Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×C5×Q32 | C2 | semidirect |
| 3. C5×#829 | C2 | semidirect |
| 4. C5×Dic24 | C2 | semidirect |
| 14. D3×Q32 | C5 | direct (N × H) |
| 18. C5×Q32 | D3 | direct (N × H) |
| 28. C3×Q32 | C2×C5 | semidirect |
| 29. #829 | C2×C5 | semidirect |
| 30. Dic24 | C2×C5 | semidirect |
| 62. Q32 | C5×D3 | direct (N × H) |
| 65. C5×D3 | Q32 | direct (N × H) |
| 85. C3×C5 | C2×Q32 | semidirect |
| 101. D3 | C5×Q32 | direct (N × H) |
| 102. C5 | D3×Q32 | direct (N × H) |
| 108. C3 | C2×C5×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q16 | 2 |
| C3×C5×Q32 | 2 |
| C5×#829 | 2 |
| C5×Dic24 | 2 |
| C5×D3×C16 | 2 |
| C2×C5×Q32 | 3 |
| D3×Q32 | 5 |