Finite Group DatabasebetaFinite Group DatabasebetaOrder 31958.
44 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C19×C292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C29×D29 | — | 19 | 1 | no | maximal, Hall |
| 3 | D551 | C29 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 4 | C29×D19 | — | 29 | 1 | no | maximal |
| 5 | C292 | D19 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C19×C29 | — | 2 | 14 | no | — |
| 7 | C19×C29 | D29 | 1 | 1 | yes | characteristic, complemented |
| 8 | C19×C29 | C2×C29 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×C29 | — | 551 | 1 | no | — |
| 10 | D29 | — | 19 | 1 | no | — |
| 11 | D19 | — | 29 | 1 | no | Hall |
| 12 | C29 | — | 2 | 14 | no | — |
| 13 | C29 | C29×D19 | 1 | 1 | yes | characteristic, complemented |
| 14 | C29 | D551 | 1 | 1 | yes | characteristic, direct product factor |
| 15 | C19 | C29×D29 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C2 | — | 551 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D551 |
| commutator, cosocle, hypocenter | C19×C29 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C19×C292 | C2 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 ◁ C29 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C292 | C2 | semidirect |
| 3. D551 | C29 | direct (N × H) |
| 5. C292 | D19 | semidirect |
| 7. C19×C29 | D29 | semidirect |
| 8. C19×C29 | C2×C29 | semidirect |
| 13. C29 | C29×D19 | semidirect |
| 14. C29 | D551 | direct (N × H) |
| 15. C19 | C29×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×C292 | 2 |
| C29×D29 | 19 |
| D551 | 29 |
| C29×D19 | 29 |