Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. C2×C5×#216 | C2 | semidirect |
| 5. C5×#836 | C2 | semidirect |
| 6. C5×#824 | C2 | semidirect |
| 7. C5×#822 | C2 | semidirect |
| 24. #5204 | C5 | direct (N × H) |
| 51. C2×#216 | C2×C5 | semidirect |
| 52. #836 | C2×C5 | semidirect |
| 53. #824 | C2×C5 | semidirect |
| 54. #822 | C2×C5 | semidirect |
| 157. C3×C5 | #473 | semidirect |
| 187. C5 | #5204 | direct (N × H) |
| 195. C3 | C5×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#137 | 2 |
| C5×#951 | 2 |
| C5×#948 | 2 |
| C2×C5×#216 | 2 |
| C5×#836 | 2 |
| C5×#824 | 2 |
| C5×#822 | 2 |
| C5×#473 | 3 |
| #5204 | 5 |