Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 3. C2×#3996 | C2 | semidirect |
| 4. #65708 | C2 | semidirect |
| 6. (C2×AGL(1,𝔽5))⋊C8 | C2 | semidirect |
| 7. #64875 | C2 | semidirect |
| 23. C5×#103 | C4 | semidirect |
| 24. #3967 | C4 | semidirect |
| 25. #3953 | C4 | semidirect |
| 26. #3941 | C4 | semidirect |
| 111. #103 | AGL(1,𝔽5) | semidirect |
| 196. C5 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4133 | 2 |
| C2×#4010 | 2 |
| C2×#3996 | 2 |
| #65708 | 2 |
| #65093 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #64875 | 2 |
| #1866 | 5 |