Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 17. C5×#106 | C4 | semidirect |
| 89. #106 | Dic5 | semidirect |
| 168. C5 | #1920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#106 | 2 |
| #65274 | 2 |
| C4⋊C4×Dic5 | 2 |
| #64771 | 2 |
| #64770 | 2 |
| #64749 | 2 |
| #1920 | 5 |