Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #65804 | C2 | semidirect |
| 3. C5×#432 | C2 | semidirect |
| 4. #65134 | C2 | semidirect |
| 5. #65028 | C2 | semidirect |
| 7. #65004 | C2 | semidirect |
| 8. #65003 | C2 | semidirect |
| 17. C2×Dic20 | C22 | semidirect |
| 24. #4015 | C22 | semidirect |
| 25. #4015 | C22 | semidirect |
| 27. C4×Dic10 | C22 | semidirect |
| 28. C5×C4⋊C8 | C22 | semidirect |
| 30. C5×#97 | C22 | semidirect |
| 32. #3948 | C22 | semidirect |
| 73. #432 | D5 | semidirect |
| 118. C4⋊C8 | C2×D5 | semidirect |
| 122. #97 | C2×D5 | semidirect |
| 202. C5 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4021 | 2 |
| #65804 | 2 |
| C5×#432 | 2 |
| #65134 | 2 |
| #65028 | 2 |
| #65020 | 2 |
| #65004 | 2 |
| #65003 | 2 |
| #3215 | 5 |