Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 6. C2×C5×#157 | C4 | semidirect |
| 7. C2×C32×C4×C5 | C4 | semidirect |
| 8. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 10. #63781 | C5 | direct (N × H) |
| 37. C2×#157 | C4×C5 | semidirect |
| 38. C2×C32×C4 | C4×C5 | semidirect |
| 39. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 49. C32×C5 | #95 | semidirect |
| 56. C2×C4×C5 | #157 | semidirect |
| 103. C32 | C5×#95 | semidirect |
| 110. C2×C4 | C5×#157 | semidirect |
| 116. C5 | #63781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#157 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| #63781 | 5 |
| C5×#95 | 9 |