Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 82 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×#870 | C2 | semidirect |
| 3. C3×C5×C4⋊C8 | C2 | semidirect |
| 6. C5×#818 | C2 | semidirect |
| 7. C5×#817 | C2 | semidirect |
| 20. #4847 | C5 | direct (N × H) |
| 25. C5×C4⋊C8 | D3 | semidirect |
| 41. #870 | C2×C5 | semidirect |
| 42. C3×C4⋊C8 | C2×C5 | semidirect |
| 45. #818 | C2×C5 | semidirect |
| 46. #817 | C2×C5 | semidirect |
| 97. C4⋊C8 | C5×D3 | semidirect |
| 138. C3×C5 | #478 | semidirect |
| 170. C5 | #4847 | direct (N × H) |
| 182. C3 | C5×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D12 | 2 |
| C5×#870 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C5×#821 | 2 |
| C5×#818 | 2 |
| C5×#817 | 2 |
| C5×#478 | 3 |
| #4847 | 5 |