Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. #65804 | C2 | semidirect |
| 3. C5×#431 | C2 | semidirect |
| 4. #65137 | C2 | semidirect |
| 5. #65020 | C2 | semidirect |
| 6. #64983 | C2 | semidirect |
| 7. #64982 | C2 | semidirect |
| 15. C2×#677 | C22 | semidirect |
| 21. #4015 | C22 | semidirect |
| 22. #4015 | C22 | semidirect |
| 24. C4×Dic10 | C22 | semidirect |
| 25. C5×C4⋊C8 | C22 | semidirect |
| 27. C4×C5×C8 | C22 | semidirect |
| 28. #3953 | C22 | semidirect |
| 65. #431 | D5 | semidirect |
| 73. C2×C4×C5 | SD16 | semidirect |
| 108. C4⋊C8 | C2×D5 | semidirect |
| 111. C4×C8 | C2×D5 | semidirect |
| 179. C2×C4 | #677 | semidirect |
| 187. C5 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4020 | 2 |
| #65804 | 2 |
| C5×#431 | 2 |
| #65137 | 2 |
| #65020 | 2 |
| #64983 | 2 |
| #64982 | 2 |
| #3208 | 5 |