Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #65686 | C2 | semidirect |
| 4. C4×#700 | C2 | semidirect |
| 5. #64875 | C2 | semidirect |
| 9. C4×C5×D4 | C4 | semidirect |
| 10. D4×Dic5 | C4 | semidirect |
| 14. #4033 | C4 | semidirect |
| 18. C4×Dic10 | C4 | semidirect |
| 19. #4008 | C4 | semidirect |
| 39. C4×AGL(1,𝔽5) | C2×C4 | semidirect |
| 41. #700 | C2×C4 | semidirect |
| 95. C4×D4 | AGL(1,𝔽5) | semidirect |
| 187. C5 | #1759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#711 | 2 |
| C2×#4008 | 2 |
| #65686 | 2 |
| C4×#700 | 2 |
| #64875 | 2 |
| #1759 | 5 |