Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #66256 | C2 | semidirect |
| 3. C2×#4013 | C2 | semidirect |
| 4. D5⋊#100 | C2 | semidirect |
| 5. #65777 | C2 | semidirect |
| 6. #65761 | C2 | semidirect |
| 19. C2×#704 | C22 | semidirect |
| 21. D5⋊M16 | C22 | semidirect |
| 22. #4013 | C22 | semidirect |
| 23. #4013 | C22 | semidirect |
| 24. #4005 | C22 | semidirect |
| 233. C5 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4144 | 2 |
| #66256 | 2 |
| C2×#4013 | 2 |
| D5⋊#100 | 2 |
| #65777 | 2 |
| #65761 | 2 |
| #2888 | 5 |