Finite Group DatabasebetaFinite Group DatabasebetaOrder 10478.
64 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C132×C31 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D403 | — | 13 | 14 | no | maximal |
| 3 | C13×C31 | D13 | 1 | 14 | yes | complemented |
| 4 | C13⋊D13 | — | 31 | 1 | no | maximal, Hall |
| 5 | C132 | D31 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | D31 | — | 169 | 1 | no | Hall |
| 7 | C31 | C13⋊D13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | D13 | — | 403 | 14 | no | — |
| 9 | C13 | D403 | 1 | 14 | yes | complemented |
| 10 | C2 | — | 5239 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C31 | C2 |
| LCS | G ▷ C132×C31 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C132×C31 | C2 | semidirect |
| 3. C13×C31 | D13 | semidirect |
| 5. C132 | D31 | semidirect |
| 7. C31 | C13⋊D13 | semidirect |
| 9. C13 | D403 | semidirect |