Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
200 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 12. #3950 | C4 | semidirect |
| 13. #3949 | C4 | semidirect |
| 108. C5 | #1946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#108 | 2 |
| #65408 | 2 |
| #65395 | 2 |
| C2×#3947 | 2 |
| #64775 | 2 |
| #1946 | 5 |