Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 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. #64888 | C2 | semidirect |
| 4. #64886 | C2 | semidirect |
| 5. #64885 | C2 | semidirect |
| 89. C5 | #2164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65411 | 2 |
| C22⋊#674 | 2 |
| #64888 | 2 |
| #64886 | 2 |
| #64885 | 2 |
| #2164 | 5 |