Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 19. C5×#107 | C4 | semidirect |
| 20. #3950 | C4 | semidirect |
| 21. #3939 | C4 | semidirect |
| 22. #3939 | C4 | semidirect |
| 101. #107 | AGL(1,𝔽5) | semidirect |
| 188. C5 | #1921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65712 | 2 |
| C4⋊C4×AGL(1,𝔽5) | 2 |
| D5×#107 | 2 |
| #64893 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #64874 | 2 |
| #1921 | 5 |