Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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×C5×D16 | C2 | semidirect |
| 2. #65440 | C2 | semidirect |
| 3. D8×Dic5 | C2 | semidirect |
| 4. C2×#3958 | C2 | semidirect |
| 5. #64782 | C2 | semidirect |
| 6. #64729 | C2 | semidirect |
| 7. #64721 | C2 | semidirect |
| 31. C5×D8 | D4 | semidirect |
| 43. C2×D16 | D5 | semidirect |
| 95. Dic5 | D16 | semidirect |
| 108. D8 | C22⋊D5 | semidirect |
| 141. C5 | #2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D16 | 2 |
| #65440 | 2 |
| D8×Dic5 | 2 |
| C2×#3958 | 2 |
| #64782 | 2 |
| #64729 | 2 |
| #64721 | 2 |
| #2206 | 5 |