Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #65901 | C2 | semidirect |
| 3. C4×C5×SD16 | C2 | semidirect |
| 4. #65464 | C2 | semidirect |
| 5. #65316 | C2 | semidirect |
| 6. #65308 | C2 | semidirect |
| 7. #65141 | C2 | semidirect |
| 8. #65107 | C2 | semidirect |
| 9. #65051 | C2 | semidirect |
| 10. #64982 | C2 | semidirect |
| 11. C8×Dic10 | C2 | semidirect |
| 88. C4×SD16 | D5 | semidirect |
| 114. Dic10 | SD16 | semidirect |
| 116. C5×C8 | #41 | semidirect |
| 233. C8 | #709 | semidirect |
| 234. C5 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65901 | 2 |
| #65887 | 2 |
| C4×C5×SD16 | 2 |
| #65464 | 2 |
| #65316 | 2 |
| #65308 | 2 |
| #65141 | 2 |
| #65107 | 2 |
| #65051 | 2 |
| #64982 | 2 |
| C8×Dic10 | 2 |
| #3392 | 5 |