Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 16. #63916 | C5 | direct (N × H) |
| 20. C2×C5×D12 | D3 | semidirect |
| 27. C5×C4⋊Dic3 | D3 | semidirect |
| 31. C2×C5×C3⋊D3 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 39. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 40. C2×C3×D12 | C2×C5 | semidirect |
| 41. C2×#626 | C2×C5 | semidirect |
| 42. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 43. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 104. C3×C4×C5 | D12 | semidirect |
| 105. C3×C4×C5 | #67 | semidirect |
| 113. C2×D12 | C5×D3 | semidirect |
| 120. C4⋊Dic3 | C5×D3 | semidirect |
| 121. C32×C5 | #121 | semidirect |
| 133. C2×C3⋊D3 | C5×D4 | semidirect |
| 137. C32×C4 | C5×D4 | semidirect |
| 184. C4×C5 | #626 | semidirect |
| 196. C3×C5 | #895 | semidirect |
| 197. C3×C5 | #938 | semidirect |
| 218. C3×C4 | C5×D12 | semidirect |
| 219. C3×C4 | C5×#67 | semidirect |
| 229. C32 | C5×#121 | semidirect |
| 252. C5 | #63916 | direct (N × H) |
| 262. C4 | C5×#626 | semidirect |
| 264. C3 | C5×#895 | semidirect |
| 265. C3 | C5×#938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C5×#626 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#938 | 3 |
| C5×#895 | 3 |
| #63916 | 5 |