Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 90 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×#907 | C2 | semidirect |
| 3. C3×C5×#108 | C2 | semidirect |
| 4. C5×#825 | C2 | semidirect |
| 5. C5×C8×Dic3 | C2 | semidirect |
| 12. C5×Dic12 | C4 | semidirect |
| 13. C5×D24 | C4 | semidirect |
| 14. C5×#204 | C4 | semidirect |
| 17. #4895 | C5 | direct (N × H) |
| 20. C5×#108 | D3 | semidirect |
| 34. #907 | C2×C5 | semidirect |
| 36. C3×#108 | C2×C5 | semidirect |
| 37. #825 | C2×C5 | semidirect |
| 38. C8×Dic3 | C2×C5 | semidirect |
| 61. Dic12 | C4×C5 | semidirect |
| 62. D24 | C4×C5 | semidirect |
| 63. #204 | C4×C5 | semidirect |
| 79. #108 | C5×D3 | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | #4895 | 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×#907 | 2 |
| C5×#904 | 2 |
| C3×C5×#108 | 2 |
| C5×#825 | 2 |
| C5×C8×Dic3 | 2 |
| C5×#443 | 3 |
| #4895 | 5 |