| Label |
Name |
Degree |
Order |
Parity |
Solvable |
Nil. class |
$\#\Aut(F/K)$ |
Transitivity |
Conj. classes |
Subfields |
Low Degree Siblings |
| 20T144 |
$C_2^5.D_{10}$ |
$20$ |
$640$ |
$-1$ |
✓ |
$-1$ |
$4$ |
$1$ |
$40$ |
$C_2$, $D_{5}$, $D_{10}$ |
20T144 x 5, 40T455 x 3, 40T464 x 6, 40T465 x 6, 40T533 x 6, 40T535 x 6, 40T544 x 6, 40T545 x 6 |
| 40T455 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$8$ |
$1$ |
$40$ |
$C_2$ x 3, $C_2^2$, $D_{5}$, $D_5$, $D_{10}$ x 2, $D_{10}$, $C_2^5.D_{10}$ x 2 |
20T144 x 6, 40T455 x 2, 40T464 x 6, 40T465 x 6, 40T533 x 6, 40T535 x 6, 40T544 x 6, 40T545 x 6 |
| 40T464 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$8$ |
$1$ |
$40$ |
$C_2$, $C_4$, $D_{5}$, $D_{10}$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$, $C_4\times D_5$, $C_2\wr D_5$, $C_2^5.D_{10}$ |
20T144 x 6, 40T455 x 3, 40T464 x 5, 40T465 x 6, 40T533 x 6, 40T535 x 6, 40T544 x 6, 40T545 x 6 |
| 40T465 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$8$ |
$1$ |
$40$ |
$C_2$, $C_4$, $D_{5}$, $D_{10}$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$, $C_4\times D_5$, $C_2\wr D_5$, $C_2^5.D_{10}$ |
20T144 x 6, 40T455 x 3, 40T464 x 6, 40T465 x 5, 40T533 x 6, 40T535 x 6, 40T544 x 6, 40T545 x 6 |
| 40T533 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$4$ |
$1$ |
$40$ |
$C_2$, $D_{5}$, $D_{10}$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$, $C_2\wr D_5$ |
20T144 x 6, 40T455 x 3, 40T464 x 6, 40T465 x 6, 40T533 x 5, 40T535 x 6, 40T544 x 6, 40T545 x 6 |
| 40T535 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$8$ |
$1$ |
$40$ |
$C_2$, $D_{5}$, $D_{10}$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$, $C_2\wr D_5$, $C_2^5.D_{10}$ x 2 |
20T144 x 6, 40T455 x 3, 40T464 x 6, 40T465 x 6, 40T533 x 6, 40T535 x 5, 40T544 x 6, 40T545 x 6 |
| 40T544 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$4$ |
$1$ |
$40$ |
$C_2$, $D_{5}$, $D_{10}$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$, $C_2\wr D_5$ |
20T144 x 6, 40T455 x 3, 40T464 x 6, 40T465 x 6, 40T533 x 6, 40T535 x 6, 40T544 x 5, 40T545 x 6 |
| 40T545 |
$C_2^5.D_{10}$ |
$40$ |
$640$ |
$1$ |
✓ |
$-1$ |
$8$ |
$1$ |
$40$ |
$C_2$, $D_{5}$, $D_{10}$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$, $C_2\wr D_5$, $C_2^5.D_{10}$ x 2 |
20T144 x 6, 40T455 x 3, 40T464 x 6, 40T465 x 6, 40T533 x 6, 40T535 x 6, 40T544 x 6, 40T545 x 5 |
