Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. C22×#688 | C2 | semidirect |
| 4. #65855 | C2 | semidirect |
| 5. #65522 | C2 | semidirect |
| 6. #65514 | C2 | semidirect |
| 7. #65372 | C2 | semidirect |
| 8. #65346 | C2 | semidirect |
| 9. #65288 | C2 | semidirect |
| 13. C5×C4⋊Q8 | C22 | semidirect |
| 14. C5×#124 | C22 | semidirect |
| 29. #3967 | C22 | semidirect |
| 30. #3967 | C22 | semidirect |
| 31. #3964 | C22 | semidirect |
| 32. C4⋊#168 | C22 | semidirect |
| 70. #536 | D5 | semidirect |
| 116. C4⋊Q8 | C2×D5 | semidirect |
| 117. #124 | C2×D5 | semidirect |
| 212. C5 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#536 | 2 |
| C2×#4095 | 2 |
| C22×#688 | 2 |
| #65855 | 2 |
| #65522 | 2 |
| #65514 | 2 |
| #65372 | 2 |
| #65346 | 2 |
| #65288 | 2 |
| #3042 | 5 |