Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. C2×#3948 | C2 | semidirect |
| 5. C2×#3947 | C2 | semidirect |
| 6. #65263 | C2 | semidirect |
| 7. C2×#3939 | C2 | semidirect |
| 15. C2×#687 | C4 | semidirect |
| 95. #168 | C22⋊C4 | semidirect |
| 200. C5 | #1973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#687 | 2 |
| C2×C5×#102 | 2 |
| #65510 | 2 |
| C2×#3948 | 2 |
| C2×#3947 | 2 |
| #65263 | 2 |
| C2×#3939 | 2 |
| #1973 | 5 |