Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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. #65382 | C2 | semidirect |
| 4. #65367 | C2 | semidirect |
| 5. #65365 | C2 | semidirect |
| 6. #65359 | C2 | semidirect |
| 7. #65331 | C2 | semidirect |
| 8. #65307 | C2 | semidirect |
| 9. C4×#681 | C2 | semidirect |
| 100. #168 | #41 | semidirect |
| 203. C5 | #3182 | 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 |
| #65382 | 2 |
| #65367 | 2 |
| #65365 | 2 |
| #65359 | 2 |
| #65331 | 2 |
| #65307 | 2 |
| C4×#681 | 2 |
| #3182 | 5 |