Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
342 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 132 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×C32×C5×Q8 | C2 | semidirect |
| 3. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 6. C5×#947 | C3 | direct (N × H) |
| 13. C3×#947 | C5 | direct (N × H) |
| 15. C2×C3×C5×Q8 | D3 | semidirect |
| 16. C2×C3×C5×Q8 | C2×C3 | semidirect |
| 21. C5×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 22. C4×C5×Dic3 | C2×C3 | semidirect |
| 30. C2×C32×Q8 | C2×C5 | semidirect |
| 32. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 33. C3×C4×Dic3 | C2×C5 | semidirect |
| 50. #947 | C3×C5 | direct (N × H) |
| 54. C2×C5×Q8 | C3×D3 | semidirect |
| 80. C2×C3×Q8 | C5×D3 | semidirect |
| 81. C2×C3×Q8 | C2×C3×C5 | semidirect |
| 86. (C2×D3)⋊C4 | C2×C3×C5 | semidirect |
| 87. C4×Dic3 | C2×C3×C5 | semidirect |
| 88. C32×C5 | #124 | semidirect |
| 134. C2×Q8 | C3×C5×D3 | semidirect |
| 139. C3×C5 | #947 | direct (N × H) |
| 140. C3×C5 | C3×#124 | semidirect |
| 159. C32 | C5×#124 | semidirect |
| 174. C5 | C3×#947 | direct (N × H) |
| 182. C3 | C5×#947 | direct (N × H) |
| 183. C3 | C3×C5×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C3×C5×D12 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C3×C5×#124 | 3 |
| C5×#947 | 3 |
| C3×#947 | 5 |