Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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. #65721 | C2 | semidirect |
| 5. #64902 | C2 | semidirect |
| 9. C5×#131 | C4 | semidirect |
| 10. #4094 | C4 | semidirect |
| 12. #4053 | C4 | semidirect |
| 16. #4047 | C4 | semidirect |
| 103. #131 | AGL(1,𝔽5) | semidirect |
| 202. C5 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#131 | 2 |
| #65795 | 2 |
| C2×#3996 | 2 |
| #65721 | 2 |
| #64902 | 2 |
| #1814 | 5 |