Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 94 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×#901 | C2 | semidirect |
| 3. C3×C4×C5×C8 | C2 | semidirect |
| 4. C5×#819 | C2 | semidirect |
| 5. C5×#805 | C2 | semidirect |
| 12. C5×Dic12 | C4 | semidirect |
| 13. C5×D24 | C4 | semidirect |
| 14. C5×#204 | C4 | semidirect |
| 17. #4700 | C5 | direct (N × H) |
| 22. C4×C5×C8 | D3 | semidirect |
| 35. #901 | C2×C5 | semidirect |
| 36. C3×C4×C8 | C2×C5 | semidirect |
| 37. #819 | C2×C5 | semidirect |
| 38. #805 | C2×C5 | semidirect |
| 61. Dic12 | C4×C5 | semidirect |
| 62. D24 | C4×C5 | semidirect |
| 63. #204 | C4×C5 | semidirect |
| 81. C4×C8 | C5×D3 | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | #4700 | direct (N × H) |
| 143. C3 | C5×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#904 | 2 |
| C5×#901 | 2 |
| C3×C4×C5×C8 | 2 |
| C5×#819 | 2 |
| C5×#805 | 2 |
| C5×#443 | 3 |
| #4700 | 5 |