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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (1-50 of 38813 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
5T4 $A_5$ $60$ $1$ 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
5T5 $S_5$ $120$ $-1$ 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T12 $\PSL(2,5)$ $60$ $1$ 5T4, 10T7, 12T33, 15T5, 20T15, 30T9
6T14 $\PGL(2,5)$ $120$ $-1$ 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
6T15 $A_6$ $360$ $1$ 6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
6T16 $S_6$ $720$ $-1$ 6T16, 10T32, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96
7T5 $\GL(3,2)$ $168$ $1$ 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
7T6 $A_7$ $2520$ $1$ 15T47 x 2, 21T33, 35T28, 42T294, 42T299
7T7 $S_7$ $5040$ $-1$ 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
8T37 $\PSL(2,7)$ $168$ $1$ 7T5 x 2, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
8T43 $\PGL(2,7)$ $336$ $-1$ 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
8T48 $C_2^3:\GL(3,2)$ $1344$ $1$ 8T48, 14T34 x 2, 28T153, 28T159 x 2, 42T210 x 2, 42T211 x 2
8T49 $A_8$ $20160$ $1$ 15T72 x 2, 28T433, 35T36
8T50 $S_8$ $40320$ $-1$ 16T1838, 28T502, 30T1153, 35T44
9T27 $\PSL(2,8)$ $504$ $1$ 28T70, 36T712
9T32 $\mathrm{P}\Gamma\mathrm{L}(2,8)$ $1512$ $1$ 27T391, 28T165, 36T2342
9T33 $A_9$ $181440$ $1$ 36T23796
9T34 $S_9$ $362880$ $-1$ 18T887, 36T28590
10T7 $A_{5}$ $60$ $1$ 5T4, 6T12, 12T33, 15T5, 20T15, 30T9
10T11 $A_5\times C_2$ $120$ $-1$ $C_2$, $A_5$ 12T75, 12T76, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61
10T12 $S_5$ $120$ $-1$ $C_2$, $S_5$ 5T5, 6T14, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
10T13 $S_5$ $120$ $-1$ 5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
10T22 $S_5\times C_2$ $240$ $-1$ $C_2$, $S_5$ 10T22, 12T123 x 2, 20T62 x 2, 20T65 x 2, 20T70, 24T570, 24T577, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2
10T26 $\PSL(2,9)$ $360$ $1$ 6T15 x 2, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
10T30 $\PGL(2,9)$ $720$ $-1$ 12T182, 20T146, 30T171, 36T1254, 40T590, 45T110
10T31 $M_{10}$ $720$ $1$ 12T181, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109
10T32 $S_{6}$ $720$ $-1$ 6T16 x 2, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96
10T34 $C_2^4 : A_5$ $960$ $1$ $A_5$ 16T1081, 20T172, 20T177, 30T214, 30T217, 40T888, 40T889, 40T932, 40T942, 40T944, 40T945
10T35 $(A_6 : C_2) : C_2$ $1440$ $-1$ 12T220, 20T201, 20T204, 20T208, 24T2960, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187
10T36 $C_2 \wr A_5$ $1920$ $-1$ $A_5$ 20T224, 20T225, 20T230, 30T344, 30T354, 32T97741, 40T1576, 40T1578, 40T1585, 40T1586, 40T1597, 40T1598, 40T1644
10T37 $(C_2^4:A_5) : C_2$ $1920$ $1$ $S_5$ 10T38, 16T1328, 20T218, 20T219, 20T222, 20T223, 20T226, 30T329, 30T332, 30T333, 30T341, 32T97736, 40T1581, 40T1582, 40T1583, 40T1584, 40T1587, 40T1588, 40T1595, 40T1596, 40T1658, 40T1659, 40T1676, 40T1677, 40T1678
10T38 $(C_2^4:A_5) : C_2$ $1920$ $-1$ $S_5$ 10T37, 16T1328, 20T218, 20T219, 20T222, 20T223, 20T226, 30T329, 30T332, 30T333, 30T341, 32T97736, 40T1581, 40T1582, 40T1583, 40T1584, 40T1587, 40T1588, 40T1595, 40T1596, 40T1658, 40T1659, 40T1676, 40T1677, 40T1678
10T39 $C_2 \wr S_5$ $3840$ $-1$ $S_5$ 10T39, 20T275, 20T279 x 2, 20T285 x 2, 20T288 x 2, 20T289 x 2, 30T517 x 2, 30T524 x 2, 32T206825 x 2, 40T2728 x 2, 40T2731 x 2, 40T2748, 40T2749, 40T2757 x 2, 40T2771 x 2, 40T2772 x 2, 40T2773 x 2, 40T2774 x 2, 40T2779 x 2, 40T2780 x 2, 40T2781 x 2, 40T2782 x 2, 40T2798, 40T2839 x 2
10T40 $A_5 \wr C_2$ $7200$ $-1$ $C_2$ 12T269, 20T363, 24T9631, 25T88, 30T652, 36T7075, 40T5410
10T41 $(A_5^2 : C_2):C_2$ $14400$ $-1$ $C_2$ 12T279, 20T456, 20T459, 24T12117, 25T101, 30T819, 36T9862, 40T10506, 40T10507, 40T10508
10T42 $A_5^2 : C_4$ $14400$ $1$ $C_2$ 12T278, 20T457, 20T461, 24T12116, 25T100, 30T817, 36T9861, 40T10509, 40T10510, 40T10511
10T43 $S_5^2 \wr C_2$ $28800$ $-1$ $C_2$ 12T288, 20T539, 20T540, 20T542, 20T544, 24T13996, 24T13997, 24T13998, 25T106, 30T1011, 36T13308, 40T14374, 40T14375, 40T14376, 40T14377, 40T14378, 40T14379, 40T14380, 40T14381
10T44 $A_{10}$ $1814400$ $1$ 45T1982
10T45 $S_{10}$ $3628800$ $-1$ 20T1007, 45T2246
11T5 $\PSL(2,11)$ $660$ $1$ 11T5, 12T179
11T6 $M_{11}$ $7920$ $1$ 12T272, 22T22
11T7 $A_{11}$ $19958400$ $1$
11T8 $S_{11}$ $39916800$ $-1$ 22T45
12T33 $A_5$ $60$ $1$ $\PSL(2,5)$ 5T4, 6T12, 10T7, 15T5, 20T15, 30T9
12T74 $S_5$ $120$ $1$ $C_2$, $\PGL(2,5)$ 5T5, 6T14, 10T12, 10T13, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
12T75 $C_2\times A_5$ $120$ $1$ $C_2$, $\PSL(2,5)$ 10T11, 12T76, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61
12T76 $C_2\times A_5$ $120$ $1$ $\PSL(2,5)$ 10T11, 12T75, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61
12T123 $C_2\times S_5$ $240$ $1$ $C_2$, $\PGL(2,5)$ 10T22 x 2, 12T123, 20T62 x 2, 20T65 x 2, 20T70, 24T570, 24T577, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2
12T124 $A_5:C_4$ $240$ $-1$ $\PGL(2,5)$ 12T124, 20T66, 24T571, 24T578, 40T178, 40T179
12T179 $\PSL(2,11)$ $660$ $1$ 11T5 x 2
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Results are complete for degrees $\leq 23$.