Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 1. C5×#559 | C2 | semidirect |
| 2. #65919 | C2 | semidirect |
| 3. #65364 | C2 | semidirect |
| 5. #65348 | C2 | semidirect |
| 6. #65346 | C2 | semidirect |
| 7. C4×#689 | C2 | semidirect |
| 8. #65316 | C2 | semidirect |
| 9. Q8×#168 | C2 | semidirect |
| 10. #65305 | C2 | semidirect |
| 11. C4×#686 | C2 | semidirect |
| 78. #559 | D5 | semidirect |
| 232. C5 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#559 | 2 |
| #65919 | 2 |
| #65364 | 2 |
| #65362 | 2 |
| #65348 | 2 |
| #65346 | 2 |
| C4×#689 | 2 |
| #65316 | 2 |
| Q8×#168 | 2 |
| #65305 | 2 |
| C4×#686 | 2 |
| #3396 | 5 |