Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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. #65167 | C2 | semidirect |
| 3. C5×#367 | C2 | semidirect |
| 5. #64721 | C2 | semidirect |
| 7. #64709 | C2 | semidirect |
| 37. #367 | D5 | semidirect |
| 109. C5 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65167 | 2 |
| #65161 | 2 |
| C5×#367 | 2 |
| #64729 | 2 |
| #64721 | 2 |
| #64711 | 2 |
| #64709 | 2 |
| #2228 | 5 |