Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 3. #64895 | C2 | semidirect |
| 8. #4130 | C4 | semidirect |
| 11. C2×C4×AGL(1,𝔽5) | C4 | semidirect |
| 12. C2×C5×M16 | C4 | semidirect |
| 13. C2×#681 | C4 | semidirect |
| 17. C2×C8×D5 | C4 | semidirect |
| 36. C4×AGL(1,𝔽5) | C2×C4 | semidirect |
| 38. C2×C5×C8 | C2×C4 | semidirect |
| 40. C2×#168 | C2×C4 | semidirect |
| 80. C2×M16 | AGL(1,𝔽5) | semidirect |
| 124. C2×C8 | C2×AGL(1,𝔽5) | semidirect |
| 136. D5 | H(3,ℤ/4) | semidirect |
| 165. C5 | C2×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4130 | 2 |
| C2×D5×M16 | 2 |
| #64895 | 2 |
| C2×H(3,ℤ/4) | 5 |