| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 10T1 |
$C_{10}$ |
$10$ |
$-1$ |
✓ |
$1$ |
$10$ |
$C_2$, $C_5$ |
|
| 10T2 |
$D_5$ |
$10$ |
$-1$ |
✓ |
$-1$ |
$4$ |
$C_2$, $D_{5}$ |
5T2 |
| 10T3 |
$D_{10}$ |
$20$ |
$-1$ |
✓ |
$-1$ |
$8$ |
$C_2$, $D_{5}$ |
10T3, 20T4 |
| 10T4 |
$F_5$ |
$20$ |
$-1$ |
✓ |
$-1$ |
$5$ |
$C_2$, $F_5$ |
5T3, 20T5 |
| 10T5 |
$F_{5}\times C_2$ |
$40$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $F_5$ |
10T5, 20T9, 20T13, 40T14 |
| 10T6 |
$D_5\times C_5$ |
$50$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$ |
10T6, 25T3 |
| 10T7 |
$A_{5}$ |
$60$ |
$1$ |
|
$-1$ |
$5$ |
|
5T4, 6T12, 12T33, 15T5, 20T15, 30T9 |
| 10T8 |
$C_2^4 : C_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_5$ |
10T8 x 2, 16T178, 20T17 x 6, 20T23, 40T57 x 3 |
| 10T9 |
$D_5^2$ |
$100$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$ |
10T9, 20T28 x 2, 25T12 |
| 10T10 |
$C_5^2 : C_4$ |
$100$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$ |
10T10, 20T27 x 2, 25T10 |
| 10T11 |
$A_5\times C_2$ |
$120$ |
$-1$ |
|
$-1$ |
$10$ |
$C_2$, $A_5$ |
12T75, 12T76, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61 |
| 10T12 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$7$ |
$C_2$, $S_5$ |
5T5, 6T14, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 10T13 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$7$ |
|
5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 10T14 |
$C_2 \times (C_2^4 : C_5)$ |
$160$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_5$ |
10T14 x 2, 20T40 x 12, 20T41 x 6, 20T44 x 3, 20T46 x 3, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3 |
| 10T15 |
$(C_2^4 : C_5) : C_2$ |
$160$ |
$1$ |
✓ |
$-1$ |
$10$ |
$D_{5}$ |
10T15 x 2, 10T16 x 3, 16T415, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146 |
| 10T16 |
$(C_2^4 : C_5) : C_2$ |
$160$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$D_{5}$ |
10T15 x 3, 10T16 x 2, 16T415, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146 |
| 10T17 |
$(C_5^2 : C_4) : C_2$ |
$200$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$ |
10T17, 20T54 x 2, 25T19, 40T169 x 2 |
| 10T18 |
$C_5^2 : C_8$ |
$200$ |
$1$ |
✓ |
$-1$ |
$11$ |
$C_2$ |
10T18 x 2, 20T56 x 3, 25T20, 40T171 x 3 |
| 10T19 |
$D_5^2 : C_2$ |
$200$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$ |
10T21 x 2, 20T48 x 2, 20T50 x 2, 20T55, 20T57 x 2, 25T21, 40T167 x 2, 40T170 |
| 10T20 |
$C_5^2 : Q_8$ |
$200$ |
$-1$ |
✓ |
$-1$ |
$8$ |
$C_2$ |
10T20 x 2, 20T47 x 3, 25T17, 40T166 x 3 |
| 10T21 |
$D_5^2 : C_2$ |
$200$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$ |
10T19, 10T21, 20T48 x 2, 20T50 x 2, 20T55, 20T57 x 2, 25T21, 40T167 x 2, 40T170 |
| 10T22 |
$S_5\times C_2$ |
$240$ |
$-1$ |
|
$-1$ |
$14$ |
$C_2$, $S_5$ |
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 |
| 10T23 |
$C_2\times (C_2^4 : D_5)$ |
$320$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$D_{5}$ |
10T23 x 5, 20T71 x 6, 20T73 x 6, 20T76 x 6, 20T81 x 3, 20T85 x 6, 20T87 x 6, 32T9313 x 2, 40T204 x 3, 40T270 x 12, 40T271 x 12, 40T272 x 3, 40T273 x 2, 40T284 x 6, 40T286 x 6, 40T288 x 3, 40T293 x 3, 40T295 x 6 |
| 10T24 |
$(C_2^4 : C_5):C_4$ |
$320$ |
$1$ |
✓ |
$-1$ |
$11$ |
$F_5$ |
10T25, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88, 32T9312, 40T206, 40T207, 40T296, 40T297, 40T298, 40T299, 40T300, 40T301, 40T302, 40T303 |
| 10T25 |
$(C_2^4 : C_5):C_4$ |
$320$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$F_5$ |
10T24, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88, 32T9312, 40T206, 40T207, 40T296, 40T297, 40T298, 40T299, 40T300, 40T301, 40T302, 40T303 |
| 10T26 |
$\PSL(2,9)$ |
$360$ |
$1$ |
|
$-1$ |
$7$ |
|
6T15 x 2, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 |
| 10T27 |
$(D_5 \wr C_2):C_2$ |
$400$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$ |
10T27 x 2, 20T90 x 3, 20T96 x 3, 20T97 x 3, 25T30, 40T393 x 3, 40T394 x 3, 40T395 x 3 |
| 10T28 |
$(C_5^2 : C_8):C_2$ |
$400$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ |
20T104, 20T107, 20T109, 20T115, 25T31, 40T397, 40T398, 40T399, 40T400 |
| 10T29 |
$((C_2^4 : C_5):C_4)\times C_2$ |
$640$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$F_5$ |
10T29, 20T129, 20T131 x 2, 20T132, 20T133, 20T134, 20T135, 20T137 x 2, 20T140, 32T34608 x 2, 40T460, 40T462, 40T473, 40T474, 40T475, 40T476, 40T487, 40T488, 40T489, 40T490, 40T557, 40T558 x 2, 40T561, 40T562, 40T563, 40T564, 40T565, 40T566, 40T567 x 2, 40T576, 40T577, 40T578, 40T579, 40T586 |
| 10T30 |
$\PGL(2,9)$ |
$720$ |
$-1$ |
|
$-1$ |
$11$ |
|
12T182, 20T146, 30T171, 36T1254, 40T590, 45T110 |
| 10T31 |
$M_{10}$ |
$720$ |
$1$ |
|
$-1$ |
$8$ |
|
12T181, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109 |
| 10T32 |
$S_{6}$ |
$720$ |
$-1$ |
|
$-1$ |
$11$ |
|
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 |
| 10T33 |
$F_5 \wr C_2$ |
$800$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$ |
20T155, 20T161, 20T167, 20T169, 25T50, 40T874, 40T875, 40T876, 40T877, 40T878, 40T879, 40T880, 40T881, 40T882, 40T883 |
| 10T34 |
$C_2^4 : A_5$ |
$960$ |
$1$ |
|
$-1$ |
$12$ |
$A_5$ |
16T1081, 20T172, 20T177, 30T214, 30T217, 40T888, 40T889, 40T932, 40T942, 40T944, 40T945 |
| 10T35 |
$(A_6 : C_2) : C_2$ |
$1440$ |
$-1$ |
|
$-1$ |
$13$ |
|
12T220, 20T201, 20T204, 20T208, 24T2960, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187 |
| 10T36 |
$C_2 \wr A_5$ |
$1920$ |
$-1$ |
|
$-1$ |
$24$ |
$A_5$ |
20T224, 20T225, 20T230, 30T344, 30T354, 32T97741, 40T1576, 40T1578, 40T1585, 40T1586, 40T1597, 40T1598, 40T1644 |
| 10T37 |
$(C_2^4:A_5) : C_2$ |
$1920$ |
$1$ |
|
$-1$ |
$18$ |
$S_5$ |
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 |
$(C_2^4:A_5) : C_2$ |
$1920$ |
$-1$ |
|
$-1$ |
$18$ |
$S_5$ |
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 |
$C_2 \wr S_5$ |
$3840$ |
$-1$ |
|
$-1$ |
$36$ |
$S_5$ |
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 |
$A_5 \wr C_2$ |
$7200$ |
$-1$ |
|
$-1$ |
$20$ |
$C_2$ |
12T269, 20T363, 24T9631, 25T88, 30T652, 36T7075, 40T5410 |
| 10T41 |
$(A_5^2 : C_2):C_2$ |
$14400$ |
$-1$ |
|
$-1$ |
$25$ |
$C_2$ |
12T279, 20T456, 20T459, 24T12117, 25T101, 30T819, 36T9862, 40T10506, 40T10507, 40T10508 |
| 10T42 |
$A_5^2 : C_4$ |
$14400$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$ |
12T278, 20T457, 20T461, 24T12116, 25T100, 30T817, 36T9861, 40T10509, 40T10510, 40T10511 |
| 10T43 |
$S_5^2 \wr C_2$ |
$28800$ |
$-1$ |
|
$-1$ |
$35$ |
$C_2$ |
12T288, 20T539, 20T540, 20T542, 20T544, 24T13996, 24T13997, 24T13998, 25T106, 30T1011, 36T13308, 40T14374, 40T14375, 40T14376, 40T14377, 40T14378, 40T14379, 40T14380, 40T14381 |
| 10T44 |
$A_{10}$ |
$1814400$ |
$1$ |
|
$-1$ |
$24$ |
|
45T1982 |
| 10T45 |
$S_{10}$ |
$3628800$ |
$-1$ |
|
$-1$ |
$42$ |
|
20T1007, 45T2246 |
Results are complete for degrees $\leq 23$.
