Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
232 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
| 159. C5 | #1493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65956 | 2 |
| #65758 | 2 |
| C2×C4×#170 | 2 |
| Q8⋊#170 | 2 |
| #64872 | 2 |
| #1493 | 5 |