Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. D5×C4⋊Q8 | C2 | semidirect |
| 3. C5×#497 | C2 | semidirect |
| 4. #65475 | C2 | semidirect |
| 5. #65471 | C2 | semidirect |
| 7. #65451 | C2 | semidirect |
| 8. #65371 | C2 | semidirect |
| 9. #65349 | C2 | semidirect |
| 10. #64994 | C2 | semidirect |
| 11. #64992 | C2 | semidirect |
| 88. #497 | D5 | semidirect |
| 247. C5 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| #66014 | 2 |
| C5×#497 | 2 |
| #65475 | 2 |
| #65471 | 2 |
| #65459 | 2 |
| #65451 | 2 |
| #65371 | 2 |
| #65349 | 2 |
| #64994 | 2 |
| #64992 | 2 |
| #3218 | 5 |