Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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. #65313 | C2 | semidirect |
| 4. #65309 | C2 | semidirect |
| 6. #64706 | C2 | semidirect |
| 7. #64699 | C2 | semidirect |
| 70. #168 | SD16 | semidirect |
| 142. C5 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#460 | 2 |
| #65365 | 2 |
| #65313 | 2 |
| #65309 | 2 |
| #64764 | 2 |
| #64706 | 2 |
| #64699 | 2 |
| #1686 | 5 |