Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×C5×D3×Q8 | C2 | semidirect |
| 3. C5×#3756 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C5×#3719 | C2 | semidirect |
| 6. C5×#3715 | C2 | semidirect |
| 7. C5×#3711 | C2 | semidirect |
| 21. #63946 | C5 | direct (N × H) |
| 23. C5×D3×Q8 | D3 | semidirect |
| 32. C5×#215 | D3 | semidirect |
| 45. C3×D3×Q8 | C2×C5 | semidirect |
| 47. #3756 | C2×C5 | semidirect |
| 48. C3×#215 | C2×C5 | semidirect |
| 49. #3719 | C2×C5 | semidirect |
| 50. #3715 | C2×C5 | semidirect |
| 51. #3711 | C2×C5 | semidirect |
| 118. D3×Q8 | C5×D3 | semidirect |
| 127. #215 | C5×D3 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #915 | semidirect |
| 203. C3×C5 | #942 | semidirect |
| 224. C32 | C5×#137 | semidirect |
| 243. C5 | #63946 | direct (N × H) |
| 252. C3 | C5×#915 | semidirect |
| 253. C3 | C5×#942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×Q8 | 2 |
| C5×#3795 | 2 |
| C5×#3756 | 2 |
| C3×C5×#215 | 2 |
| C5×#3719 | 2 |
| C5×#3715 | 2 |
| C5×#3711 | 2 |
| C5×#942 | 3 |
| C5×#915 | 3 |
| #63946 | 5 |