Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #41×Dic5 | C2 | semidirect |
| 3. C2×#4097 | C2 | semidirect |
| 4. C2×#4082 | C2 | semidirect |
| 5. #65504 | C2 | semidirect |
| 6. #65455 | C2 | semidirect |
| 7. #65442 | C2 | semidirect |
| 8. #65409 | C2 | semidirect |
| 9. #65407 | C2 | semidirect |
| 19. Q8×Dic5 | C22 | semidirect |
| 20. C2×#689 | C22 | semidirect |
| 25. D4×Dic5 | C22 | semidirect |
| 26. C2×#687 | C22 | semidirect |
| 33. #3948 | C22 | semidirect |
| 34. #3946 | C22 | semidirect |
| 229. C5 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×AGL(1,ℤ/8) | 2 |
| #41×Dic5 | 2 |
| C2×#4097 | 2 |
| C2×#4082 | 2 |
| #65504 | 2 |
| #65455 | 2 |
| #65442 | 2 |
| #65409 | 2 |
| #65407 | 2 |
| #3040 | 5 |