Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
588 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 211 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. C3×C4×C5×Q8 | C2 | semidirect |
| 3. Q8×Dic15 | C2 | semidirect |
| 4. #91782 | C2 | semidirect |
| 5. C4⋊C4×D15 | C2 | semidirect |
| 6. C4×D60 | C2 | semidirect |
| 7. #91761 | C2 | semidirect |
| 10. #6821 | C4 | semidirect |
| 24. C4×C5×Q8 | D3 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 38. D60 | C2×C4 | semidirect |
| 40. C4×D15 | C2×C4 | semidirect |
| 42. C3×C4×Q8 | D5 | semidirect |
| 86. C5×Q8 | C4×D3 | semidirect |
| 98. C4×Q8 | D15 | semidirect |
| 108. C3×Q8 | C4×D5 | semidirect |
| 141. C3×C5 | #520 | semidirect |
| 157. Q8 | C4×D15 | semidirect |
| 171. C5 | #5574 | semidirect |
| 182. C3 | #65908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6821 | 2 |
| C3×C4×C5×Q8 | 2 |
| Q8×Dic15 | 2 |
| #91782 | 2 |
| C4⋊C4×D15 | 2 |
| C4×D60 | 2 |
| #91761 | 2 |
| #65908 | 3 |
| #5574 | 5 |