Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #65358 | C2 | semidirect |
| 4. #65354 | C2 | semidirect |
| 5. #65349 | C2 | semidirect |
| 6. #65344 | C2 | semidirect |
| 7. #65341 | C2 | semidirect |
| 9. C4×#689 | C2 | semidirect |
| 10. C4×#687 | C2 | semidirect |
| 11. C4×#681 | C2 | semidirect |
| 235. C5 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#529 | 2 |
| #65804 | 2 |
| #65358 | 2 |
| #65354 | 2 |
| #65349 | 2 |
| #65344 | 2 |
| #65341 | 2 |
| #65331 | 2 |
| C4×#689 | 2 |
| C4×#687 | 2 |
| C4×#681 | 2 |
| #3172 | 5 |