Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #65804 | C2 | semidirect |
| 3. #65517 | C2 | semidirect |
| 5. #65349 | C2 | semidirect |
| 6. #65344 | C2 | semidirect |
| 7. #65343 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 18. C2×#689 | C22 | semidirect |
| 24. #4015 | C22 | semidirect |
| 25. #4015 | C22 | semidirect |
| 27. C4×Dic10 | C22 | semidirect |
| 28. #3967 | C22 | semidirect |
| 31. C4⋊#168 | C22 | semidirect |
| 32. #3935 | C22 | semidirect |
| 202. C5 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#124 | 2 |
| #65804 | 2 |
| #65517 | 2 |
| #65507 | 2 |
| #65349 | 2 |
| #65344 | 2 |
| #65343 | 2 |
| #65215 | 2 |
| #3215 | 5 |