Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 126 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. C22×C3×C5×C8 | C2 | semidirect |
| 3. C5×#926 | C2 | semidirect |
| 4. C5×#821 | C2 | semidirect |
| 5. C5×#816 | C2 | semidirect |
| 10. C5×#235 | C4 | semidirect |
| 19. #5113 | C5 | direct (N × H) |
| 21. C22×C5×C8 | D3 | semidirect |
| 41. C22×C3×C8 | C2×C5 | semidirect |
| 42. #926 | C2×C5 | semidirect |
| 43. #821 | C2×C5 | semidirect |
| 44. #816 | C2×C5 | semidirect |
| 71. #235 | C4×C5 | semidirect |
| 96. C22×C8 | C5×D3 | semidirect |
| 141. C3×C5 | #416 | semidirect |
| 175. C5 | #5113 | direct (N × H) |
| 186. C3 | C5×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#235 | 2 |
| C22×C3×C5×C8 | 2 |
| C5×#926 | 2 |
| C5×#821 | 2 |
| C5×#816 | 2 |
| C5×#416 | 3 |
| #5113 | 5 |