Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #65733 | C2 | semidirect |
| 2. #65731 | C2 | semidirect |
| 4. #64906 | C2 | semidirect |
| 5. #64903 | C2 | semidirect |
| 6. ΓL(1,𝔽81) | C2 | semidirect |
| 7. #64845 | C2 | semidirect |
| 18. C5×D16 | C4 | semidirect |
| 19. #3959 | C4 | semidirect |
| 20. #3958 | C4 | semidirect |
| 21. #3932 | C4 | semidirect |
| 35. C5×D8 | C2×C4 | semidirect |
| 38. Dic20 | C2×C4 | semidirect |
| 42. C5×C16 | C2×C4 | semidirect |
| 43. #672 | C2×C4 | semidirect |
| 74. D16 | AGL(1,𝔽5) | semidirect |
| 101. D8 | C2×AGL(1,𝔽5) | semidirect |
| 112. C16 | C2×AGL(1,𝔽5) | semidirect |
| 134. C5 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65733 | 2 |
| #65731 | 2 |
| #65200 | 2 |
| #64906 | 2 |
| #64903 | 2 |
| ΓL(1,𝔽81) | 2 |
| #64845 | 2 |
| AGL(1,ℤ/16) | 5 |