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 |
|---|---|---|
| 1. C5×#556 | C2 | semidirect |
| 3. #65376 | C2 | semidirect |
| 4. #65367 | C2 | semidirect |
| 5. #65338 | C2 | semidirect |
| 6. #65333 | C2 | semidirect |
| 7. C4×#688 | C2 | semidirect |
| 8. #65309 | C2 | semidirect |
| 9. #65301 | C2 | semidirect |
| 10. #65292 | C2 | semidirect |
| 11. #65284 | C2 | semidirect |
| 75. #556 | D5 | 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×#556 | 2 |
| #65889 | 2 |
| #65376 | 2 |
| #65367 | 2 |
| #65338 | 2 |
| #65333 | 2 |
| C4×#688 | 2 |
| #65309 | 2 |
| #65301 | 2 |
| #65292 | 2 |
| #65284 | 2 |
| #3353 | 5 |