Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. C5×#431 | C2 | semidirect |
| 3. #65214 | C2 | semidirect |
| 4. #64703 | C2 | semidirect |
| 14. C5×C4⋊C8 | C22 | semidirect |
| 19. C4×#168 | C22 | semidirect |
| 28. C2×D20 | C8 | semidirect |
| 45. #431 | D5 | semidirect |
| 81. C4⋊C8 | C2×D5 | semidirect |
| 153. C5 | #1478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D20 | 2 |
| C5×#431 | 2 |
| #65214 | 2 |
| #64703 | 2 |
| #1478 | 5 |