Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C2×D80 | C2 | semidirect |
| 2. #64984 | C2 | semidirect |
| 3. C4×D40 | C2 | semidirect |
| 4. C5×C4⋊C16 | C2 | semidirect |
| 5. #64729 | C2 | semidirect |
| 31. D40 | D4 | semidirect |
| 36. C4⋊C16 | D5 | semidirect |
| 72. C4×C5 | D16 | semidirect |
| 113. C5 | #2206 | semidirect |
| 123. C4 | D80 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D80 | 2 |
| #64984 | 2 |
| C4×D40 | 2 |
| C5×C4⋊C16 | 2 |
| #64729 | 2 |
| #2206 | 5 |