Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
280 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 2. C5×#3797 | C2 | semidirect |
| 3. C3×C5×#214 | C2 | semidirect |
| 4. C5×#3719 | C2 | semidirect |
| 5. C5×#3712 | C2 | semidirect |
| 16. #63931 | C5 | direct (N × H) |
| 22. C5×#214 | D3 | semidirect |
| 33. #3797 | C2×C5 | semidirect |
| 34. C3×#214 | C2×C5 | semidirect |
| 35. #3719 | C2×C5 | semidirect |
| 36. #3712 | C2×C5 | semidirect |
| 88. #214 | C5×D3 | semidirect |
| 91. C32×C5 | #137 | semidirect |
| 145. C3×C5 | #915 | semidirect |
| 161. C32 | C5×#137 | semidirect |
| 177. C5 | #63931 | direct (N × H) |
| 185. C3 | C5×#915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3830 | 2 |
| C5×#3797 | 2 |
| C3×C5×#214 | 2 |
| C5×#3719 | 2 |
| C5×#3712 | 2 |
| C5×#915 | 3 |
| #63931 | 5 |