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×C3×C4×C5×D3 | C2 | semidirect |
| 3. C5×#3750 | C2 | semidirect |
| 4. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C5×Dic3⋊Dic3 | C2 | semidirect |
| 6. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 7. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 19. #63905 | C5 | direct (N × H) |
| 23. C2×C4×C5×D3 | D3 | semidirect |
| 29. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 48. C2×C3×C4×D3 | C2×C5 | semidirect |
| 50. #3750 | C2×C5 | semidirect |
| 51. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 52. Dic3⋊Dic3 | C2×C5 | semidirect |
| 53. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 54. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 130. C2×C4×D3 | C5×D3 | semidirect |
| 136. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 142. C32×C5 | #123 | semidirect |
| 224. C3×C5 | #883 | semidirect |
| 225. C3×C5 | #929 | semidirect |
| 259. C32 | C5×#123 | semidirect |
| 282. C5 | #63905 | direct (N × H) |
| 296. C3 | C5×#883 | semidirect |
| 297. C3 | C5×#929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C2×C5×#625 | 2 |
| C5×#3750 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#929 | 3 |
| C5×#883 | 3 |
| #63905 | 5 |