Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 174 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×ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 5. ΓL(1,𝔽16)⋊Q8 | C2 | semidirect |
| 7. AGL(1,𝔽5)×Dic6 | C2 | semidirect |
| 9. Q8×D15 | C4 | semidirect |
| 10. C5×D3×Q8 | C4 | semidirect |
| 13. D15⋊Q8 | C4 | semidirect |
| 14. D3×Dic10 | C4 | semidirect |
| 30. Q8×AGL(1,𝔽5) | D3 | semidirect |
| 90. D3×Q8 | AGL(1,𝔽5) | semidirect |
| 175. C3×C5 | #519 | semidirect |
| 215. C5 | #5572 | semidirect |
| 229. C3 | #66262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×D5 | 2 |
| Q8×ΓL(1,𝔽16) | 2 |
| C3×Q8×AGL(1,𝔽5) | 2 |
| #91909 | 2 |
| ΓL(1,𝔽16)⋊Q8 | 2 |
| #91907 | 2 |
| AGL(1,𝔽5)×Dic6 | 2 |
| #66262 | 3 |
| #5572 | 5 |