Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 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. #65138 | C2 | semidirect |
| 4. #65120 | C2 | semidirect |
| 6. #64706 | C2 | semidirect |
| 7. #64700 | C2 | semidirect |
| 140. C5 | #1702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65364 | 2 |
| #65359 | 2 |
| #65138 | 2 |
| #65120 | 2 |
| C5×#331 | 2 |
| #64706 | 2 |
| #64700 | 2 |
| #1702 | 5 |