Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. C4×C5×M16 | C2 | semidirect |
| 4. #65408 | C2 | semidirect |
| 5. C2×#3935 | C2 | semidirect |
| 6. #64994 | C2 | semidirect |
| 7. #64979 | C2 | semidirect |
| 51. C4×M16 | D5 | semidirect |
| 139. C5 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#709 | 2 |
| C4×C5×M16 | 2 |
| #65418 | 2 |
| #65408 | 2 |
| C2×#3935 | 2 |
| #64994 | 2 |
| #64979 | 2 |
| #2923 | 5 |