Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 2. #65757 | C2 | semidirect |
| 3. #64927 | C2 | semidirect |
| 13. #4002 | C22 | semidirect |
| 109. C5 | #1533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4093 | 2 |
| #65757 | 2 |
| #64927 | 2 |
| #1533 | 5 |