Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 1. C2×C5×#638 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C2×C5×#625 | C2 | semidirect |
| 5. C5×Dic32 | C2 | semidirect |
| 16. #63979 | C5 | direct (N × H) |
| 22. C2×C5×#67 | D3 | semidirect |
| 33. C5×C3⋊Dic3 | D4 | semidirect |
| 34. C3×C5×Dic3 | D4 | semidirect |
| 36. C2×#638 | C2×C5 | semidirect |
| 37. C2×C3×#67 | C2×C5 | semidirect |
| 38. C2×#626 | C2×C5 | semidirect |
| 39. C2×#625 | C2×C5 | semidirect |
| 40. Dic32 | C2×C5 | semidirect |
| 99. C5×Dic3 | #67 | semidirect |
| 105. C2×#67 | C5×D3 | semidirect |
| 108. C32×C5 | #127 | semidirect |
| 126. C3⋊Dic3 | C5×D4 | semidirect |
| 127. C3×Dic3 | C5×D4 | semidirect |
| 178. C3×C5 | #940 | semidirect |
| 200. Dic3 | C5×#67 | semidirect |
| 206. C32 | C5×#127 | semidirect |
| 227. C5 | #63979 | direct (N × H) |
| 239. C3 | C5×#940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×C5×#626 | 2 |
| C2×C5×#625 | 2 |
| C5×Dic32 | 2 |
| C5×#940 | 3 |
| #63979 | 5 |