Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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. #64747 | C2 | semidirect |
| 6. C5×#117 | C4 | semidirect |
| 7. C2×C5×C22⋊C4 | C4 | semidirect |
| 47. #117 | Dic5 | semidirect |
| 49. C2×C22⋊C4 | Dic5 | semidirect |
| 99. C5 | #1828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#518 | 2 |
| C2×#3966 | 2 |
| #64747 | 2 |
| #1828 | 5 |