Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 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. C5×#938 | C2 | semidirect |
| 2. C2×C5×#213 | C2 | semidirect |
| 3. C2×C5×D3×C8 | C2 | semidirect |
| 4. C5×#895 | C2 | semidirect |
| 5. C3×C5×#102 | C2 | semidirect |
| 6. C5×#821 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 22. #4775 | C5 | direct (N × H) |
| 29. C5×#102 | D3 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 47. #938 | C2×C5 | semidirect |
| 48. C2×#213 | C2×C5 | semidirect |
| 49. C2×D3×C8 | C2×C5 | semidirect |
| 50. #895 | C2×C5 | semidirect |
| 51. C3×#102 | C2×C5 | semidirect |
| 52. #821 | C2×C5 | semidirect |
| 53. #807 | C2×C5 | semidirect |
| 77. C2×C5×D3 | D8 | semidirect |
| 119. #102 | C5×D3 | semidirect |
| 142. C3⋊C8 | C5×D4 | semidirect |
| 171. C3×C5 | #466 | semidirect |
| 181. C2×D3 | C5×D8 | semidirect |
| 216. C5 | #4775 | direct (N × H) |
| 232. C3 | C5×#466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#938 | 2 |
| C2×C5×#213 | 2 |
| C2×C5×D3×C8 | 2 |
| C5×#895 | 2 |
| C3×C5×#102 | 2 |
| C5×#821 | 2 |
| C5×#807 | 2 |
| C5×#466 | 3 |
| #4775 | 5 |