Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
588 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 240 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. Q8×Dic15 | C2 | semidirect |
| 3. C5×Q8×Dic3 | C2 | semidirect |
| 4. #91434 | C2 | semidirect |
| 5. Dic3×D20 | C2 | semidirect |
| 6. D5×C4⋊Dic3 | C2 | semidirect |
| 7. #91357 | C2 | semidirect |
| 10. C3×#713 | C4 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 38. C3×D20 | C2×C4 | semidirect |
| 39. C3×C4×D5 | C2×C4 | semidirect |
| 43. Q8×Dic3 | D5 | semidirect |
| 49. #713 | Dic3 | semidirect |
| 86. C5×Q8 | C2×Dic3 | semidirect |
| 93. D20 | C2×Dic3 | semidirect |
| 95. C4×D5 | C2×Dic3 | semidirect |
| 108. C3×Q8 | C4×D5 | semidirect |
| 141. C3×C5 | #520 | semidirect |
| 157. Q8 | D5×Dic3 | semidirect |
| 171. C5 | #5827 | 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×C3×#713 | 2 |
| Q8×Dic15 | 2 |
| C5×Q8×Dic3 | 2 |
| #91434 | 2 |
| Dic3×D20 | 2 |
| D5×C4⋊Dic3 | 2 |
| #91357 | 2 |
| #65908 | 3 |
| #5827 | 5 |