Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
144 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 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. #65725 | C2 | semidirect |
| 3. #64898 | C2 | semidirect |
| 4. #64889 | C2 | semidirect |
| 5. #64886 | C2 | semidirect |
| 89. C5 | #2171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65725 | 2 |
| #65184 | 2 |
| #64898 | 2 |
| #64889 | 2 |
| #64886 | 2 |
| #2171 | 5 |