Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
218 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. Q8⋊#170 | C2 | semidirect |
| 5. #64872 | C2 | semidirect |
| 154. C5 | #1485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65956 | 2 |
| C4×#704 | 2 |
| #65748 | 2 |
| Q8⋊#170 | 2 |
| #64872 | 2 |
| #1485 | 5 |