Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 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. C2×C5×#204 | C2 | semidirect |
| 3. C4×C5×Dic6 | C2 | semidirect |
| 4. C3×C5×C4⋊C8 | C2 | semidirect |
| 5. C5×#821 | C2 | semidirect |
| 17. #4848 | C5 | direct (N × H) |
| 21. C5×C4⋊C8 | D3 | semidirect |
| 34. C5×Dic6 | D4 | semidirect |
| 36. C2×#204 | C2×C5 | semidirect |
| 38. C4×Dic6 | C2×C5 | semidirect |
| 39. C3×C4⋊C8 | C2×C5 | semidirect |
| 40. #821 | C2×C5 | semidirect |
| 57. C3×C4×C5 | SD16 | semidirect |
| 88. C4⋊C8 | C5×D3 | semidirect |
| 105. Dic6 | C5×D4 | semidirect |
| 114. C4×C5 | #204 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 133. C3×C4 | C5×SD16 | semidirect |
| 159. C5 | #4848 | direct (N × H) |
| 167. C4 | C5×#204 | semidirect |
| 170. C3 | C5×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#204 | 2 |
| C5×#874 | 2 |
| C4×C5×Dic6 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C5×#821 | 2 |
| C5×#460 | 3 |
| #4848 | 5 |