Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 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. #91989 | C2 | semidirect |
| 3. C2×#6758 | C2 | semidirect |
| 4. #91239 | C2 | semidirect |
| 5. #91237 | C2 | semidirect |
| 7. C3×C5×#41 | C4 | semidirect |
| 9. C3×Q8×D5 | C4 | semidirect |
| 13. C3×D4×D5 | C4 | semidirect |
| 15. C3×#709 | C4 | semidirect |
| 21. C4×ΓL(1,𝔽16) | C22 | semidirect |
| 23. #6758 | C22 | semidirect |
| 60. C5×#41 | Dic3 | semidirect |
| 62. Q8×D5 | Dic3 | semidirect |
| 66. D4×D5 | Dic3 | semidirect |
| 68. #709 | Dic3 | semidirect |
| 97. C3×#41 | AGL(1,𝔽5) | semidirect |
| 189. #41 | ΓL(1,𝔽16) | semidirect |
| 201. C3×C5 | #421 | semidirect |
| 253. C5 | #5236 | semidirect |
| 268. C3 | #65795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×#41 | 2 |
| #91989 | 2 |
| C2×#6758 | 2 |
| #91239 | 2 |
| #91237 | 2 |
| #65795 | 3 |
| #5236 | 5 |