Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
316 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×Q32 | C2 | semidirect |
| 3. C5×Dic3×Q16 | C2 | semidirect |
| 5. C5×#4564 | C2 | semidirect |
| 7. C5×Dic3⋊C16 | C2 | semidirect |
| 22. #71498 | C5 | direct (N × H) |
| 23. C2×C5×Q32 | D3 | semidirect |
| 50. C2×C3×Q32 | C2×C5 | semidirect |
| 52. Dic3×Q16 | C2×C5 | semidirect |
| 54. #4564 | C2×C5 | semidirect |
| 56. Dic3⋊C16 | C2×C5 | semidirect |
| 120. C2×Q32 | C5×D3 | semidirect |
| 238. C3×C5 | #2211 | semidirect |
| 274. C5 | #71498 | direct (N × H) |
| 286. C3 | C5×#2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q32 | 2 |
| C5×#5191 | 2 |
| C5×Dic3×Q16 | 2 |
| C2×C5×#828 | 2 |
| C5×#4564 | 2 |
| C5×#4509 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#2211 | 3 |
| #71498 | 5 |