Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×C8×AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊C8 | C2 | semidirect |
| 8. C22×#170 | C4 | semidirect |
| 11. C2×D5⋊C8 | C4 | semidirect |
| 17. C5×C22⋊C8 | C4 | semidirect |
| 18. C22⋊#168 | C4 | semidirect |
| 19. #3952 | C4 | semidirect |
| 31. C22⋊AGL(1,𝔽5) | C8 | semidirect |
| 57. C2×AGL(1,𝔽5) | C2×C8 | semidirect |
| 72. #170 | C22⋊C4 | semidirect |
| 86. C22⋊C8 | AGL(1,𝔽5) | semidirect |
| 91. C22×C5 | C4×C8 | semidirect |
| 96. C2×D5 | C4×C8 | semidirect |
| 161. C5 | C8×C22⋊C4 | semidirect |
| 171. C22 | C8×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5⋊C8 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 2 |
| C2×C8×AGL(1,𝔽5) | 2 |
| D5×C22⋊C8 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| C8×C22⋊C4 | 5 |