Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 18. C2×C5×Q16 | C4 | semidirect |
| 19. C2×#689 | C4 | semidirect |
| 20. C2×#689 | C4 | semidirect |
| 23. C2×Dic20 | C4 | semidirect |
| 89. C2×AGL(1,𝔽5) | Q16 | semidirect |
| 126. C2×Q16 | AGL(1,𝔽5) | semidirect |
| 248. C5 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽5) | 2 |
| C2×D5×Q16 | 2 |
| (C2×AGL(1,𝔽5))⋊Q8 | 2 |
| C2×#4009 | 2 |
| #64893 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #1878 | 5 |