Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
158 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. #64884 | C2 | semidirect |
| 5. #64883 | C2 | semidirect |
| 6. #64882 | C2 | semidirect |
| 7. #64881 | C2 | semidirect |
| 134. C5 | #1574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65758 | 2 |
| #65748 | 2 |
| #65007 | 2 |
| #64884 | 2 |
| #64883 | 2 |
| #64882 | 2 |
| #64881 | 2 |
| #1574 | 5 |