Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C2×C5×#627 | C2 | semidirect |
| 3. C5×#3757 | C2 | semidirect |
| 4. C3×C5×#217 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 6. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 7. C5×Dic32 | C2 | semidirect |
| 19. #63959 | C5 | direct (N × H) |
| 30. C5×#217 | D3 | semidirect |
| 49. C2×#627 | C2×C5 | semidirect |
| 50. #3757 | C2×C5 | semidirect |
| 51. C3×#217 | C2×C5 | semidirect |
| 52. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 53. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 54. Dic32 | C2×C5 | semidirect |
| 139. #217 | C5×D3 | semidirect |
| 144. C32×C5 | #124 | semidirect |
| 227. C3×C5 | #885 | semidirect |
| 228. C3×C5 | #936 | semidirect |
| 264. C32 | C5×#124 | semidirect |
| 288. C5 | #63959 | direct (N × H) |
| 302. C3 | C5×#885 | semidirect |
| 303. C3 | C5×#936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#67 | 2 |
| C2×C5×#627 | 2 |
| C5×#3757 | 2 |
| C3×C5×#217 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×Dic32 | 2 |
| C5×#936 | 3 |
| C5×#885 | 3 |
| #63959 | 5 |