Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C2×C5×Dic12 | C2 | semidirect |
| 4. C4×C5×Dic6 | C2 | semidirect |
| 5. C3×C5×C4⋊C8 | C2 | semidirect |
| 7. C5×#816 | C2 | semidirect |
| 22. #4845 | C5 | direct (N × H) |
| 27. C5×C4⋊C8 | D3 | semidirect |
| 45. C2×Dic12 | C2×C5 | semidirect |
| 48. C4×Dic6 | C2×C5 | semidirect |
| 49. C3×C4⋊C8 | C2×C5 | semidirect |
| 51. #816 | C2×C5 | semidirect |
| 109. C4⋊C8 | C5×D3 | semidirect |
| 155. C3×C5 | #464 | semidirect |
| 190. C5 | #4845 | direct (N × H) |
| 202. C3 | C5×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic12 | 2 |
| C2×C5×#204 | 2 |
| C5×#875 | 2 |
| C4×C5×Dic6 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C5×#821 | 2 |
| C5×#816 | 2 |
| C5×#464 | 3 |
| #4845 | 5 |