Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
448 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 448 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. #64893 | C2 | semidirect |
| 9. #4130 | C4 | semidirect |
| 12. C2×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 16. C2×C5×M16 | C4 | semidirect |
| 17. C2×#681 | C4 | semidirect |
| 20. C2×#676 | C4 | semidirect |
| 43. C4⋊AGL(1,𝔽5) | C2×C4 | semidirect |
| 46. C2×C5×C8 | C2×C4 | semidirect |
| 48. C2×#168 | C2×C4 | semidirect |
| 95. C2×M16 | AGL(1,𝔽5) | semidirect |
| 147. C2×C8 | C2×AGL(1,𝔽5) | semidirect |
| 195. C5 | #1736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4130 | 2 |
| C22×C4⋊AGL(1,𝔽5) | 2 |
| C2×D5×M16 | 2 |
| #64893 | 2 |
| #1736 | 5 |