Finite Group DatabasebetaFinite Group DatabasebetaOrder 10830.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11762245⋊C5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | (C19⋊D19)⋊C5 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | #14524206 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C192⋊C5 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | #11762245 | C2×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C19⋊D19 | C3×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C192 | C2×C3×C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | D19⋊C3 | — | 95 | 4 | no | — |
| 9 | C19⋊C3 | — | 95 | 4 | no | — |
| 10 | D19 | — | 95 | 4 | no | — |
| 11 | C2×C3×C5 | — | 361 | 1 | no | maximal, Hall |
| 12 | C19 | — | 5 | 4 | no | — |
| 13 | C3×C5 | — | 361 | 1 | no | Hall |
| 14 | C2×C5 | — | 361 | 1 | no | Hall |
| 15 | C2×C3 | — | 361 | 1 | no | Hall |
| 16 | C5 | — | 361 | 1 | no | Sylow |
| 17 | C3 | — | 361 | 1 | no | Sylow |
| 18 | C2 | — | 361 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11762245⋊C5 | C2 | semidirect |
| 2. (C19⋊D19)⋊C5 | C3 | semidirect |
| 3. #14524206 | C5 | semidirect |
| 4. C192⋊C5 | C2×C3 | semidirect |
| 5. #11762245 | C2×C5 | semidirect |
| 6. C19⋊D19 | C3×C5 | semidirect |
| 7. C192 | C2×C3×C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762245⋊C5 | 2 |
| (C19⋊D19)⋊C5 | 3 |
| #14524206 | 5 |
| C2×C3×C5 | 361 |