Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
274 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 89 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. #65224 | C2 | semidirect |
| 4. #64749 | C2 | semidirect |
| 5. #64744 | C2 | semidirect |
| 156. C5 | #2071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#390 | 2 |
| C2×#3964 | 2 |
| #65224 | 2 |
| #64749 | 2 |
| #64744 | 2 |
| #2071 | 5 |