Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 4. (C2×AGL(1,𝔽5))⋊C8 | C2 | semidirect |
| 7. C22×#170 | C4 | semidirect |
| 14. C2×D5⋊C8 | C4 | semidirect |
| 16. C2×C5×M16 | C4 | semidirect |
| 17. C2×#681 | C4 | semidirect |
| 20. C2×#676 | C4 | semidirect |
| 89. C2×M16 | AGL(1,𝔽5) | semidirect |
| 181. C5 | #1729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4130 | 2 |
| C22×D5⋊C8 | 2 |
| C2×D5×M16 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #1729 | 5 |