Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 334 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×#627 | C2 | semidirect |
| 3. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 4. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 14. #63915 | C5 | direct (N × H) |
| 20. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 32. C2×#627 | C2×C5 | semidirect |
| 34. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 35. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 36. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 87. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 90. C32×C5 | #124 | semidirect |
| 145. C3×C5 | #885 | semidirect |
| 166. C32 | C5×#124 | semidirect |
| 182. C5 | #63915 | direct (N × H) |
| 192. 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×#627 | 2 |
| C2×C5×#625 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#885 | 3 |
| #63915 | 5 |