Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
396 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 2. C2×#4013 | C2 | semidirect |
| 3. #65758 | C2 | semidirect |
| 4. C4×#704 | C2 | semidirect |
| 42. #704 | D4 | semidirect |
| 112. C4×C5 | #100 | semidirect |
| 114. Dic5 | #100 | semidirect |
| 181. C5 | #1965 | semidirect |
| 200. C4 | #4013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4086 | 2 |
| C2×#4013 | 2 |
| #65758 | 2 |
| C4×#704 | 2 |
| #1965 | 5 |