Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
388 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 137 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. C5×#343 | C2 | semidirect |
| 4. #64774 | C2 | semidirect |
| 5. #64750 | C2 | semidirect |
| 14. D5×M16 | C4 | semidirect |
| 47. #343 | D5 | semidirect |
| 154. C5 | #1742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×M16 | 2 |
| C2×#4038 | 2 |
| C5×#343 | 2 |
| #64774 | 2 |
| #64750 | 2 |
| #1742 | 5 |