Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
9T1 |
$C_9$ |
$9$ |
$1$ |
✓ |
$1$ |
$9$ |
$C_3$ |
|
9T2 |
$C_3^2$ |
$9$ |
$1$ |
✓ |
$1$ |
$9$ |
$C_3$ x 4 |
|
9T3 |
$D_{9}$ |
$18$ |
$1$ |
✓ |
$-1$ |
$6$ |
$S_3$ |
18T5 |
9T4 |
$S_3\times C_3$ |
$18$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_3$, $S_3$ |
6T5, 18T3 |
9T5 |
$C_3^2:C_2$ |
$18$ |
$1$ |
✓ |
$-1$ |
$6$ |
$S_3$ x 4 |
18T4 |
9T6 |
$C_9:C_3$ |
$27$ |
$1$ |
✓ |
$2$ |
$11$ |
$C_3$ |
27T5 |
9T7 |
$C_3^2:C_3$ |
$27$ |
$1$ |
✓ |
$2$ |
$11$ |
$C_3$ |
9T7 x 3, 27T3 |
9T8 |
$S_3^2$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$S_3$ x 2 |
6T9, 12T16, 18T9, 18T11 x 2, 36T13 |
9T10 |
$(C_9:C_3):C_2$ |
$54$ |
$1$ |
✓ |
$-1$ |
$10$ |
$S_3$ |
18T18, 27T14 |
9T11 |
$C_3^2 : C_6$ |
$54$ |
$1$ |
✓ |
$-1$ |
$10$ |
$S_3$ |
9T13, 18T20, 18T21, 18T22, 27T11 |
9T12 |
$(C_3^2:C_3):C_2$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$S_3$ |
9T12 x 3, 18T24 x 4, 27T6 |
9T13 |
$C_3^2 : S_3 $ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_3$ |
9T11, 18T20, 18T21, 18T22, 27T11 |
9T17 |
$C_3 \wr C_3 $ |
$81$ |
$1$ |
✓ |
$3$ |
$17$ |
$C_3$ |
9T17 x 2, 27T19, 27T21, 27T27 x 3 |
9T18 |
$C_3^2 : D_{6} $ |
$108$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$S_3$ |
9T18, 18T51 x 2, 18T55 x 2, 18T56, 18T57 x 2, 27T29, 36T87 x 2, 36T90 |
9T20 |
$C_3 \wr S_3 $ |
$162$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_3$ |
9T20 x 2, 18T86 x 3, 27T37, 27T50 x 3, 27T70 |
9T21 |
$(C_3^3:C_3):C_2$ |
$162$ |
$1$ |
✓ |
$-1$ |
$13$ |
$S_3$ |
9T21 x 2, 18T88 x 3, 27T51 x 3, 27T52, 27T67 |
9T22 |
$(C_3^3:C_3):C_2$ |
$162$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$C_3$ |
9T22 x 2, 18T85 x 3, 27T53 x 3, 27T62, 27T63 |
9T24 |
$((C_3^3:C_3):C_2):C_2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$ |
9T24 x 2, 18T129 x 3, 18T136 x 3, 18T137 x 3, 27T121, 27T128 x 3, 27T129, 36T502 x 3 |
9T25 |
$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3$ |
12T132 x 2, 12T133, 18T141 x 2, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
9T28 |
$S_3 \wr C_3 $ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_3$ |
12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
9T29 |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$ |
12T175, 18T219, 18T220, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
9T30 |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
$648$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$ |
12T177 x 2, 12T178, 18T217, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
9T31 |
$S_3\wr S_3$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_3$ |
12T213, 18T300, 18T303, 18T311, 18T312, 18T314, 18T315, 18T319, 18T320, 24T2893, 24T2894, 24T2895, 24T2912, 27T296, 27T298, 36T2197, 36T2198, 36T2199, 36T2201, 36T2202, 36T2210, 36T2211, 36T2212, 36T2213, 36T2214, 36T2215, 36T2216, 36T2217, 36T2218, 36T2219, 36T2220, 36T2225, 36T2226, 36T2229, 36T2305 |
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 |
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 |
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 |
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 |
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 |
Results are complete for degrees $\leq 23$.