Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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×#946 | C2 | semidirect |
| 2. C2×C5×#215 | C2 | semidirect |
| 3. C2×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×C5×#103 | C2 | semidirect |
| 6. C5×#821 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 22. #4812 | C5 | direct (N × H) |
| 28. C5×#103 | D3 | semidirect |
| 45. C5×C3⋊C8 | D4 | semidirect |
| 46. #946 | C2×C5 | semidirect |
| 47. C2×#215 | C2×C5 | semidirect |
| 48. C2×ΓL(1,𝔽25) | C2×C5 | semidirect |
| 50. C3×#103 | C2×C5 | semidirect |
| 51. #821 | C2×C5 | semidirect |
| 52. #807 | C2×C5 | semidirect |
| 114. #103 | C5×D3 | semidirect |
| 136. C3⋊C8 | C5×D4 | semidirect |
| 163. C3×C5 | #468 | semidirect |
| 203. C5 | #4812 | direct (N × H) |
| 217. C3 | C5×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#946 | 2 |
| C2×C5×#215 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C5×#895 | 2 |
| C3×C5×#103 | 2 |
| C5×#821 | 2 |
| C5×#807 | 2 |
| C5×#468 | 3 |
| #4812 | 5 |