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. D5⋊#208 | C2 | semidirect |
| 4. #91237 | C2 | semidirect |
| 6. C2×C3×C5×D4 | C4 | semidirect |
| 11. C3×#711 | C4 | semidirect |
| 14. C2×C3×Dic10 | C4 | semidirect |
| 18. C4×ΓL(1,𝔽16) | C22 | semidirect |
| 19. #6758 | C22 | semidirect |
| 49. C2×C5×D4 | Dic3 | semidirect |
| 54. #711 | Dic3 | semidirect |
| 57. C2×Dic10 | Dic3 | semidirect |
| 83. C2×C3×D4 | AGL(1,𝔽5) | semidirect |
| 157. C2×D4 | ΓL(1,𝔽16) | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | #5236 | semidirect |
| 221. C3 | #65769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#711 | 2 |
| #91989 | 2 |
| D5⋊#208 | 2 |
| #91237 | 2 |
| #65769 | 3 |
| #5236 | 5 |