| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 40T1 |
$C_{40}$ |
$40$ |
$-1$ |
✓ |
$1$ |
$40$ |
$C_2$, $C_4$, $C_5$, $C_8$, $C_{10}$, $C_{20}$ |
|
| 40T2 |
$C_2\times C_{20}$ |
$40$ |
$1$ |
✓ |
$1$ |
$40$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_5$, $C_4\times C_2$, $C_{10}$ x 3, $C_{20}$ x 2, $C_2\times C_{10}$ |
|
| 40T3 |
$C_5:C_8$ |
$40$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_4$, $D_{5}$, $C_8$, $D_5$, $C_5:C_4$ |
|
| 40T4 |
$C_{10}:C_4$ |
$40$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{5}$, $C_4\times C_2$, $D_5$, $D_{10}$ x 2, $C_5:C_4$ x 2, $D_{10}$ |
|
| 40T5 |
$C_5\times Q_8$ |
$40$ |
$1$ |
✓ |
$2$ |
$25$ |
$C_2$ x 3, $C_2^2$, $C_5$, $Q_8$, $C_{10}$ x 3, $C_2\times C_{10}$ |
|
| 40T6 |
$C_5\times D_4$ |
$40$ |
$1$ |
✓ |
$2$ |
$25$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $C_5$, $D_4$, $C_{10}$ x 3, $C_2\times C_{10}$, $C_5\times D_4$ x 2 |
20T12 x 2 |
| 40T7 |
$C_2^2\times C_{10}$ |
$40$ |
$1$ |
✓ |
$1$ |
$40$ |
$C_2$ x 7, $C_2^2$ x 7, $C_5$, $C_2^3$, $C_{10}$ x 7, $C_2\times C_{10}$ x 7 |
|
| 40T8 |
$C_5:Q_8$ |
$40$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8$, $D_5$, $D_{10}$ x 2, $D_{10}$ |
|
| 40T9 |
$C_4\times D_5$ |
$40$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{5}$, $C_4\times C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$, $C_4\times D_5$ x 2 |
20T6 x 2 |
| 40T10 |
$C_2\times D_{10}$ |
$40$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{5}$, $C_2^3$, $D_5$, $D_{10}$ x 6, $D_{10}$ x 3, $C_2\times D_{10}$ x 4 |
20T8 x 4 |
| 40T11 |
$C_5:D_4$ |
$40$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4$, $D_5$, $D_{10}$ x 2, $D_{10}$, $C_5:D_4$, $C_5:D_4$ |
20T7, 20T11 |
| 40T12 |
$D_{20}$ |
$40$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4$, $D_5$, $D_{10}$ x 2, $D_{10}$, $D_{20}$ x 2 |
20T10 x 2 |
| 40T13 |
$C_5:C_8$ |
$40$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_4$, $F_5$, $C_8$, $F_5$, $F_5$ |
|
| 40T14 |
$C_2\times F_5$ |
$40$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $F_5$, $C_4\times C_2$, $F_5$, $F_{5}\times C_2$ x 2, $F_5$, $C_2\times F_5$, $C_2\times F_5$ |
10T5 x 2, 20T9, 20T13 |
| 40T15 |
$C_5\times \OD_{16}$ |
$80$ |
$-1$ |
✓ |
$2$ |
$50$ |
$C_2$, $C_4$, $C_5$, $C_8:C_2$, $C_{10}$, $C_{20}$ |
|
| 40T16 |
$C_2^2:C_{20}$ |
$80$ |
$1$ |
✓ |
$2$ |
$50$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_5$, $C_2^2:C_4$, $C_{10}$, $C_{20}$, $C_5\times D_4$ x 2 |
40T16 |
| 40T17 |
$C_{20}.C_4$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_4$, $D_{5}$, $C_8:C_2$, $D_5$, $C_5:C_4$ |
|
| 40T18 |
$C_{10}.D_4$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{5}$, $C_2^2:C_4$, $D_5$, $C_5:C_4$, $C_5:D_4$ x 2 |
40T18 |
| 40T19 |
$D_4:C_{10}$ |
$80$ |
$1$ |
✓ |
$2$ |
$50$ |
$C_2$ x 3, $C_2^2$, $C_5$, $Q_8:C_2$, $C_{10}$ x 3, $C_2\times C_{10}$ |
40T19 x 2 |
| 40T20 |
$D_4\times C_{10}$ |
$80$ |
$1$ |
✓ |
$2$ |
$50$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $C_5$, $D_4\times C_2$, $C_{10}$ x 3, $C_2\times C_{10}$, $C_5\times D_4$ x 2 |
40T20 x 3 |
| 40T21 |
$D_4:D_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8:C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$ |
40T21, 40T35 |
| 40T22 |
$D_4\times D_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4\times C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$, $D_4\times D_5$ x 2 |
20T21 x 4, 40T22, 40T39 x 2, 40T40 x 2 |
| 40T23 |
$D_{20}:C_2$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8:C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$ |
40T37 x 2 |
| 40T24 |
$C_{10}:D_4$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4\times C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$, $C_5:D_4$ x 2 |
40T24, 40T33 x 2 |
| 40T25 |
$C_5:\OD_{16}$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_4$, $F_5$, $C_8:C_2$, $F_5$, $F_5$ |
|
| 40T26 |
$D_{10}:C_4$ |
$80$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_4$, $D_{4}$ x 2, $F_5$, $C_2^2:C_4$, $F_5$, $F_5$, $D_{10}:C_4$ x 2 |
20T19 x 2, 20T22 x 2, 40T45, 40T55 x 2 |
| 40T27 |
$C_8\times D_5$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $C_4$, $D_{5}$, $C_8$, $D_{10}$, $C_4\times D_5$ |
40T27 |
| 40T28 |
$C_{40}:C_2$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_4$, $D_{5}$, $C_8:C_2$, $D_{10}$, $C_4\times D_5$ |
|
| 40T29 |
$C_4\times D_{10}$ |
$80$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{5}$, $C_4\times C_2$, $D_{10}$ x 3, $C_4\times D_5$ x 2, $C_2\times D_{10}$ |
40T29 x 3 |
| 40T30 |
$D_{10}:C_4$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{5}$, $C_2^2:C_4$, $D_{10}$, $C_4\times D_5$, $C_5:D_4$, $D_{20}$ |
40T30 |
| 40T31 |
$Q_8:D_5$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{5}$, $QD_{16}$, $D_{10}$, $C_5:D_4$ |
|
| 40T32 |
$C_5:D_8$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{5}$, $D_{8}$, $D_{10}$, $C_5:D_4$ |
40T48 |
| 40T33 |
$C_{10}:D_4$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4\times C_2$, $D_{10}$ x 3, $C_5:D_4$ x 2, $C_2\times D_{10}$ |
40T24 x 2, 40T33 |
| 40T34 |
$Q_8\times D_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8$, $D_{10}$ x 3, $C_2\times D_{10}$ |
40T34 |
| 40T35 |
$D_4:D_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8:C_2$, $D_{10}$ x 3, $C_2\times D_{10}$ |
40T21 x 2 |
| 40T36 |
$D_{20}:C_2$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8:C_2$, $D_{10}$ x 3, $C_2\times D_{10}$ |
40T36 x 2 |
| 40T37 |
$D_{20}:C_2$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8:C_2$, $D_{10}$ x 3, $C_2\times D_{10}$ |
40T23, 40T37 |
| 40T38 |
$C_2\times D_{20}$ |
$80$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4\times C_2$, $D_{10}$ x 3, $C_2\times D_{10}$, $D_{20}$ x 2 |
40T38 x 3 |
| 40T39 |
$D_4\times D_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4\times C_2$, $D_{10}$ x 3, $C_2\times D_{10}$, $D_4\times D_5$ x 2 |
20T21 x 4, 40T22 x 2, 40T39, 40T40 x 2 |
| 40T40 |
$D_4\times D_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{5}$, $D_4$, $D_{10}$ x 3, $C_2\times D_{10}$, $D_4\times D_5$ x 2 |
20T21 x 4, 40T22 x 2, 40T39 x 2, 40T40 |
| 40T41 |
$C_2^2\times D_{10}$ |
$80$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{5}$, $C_2^3$, $D_{10}$ x 7, $C_2\times D_{10}$ x 7 |
40T41 x 7 |
| 40T42 |
$D_5:C_8$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $F_5$, $C_8$, $F_5$, $C_2\times F_5$ |
40T42 |
| 40T43 |
$C_{20}.C_4$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_4$, $F_5$, $C_8:C_2$, $F_5$, $C_2\times F_5$ |
|
| 40T44 |
$C_2^2\times F_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $F_5$, $C_4\times C_2$, $F_5$, $F_{5}\times C_2$ x 2, $C_2\times F_5$ x 2, $C_2\times F_5$ |
20T16 x 4, 40T44 x 2, 40T56 |
| 40T45 |
$D_{10}:C_4$ |
$80$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_4$, $D_{4}$ x 2, $F_5$, $C_2^2:C_4$, $F_5$, $C_2\times F_5$, $D_{10}:C_4$ x 2 |
20T19 x 2, 20T22 x 2, 40T26, 40T55 x 2 |
| 40T46 |
$D_{40}$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$23$ |
$C_2$, $D_{4}$, $D_{5}$, $D_{8}$, $D_{10}$, $D_{20}$ |
40T46 |
| 40T47 |
$C_{40}:C_2$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$23$ |
$C_2$, $D_{4}$, $D_{5}$, $QD_{16}$, $D_{10}$, $D_{20}$ |
|
| 40T48 |
$C_5:D_8$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{5}$, $D_{8}$, $D_5$, $C_5:D_4$ |
40T32 |
| 40T49 |
$C_5:\SD_{16}$ |
$80$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{5}$, $QD_{16}$, $D_5$, $C_5:D_4$ |
|
| 40T50 |
$C_5\times D_8$ |
$80$ |
$-1$ |
✓ |
$3$ |
$35$ |
$C_2$, $D_{4}$, $C_5$, $D_{8}$, $C_{10}$, $C_5\times D_4$ |
40T50 |
Results are complete for degrees $\leq 23$.
