Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C5×#3797 | C2 | semidirect |
| 3. C5×#3743 | C2 | semidirect |
| 4. C3×C5×Dic12 | C2 | semidirect |
| 5. C3×C5×#204 | C2 | semidirect |
| 6. C5×#3718 | C2 | semidirect |
| 7. C5×#3715 | C2 | semidirect |
| 21. #63811 | C5 | direct (N × H) |
| 32. C5×Dic12 | D3 | semidirect |
| 33. C5×#204 | D3 | semidirect |
| 45. #3797 | C2×C5 | semidirect |
| 47. #3743 | C2×C5 | semidirect |
| 48. C3×Dic12 | C2×C5 | semidirect |
| 49. C3×#204 | C2×C5 | semidirect |
| 50. #3718 | C2×C5 | semidirect |
| 51. #3715 | C2×C5 | semidirect |
| 127. Dic12 | C5×D3 | semidirect |
| 128. #204 | C5×D3 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #915 | semidirect |
| 204. C3×C5 | #918 | semidirect |
| 225. C32 | C5×#137 | semidirect |
| 245. C5 | #63811 | direct (N × H) |
| 254. C3 | C5×#915 | semidirect |
| 255. C3 | C5×#918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3797 | 2 |
| C5×#3796 | 2 |
| C5×#3743 | 2 |
| C3×C5×Dic12 | 2 |
| C3×C5×#204 | 2 |
| C5×#3718 | 2 |
| C5×#3715 | 2 |
| C5×#918 | 3 |
| C5×#915 | 3 |
| #63811 | 5 |