Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 2. C3×C5×C22⋊Q8 | C2 | semidirect |
| 3. C2×C5×#216 | C2 | semidirect |
| 4. C2×C5×#215 | C2 | semidirect |
| 5. C5×#830 | C2 | semidirect |
| 6. C5×#810 | C2 | semidirect |
| 7. C5×#809 | C2 | semidirect |
| 24. #5047 | C5 | direct (N × H) |
| 28. C5×C22⋊Q8 | D3 | semidirect |
| 52. C3×C22⋊Q8 | C2×C5 | semidirect |
| 53. C2×#216 | C2×C5 | semidirect |
| 54. C2×#215 | C2×C5 | semidirect |
| 55. #830 | C2×C5 | semidirect |
| 56. #810 | C2×C5 | semidirect |
| 57. #809 | C2×C5 | semidirect |
| 124. C22⋊Q8 | C5×D3 | semidirect |
| 180. C3×C5 | #452 | semidirect |
| 223. C5 | #5047 | direct (N × H) |
| 237. C3 | C5×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#235 | 2 |
| C3×C5×C22⋊Q8 | 2 |
| C2×C5×#216 | 2 |
| C2×C5×#215 | 2 |
| C5×#830 | 2 |
| C5×#810 | 2 |
| C5×#809 | 2 |
| C5×#452 | 3 |
| #5047 | 5 |