Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 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×C3×C5×SD16 | C2 | semidirect |
| 2. C5×#946 | C2 | semidirect |
| 4. C2×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 6. C5×#832 | C2 | semidirect |
| 7. C5×#818 | C2 | semidirect |
| 22. #5174 | C5 | direct (N × H) |
| 23. C2×C5×SD16 | D3 | semidirect |
| 44. C3×C5×C8 | D4 | semidirect |
| 46. C2×C3×SD16 | C2×C5 | semidirect |
| 47. #946 | C2×C5 | semidirect |
| 49. C2×ΓL(1,𝔽25) | C2×C5 | semidirect |
| 50. #835 | C2×C5 | semidirect |
| 51. #832 | C2×C5 | semidirect |
| 52. #818 | C2×C5 | semidirect |
| 108. C5×C8 | #67 | semidirect |
| 109. C2×SD16 | C5×D3 | semidirect |
| 135. C3×C8 | C5×D4 | semidirect |
| 163. C3×C5 | #468 | semidirect |
| 197. C8 | C5×#67 | semidirect |
| 203. C5 | #5174 | 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 |
|---|---|
| C2×C3×C5×SD16 | 2 |
| C5×#946 | 2 |
| C5×#938 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C5×#835 | 2 |
| C5×#832 | 2 |
| C5×#818 | 2 |
| C5×#468 | 3 |
| #5174 | 5 |