Rubik's Cube Orders Table

Here's the idea behind this: starting from the starting sequence, any sequence of moves will eventually bring you back there when performed enough times. The 'order' of a move sequence is the smallest positive integer n such that, starting with a solved cube, performing that move sequence n times will bring you back to the solved state. This page is a table of the shortest known (by me) sequences that have specific orders. A cell is left blank if I don't know any sequence with that order, and I only listed the rows for which I know at least one sequence on one of the cubes.

Before you begin, you might want to read up on the normal cubing notation. I'm using a lowercase letter (such as r) to mean a double-layer move, and an uppercase letter with a number in front (such as 2R) to mean a move of the 2nd layer on the R side.

I generated most of this table with a computer program that searched through all sequences of a certain length; I checked all 2x2 and 3x3 sequences of up to 5 moves, and all 4x4 sequences of up to 4 moves. It's possible that I may have missed some orders, though. If you have anything to add (or can improve on the length of some of these sequences), please let me know.

Order	2x2x2	3x3x3	4x4x4
2	R2	R2	R2
3	R2 U2	R u' z'	r2 u2
4	R	R	R
5	R U R' U	R U R' U	R U R' U
6	R U2	R2 U2	R2 U2
7	R U' F2	F U R U'	r u' f2
8	R L2 U2	R y2	R y2
9	R U'	R' U' F2	r u'
10	R U F	R2 u' f2	R2 3u' 3f2
11		U B E F' R' B' E2 F y'	U B E F' R' B' E2 F y'
12	R L y	R2 u2	R2 3u2
13			(2R 3u' L 2F 3u)4
14		R U2 r f2	R U2 3r 3f2
15	R U	R2 r U' S	r u
16		R U R2 d'	R L' 2U
17			(R u' r' S)4
18	R L U	R U r2	R U 3r2
19			(R 2U f' 3u L')3
20		R U R' D2	R 2U
21	R L2 U	R2 U R2 F	r l2 u
22		R L2 U D' F	R L2 U D' F
24		R2 y	R2 y
23			(r' 3u2 L2 3u L' f)3
26			(2R 3u' L 2F 3u)2
28		R U2 f'	2R 2U
30	R L2 y	R U2	R U2
33		R' L U F'	R' L U F'
34			(R u' r' S)2
35		R2 U R2 D'	R2 U R2 D'
36	R y	R L u	r y
38			(R 2U r' 2D)2
39			(R' U2 F' u)2
40		r' u2 f2	r E
42		r2 U	3r2 U
44		R L' U F'	2R 2U S2
45	R L2 U'	R u' S	R 3u' S
46			(R 2U 3r 2F)2
48		R L u f	R L 2U
51			(R U' F d')2
52			2R 3u' L 2F 3u
55		R L2 U' F2 B' D'	R L2 U' F2 B' D'
56		R y2 S	R y2 S
57			R 2U f' 3u L'
60		R2 u	R2 3u
63		R U'	R U'
65			(R U f U')2
66		R U r u2	r2 2U S
68			R u' r' S
69			r' 3u2 L2 3u L' f
70		r u f	3r 3u 3f
72		R U' S	R U' S
76			R 2U r' 2D
77		R U L F'	R U L F'
78			R' U2 F' u
80		R U F	r 2U
84		F U R	F U R
85			(r 3u 2R' 3f)2
88		R L u' f2	R' 2U 2F'
90		R L U	R L U
91			(R 2D 3u' L f')3
92			R 2U 3r 2F
95			(R2 3u' L f' 3u L')2
99		R2 U2 r u	R2 U2 3r 3u
102			R U' F d'
104			R u r' 2D
105		R U	R U
110		R' u R f2	R' u R f2
112		R2 L U L' u	R l' 2U
114			R2 l 3u' L f
115			(r 2U M 3u)3
117			(R' U2 F' 2U)2
119			r 3u L' 2R' 3u'
120		r U	3r U
126		R' U' f2	R' U' 3f2
130			R U f U'
132		R2 u f	R2 3u 3f
133			r 3u' L 2R2 u
136			R2 r' 2U 2F'
138			r' u' 3f2 L2 3f' L
140		r U' F2	3r U' F2
143			(R U' r' 2D)4
144		R L' u	R L' 3u
152			R2 U F' l'
153			R u' 2F'
154		R r2 U f2	R 3r2 U 3f2
156			r' 2U 2F
161			R2 l 3u L' d
165		r u M' E'	r 2U' 3b
168		R L2 U	R L2 U
170			r 3u 2R' 3f
171			R2 u r E
176			2R 2L2 y
180		R L' U	R L' U
182			(R u' r' 2D')2
184			(r u' 3f L' 2D2)2
187			(r' u 2U2 3f' L)3
190			R2 3u' L f' 3u L'
195			R2 U r' 2B
198		R r2 U' u2	r 3u' S'
204			2R 2U 3f'
207			r 2U 3l' 3u' L
208			R U r' 2U
209			(r2 u S u)3
210		R U l2	R U 3l2
220		R2 r' u f	2R 3u
221			(R u r E2)6
228			R2 U2 f' 3u'
230			(R' U F' l2)3
231		R r U' f	R 3r U' 3f
234			R' U2 F' 2U
238			r E2 3f L' 3f'
240		x y F	R u
247			(r 3u2 L2 f2 3u)4
252		r U'	3r U'
253			(r 2U 3l' E)4
255			R u 2F'
260			R U r' 2D
264			r 2U' 2F'
266			(R U' r' d)2
272			r E 3u' L 3f2
273			R 2D 3u' L f'
276			R' u' l' 3f
280		R U2 R2 y	R u f
285			R u 2R E2
286			(R U' r' 2D)2
299			(2R' 3u L' 2F2 3u2 L2)6
304			R2 2U l 3f' L
306			R U' F' l
308			r 2U S2
312			r' 2U 2F'
315		R B L F	R u' 2F
322			2R 3u2 L2 3f L' 2U'
323			(R 2U' f' 3u L')3
330		R r2 U u2	R u' 3f
336		R l2 u	R 3l2 3u
340			R 2U' r' E'
342			R U F' r2
345			r 2U M 3u
357			R u d2 2L
360		F U R'	F U R'
364			R u' r' 2D'
368			r u' 3f L' 2D2
374			(R 2U' l E')2
380			R2 r' u 3f
385			r 3u L' u' 3u' L
390			R U f'
391			(R' u' r2 3f' L)6
396		R L2 U2 y	r2 3u 3f
399			R2 l u 2D2
408			R U F2 d'
414			R2 u r2 3f'
418			(R u r' 2D2)2
420		f u r	3f 3u 3r
429			(R L u f2)2
437			(r 3u2 L2 3u' f2)4
440			r E S
442			(R u r E2)3
455			r 2D' 3u L' 3u'
456			R u F2 2U
460			(R' r2 u2 3f' L)2
462		r u' f2	3r 3u' 3f2
468			R' U' F' d2
476			R u' 3b2
483			R2 U2 l f'
494			(r 3u2 L2 f2 3u)2
495		R2 L2 U F' U2	r u' S
504		R u z2	R 3u z2
506			(r 2U 3l' E)2
510			R2 U F r'
520			R U2 l' 3u'
528			R U2 r2 f
532			R U' r' d
546			R u2 d 2F
552			R U F' l2
560			2R y
561			r' u 2U2 3f' L
570			R' U F' r2
572			R U' r' 2D
585			R u' 2L
595			2R 2U' 3f' L 3u L'
598			(2R' 3u L' 2F2 3u2 L2)3
612			R' U' F2 d'
616			R U' F' u
624			R' U2 u f'
627			r2 u S u
630		R U z2	R U z2
644			R u' 3r' d'
646			(r' 2D f 3u' L)2
660		R L2 y	R L2 y
663			(R u r E2)2
665			(R2 U f' 2D')2
680			R2 2U 2F 3l'
684			R U' F2 d'
690			R' U F' l2
693			R u' 2L'
714			R' L2 u' 2D'
715			(r' u' 2F2)3
720		R2 r U' y2	R u'
728			R L2 u' 3f
741			(R r 3u 2F')2
748			R 2U' l E'
759			(r' u 3f' L 3d)2
760			R' 2U 3l 2F
765			R2 U l' 2D
770			R U r' 3d'
780			R' L2 u2 3f
782			(R' u' r2 3f' L)3
792			R' U' f
798			R2 u f'
805			(R2 u2 r' 3f)2
816			R2 U' r f'
819			R u' 2R E2
828			R U' F' d2
836			R u r' 2D2
840		R r2 u'	R 3r2 3u'
855			R u2 d' 2L
858			R L u f2
874			(r 3u2 L2 3u' f2)2
880			R u2 L2 E
884			(r 3u' L 3f L' 2D')2
897			(2R' 3u L' 2F2 3u2 L2)2
910			R U r' d2
912			R U2 l 2F
920			R' r2 u2 3f' L
924			R 2U 3b2
935			R U r' f
936			R U' f'
952			R2 U' 2R 3f
966			R2 l u 3f2
969			R 2U' f' 3u L'
988			r 3u2 L2 f2 3u
990		R l2 u' S'	R U l
1001			(r u2 3d' 3f2 L2)2
1008			r U' 2L'
1012			r 2U 3l' E
1020			R2 u 3f
1035			r' u' 3f2 E'
1040			R r 3u2 3f'
1045			R u r' 3u
1064			R U r 3f
1071			R2 2U' r 3f
1092			R2 u 2F
1104			R' r2 3u 3f2
1105			(R 2U 2R' 3d)3
1122			R U r 2D'
1140			R' U F2 d'
1144			R' D2 f2 3u' L
1155			R u 2L
1170			R l u'
1173			(R' u' r2 3f' L)2
1190			r u 2L' 3f
1196			(R2 U' l f)2
1197			R' 2U f' 3d2
1224			R2 U F' r
1232			R2 U f' 2L
1235			(r u 2L2 2D2)3
1254			R u 2F 3u
1260		R y	R y
1265			(R' U l' f)6
1287			R2 u' f'
1288			R U2 l' f
1292			r' 2D f 3u' L
1309			R 2L 3u L' u'
1311			(r u S2 3f L')2
1320			r 2L2 3u
1326			R u r E2
1330			R2 U f' 2D'
1360			r u 3f
1365			R L2 u 2D'
1368			R l' u'
1380			R' 2U' 2R' 3f'
1386			R L2 U2 f'
1428			R2 U d2 3f
1430			(R u r' 2D')2
1449			R2 u' l' 3f2
1456			R U2 f' 2B'
1463			(R2 u l E2)3
1482			R r 3u 2F'
1495			(R' 2U 2R 3f')3
1496			r 3u' 3f L' u
1518			r' u 3f' L 3d
1520			R2 l' u 3f'
1530			R' L2 u 3f'
1540			R 2U 2R' S'
1547			(R2 l u f2)3
1560			r 3u 3b
1564			(R U2 l f)2
1584			R U2 r2 3u
1596			R2 U F2 l
1610			R2 u2 r' 3f
1615			(r 2U' 3f 3d)2
1638			R2 u 3b
1656			R2 u l 3f2
1672			r2 3u2 L2 f 2U
1680			R u 3f2
1683			(R' u2 2D' 3f')2
1710			R U' r f
1716			R' r' 2U 3f'
1729			R' U r' f
1748			r 3u2 L2 3u' f2
1768			r 3u' L 3f L' 2D'
1771			R u' 2R' 3f2
1785			R U l' f'
1794			2R' 3u L' 2F2 3u2 L2
1820			R2 r u f2
1840			r2 3u' L 3f' 3u L'
1848			R' U2 f
1870			R2 u2 f' 2U
1872			R U l 2F'
1881			R' u 2L2 2F
1904			R2 u 3f2 3r
1932			R2 U2 d f'
1938			R2 u r' 3u2
1955			(r 3u2 3f2 L2 b')3
1976			r 2U 3u L' u2
1980			R U l'
1989			R u' E2 2L
1995			R2 U f' 2U
2002			r u2 3d' 3f2 L2
2024			R' l' u f2
2040			r u S2
2070			R2 r' 2U' 3f'
2090			R u f 2B
2093			(R2 u 2R2 3f')2
2128			R U' r f'
2142			R2 U l 3f2
2145			r' u' 2F2
2184			r u2 3d
2185			(r 2U' M2 3f)3
2210			(r u 2R' 3u' L)2
2223			(R l u 2D2)2
2244			R u 3r' 2D
2261			(2R 3u L' 3f' L E2)2
2277			r 2U' M 3u'
2280			R U' r' 3f'
2288			2R2 3d 3f' L 3u' L
2310			R u' x
2340			R2 L r 3u
2346			R' u' r2 3f' L
2380			R u r' E
2392			R2 U' l f
2394			r u' 2F2
2415			r u' 3f2
2431			(r u 2L2 S')15
2448			R u' f'
2470			(r 3u 3f' M2)3
2508			R2 U' d2 f
2520		R L2 U' F' d	R2 u x
2530			(R' U l' f)3
2574			r u2 3b
2576			R r2 3u 3f2
2584			r u 3r 3u' L
2618			r E 3u' L 3f
2622			r u S2 3f L'
2640			r 3u S'
2652			R U' r 2D'
2660			R' r' u' 3f
2691			(r2 2U' 3f' L b')2
2717			(r2 d 3f' 3u2 L2)18
2730			R' L2 U' f
2736			R 2U2 3f'
2737			r' u 3r' 3f
2760			R' U l2 3f
2772			R L U f
2805			R2 r u' 2F2
2856			R2 U2 f' 3d
2860			R u r' 2D'
2898			r 2U2 3f'
2907			R2 U2 u f'
2926			(R' 2U 3f L' u')2
2964			R r 2U' 3f
2990			(r u' 3f L' 2D')2
3003			R L' r u'
3036			R u2 2R' 3f
3059			(r2 3u L' u' 3f')2
3060			R' L2 u' f'
3080			R u' r2 3f2
3094			(R u r f)2
3120			R U r y
3128			R U2 l f
3135			(r u 2L)2
3192			R2 U2 r' f
3220			R u r' 3d'
3230			r 2U' 3f 3d
3276			r 3u'
3289			(r' 3u2 L2 u 3f2)4
3312			R u r 3f'
3315			R 2U 2R' 3d
3366			R' u2 2D' 3f'
3420			r 3u' 3f'
3432			R u2 r2 3d
3458			r u2 3f'
3465			R u 2L'
3496			R u l 3f2
3519			(R' u2 3f' 2L')2
3542			r u2 3b'
3570			R2 U2 u 3l'
3588			r' 3u2 L2 u' 2F
3640			R2 u 3r' 3d'
3696			r 2U 3b2
3705			r u 2L2 2D2
3740			R u r' S'
3762			R l u
3795			(R' U l' f)2
3864			R2 u' 2L' 3f
3876			r2 u 2R2 3f
3910			(R2 u 3f L' 2L)3
3927			R l u' 3f
3933			r' u2 f' M2
3960			R2 U r 3d
3978			R' u 2F2 3f'
3990			R' U' u' 3f
4004			R2 2U f 3u'
4080			r' u' 2F
4095			R2 r u' E2
4140			R r2 2U' 3f'
4180			R2 3u' L r' f'
4186			R2 u 2R2 3f'
4284			R' U2 f' E
4290			R' U u2 2F
4368			R U2 r2 3u'
4370			(r2 u' B f L')3
4389			R2 u l E2
4420			r u 2R' 3u' L
4446			R l u 2D2
4485			R' 2U 2R 3f'
4488			r u2 3r u'
4522			2R 3u L' 3f' L E2
4554			R' u l' f2
4560			R 2U 3f
4620			R2 u f
4641			R2 l u f2
4680			R2 U r d
4692			R2 U' d' f'
4760			R2 u' f 3d
4788			R' U' l 2F
4830			R2 U' d f'
4845			r u 2L2
4862			(r2 u' 3u' L 3f)9
4940			(R u f 2L')2
5005			(R 2L2 3u L' u')2
5016			R2 U r' d
5040			R2 u x'
5060			(r' 2D' f2 3u L')2
5148			R U d' 3f'
5187			r u2 f' M2
5236			R u' 3r 3f'
5244			R' u' 3f' L 2L'
5304			R2 r' 3u' L f2
5313			r' 2U 3f 3d2
5320			R u 3f
5355			R2 l u' z2
5382			r2 2U' 3f' L b'
5434			(r2 d 3f' 3u2 L2)9
5460			R u 2F2
5474			(r u2 3u' L 3f')2
5520			R2 U l' f
5544			R2 U2 r d'
5610			R' u r2 2F2
5712			R U2 f2 b
5720			R U2 l 3f
5796			R l u 3f'
5814			r 3u z2
5852			R' 2U 3f L' u'
5865			r 3u2 3f2 L2 b'
5928			R U2 f 3l
5980			r u' 3f L' 2D'
5985			R u' 2L 3d2
6006			R2 l 3u
6072			R2 3u L' f' r
6118			r2 3u L' u' 3f'
6120			R2 L2 u f
6160			R2 U d f'
6188			R u r f
6270			r u 2L
6279			R2 u' r 3f L'
6384			R' L2 u2 3f'
6435			R2 l u'
6440			r d' 3f2 L2 3u2 L2
6460			R2 U' 3f L' r'
6545			r u' 2R2 3f2
6552			r2 3u 3f'
6555			r 2U' M2 3f
6578			(r' 3u2 L2 u 3f2)2
6630			R' U' f' 3f2 L2
6732			R L u 2D
6783			R2 l u
6840			r 3u
6864			R u2 3f' 3b2
6916			(2R' 2U2 3u L' 3f L')2
6930			R l2 u'
7038			R' u2 3f' 2L'
7084			r 3u' L f' 3u L'
7140			R u 3f'
7176			r2 u' 3f L' u
7245			r 2U 3f'
7280			r' u 2L 3f2
7293			(r u 2L2 S')5
7315			(R2 u' 3f E')2
7410			r 3u 3f' M2
7480			R L2 u f'
7524			R U2 f 2D'
7590			R' U l' f
7728			R' u r 3f'
7735			r 3u L' u' 2D2
7752			R u2 l 3f
7820			(r 2U2 3f)3
7854			R u2 3d 2F
7866			R2 3u L' r' f
7920			R L r 3u'
7956			R U' u' 3f
7980			R2 U2 r 3d
8008			R' r2 3u' L f
8151			(r2 d 3f' 3u2 L2)6
8190			R2 U r' f'
8211			r u 3f' L E2
8280			R u' 3r2 2F
8360			(R U r' 3f)3
8372			(r' u' 3f L' 3u)2
8415			R2 u l' S2
8568			R2 U2 r 3d'
8580			f R b D u'
8645			(R2 u' 3f 2U2)2
8740			(r 2U' 3f2 3d)3
8778			R U 3f' L 2U'
8840			r 2U f2 3u' L
8855			(R' 3u2 L2 2L' f')3
8892			R2 U2 l 3d
8970			r 2U 3r 3f
9009			r u' M'
9044			R 3u' r 3f'
9108			R l' u f2
9177			r u l2 E
9240			R L r y
9282			R2 l2 3u L' 2F
9360			R2 u L' 2F'
9384			r' 2D 3f' L 3u L'
9405			R u 2R2 2F'
9520			r' 3u2 L2 f' 3f' L
9576			R l' u' 2F'
9660			R U d f'
9690			R l' u' z2
9724			(r 3u2 L2 3l' u)6
9867			(r' 2U 2L2 3f)3
9880			R u f 2L'
9945			R2 l u' E2
10010			R 2L2 3u L' u'
10120			r' 2D' f2 3u L'
10296			R2 U' f' 3u'
10374			R' U r' 3f
10465			(R2 l 3u2 L2 f')3
10472			r' u 3f L' f'
10488			r 3u2 3f' L 2U
10626			r' 2U' 3r' 3f'
10640			2R 2U' 3f L' 3d2
10710			R 2U 3f'
10764			R' u' 3r2 2F
10868			(2R' 3u' L 3f' L 2U2)7
10920			R2 u 3b'
10948			r u2 3u' L 3f'
11088			2R 3u 3b'
11115			R2 U2 l d
11220			R U2 l' 3d
11305			r 3u L' S u'
11385			r' u 2L' 2F
11440			(r 3u 2L' 3f')3
11592			R2 l' u f2
11628			R u2 l 3d
11704			r 3u' L 2F2 u
11730			R2 u 3f L' 2L
11781			R u' l 3f'
11960			R' u l 3f2
11970			r 3u' 3d2
12012			R2 U l' y
12155			(r u 2L2 S')3
12236			2R 3u' L 3f' L 2B2
12240			R' U' d' 2F
12376			(R d' f2 3u2 L2)3
12540			R U' l' 3f'
12558			r u2 3f2 L2 3f
12870			R U2 l d'
12880			(R' 3u2 L2 l' f')3
12920			r' 2D2 3f' L 3u L'
13090			r 3u 3f
13104			R u2 L2 3u'
13110			r2 u' B f L'
13156			r' 3u2 L2 u 3f2
13167			R U2 f' 2L'
13260			R u 2R' 3f2
13455			R2 u 3r 2F
13464			R u 2F2 3r2
13566			R l2 2U' 3f
13585			(r 3u L' 2L2 u)9
13680			R2 U' l 2F
13685			R u' 3f2 2L'
13832			2R' 2U2 3u L' 3f L'
13860			R' u f
13923			2R 2U' 3r 3d'
14076			R2 U d' f'
14168			(R2 3u' L 2R' f2)3
14280			r 3u S2
14490			R U l' f
14535			2R 2U' 3f L' E2
14586			(r2 u' 3u' L 3f)3
14630			R2 u' 3f E'
14820			R2 u 3f 2U2
15015			R2 r u'
15048			R' u l' 3f2
15180			R' 3u' L 2R f'
15295			2R 3u' L 2U 3f' L
15470			2R 2U2 3f' L 3u L'
15561			R2 U' f' 2L
15708			R2 u f2 3b
15732			r 2U 3l' 3u'
15912			R U l' z'
15939			r' 2U2 2F' 3u
15960			R2 U r' E
16016			r' u 2L' 3f2
16302			(r2 d 3f' 3u2 L2)3
16380			r 3u' M2
16422			R' l2 2U' 3f'
16560			R2 U' l f'
16744			r' u' 3f L' 3u
16830			R l' u z2
17017			(R2 r u2 d')3
17136			R2 U f2 3l'
17160			R2 U' f 3u'
17290			R2 u' 3f 2U2
17556			R U2 l2 f'
17595			r u' 3l2 E'
17710			(r u 3l2 E)3
17784			r 2L2 y
17940			R2 u 2R2 3f
18018			R' u' f 3u2
18216			r2 u' 2F2 3f'
18354			r E 3u' L f'
18480			R2 U' f' 3b2
18564			r 3u 2L2 3f2
18810			R l u' E2
18837			r' u' 2F2 3f2 L2
19019			(2R' 3u' L 3f' L 2U2)4
19152			r u2 S2 3f L'
19320			r u2 3f' E2
19380			R2 U' f 3l
19448			(r 3u2 L2 3l' u)3
19635			R2 U2 r f
19665			r 2U l2 3u'
19890			R 2U' 3l2 3f'
20020			r 2U 3f' L d
20349			(r d2 3f 3u' L)2
20592			R U2 f2 3d
20748			R2 u 3f 2U'
20930			(R2 r u2 3f)2
21252			R' l u2 3f' L
21420			R L2 u' f'
21528			R2 u' 3r' 2F2
21840			R u' r2 3f
21879			(r2 u' 3u' L 3f)2
21945			2R' 2U 3l2 3f L'
22230			R2 U2 u 3l
22440			R u d2 3f'
22610			r 3u2 M2 3f'
22770			R' r2 2U' 3f'
23023			r u 3r 3f
23184			r 2U 2L 3f'
23205			R2 L2 r u'
23460			r 2U2 3f
23562			R' u' 2F' 3d2
23940			R2 U l' 2F'
24024			R u 2R2 3f' L
24453			(r2 d 3f' 3u2 L2)2
24633			r' 2U M2 3f
25080			R U r' 3f
25116			R' 2L 3u' L f
25740			R' L2 u' 3f'
25935			R' u r2 2F'
26180			R L' u 3f'
26220			r 2U' 3f2 3d
26334			R 2U' 3f 3l2
26520			r u 2F E'
26565			R' 3u2 L2 2L' f'
26910			R2 u2 2L' 3f L'
27132			R2 U2 u 3f
27170			(R' u 2F' z2)6
27720			r M2 y
27846			R2 u' 3l' 3f2
28560			R2 u F' d'
28980			R' U' d f'
29070			R 2U M2 3f'
29172			(r 3u2 L2 3l' u)2
29260			r' 2U' 3f L' u'
29601			r' 2U 2L2 3f
29640			R2 l y
30030			R L u 3f'
30360			r 2U' 3f2 3u L'
30940			R' U' r' 3f'
31122			r' u' 2L2 3f
31395			R2 l 3u2 L2 f'
31416			r2 u 2F 3l
31878			(r 2L2 3u' L 2D')2
31920			R l' 3u L' S2
32604			(R' u 2F' z2)5
32760			r 2U2 3b'
32844			r' 3u2 L2 f' E'
33660			R 2R' 3u'
33915			r u 3l2
34034			(r2 u 3r' 3f2)3
34320			r 3u 2L' 3f'
34580			R u' 2L2 z
35112			R2 u2 l 3f'
35190			R2 2U2 l 3f'
35420			(r' u' 3f' L 2F2)3
35880			R' U2 l f'
36036			r 3u 3b2
36465			r u 2L2 S'
36708			R' r2 3u L' f'
37128			R d' f2 3u2 L2
37620			R2 U 2F' 3l'
37674			R2 l' u 3f2
38038			(2R' 3u' L 3f' L 2U2)2
38640			R' 3u2 L2 l' f'
39270			R2 l' 2U2 3f'
39330			r 3u 2F2 3u2 L2
39780			R' U2 u' 3f'
40040			R u2 M2 f'
40698			r d2 3f 3u' L
40755			(r 3u L' 2L2 u)3
41055			r 2D2 f 3u2 L2
41496			R' U u 3f
41860			R2 r u2 3f
42504			R2 3u' L 2R' f2
42840			R u' M
43758			r2 u' 3u' L 3f
43890			R U u 3f'
44460			R2 r u 3d'
45045			R2 r u
45220			2R' 3u L' 3f L' 2U2
45540			r 3u' 3f2 L2 b2
45885			r D u L' 3f2
46410			r 3u 3d2
47124			R 3u L' 2R2 2F
47880			R l' u' 3r2
48048			R2 U' f2 3l'
48906			r2 d 3f' 3u2 L2
50232			R2 l' 3u L' f
51051			R2 r u2 d'
51480			R u r d'
51870			R' l u2 f'
52360			r u 3u L' 3u
52668			R' u 3f' 2L2
53130			r u 3l2 E
53820			r2 2U 3f2 L2 3f' L
54340			(R' u 2F' z2)3
55440			R2 r' 2U2 3f'
55692			R' U' r 3f
57057			(R u 2F' 3l2)5
57960			R' u2 2L 3f
58140			r 3u M 3u2
58344			r 3u2 L2 3l' u
58520			2R' 3u' L 2D 3f2
58905			R2 u M f'
60060			R U d 3f'
61880			2R 3u L' F' L
62244			R' U' l 3f
62790			R' l2 u 3f' L
63756			r 2L2 3u' L 2D'
65520			R2 U 2F2 3l'
65835			R2 r u' 3f2
67320			R2 u' 3f 3r
67830			r2 2U 3f' 3u
68068			(R d' 2L' 3u2 L2)3
69069			r 2U' 3f2 L2 3u
69160			r' u' 3r 3f L'
69615			r u' M2
70380			r2 E' 3f L' 2F'
70840			(2R2 x' 3u' L 2F)3
72072			r u 2F' u2
75240			R2 l 3u 3f
75348			r 2D 3f' L 3u L'
76076			2R' 3u' L 3f' L 2U2
77805			(r2 3u L' 3f' L 2D)2
78540			R' u2 2F 3d'
78660			r2 3u L' 3f' L 2F
79560			R2 2U 3r' 3u'
79695			(R 3u2 L2 2R f)2
81396			r u 3d' 3f2
81510			(R' u 2F' z2)2
85085			(r d 3f2 L2 3u L')3
85680			R u r d
87780			r l2 3u S2
88920			R u2 2R' 3d'
90090			R2 L2 u 3f
91080			r2 2D2 2F 3u L'
92820			R u 3f' 2U2
94185			(R' 2U l2 3f)2
94248			r' u M2 3f L'
95095			(R u 2F' 3l2)3
95760			R2 u' 3f2 3r
101745			r u' 3l2
102102			r2 u 3r' 3f2
102960			r u2 2R 3d'
103740			r2 3u 2R 3f L'
106260			r' u' 3f' L 2F2
109395			(R2 r u d2)7
117810			r l2 2U2 3u'
120120			R2 u' l' 2F'
122265			r 3u L' 2L2 u
125580			r' u 2F 3u2 L2
131670			R 2U L2 3f'
135660			R2 l u' 3d2
139230			R2 u E2 3l'
144144			r' u2 3u' L 3f
153153			R 2L 3u2 L2 d
155610			r2 3u L' 3f' L 2D
157080			R2 l2 u 3r'
159390			R 3u2 L2 2R f
163020			R' u 2F' z2
175560			R2 u f 3d'
180180			R l' u' S2
185640			r' u' 3r 3f2 L2
188370			R' 2U l2 3f
203490			r l2 2U2 3f'
204204			R d' 2L' 3u2 L2
212520			2R2 x' 3u' L 2F
235620			R l u' S'
244530			R2 r d' 3u2 L2
255255			r d 3f2 L2 3u L'
263340			r' 2D' 3u L' 3f' L
278460			R l u' 3r2
285285			R u 2F' 3l2
306306			r u M2 z2
311220			R u 3f L' 3r2
360360			r d 3l' 3u2 L2
471240			R l' u 3r2
765765			R2 r u d2