Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 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. #65705 | C2 | semidirect |
| 2. #65702 | C2 | semidirect |
| 4. #64884 | C2 | semidirect |
| 5. #170⋊C8 | C2 | semidirect |
| 6. #64871 | C2 | semidirect |
| 7. #64871 | C2 | semidirect |
| 60. D20 | M16 | semidirect |
| 69. #170 | D8 | semidirect |
| 147. C5 | #1581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65705 | 2 |
| #65702 | 2 |
| #65161 | 2 |
| #64884 | 2 |
| #170⋊C8 | 2 |
| #64871 | 2 |
| #1581 | 5 |