Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 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 |
|---|---|---|
| 2. #65368 | C2 | semidirect |
| 5. #64767 | C2 | semidirect |
| 6. #64701 | C2 | semidirect |
| 7. #64699 | C2 | semidirect |
| 67. #168 | SD16 | semidirect |
| 136. C5 | #1691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#461 | 2 |
| #65368 | 2 |
| #65301 | 2 |
| #65297 | 2 |
| #64767 | 2 |
| #64701 | 2 |
| #64699 | 2 |
| #1691 | 5 |