Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
184 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 114 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. #64859 | C2 | semidirect |
| 5. C4×#674 | C2 | semidirect |
| 9. #3998 | C4 | semidirect |
| 10. C2×#674 | C4 | semidirect |
| 88. C5 | #2108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3998 | 2 |
| C22×#674 | 2 |
| #65286 | 2 |
| #64859 | 2 |
| C4×#674 | 2 |
| #2108 | 5 |