Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #65876 | C2 | semidirect |
| 3. #65383 | C2 | semidirect |
| 4. #65367 | C2 | semidirect |
| 5. #65331 | C2 | semidirect |
| 6. #65324 | C2 | semidirect |
| 7. C4×#687 | C2 | semidirect |
| 8. #65301 | C2 | semidirect |
| 9. #65296 | C2 | semidirect |
| 10. #65259 | C2 | semidirect |
| 11. #65253 | C2 | semidirect |
| 111. #168 | #41 | semidirect |
| 222. C5 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#547 | 2 |
| #65876 | 2 |
| #65383 | 2 |
| #65367 | 2 |
| #65331 | 2 |
| #65324 | 2 |
| C4×#687 | 2 |
| #65301 | 2 |
| #65296 | 2 |
| #65259 | 2 |
| #65253 | 2 |
| #3353 | 5 |