Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 142 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. C5×#926 | C2 | semidirect |
| 3. C22×C5×C3⋊C8 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 5. C5×#832 | C2 | semidirect |
| 8. C3×C5×#41 | C4 | semidirect |
| 19. #5233 | C5 | direct (N × H) |
| 41. #926 | C2×C5 | semidirect |
| 42. C22×C3⋊C8 | C2×C5 | semidirect |
| 43. #835 | C2×C5 | semidirect |
| 44. #832 | C2×C5 | semidirect |
| 46. C5×#41 | Dic3 | semidirect |
| 69. C3×#41 | C4×C5 | semidirect |
| 130. #41 | C5×Dic3 | semidirect |
| 141. C3×C5 | #416 | semidirect |
| 175. C5 | #5233 | 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×C3×C5×#41 | 2 |
| C5×#926 | 2 |
| C22×C5×C3⋊C8 | 2 |
| C5×#835 | 2 |
| C5×#832 | 2 |
| C5×#416 | 3 |
| #5233 | 5 |