Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×C5×C22⋊Q8 | C2 | semidirect |
| 3. #65516 | C2 | semidirect |
| 4. C2×C22⋊#168 | C2 | semidirect |
| 5. #65337 | C2 | semidirect |
| 6. #65335 | C2 | semidirect |
| 7. #65332 | C2 | semidirect |
| 8. #65257 | C2 | semidirect |
| 9. C22×C5×Q8 | C22 | semidirect |
| 16. C5×C22⋊Q8 | C22 | semidirect |
| 18. C2×C5×C4⋊C4 | C22 | semidirect |
| 20. C2×#688 | C22 | semidirect |
| 27. C22×#168 | C22 | semidirect |
| 28. #3967 | C22 | semidirect |
| 30. C22⋊#168 | C22 | semidirect |
| 31. #3941 | C22 | semidirect |
| 32. #3940 | C22 | semidirect |
| 68. C2×C22⋊Q8 | D5 | semidirect |
| 78. C23×C5 | SD16 | semidirect |
| 109. C22×Q8 | C2×D5 | semidirect |
| 118. C22⋊Q8 | C2×D5 | semidirect |
| 125. C2×C4⋊C4 | C2×D5 | semidirect |
| 202. C23 | #688 | semidirect |
| 229. C5 | #3187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊Q8 | 2 |
| C2×#4076 | 2 |
| #65516 | 2 |
| C2×C22⋊#168 | 2 |
| #65337 | 2 |
| #65335 | 2 |
| #65332 | 2 |
| #65257 | 2 |
| #3187 | 5 |