Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C5×#536 | C2 | semidirect |
| 2. C2×#4097 | C2 | semidirect |
| 4. C22×#689 | C2 | semidirect |
| 5. C2×#4088 | C2 | semidirect |
| 6. #65860 | C2 | semidirect |
| 7. #65381 | C2 | semidirect |
| 8. #65375 | C2 | semidirect |
| 9. #65349 | C2 | semidirect |
| 10. #65348 | C2 | semidirect |
| 11. #65286 | C2 | semidirect |
| 94. #536 | D5 | semidirect |
| 266. C5 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#536 | 2 |
| C2×#4097 | 2 |
| C2×#4096 | 2 |
| C22×#689 | 2 |
| C2×#4088 | 2 |
| #65860 | 2 |
| #65381 | 2 |
| #65375 | 2 |
| #65349 | 2 |
| #65348 | 2 |
| #65286 | 2 |
| #3156 | 5 |