Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. C5×#550 | C2 | semidirect |
| 2. #65897 | C2 | semidirect |
| 3. #65527 | C2 | semidirect |
| 4. #65522 | C2 | semidirect |
| 5. #65361 | C2 | semidirect |
| 6. #65359 | C2 | semidirect |
| 7. #65327 | C2 | semidirect |
| 8. #65324 | C2 | semidirect |
| 9. C4×#688 | C2 | semidirect |
| 10. #65310 | C2 | semidirect |
| 11. D4×#168 | C2 | semidirect |
| 78. #550 | D5 | semidirect |
| 239. C5 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#550 | 2 |
| #65897 | 2 |
| #65527 | 2 |
| #65522 | 2 |
| #65361 | 2 |
| #65359 | 2 |
| #65327 | 2 |
| #65324 | 2 |
| C4×#688 | 2 |
| #65310 | 2 |
| D4×#168 | 2 |
| #3305 | 5 |