Finite Group DatabasebetaFinite Group DatabasebetaOrder 31730.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×C19×C167 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C19×D167 | — | 5 | 1 | no | maximal, Hall |
| 3 | C19×C167 | D5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D835 | C19 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C5×C167 | C2×C19 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D167 | — | 5 | 1 | no | Hall |
| 7 | D5×C19 | — | 167 | 1 | no | maximal, Hall |
| 8 | C167 | D5×C19 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C5×C19 | D167 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | C2×C19 | — | 835 | 1 | no | Hall |
| 11 | C19 | D835 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 12 | D5 | — | 167 | 1 | no | Hall |
| 13 | C5 | C19×D167 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 835 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D835 |
| commutator, cosocle, hypocenter | C5×C167 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C167 | C2 |
| LCS | G ▷ C5×C167 | |
| UCS | C1 ◁ C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C19×C167 | C2 | semidirect |
| 3. C19×C167 | D5 | semidirect |
| 4. D835 | C19 | direct (N × H) |
| 5. C5×C167 | C2×C19 | semidirect |
| 8. C167 | D5×C19 | semidirect |
| 9. C5×C19 | D167 | semidirect |
| 11. C19 | D835 | direct (N × H) |
| 13. C5 | C19×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C19×C167 | 2 |
| C19×D167 | 5 |
| D835 | 19 |
| D5×C19 | 167 |