Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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. #64768 | C2 | semidirect |
| 112. C5 | #2135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#536 | 2 |
| #65526 | 2 |
| #64768 | 2 |
| #2135 | 5 |