Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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. #65721 | C2 | semidirect |
| 4. #64895 | C2 | semidirect |
| 7. C2×C5×M16 | C4 | semidirect |
| 8. C22×#168 | C4 | semidirect |
| 11. C2×#676 | C4 | semidirect |
| 13. C2×C8×D5 | C4 | semidirect |
| 77. C2×M16 | AGL(1,𝔽5) | semidirect |
| 152. C5 | #1812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4053 | 2 |
| #65745 | 2 |
| #65721 | 2 |
| #64895 | 2 |
| #1812 | 5 |