Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 100 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×D12 | C2 | semidirect |
| 2. C2×C5×#625 | C2 | semidirect |
| 3. C2×C5×#625 | C2 | semidirect |
| 4. C2×C5×D3×Dic3 | C2 | semidirect |
| 5. C5×#3750 | C2 | semidirect |
| 6. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 21. #63885 | C5 | direct (N × H) |
| 28. C2×C5×D12 | D3 | semidirect |
| 33. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 46. C2×C3×C5×D3 | D4 | semidirect |
| 49. C5×C3⋊Dic3 | D4 | semidirect |
| 52. C2×C3×D12 | C2×C5 | semidirect |
| 53. C2×#625 | C2×C5 | semidirect |
| 54. C2×#625 | C2×C5 | semidirect |
| 55. C2×D3×Dic3 | C2×C5 | semidirect |
| 56. #3750 | C2×C5 | semidirect |
| 57. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 58. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 130. C2×C5×D3 | #67 | semidirect |
| 148. C2×D12 | C5×D3 | semidirect |
| 153. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 157. C32×C5 | #121 | semidirect |
| 178. C2×C3×D3 | C5×D4 | semidirect |
| 181. C3⋊Dic3 | C5×D4 | semidirect |
| 252. C3×C5 | #884 | semidirect |
| 253. C3×C5 | #939 | semidirect |
| 274. C2×D3 | C5×#67 | semidirect |
| 292. C32 | C5×#121 | semidirect |
| 319. C5 | #63885 | direct (N × H) |
| 335. C3 | C5×#884 | semidirect |
| 336. C3 | C5×#939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D12 | 2 |
| C2×C5×#625 | 2 |
| C2×C5×D3×Dic3 | 2 |
| C5×#3750 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#939 | 3 |
| C5×#884 | 3 |
| #63885 | 5 |