Finite Group DatabasebetaFinite Group DatabasebetaOrder 15717.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C132×C31 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | #11925882 | — | 13 | 1 | no | maximal |
| 3 | #11925881 | — | 13 | 1 | no | maximal |
| 4 | #92789 | — | 31 | 1 | no | maximal, Hall |
| 5 | C13×C31 | — | 3 | 4 | no | — |
| 6 | C13×C31 | C13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 7 | C13×C31 | C13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | C132 | C31⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C31⋊C3 | — | 169 | 1 | no | Hall |
| 10 | C13⋊C3 | — | 403 | 1 | no | — |
| 11 | C13⋊C3 | — | 403 | 1 | no | — |
| 12 | C31 | #92789 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C13 | — | 3 | 4 | no | — |
| 14 | C13 | #11925881 | 1 | 1 | yes | characteristic, complemented |
| 15 | C13 | #11925882 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3 | — | 5239 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C31 | C3 |
| LCS | G ▷ C132×C31 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C132×C31 | C3 | semidirect |
| 6. C13×C31 | C13⋊C3 | semidirect |
| 7. C13×C31 | C13⋊C3 | semidirect |
| 8. C132 | C31⋊C3 | semidirect |
| 12. C31 | #92789 | semidirect |
| 14. C13 | #11925881 | semidirect |
| 15. C13 | #11925882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C132×C31 | 3 |
| #11925882 | 13 |
| #11925881 | 13 |
| #92789 | 31 |