Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 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. #66056 | C2 | semidirect |
| 3. C5×#486 | C2 | semidirect |
| 4. #65373 | C2 | semidirect |
| 5. #65364 | C2 | semidirect |
| 6. #65051 | C2 | semidirect |
| 7. #65050 | C2 | semidirect |
| 8. #65049 | C2 | semidirect |
| 9. #65047 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. C8×Dic10 | C2 | semidirect |
| 78. #486 | D5 | semidirect |
| 110. Dic10 | SD16 | semidirect |
| 111. Dic10 | #41 | semidirect |
| 228. C5 | #3362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66056 | 2 |
| #66052 | 2 |
| C5×#486 | 2 |
| #65373 | 2 |
| #65364 | 2 |
| #65051 | 2 |
| #65050 | 2 |
| #65049 | 2 |
| #65047 | 2 |
| C4×#677 | 2 |
| C8×Dic10 | 2 |
| #3362 | 5 |