Finite Group DatabasebetaFinite Group DatabasebetaOrder 36518.
136 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C19×C312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C2×C312 | — | 19 | 1 | no | maximal, Hall |
| 3 | C31×D19 | C31 | 1 | 32 | yes | maximal, direct product factor |
| 4 | C312 | D19 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 5 | C19×C31 | C2×C31 | 1 | 32 | yes | complemented |
| 6 | C2×C31 | — | 19 | 32 | no | — |
| 7 | D19 | C312 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 8 | C31 | C31×D19 | 1 | 32 | yes | direct product factor |
| 9 | C19 | C2×C312 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2 | — | 19 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C312 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C312 |
| Frattini | C1 | G |
| Fitting, socle | C19×C312 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C312 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C312 | C2 | semidirect |
| 3. C31×D19 | C31 | direct (N × H) |
| 4. C312 | D19 | direct (N × H) |
| 5. C19×C31 | C2×C31 | semidirect |
| 7. D19 | C312 | direct (N × H) |
| 8. C31 | C31×D19 | direct (N × H) |
| 9. C19 | C2×C312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×C312 | 2 |
| C2×C312 | 19 |
| C31×D19 | 31 |