Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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. #64882 | C2 | semidirect |
| 49. C5×C8 | M16 | semidirect |
| 51. #168 | M16 | semidirect |
| 109. C8 | #704 | semidirect |
| 110. C5 | #1567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65758 | 2 |
| C2×C8×Dic5 | 2 |
| #64884 | 2 |
| #64882 | 2 |
| #1567 | 5 |