Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
168 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C5×#446 | C2 | semidirect |
| 3. #65309 | C2 | semidirect |
| 6. #64702 | C2 | semidirect |
| 7. #64678 | C2 | semidirect |
| 46. #446 | D5 | semidirect |
| 68. C5×C8 | SD16 | semidirect |
| 141. C8 | #688 | 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×#446 | 2 |
| #65316 | 2 |
| #65309 | 2 |
| #64982 | 2 |
| #64705 | 2 |
| #64702 | 2 |
| #64678 | 2 |
| #1686 | 5 |