Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 21. C4⋊#168 | C4 | semidirect |
| 170. C5 | #1949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C4⋊C4 | 2 |
| C2×#3940 | 2 |
| C2×#3939 | 2 |
| #65225 | 2 |
| C2×C4⋊#168 | 2 |
| #64749 | 2 |
| #1949 | 5 |