Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 62 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×#919 | C2 | semidirect |
| 2. C3×C5×Q32 | C2 | semidirect |
| 3. C5×#828 | C2 | semidirect |
| 4. C5×D48 | C2 | semidirect |
| 5. C5×D3×C16 | C2 | semidirect |
| 14. #4919 | C5 | direct (N × H) |
| 16. C5×Q32 | D3 | semidirect |
| 27. #919 | C2×C5 | semidirect |
| 28. C3×Q32 | C2×C5 | semidirect |
| 29. #828 | C2×C5 | semidirect |
| 30. D48 | C2×C5 | semidirect |
| 31. D3×C16 | C2×C5 | semidirect |
| 60. Q32 | C5×D3 | semidirect |
| 86. C3×C5 | #508 | semidirect |
| 105. C5 | #4919 | direct (N × H) |
| 111. C3 | C5×#508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#919 | 2 |
| C3×C5×Q32 | 2 |
| C5×#828 | 2 |
| C5×D48 | 2 |
| C5×D3×C16 | 2 |
| C5×#508 | 3 |
| #4919 | 5 |