Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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. C5×#544 | C2 | semidirect |
| 4. #64752 | C2 | semidirect |
| 5. #64750 | C2 | semidirect |
| 26. C2×D20 | Q8 | semidirect |
| 39. #544 | D5 | semidirect |
| 140. C5 | #2027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#544 | 2 |
| #65290 | 2 |
| #65277 | 2 |
| #64752 | 2 |
| #64750 | 2 |
| #2027 | 5 |