Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. C5×#3724 | C2 | semidirect |
| 5. C5×Dic3⋊Dic3 | C2 | semidirect |
| 6. C5×Dic3⋊Dic3 | C2 | semidirect |
| 7. C5×Dic32 | C2 | semidirect |
| 17. #63956 | C5 | direct (N × H) |
| 47. #3724 | C2×C5 | semidirect |
| 48. Dic3⋊Dic3 | C2×C5 | semidirect |
| 49. Dic3⋊Dic3 | C2×C5 | semidirect |
| 50. Dic32 | C2×C5 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #879 | semidirect |
| 200. C3×C5 | #879 | semidirect |
| 231. C32 | C5×#126 | semidirect |
| 251. C5 | #63956 | direct (N × H) |
| 263. C3 | C5×#879 | semidirect |
| 264. C3 | C5×#879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3757 | 2 |
| C3×C5×#217 | 2 |
| C5×#3724 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×Dic32 | 2 |
| C5×#879 | 3 |
| #63956 | 5 |