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 |
|---|---|---|
| 1. C2×C5×#627 | C2 | semidirect |
| 3. C5×#3752 | C2 | semidirect |
| 4. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C4×C5×Dic3 | C2 | semidirect |
| 6. C5×#3722 | C2 | semidirect |
| 7. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 19. #63852 | C5 | direct (N × H) |
| 33. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 34. C4×C5×Dic3 | D3 | semidirect |
| 48. C2×#627 | C2×C5 | semidirect |
| 50. #3752 | C2×C5 | semidirect |
| 51. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 52. C3×C4×Dic3 | C2×C5 | semidirect |
| 53. #3722 | C2×C5 | semidirect |
| 54. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 142. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 143. C4×Dic3 | C5×D3 | semidirect |
| 144. C32×C5 | #124 | semidirect |
| 227. C3×C5 | #875 | semidirect |
| 228. C3×C5 | #885 | semidirect |
| 264. C32 | C5×#124 | semidirect |
| 288. C5 | #63852 | direct (N × H) |
| 302. C3 | C5×#875 | semidirect |
| 303. C3 | C5×#885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#627 | 2 |
| C2×C5×#626 | 2 |
| C5×#3752 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C5×#3722 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#885 | 3 |
| C5×#875 | 3 |
| #63852 | 5 |