Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
300 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C5×#103 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 6. C5×#816 | C2 | semidirect |
| 7. C5×#810 | C2 | semidirect |
| 11. C5×D3×Q8 | C4 | semidirect |
| 23. #4802 | C5 | direct (N × H) |
| 30. C5×#103 | D3 | semidirect |
| 51. C3×#103 | C2×C5 | semidirect |
| 52. #835 | C2×C5 | semidirect |
| 53. #816 | C2×C5 | semidirect |
| 54. #810 | C2×C5 | semidirect |
| 83. D3×Q8 | C4×C5 | semidirect |
| 118. #103 | C5×D3 | semidirect |
| 165. C3×C5 | #419 | semidirect |
| 202. C5 | #4802 | direct (N × H) |
| 214. C3 | C5×#419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C5×#892 | 2 |
| C3×C5×#103 | 2 |
| C5×#835 | 2 |
| C5×#816 | 2 |
| C5×#810 | 2 |
| C5×#419 | 3 |
| #4802 | 5 |