Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 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. #66062 | C2 | semidirect |
| 3. C5×#461 | C2 | semidirect |
| 4. #65460 | C2 | semidirect |
| 5. #65452 | C2 | semidirect |
| 6. #65372 | C2 | semidirect |
| 7. #65297 | C2 | semidirect |
| 8. #65131 | C2 | semidirect |
| 9. D5×C4⋊C8 | C2 | semidirect |
| 10. #65096 | C2 | semidirect |
| 11. #65080 | C2 | semidirect |
| 91. #461 | D5 | semidirect |
| 122. C4×D5 | SD16 | semidirect |
| 257. C5 | #3246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| #65882 | 2 |
| C5×#461 | 2 |
| #65460 | 2 |
| #65452 | 2 |
| #65372 | 2 |
| #65297 | 2 |
| #65131 | 2 |
| D5×C4⋊C8 | 2 |
| #65096 | 2 |
| #65080 | 2 |
| #3246 | 5 |