Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 112 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×C5×D12 | C2 | semidirect |
| 2. C2×C5×#625 | C2 | semidirect |
| 3. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 10. #63914 | C5 | direct (N × H) |
| 13. C2×C5×D12 | D3 | semidirect |
| 19. C32×C4×C5 | D4 | semidirect |
| 20. C5×C3⋊Dic3 | D4 | semidirect |
| 22. C2×C3×D12 | C2×C5 | semidirect |
| 23. C2×#625 | C2×C5 | semidirect |
| 24. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 53. C3×C4×C5 | #67 | semidirect |
| 58. C2×D12 | C5×D3 | semidirect |
| 61. C32×C5 | #127 | semidirect |
| 70. C32×C4 | C5×D4 | semidirect |
| 71. C3⋊Dic3 | C5×D4 | semidirect |
| 92. C4×C5 | #625 | semidirect |
| 100. C3×C5 | #940 | semidirect |
| 108. C3×C4 | C5×#67 | semidirect |
| 114. C32 | C5×#127 | semidirect |
| 126. C5 | #63914 | direct (N × H) |
| 131. C4 | C5×#625 | semidirect |
| 133. C3 | C5×#940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D12 | 2 |
| C2×C5×#625 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#940 | 3 |
| #63914 | 5 |