Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4133 | C2 | semidirect |
| 3. C2×#4010 | C2 | semidirect |
| 4. #65776 | C2 | semidirect |
| 5. C2×#4008 | C2 | semidirect |
| 6. #64896 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽5))⋊C8 | C2 | semidirect |
| 18. C2×C5×SD16 | C4 | semidirect |
| 19. C2×#689 | C4 | semidirect |
| 20. C2×#686 | C4 | semidirect |
| 23. C2×#677 | C4 | semidirect |
| 119. C2×SD16 | AGL(1,𝔽5) | semidirect |
| 235. C5 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4133 | 2 |
| C2×#4062 | 2 |
| C2×#4010 | 2 |
| #65776 | 2 |
| C2×#4008 | 2 |
| #64896 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #1876 | 5 |