Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. C3×C5×#106 | C2 | semidirect |
| 5. C5×#816 | C2 | semidirect |
| 6. C5×#810 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 20. #4868 | C5 | direct (N × H) |
| 24. C5×#106 | D3 | semidirect |
| 43. C3×#106 | C2×C5 | semidirect |
| 45. #816 | C2×C5 | semidirect |
| 46. #810 | C2×C5 | semidirect |
| 47. #807 | C2×C5 | semidirect |
| 98. #106 | C5×D3 | semidirect |
| 141. C3×C5 | #485 | semidirect |
| 174. C5 | #4868 | direct (N × H) |
| 186. C3 | C5×#485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#897 | 2 |
| C5×#892 | 2 |
| C3×C5×#106 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#816 | 2 |
| C5×#810 | 2 |
| C5×#807 | 2 |
| C5×#485 | 3 |
| #4868 | 5 |