Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 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. #64929 | C2 | semidirect |
| 4. #64855 | C2 | semidirect |
| 120. D5 | #356 | semidirect |
| 144. C5 | C2×#356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| D5⋊#101 | 2 |
| #64929 | 2 |
| #64855 | 2 |
| C2×#356 | 5 |