Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 208 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×#815 | C2 | semidirect |
| 8. C3×C5×Q16 | C4 | semidirect |
| 9. C3×C5×SD16 | C4 | semidirect |
| 10. C3×C5×D8 | C4 | semidirect |
| 17. #5197 | C5 | direct (N × H) |
| 34. #948 | C2×C5 | semidirect |
| 35. #837 | C2×C5 | semidirect |
| 36. #819 | C2×C5 | semidirect |
| 37. #815 | C2×C5 | semidirect |
| 39. C5×Q16 | Dic3 | semidirect |
| 40. C5×SD16 | Dic3 | semidirect |
| 41. C5×D8 | Dic3 | semidirect |
| 56. C3×Q16 | C4×C5 | semidirect |
| 57. C3×SD16 | C4×C5 | semidirect |
| 58. C3×D8 | C4×C5 | semidirect |
| 100. Q16 | C5×Dic3 | semidirect |
| 101. SD16 | C5×Dic3 | semidirect |
| 102. D8 | C5×Dic3 | semidirect |
| 109. C3×C5 | #444 | semidirect |
| 132. C5 | #5197 | direct (N × H) |
| 139. C3 | C5×#444 | 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×#815 | 2 |
| C5×#444 | 3 |
| #5197 | 5 |