Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 120 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×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 14. #63911 | C5 | direct (N × H) |
| 21. C2×C5×D12 | D3 | semidirect |
| 23. C4×C5×Dic3 | D3 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 30. C3×C5×Dic3 | D4 | semidirect |
| 32. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 33. C2×C3×D12 | C2×C5 | semidirect |
| 34. C2×#626 | C2×C5 | semidirect |
| 35. C3×C4×Dic3 | C2×C5 | semidirect |
| 85. C3×C4×C5 | D12 | semidirect |
| 86. C3×C4×C5 | #67 | semidirect |
| 87. C5×Dic3 | D12 | semidirect |
| 94. C2×D12 | C5×D3 | semidirect |
| 96. C4×Dic3 | C5×D3 | semidirect |
| 97. C32×C5 | #127 | semidirect |
| 110. C32×C4 | C5×D4 | semidirect |
| 111. C3×Dic3 | C5×D4 | semidirect |
| 147. C4×C5 | #626 | semidirect |
| 157. C3×C5 | #874 | semidirect |
| 158. C3×C5 | #940 | semidirect |
| 174. C3×C4 | C5×D12 | semidirect |
| 175. C3×C4 | C5×#67 | semidirect |
| 176. Dic3 | C5×D12 | semidirect |
| 181. C32 | C5×#127 | semidirect |
| 200. C5 | #63911 | direct (N × H) |
| 207. C4 | C5×#626 | semidirect |
| 209. C3 | C5×#874 | semidirect |
| 210. C3 | C5×#940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C5×#626 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C5×#940 | 3 |
| C5×#874 | 3 |
| #63911 | 5 |