Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 2. C2×C5×D3×C8 | C2 | semidirect |
| 3. C5×#892 | C2 | semidirect |
| 4. C3×C5×#102 | C2 | semidirect |
| 5. C5×#832 | C2 | semidirect |
| 6. C5×#816 | C2 | semidirect |
| 7. C5×#810 | C2 | semidirect |
| 13. C5×#237 | C4 | semidirect |
| 23. #4772 | C5 | direct (N × H) |
| 30. C5×#102 | D3 | semidirect |
| 49. C2×D3×C8 | C2×C5 | semidirect |
| 50. #892 | C2×C5 | semidirect |
| 51. C3×#102 | C2×C5 | semidirect |
| 52. #832 | C2×C5 | semidirect |
| 53. #816 | C2×C5 | semidirect |
| 54. #810 | C2×C5 | semidirect |
| 87. #237 | C4×C5 | semidirect |
| 120. #102 | C5×D3 | semidirect |
| 170. C3×C5 | #416 | semidirect |
| 211. C5 | #4772 | direct (N × H) |
| 225. C3 | C5×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#237 | 2 |
| C2×C5×D3×C8 | 2 |
| C5×#892 | 2 |
| C3×C5×#102 | 2 |
| C5×#832 | 2 |
| C5×#816 | 2 |
| C5×#810 | 2 |
| C5×#416 | 3 |
| #4772 | 5 |