Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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. C4×#704 | C2 | semidirect |
| 4. #64919 | C2 | semidirect |
| 15. #4013 | C4 | semidirect |
| 36. #704 | C2×C4 | semidirect |
| 108. Dic5 | #100 | semidirect |
| 170. C5 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4027 | 2 |
| C2×#4013 | 2 |
| C4×#704 | 2 |
| #64919 | 2 |
| C4×#100 | 5 |