Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
298 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 19. #63839 | C5 | direct (N × H) |
| 38. C5×C3⋊Dic3 | Q8 | semidirect |
| 42. C3×C5×Dic3 | Q8 | semidirect |
| 111. C5×Dic3 | Dic6 | semidirect |
| 128. C32×C5 | C4⋊Q8 | semidirect |
| 141. C3⋊Dic3 | C5×Q8 | semidirect |
| 145. C3×Dic3 | C5×Q8 | semidirect |
| 196. C3×C5 | #888 | semidirect |
| 197. C3×C5 | #944 | semidirect |
| 216. Dic3 | C5×Dic6 | semidirect |
| 221. C32 | C5×C4⋊Q8 | semidirect |
| 240. C5 | #63839 | direct (N × H) |
| 250. C3 | C5×#888 | semidirect |
| 251. C3 | C5×#944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Dic6 | 2 |
| C2×C5×#627 | 2 |
| C5×#3750 | 2 |
| C3×C5×Dic3⋊C4 | 2 |
| C5×#3724 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×Dic32 | 2 |
| C5×#944 | 3 |
| C5×#888 | 3 |
| #63839 | 5 |