Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×#4090 | C2 | semidirect |
| 3. C5×#448 | C2 | semidirect |
| 4. #65516 | C2 | semidirect |
| 5. #65464 | C2 | semidirect |
| 6. #65451 | C2 | semidirect |
| 7. #65329 | C2 | semidirect |
| 8. #65107 | C2 | semidirect |
| 9. #65081 | C2 | semidirect |
| 10. #65027 | C2 | semidirect |
| 11. #65007 | C2 | semidirect |
| 95. #448 | D5 | semidirect |
| 119. C2×Dic5 | SD16 | semidirect |
| 266. C5 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4090 | 2 |
| #65930 | 2 |
| C5×#448 | 2 |
| #65516 | 2 |
| #65464 | 2 |
| #65451 | 2 |
| #65329 | 2 |
| #65107 | 2 |
| #65081 | 2 |
| #65027 | 2 |
| #65007 | 2 |
| #3206 | 5 |