Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
342 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 92 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×#634 | C2 | semidirect |
| 3. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 5. C5×Dic32 | C2 | semidirect |
| 14. #63913 | C5 | direct (N × H) |
| 21. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 32. C2×#634 | C2×C5 | semidirect |
| 34. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 35. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 36. Dic32 | C2×C5 | semidirect |
| 88. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 90. C32×C5 | #124 | semidirect |
| 144. C3×C5 | #885 | semidirect |
| 164. C32 | C5×#124 | semidirect |
| 179. C5 | #63913 | direct (N × H) |
| 189. C3 | C5×#885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#634 | 2 |
| C2×C5×#625 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×Dic32 | 2 |
| C5×#885 | 3 |
| #63913 | 5 |