Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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. C5×#948 | C2 | semidirect |
| 3. C5×#837 | C2 | semidirect |
| 4. C5×#819 | C2 | semidirect |
| 5. C5×C8×Dic3 | C2 | semidirect |
| 8. C3×C5×Q16 | C4 | semidirect |
| 9. C3×C5×SD16 | C4 | semidirect |
| 10. C3×C5×D8 | C4 | semidirect |
| 17. #5196 | C5 | direct (N × H) |
| 35. #948 | C2×C5 | semidirect |
| 36. #837 | C2×C5 | semidirect |
| 37. #819 | C2×C5 | semidirect |
| 38. C8×Dic3 | C2×C5 | semidirect |
| 40. C5×Q16 | Dic3 | semidirect |
| 41. C5×SD16 | Dic3 | semidirect |
| 42. C5×D8 | Dic3 | semidirect |
| 57. C3×Q16 | C4×C5 | semidirect |
| 58. C3×SD16 | C4×C5 | semidirect |
| 59. C3×D8 | C4×C5 | semidirect |
| 103. Q16 | C5×Dic3 | semidirect |
| 104. SD16 | C5×Dic3 | semidirect |
| 105. D8 | C5×Dic3 | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | #5196 | direct (N × H) |
| 143. C3 | C5×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#135 | 2 |
| C5×#948 | 2 |
| C5×#837 | 2 |
| C5×#819 | 2 |
| C5×C8×Dic3 | 2 |
| C5×#443 | 3 |
| #5196 | 5 |