Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 164 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×D3×Q16 | C2 | semidirect |
| 3. C3×C5×SD32 | C2 | semidirect |
| 4. C5×#829 | C2 | semidirect |
| 5. C5×#827 | C2 | semidirect |
| 6. C5×Dic24 | C2 | semidirect |
| 7. C5×#798 | C2 | semidirect |
| 20. #4915 | C5 | direct (N × H) |
| 26. C5×SD32 | D3 | semidirect |
| 39. D3×Q16 | C2×C5 | semidirect |
| 41. C3×SD32 | C2×C5 | semidirect |
| 42. #829 | C2×C5 | semidirect |
| 43. #827 | C2×C5 | semidirect |
| 44. Dic24 | C2×C5 | semidirect |
| 45. #798 | C2×C5 | semidirect |
| 92. SD32 | C5×D3 | semidirect |
| 126. C3×C5 | #510 | semidirect |
| 151. C5 | #4915 | direct (N × H) |
| 159. C3 | C5×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q16 | 2 |
| C5×#912 | 2 |
| C3×C5×SD32 | 2 |
| C5×#829 | 2 |
| C5×#827 | 2 |
| C5×Dic24 | 2 |
| C5×#798 | 2 |
| C5×#510 | 3 |
| #4915 | 5 |