Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
314 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. #65709 | C2 | semidirect |
| 3. #65707 | C2 | semidirect |
| 111. C5 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66022 | 2 |
| #65709 | 2 |
| #65707 | 2 |
| #65706 | 2 |
| #65683 | 2 |
| #2987 | 5 |