Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 118 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×Q8×Dic3 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 6. C5×#817 | C2 | semidirect |
| 7. C5×C8×Dic3 | C2 | semidirect |
| 12. C3×C5×SD16 | C4 | semidirect |
| 21. Dic3×SD16 | C5 | direct (N × H) |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 41. C3×C5×C8 | C2×C4 | semidirect |
| 44. Q8×Dic3 | C2×C5 | semidirect |
| 46. #835 | C2×C5 | semidirect |
| 48. #817 | C2×C5 | semidirect |
| 49. C8×Dic3 | C2×C5 | semidirect |
| 53. C5×SD16 | Dic3 | direct (N × H) |
| 73. C5×Dic3 | SD16 | direct (N × H) |
| 77. C3×SD16 | C4×C5 | semidirect |
| 88. C5×Q8 | C2×Dic3 | semidirect |
| 99. C5×C8 | C2×Dic3 | semidirect |
| 113. C3×Q8 | C2×C4×C5 | semidirect |
| 123. C3×C8 | C2×C4×C5 | semidirect |
| 139. SD16 | C5×Dic3 | direct (N × H) |
| 148. C3×C5 | C4×SD16 | semidirect |
| 159. Dic3 | C5×SD16 | direct (N × H) |
| 166. Q8 | C2×C5×Dic3 | semidirect |
| 177. C8 | C2×C5×Dic3 | semidirect |
| 182. C5 | Dic3×SD16 | direct (N × H) |
| 194. C3 | C4×C5×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD16 | 2 |
| C5×Q8×Dic3 | 2 |
| C5×D4×Dic3 | 2 |
| C5×#835 | 2 |
| C5×#832 | 2 |
| C5×#817 | 2 |
| C5×C8×Dic3 | 2 |
| C4×C5×SD16 | 3 |
| Dic3×SD16 | 5 |