| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 18T81 |
$C_3^3:C_6$ |
$162$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3\times C_3$ |
18T76, 18T78, 18T81, 27T48, 27T60 x 3 |
| 18T118 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3^2$ |
18T118, 18T126 x 2, 27T125 x 2, 36T493 x 2, 36T499 x 2 |
| 18T131 |
$(C_3\times \He_3):C_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$ |
18T131 x 3, 36T504 x 4 |
| 18T141 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3$, $A_4$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
9T25, 12T132 x 2, 12T133, 18T141, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 18T199 |
$C_2\times C_3^3:A_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_3$, $A_4\times C_2$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
18T199, 18T201, 18T205, 24T1516 x 2, 24T1518, 36T1073 x 2, 36T1074 x 2, 36T1075, 36T1076, 36T1077, 36T1078 |
| 18T215 |
$C_3^2.\SOPlus(4,2)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:D_4$ |
18T215, 36T1116 x 2, 36T1117 x 2, 36T1118 x 2, 36T1186 |
| 20T40 |
$C_2\wr C_5$ |
$160$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_5$, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 2 |
10T14 x 3, 20T40 x 11, 20T41 x 6, 20T44 x 3, 20T46 x 3, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3 |
| 20T60 |
$C_5:D_{20}$ |
$200$ |
$-1$ |
✓ |
$-1$ |
$29$ |
$C_2$, $D_{4}$, $D_5^2$ |
20T60 x 3, 40T163 x 2 |
| 20T74 |
$C_2^5:C_{10}$ |
$320$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_5$, $C_2 \times (C_2^4 : C_5)$ x 3 |
20T72 x 6, 20T74 x 35, 20T86 x 9, 40T202 x 3, 40T274 x 72, 40T275 x 36, 40T276 x 36, 40T277 x 18, 40T278 x 18, 40T292 x 9 |
| 20T95 |
$D_5^2:C_4$ |
$400$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $D_{4}$, $D_5^2 : C_2$ |
20T93 x 2, 20T94 x 2, 20T95, 40T330 x 2, 40T335, 40T337, 40T339, 40T341, 40T364, 40T367, 40T372 x 2 |
| 20T101 |
$D_{10}:F_5$ |
$400$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $D_{4}$, $(C_5^2 : C_4) : C_2$ |
20T101 x 3, 40T357 x 2, 40T360 x 2 |
| 20T108 |
$C_{10}.(C_2\times F_5)$ |
$400$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $D_{4}$, $(C_5^2 : C_4) : C_2$ |
20T108 x 3, 40T356 x 2, 40T361 x 2 |
| 20T112 |
$(C_5\times C_{10}).Q_8$ |
$400$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $D_{4}$, $C_5^2 : Q_8$ |
20T111 x 2, 20T112 x 3, 40T322, 40T323 x 2, 40T324, 40T326 x 2 |
| 20T136 |
$C_2^6:D_5$ |
$640$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$D_{5}$, $C_2\times (C_2^4 : D_5)$ |
20T136 x 11, 20T139 x 3, 20T142 x 3, 40T457 x 3, 40T467 x 3, 40T468 x 3, 40T481 x 3, 40T482 x 3, 40T527 x 3, 40T528 x 6, 40T529 x 12, 40T536 x 3, 40T539 x 6, 40T546 x 3, 40T548 x 6, 40T556 x 12, 40T569 x 3, 40T573 x 12, 40T574 x 12, 40T581 x 12 |
| 20T150 |
$A_6.C_2$ |
$720$ |
$-1$ |
|
$-1$ |
$8$ |
$M_{10}$ |
10T31, 12T181, 20T148, 20T150, 30T162, 36T1253, 40T591, 45T109 |
| 20T157 |
$D_5^2.D_4$ |
$800$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $D_{4}$, $(D_5 \wr C_2):C_2$ |
20T157 x 3, 40T682, 40T687, 40T694 x 2, 40T725 x 2, 40T728, 40T729, 40T739 x 2, 40T746, 40T753, 40T759 x 2 |
| 20T197 |
$A_6.C_2^2$ |
$1440$ |
$-1$ |
|
$-1$ |
$16$ |
$M_{10}$ |
20T197, 20T202 x 2, 24T2954, 40T1187, 40T1188, 40T1192 x 4 |
| 20T200 |
$A_6:C_4$ |
$1440$ |
$-1$ |
|
$-1$ |
$22$ |
$\PGL(2,9)$ |
20T200, 24T2957, 40T1180, 40T1181 |
| 20T245 |
$C_2^5.C_2^4:C_5$ |
$2560$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_5$, $C_2^4 : C_5$ |
20T245 x 15, 40T1893 x 2, 40T1925 x 4, 40T1939 x 8, 40T1941 x 8, 40T1944 x 8, 40T1949 x 8, 40T1952 x 8, 40T1953 x 8, 40T2035 x 8, 40T2271 x 16, 40T2272 x 16, 40T2273 x 32 |
| 20T265 |
$A_6.D_4$ |
$2880$ |
$-1$ |
|
$-1$ |
$23$ |
$(A_6 : C_2) : C_2$ |
20T265 x 3, 24T5336 x 2, 40T2328, 40T2331 x 2, 40T2345, 40T2349 x 2, 40T2368 x 2 |
| 20T303 |
$C_2^5.C_2\wr C_5$ |
$5120$ |
$-1$ |
✓ |
$-1$ |
$50$ |
$C_5$, $C_2 \times (C_2^4 : C_5)$ |
20T303 x 15, 40T3647 x 4, 40T3896 x 4, 40T3965 x 8, 40T3975 x 8, 40T3982 x 8, 40T3983 x 8, 40T4011 x 8, 40T4017 x 8, 40T4024 x 8, 40T4029 x 8, 40T4073 x 2, 40T4086 x 2, 40T4216 x 4, 40T4283 x 4, 40T4298 x 8, 40T4305 x 8, 40T4316 x 8, 40T4334 x 8, 40T4416 x 4, 40T4522 x 8, 40T4706 x 8, 40T4709 x 8, 40T5033 x 16, 40T5034 x 16, 40T5035 x 16, 40T5036 x 16, 40T5037 x 32, 40T5038 x 32 |
| 21T22 |
$C_3\times \GL(3,2)$ |
$504$ |
$1$ |
|
$-1$ |
$18$ |
$C_3$, $\GL(3,2)$ |
21T22, 24T1355 x 2, 24T1356, 42T96 x 2, 42T103 x 2 |
| 21T27 |
$S_3\times \GL(3,2)$ |
$1008$ |
$-1$ |
|
$-1$ |
$18$ |
$S_3$, $\GL(3,2)$ |
21T27, 24T2671, 42T169 x 2, 42T170 x 2, 42T171 x 2, 42T175 x 2 |
| 21T67 |
$\PSL(3,4)$ |
$20160$ |
$1$ |
|
$-1$ |
$10$ |
|
21T67 |
| 21T85 |
$\PSL(3,4).C_2$ |
$40320$ |
$-1$ |
|
$-1$ |
$14$ |
|
21T85, 42T930 x 2 |
| 21T91 |
$\PGL(3,4)$ |
$60480$ |
$1$ |
|
$-1$ |
$22$ |
|
21T91 |
| 21T103 |
$\PSL(3,4).S_3$ |
$120960$ |
$-1$ |
|
$-1$ |
$20$ |
|
21T103, 42T1277 x 2 |
| 21T143 |
$\PSL(2,7)\wr C_3$ |
$14224896$ |
$1$ |
|
$-1$ |
$88$ |
$C_3$ |
21T143, 24T24055, 42T2782 x 2 |
| 21T146 |
$\PSL(2,7)\wr S_3$ |
$28449792$ |
$-1$ |
|
$-1$ |
$98$ |
$S_3$ |
21T146, 24T24314, 42T3078 x 2, 42T3079 x 2, 42T3080 x 2 |
| 22T13 |
$C_2\times \PSL(2,11)$ |
$1320$ |
$-1$ |
|
$-1$ |
$16$ |
$C_2$, $\PSL(2,11)$ |
22T13, 24T2948 |
| 22T40 |
$\PSL(2,11)\wr C_2$ |
$871200$ |
$-1$ |
|
$-1$ |
$44$ |
$C_2$ |
22T40, 24T21362 |
Results are complete for degrees $\leq 23$.
