| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
$\#\Aut(F/K)$ |
Conj. classes |
Subfields |
Low Degree Siblings |
| 5T5 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$1$ |
$7$ |
|
6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 6T14 |
$\PGL(2,5)$ |
$120$ |
$-1$ |
|
$-1$ |
$1$ |
$7$ |
|
5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 10T12 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$2$ |
$7$ |
$C_2$, $S_5$ |
5T5, 6T14, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 10T13 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$1$ |
$7$ |
|
5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 12T74 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$2$ |
$7$ |
$C_2$, $\PGL(2,5)$ |
5T5, 6T14, 10T12, 10T13, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 15T10 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$1$ |
$7$ |
$S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 20T30 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$2$ |
$7$ |
$S_5$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 20T32 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$2$ |
$7$ |
$C_2$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 20T35 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$2$ |
$7$ |
$S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 24T202 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$4$ |
$7$ |
$C_2$, $\PGL(2,5)$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 30T22, 30T25, 30T27, 40T62 |
| 30T22 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$2$ |
$7$ |
$S_5$, $\PGL(2,5)$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T25, 30T27, 40T62 |
| 30T25 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$6$ |
$7$ |
$C_2$, $S_5$, $S_5$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T27, 40T62 |
| 30T27 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$2$ |
$7$ |
$S_5$, $S_5$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 40T62 |
| 40T62 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$4$ |
$7$ |
$C_2$, $S_5$, $S_5$, $S_5$, $S_5$, $S_5$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27 |
