Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
128 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 8. #3996 | C4 | semidirect |
| 11. C5×M32 | C4 | semidirect |
| 12. #3944 | C4 | semidirect |
| 52. M32 | AGL(1,𝔽5) | semidirect |
| 99. C5 | #1389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3996 | 2 |
| #65721 | 2 |
| D5×M32 | 2 |
| #1389 | 5 |