Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 2. C2×C3×C5×Q16 | C2 | semidirect |
| 4. C2×C5×#216 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 7. C5×#816 | C2 | semidirect |
| 24. #5186 | C5 | direct (N × H) |
| 27. C2×C5×Q16 | D3 | semidirect |
| 52. C2×C3×Q16 | C2×C5 | semidirect |
| 54. C2×#216 | C2×C5 | semidirect |
| 55. #835 | C2×C5 | semidirect |
| 57. #816 | C2×C5 | semidirect |
| 77. C2×C5×D3 | Q16 | semidirect |
| 121. C2×Q16 | C5×D3 | semidirect |
| 175. C3×C5 | #451 | semidirect |
| 179. C2×D3 | C5×Q16 | semidirect |
| 214. C5 | #5186 | direct (N × H) |
| 226. C3 | C5×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C2×C3×C5×Q16 | 2 |
| C5×#946 | 2 |
| C2×C5×#216 | 2 |
| C5×#835 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#816 | 2 |
| C5×#451 | 3 |
| #5186 | 5 |