Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. #64884 | C2 | semidirect |
| 4. #64881 | C2 | semidirect |
| 105. C5 | #1568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65759 | 2 |
| C2×C8×Dic5 | 2 |
| #64884 | 2 |
| #64881 | 2 |
| #1568 | 5 |