Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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×C3×C5×Q16 | C2 | semidirect |
| 2. C5×#947 | C2 | semidirect |
| 3. C2×C5×#215 | C2 | semidirect |
| 5. C5×C8×Dic3 | C2 | semidirect |
| 16. #5191 | C5 | direct (N × H) |
| 17. C2×C5×Q16 | D3 | semidirect |
| 32. C2×C3×Q16 | C2×C5 | semidirect |
| 33. #947 | C2×C5 | semidirect |
| 34. C2×#215 | C2×C5 | semidirect |
| 36. C8×Dic3 | C2×C5 | semidirect |
| 73. C2×Q16 | C5×D3 | semidirect |
| 107. C3×C5 | #495 | semidirect |
| 131. C5 | #5191 | direct (N × H) |
| 139. C3 | C5×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C5×#947 | 2 |
| C2×C5×#215 | 2 |
| C2×C5×D24 | 2 |
| C5×C8×Dic3 | 2 |
| C5×#495 | 3 |
| #5191 | 5 |