Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 402 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×C3×C4×C5×D3 | C2 | semidirect |
| 3. C2×C5×#625 | C2 | semidirect |
| 4. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 16. #63908 | C5 | direct (N × H) |
| 21. C2×C5×D12 | D3 | semidirect |
| 22. C2×C4×C5×D3 | D3 | semidirect |
| 34. C2×C3×C5×D3 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 39. C2×C3×D12 | C2×C5 | semidirect |
| 40. C2×C3×C4×D3 | C2×C5 | semidirect |
| 41. C2×#625 | C2×C5 | semidirect |
| 42. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 43. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 96. C2×C5×D3 | D12 | semidirect |
| 99. C3×C4×C5 | #67 | semidirect |
| 100. C3×C4×C5 | #67 | semidirect |
| 109. C2×D12 | C5×D3 | semidirect |
| 110. C2×C4×D3 | C5×D3 | semidirect |
| 116. C32×C5 | #121 | semidirect |
| 131. C2×C3×D3 | C5×D4 | semidirect |
| 132. C32×C4 | C5×D4 | semidirect |
| 176. C4×C5 | #625 | semidirect |
| 188. C3×C5 | #930 | semidirect |
| 189. C3×C5 | #938 | semidirect |
| 204. C2×D3 | C5×D12 | semidirect |
| 207. C3×C4 | C5×#67 | semidirect |
| 208. C3×C4 | C5×#67 | semidirect |
| 218. C32 | C5×#121 | semidirect |
| 240. C5 | #63908 | direct (N × H) |
| 250. C4 | C5×#625 | semidirect |
| 252. C3 | C5×#930 | semidirect |
| 253. C3 | C5×#938 | 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×C3×C4×C5×D3 | 2 |
| C2×C5×#625 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#938 | 3 |
| C5×#930 | 3 |
| #63908 | 5 |