Finite Group DatabasebetaFinite Group DatabasebetaOrder 31694.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C13×C23×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C23×D53 | — | 13 | 1 | no | maximal, Hall |
| 3 | D689 | C23 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C23×C53 | D13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C13×C53 | C2×C23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C23×D13 | — | 53 | 1 | no | maximal, Hall |
| 7 | C13×C23 | D53 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D53 | — | 13 | 1 | no | Hall |
| 9 | C53 | C23×D13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2×C23 | — | 689 | 1 | no | Hall |
| 11 | D13 | — | 53 | 1 | no | Hall |
| 12 | C23 | D689 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 13 | C13 | C23×D53 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 689 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D689 |
| commutator, cosocle, hypocenter | C13×C53 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C53 | C2 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×C23×C53 | C2 | semidirect |
| 3. D689 | C23 | direct (N × H) |
| 4. C23×C53 | D13 | semidirect |
| 5. C13×C53 | C2×C23 | semidirect |
| 7. C13×C23 | D53 | semidirect |
| 9. C53 | C23×D13 | semidirect |
| 12. C23 | D689 | direct (N × H) |
| 13. C13 | C23×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×C23×C53 | 2 |
| C23×D53 | 13 |
| D689 | 23 |
| C23×D13 | 53 |