Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
322 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 100 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. C5×#3750 | C2 | semidirect |
| 5. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 6. C5×#3724 | C2 | semidirect |
| 19. #63899 | C5 | direct (N × H) |
| 29. C5×C4⋊Dic3 | D3 | semidirect |
| 38. C2×C3×C5×D3 | Q8 | semidirect |
| 46. C2×#627 | C2×C5 | semidirect |
| 48. #3750 | C2×C5 | semidirect |
| 50. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 51. #3724 | C2×C5 | semidirect |
| 104. C2×C5×D3 | Dic6 | semidirect |
| 129. C4⋊Dic3 | C5×D3 | semidirect |
| 135. C32×C5 | C22⋊Q8 | semidirect |
| 148. C2×C3×D3 | C5×Q8 | semidirect |
| 210. C3×C5 | #878 | semidirect |
| 211. C3×C5 | #896 | semidirect |
| 220. C2×D3 | C5×Dic6 | semidirect |
| 240. C32 | C5×C22⋊Q8 | semidirect |
| 261. C5 | #63899 | direct (N × H) |
| 273. C3 | C5×#878 | semidirect |
| 274. C3 | C5×#896 | 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×D3×Dic3 | 2 |
| C5×#3750 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C5×#3724 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#896 | 3 |
| C5×#878 | 3 |
| #63899 | 5 |