Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
156 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. #65380 | C2 | semidirect |
| 4. #64968 | C2 | semidirect |
| 5. #64766 | C2 | semidirect |
| 7. #64678 | C2 | semidirect |
| 136. C5 | #1698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#486 | 2 |
| #65380 | 2 |
| #65364 | 2 |
| #64968 | 2 |
| #64766 | 2 |
| #64764 | 2 |
| #64678 | 2 |
| #1698 | 5 |