Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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. #65804 | C2 | semidirect |
| 3. #65528 | C2 | semidirect |
| 4. #65381 | C2 | semidirect |
| 5. #65370 | C2 | semidirect |
| 6. #65365 | C2 | semidirect |
| 7. #65359 | C2 | semidirect |
| 8. #65343 | C2 | semidirect |
| 9. #65214 | C2 | semidirect |
| 203. C5 | #3210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| #65804 | 2 |
| #65528 | 2 |
| #65381 | 2 |
| #65370 | 2 |
| #65365 | 2 |
| #65359 | 2 |
| #65343 | 2 |
| #65214 | 2 |
| #3210 | 5 |