Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
260 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 64 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. #65721 | C2 | semidirect |
| 3. D5⋊M32 | C2 | semidirect |
| 4. #64904 | C2 | semidirect |
| 7. C2×C5×D8 | C4 | semidirect |
| 11. D5×D8 | C4 | semidirect |
| 13. C2×D40 | C4 | semidirect |
| 16. #3994 | C22 | semidirect |
| 19. D5⋊C16 | C22 | semidirect |
| 80. C2×D8 | AGL(1,𝔽5) | semidirect |
| 157. C5 | #2140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D8 | 2 |
| #65721 | 2 |
| D5⋊M32 | 2 |
| #64904 | 2 |
| #2140 | 5 |