| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 17T3 |
$C_{17}:C_{4}$ |
$68$ |
$1$ |
✓ |
$-1$ |
$8$ |
|
|
| 18T25 |
$C_6\times A_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$ x 4, $A_4\times C_2$, $C_3^2$ |
24T71 x 3, 36T18, 36T31 |
| 18T26 |
$C_2^2:C_{18}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $A_4\times C_2$, $C_9$ |
36T16, 36T30 |
| 18T27 |
$C_2\times C_3^2:C_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $C_3^2:C_4$ |
12T40 x 2, 12T41 x 2, 18T27, 24T76 x 2, 36T35, 36T36 |
| 18T28 |
$F_9$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_3^2:C_8$ |
9T15, 12T46, 24T81, 36T49 |
| 18T29 |
$S_3\times D_6$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 2, $D_{6}$ x 2, $S_3^2$ |
12T37 x 2, 18T29 x 3, 24T73, 36T34 x 2, 36T40 x 4 |
| 18T30 |
$C_3\times S_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_3$, $S_3$, $S_4$, $S_3\times C_3$ |
12T45, 18T33, 24T80, 24T84, 36T20, 36T52 |
| 18T31 |
$S_3\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $S_3$, $A_4$, $S_3\times C_3$ |
12T43, 18T32, 24T78, 24T83, 36T21, 36T50, 36T51 |
| 18T32 |
$S_3\times A_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$ |
12T43, 18T31, 24T78, 24T83, 36T21, 36T50, 36T51 |
| 18T33 |
$C_3\times S_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_3$, $S_3$, $S_4$, $S_3\times C_3$ |
12T45, 18T30, 24T80, 24T84, 36T20, 36T52 |
| 18T34 |
$\SOPlus(4,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_3^2:D_4$, $S_3^2:C_2$ |
6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
| 18T35 |
$\PSU(3,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $C_3^2:Q_8$ |
9T14, 12T47, 18T35 x 2, 24T82, 36T55 |
| 18T36 |
$\SOPlus(4,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3^2:C_2$ |
6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 24T72 x 2, 36T53, 36T54 x 2 |
| 18T37 |
$C_3:S_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$S_3$ x 4, $S_4$, $C_3^2:C_2$ |
12T44 x 3, 18T40, 24T79 x 3, 36T23, 36T56 |
| 18T38 |
$C_2^2:D_9$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$S_3$, $S_4$, $D_{9}$ |
18T39, 36T25, 36T57 |
| 18T39 |
$C_2^2:D_9$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$S_3$, $S_4$, $D_{9}$ |
18T38, 36T25, 36T57 |
| 18T40 |
$C_3:S_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$S_3$ x 4, $S_4$, $C_3^2:C_2$ |
12T44 x 3, 18T37, 24T79 x 3, 36T23, 36T56 |
| 18T41 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $C_3^2 : C_6$ |
18T41, 18T42 x 2, 36T71, 36T73, 36T75 |
| 18T42 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3$, $C_6$, $C_3^2 : S_3 $ |
18T41 x 2, 18T42, 36T71, 36T73, 36T75 |
| 18T43 |
$C_3\times S_3^2$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $C_6$, $S_3^2$ |
12T70, 18T46 x 2, 27T36, 36T80, 36T82 x 2, 36T92 |
| 18T44 |
$C_3^2:C_{12}$ |
$108$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_3$, $C_6$, $C_3^2:C_4$ |
12T73 x 2, 18T44, 27T33, 36T81 x 2, 36T95 x 2 |
| 18T45 |
$C_{18}:C_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $(C_9:C_3):C_2$ |
18T45, 36T67 |
| 18T46 |
$C_3\times S_3^2$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $S_3$, $D_{6}$, $S_3\times C_3$ |
12T70, 18T43, 18T46, 27T36, 36T80, 36T82 x 2, 36T92 |
| 18T47 |
$C_3^2.A_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $C_9:C_3$ |
18T47 x 2, 36T83 |
| 18T48 |
$C_3^2:A_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $C_3^2:C_3$ |
18T48 x 2, 36T84, 36T97 x 3 |
| 18T49 |
$\He_3:C_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_3^2:C_4$ |
18T49, 27T32, 36T85 x 2 |
| 18T50 |
$S_3\times D_9$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $D_{6}$ |
27T30, 36T86 |
| 18T51 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $S_3$, $S_3$, $C_3^2 : D_{6} $ |
9T18 x 2, 18T51, 18T55 x 2, 18T56, 18T57 x 2, 27T29, 36T87 x 2, 36T90 |
| 18T52 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $(C_3^2:C_3):C_2$ |
18T52 x 7, 36T79 x 4 |
| 18T53 |
$C_3:S_3^2$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $S_3$, $S_3^2$ |
12T71, 18T53 x 2, 27T35, 36T88 x 3, 36T93 |
| 18T54 |
$C_3^3:C_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $S_3$, $C_3^2:C_4$ |
12T72 x 2, 18T54, 27T31, 36T89 x 2, 36T94 x 2 |
| 18T55 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $S_3$, $D_{6}$, $C_3^2 : D_{6} $ |
9T18 x 2, 18T51 x 2, 18T55, 18T56, 18T57 x 2, 27T29, 36T87 x 2, 36T90 |
| 18T56 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $S_3^2$ |
9T18 x 2, 18T51 x 2, 18T55 x 2, 18T57 x 2, 27T29, 36T87 x 2, 36T90 |
| 18T57 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $S_3$, $D_{6}$, $C_3^2 : D_{6} $ |
9T18 x 2, 18T51 x 2, 18T55 x 2, 18T56, 18T57, 27T29, 36T87 x 2, 36T90 |
| 18T58 |
$C_3:S_3^2$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $D_{6}$, $S_3^2$ x 3 |
18T58 x 3, 27T34, 36T91 x 4 |
| 19T4 |
$C_{19}:C_{6}$ |
$114$ |
$-1$ |
✓ |
$-1$ |
$9$ |
|
|
| 20T16 |
$C_2^2\times F_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $F_5$, $F_{5}\times C_2$ x 3 |
20T16 x 3, 40T44 x 3, 40T56 |
| 20T17 |
$C_2^4:C_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_5$, $C_2^4 : C_5$ x 2 |
10T8 x 3, 16T178, 20T17 x 5, 20T23, 40T57 x 3 |
| 20T18 |
$C_{20}:C_4$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $D_{4}$, $F_5$, $F_{5}\times C_2$ |
20T18, 40T52, 40T54 |
| 20T19 |
$D_{10}:C_4$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $D_{4}$, $F_5$, $F_{5}\times C_2$ |
20T19, 20T22 x 2, 40T26, 40T45, 40T55 x 2 |
| 20T20 |
$C_4\times F_5$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $F_5$, $F_{5}\times C_2$ |
20T20 x 3, 40T53 x 2 |
| 20T21 |
$D_4\times D_5$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $D_{4}$, $D_{5}$, $D_{10}$ |
20T21 x 3, 40T22 x 2, 40T39 x 2, 40T40 x 2 |
| 20T22 |
$D_{10}:C_4$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $D_{4}$, $F_5$, $F_5$ |
20T19 x 2, 20T22, 40T26, 40T45, 40T55 x 2 |
| 20T23 |
$C_2^4:C_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_5$, $C_2^4 : C_5$ x 3 |
10T8 x 3, 16T178, 20T17 x 6, 40T57 x 3 |
| 20T24 |
$C_5\times D_{10}$ |
$100$ |
$1$ |
✓ |
$-1$ |
$40$ |
$C_2$ x 3, $C_2^2$, $D_5\times C_5$ |
20T24 |
| 20T25 |
$C_5:C_{20}$ |
$100$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$C_2$, $C_4$, $D_5\times C_5$ |
20T25 |
| 20T26 |
$C_5:F_5$ |
$100$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $C_4$ |
25T11 |
| 20T27 |
$C_5:F_5$ |
$100$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_4$, $C_5^2 : C_4$ |
10T10 x 2, 20T27, 25T10 |
| 20T28 |
$D_5^2$ |
$100$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_5^2$ |
10T9 x 2, 20T28, 25T12 |
| 20T29 |
$C_5\times F_5$ |
$100$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$C_2$, $C_4$ |
25T7 |
Results are complete for degrees $\leq 23$.
