Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 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. C3×C5×#494 | C2 | semidirect |
| 4. C5×#4547 | C2 | semidirect |
| 5. C5×#4458 | C2 | semidirect |
| 18. #71305 | C5 | direct (N × H) |
| 19. C5×#494 | D3 | semidirect |
| 39. C3×#494 | C2×C5 | semidirect |
| 42. #4547 | C2×C5 | semidirect |
| 43. #4458 | C2×C5 | semidirect |
| 65. C5×D12 | Q16 | semidirect |
| 98. #494 | C5×D3 | semidirect |
| 169. D12 | C5×Q16 | semidirect |
| 202. C3×C5 | #1669 | semidirect |
| 238. C5 | #71305 | direct (N × H) |
| 250. C3 | C5×#1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#494 | 2 |
| C5×#5087 | 2 |
| C5×C8×D12 | 2 |
| C5×#4547 | 2 |
| C5×#4458 | 2 |
| C5×#1669 | 3 |
| #71305 | 5 |