Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
806 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 169 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. C22×C5×#41 | C2 | semidirect |
| 2. C2×#4095 | C2 | semidirect |
| 3. C2×#4076 | C2 | semidirect |
| 4. #65527 | C2 | semidirect |
| 5. #65521 | C2 | semidirect |
| 6. #65516 | C2 | semidirect |
| 7. #65506 | C2 | semidirect |
| 8. #65496 | C2 | semidirect |
| 13. C2×C5×#41 | C22 | semidirect |
| 14. C22×C5×Q8 | C22 | semidirect |
| 16. C22×C5×D4 | C22 | semidirect |
| 20. C22×D20 | C22 | semidirect |
| 22. C2×#688 | C22 | semidirect |
| 23. C2×#686 | C22 | semidirect |
| 27. #4076 | C22 | semidirect |
| 29. C2×C4⋊Dic5 | C22 | semidirect |
| 30. C2×#681 | C22 | semidirect |
| 31. #3967 | C22 | semidirect |
| 32. #3964 | C22 | semidirect |
| 33. C22⋊#168 | C22 | semidirect |
| 34. C22⋊#168 | C22 | semidirect |
| 44. C5×#41 | D4 | semidirect |
| 80. C22×#41 | D5 | semidirect |
| 104. C5×Q8 | C2×D4 | semidirect |
| 109. C5×D4 | C2×D4 | semidirect |
| 135. C2×#41 | C2×D5 | semidirect |
| 136. C22×Q8 | C2×D5 | semidirect |
| 140. C22×D4 | C2×D5 | semidirect |
| 170. C22×C5 | AGL(1,ℤ/8) | semidirect |
| 190. #41 | C22⋊D5 | semidirect |
| 250. Q8 | C2×C22⋊D5 | semidirect |
| 259. D4 | C2×C22⋊D5 | semidirect |
| 277. C5 | #3006 | semidirect |
| 294. C22 | #4095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41 | 2 |
| C2×#4095 | 2 |
| C2×#4076 | 2 |
| #65527 | 2 |
| #65521 | 2 |
| #65516 | 2 |
| #65506 | 2 |
| #65496 | 2 |
| #3006 | 5 |