Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 20. #3939 | C4 | semidirect |
| 81. #168 | C4⋊C4 | semidirect |
| 172. C5 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#389 | 2 |
| C2×#3940 | 2 |
| C2×#3939 | 2 |
| #65217 | 2 |
| C2×#3935 | 2 |
| #64749 | 2 |
| #1943 | 5 |