Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 1. C2×C5×#124 | C2 | semidirect |
| 2. #65813 | C2 | semidirect |
| 3. #65517 | C2 | semidirect |
| 4. #65516 | C2 | semidirect |
| 5. #65507 | C2 | semidirect |
| 7. #65348 | C2 | semidirect |
| 8. #65346 | C2 | semidirect |
| 9. #65345 | C2 | semidirect |
| 10. #65343 | C2 | semidirect |
| 11. #65214 | C2 | semidirect |
| 21. C2×#689 | C22 | semidirect |
| 22. C2×#688 | C22 | semidirect |
| 30. #4021 | C22 | semidirect |
| 31. C4×D20 | C22 | semidirect |
| 33. #4016 | C22 | semidirect |
| 34. C4×Dic10 | C22 | semidirect |
| 35. #3967 | C22 | semidirect |
| 36. #3967 | C22 | semidirect |
| 41. C4⋊#168 | C22 | semidirect |
| 42. C4×#168 | C22 | semidirect |
| 86. C2×#124 | D5 | semidirect |
| 259. C5 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#124 | 2 |
| #65813 | 2 |
| #65517 | 2 |
| #65516 | 2 |
| #65507 | 2 |
| #65506 | 2 |
| #65348 | 2 |
| #65346 | 2 |
| #65345 | 2 |
| #65343 | 2 |
| #65214 | 2 |
| #3211 | 5 |