Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 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. C2×#4070 | C2 | semidirect |
| 3. C5×#407 | C2 | semidirect |
| 4. #65426 | C2 | semidirect |
| 5. #65423 | C2 | semidirect |
| 6. #65028 | C2 | semidirect |
| 7. #65027 | C2 | semidirect |
| 8. #65024 | C2 | semidirect |
| 9. #65022 | C2 | semidirect |
| 10. #65012 | C2 | semidirect |
| 11. #65011 | C2 | semidirect |
| 32. C2×Dic20 | C22 | semidirect |
| 33. C2×#677 | C22 | semidirect |
| 37. #3953 | C22 | semidirect |
| 38. #3950 | C22 | semidirect |
| 39. #3949 | C22 | semidirect |
| 40. #3948 | C22 | semidirect |
| 41. #3948 | C22 | semidirect |
| 42. #3948 | C22 | semidirect |
| 95. #407 | D5 | semidirect |
| 268. C5 | #3196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66125 | 2 |
| C2×#4070 | 2 |
| C5×#407 | 2 |
| #65426 | 2 |
| #65423 | 2 |
| #65028 | 2 |
| #65027 | 2 |
| #65024 | 2 |
| #65022 | 2 |
| #65012 | 2 |
| #65011 | 2 |
| #3196 | 5 |