Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
410 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
| 2. C2×C5×#626 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C2×C5×#625 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 6. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C5×Dic3⋊Dic3 | C2 | semidirect |
| 21. #63906 | C5 | direct (N × H) |
| 29. C2×C4×C5×D3 | D3 | semidirect |
| 34. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 46. C2×C3×C5×D3 | D4 | semidirect |
| 50. C3×C5×Dic3 | D4 | semidirect |
| 52. C2×C3×C4×D3 | C2×C5 | semidirect |
| 53. C2×#626 | C2×C5 | semidirect |
| 54. C2×#626 | C2×C5 | semidirect |
| 55. C2×#625 | C2×C5 | semidirect |
| 56. #3752 | C2×C5 | semidirect |
| 57. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 58. Dic3⋊Dic3 | C2×C5 | semidirect |
| 133. C2×C5×D3 | D12 | semidirect |
| 143. C5×Dic3 | #67 | semidirect |
| 151. C2×C4×D3 | C5×D3 | semidirect |
| 156. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 159. C32×C5 | #121 | semidirect |
| 180. C2×C3×D3 | C5×D4 | semidirect |
| 184. C3×Dic3 | C5×D4 | semidirect |
| 255. C3×C5 | #884 | semidirect |
| 256. C3×C5 | #930 | semidirect |
| 280. C2×D3 | C5×D12 | semidirect |
| 290. Dic3 | C5×#67 | semidirect |
| 297. C32 | C5×#121 | semidirect |
| 325. C5 | #63906 | direct (N × H) |
| 341. C3 | C5×#884 | semidirect |
| 342. C3 | C5×#930 | 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×#626 | 2 |
| C2×C5×#625 | 2 |
| C5×#3752 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×#930 | 3 |
| C5×#884 | 3 |
| #63906 | 5 |