Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
248 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 84 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. #64872 | C2 | semidirect |
| 28. C2×Dic10 | C8 | semidirect |
| 139. C5 | #1479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4033 | 2 |
| #65748 | 2 |
| #64872 | 2 |
| #1479 | 5 |