Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
366 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 92 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×C4×C5×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C3×C5×Dic3⋊C4 | C2 | semidirect |
| 5. C5×Dic3⋊Dic3 | C2 | semidirect |
| 6. C5×#3722 | C2 | semidirect |
| 7. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 19. #63853 | C5 | direct (N × H) |
| 31. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 34. C5×Dic3⋊C4 | D3 | semidirect |
| 48. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 50. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 51. C3×Dic3⋊C4 | C2×C5 | semidirect |
| 52. Dic3⋊Dic3 | C2×C5 | semidirect |
| 53. #3722 | C2×C5 | semidirect |
| 54. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 141. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 144. Dic3⋊C4 | C5×D3 | semidirect |
| 145. C32×C5 | #123 | semidirect |
| 229. C3×C5 | #883 | semidirect |
| 230. C3×C5 | #894 | semidirect |
| 266. C32 | C5×#123 | semidirect |
| 290. C5 | #63853 | direct (N × H) |
| 304. C3 | C5×#883 | semidirect |
| 305. C3 | C5×#894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C5×#626 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C5×Dic3⋊C4 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×#3722 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#894 | 3 |
| C5×#883 | 3 |
| #63853 | 5 |