Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 258 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. #65764 | C2 | direct (N × H) |
| 4. C2×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 7. C23×C4×C5 | C4 | semidirect |
| 8. C23×Dic5 | C4 | semidirect |
| 10. C22×C4×D5 | C4 | semidirect |
| 11. C22×C4×D5 | C4 | semidirect |
| 16. (C2×AGL(1,𝔽5))⋊C4 | C22 | semidirect |
| 30. C22×C4×C5 | C2×C4 | semidirect |
| 33. C22×Dic5 | C2×C4 | semidirect |
| 39. C2×C4×D5 | C2×C4 | semidirect |
| 82. C23×C4 | AGL(1,𝔽5) | semidirect |
| 127. C22×C4 | C2×AGL(1,𝔽5) | semidirect |
| 130. C2×C5 | #381 | semidirect |
| 134. D5 | #381 | semidirect |
| 164. C5 | C2×#381 | semidirect |
| 188. C2 | #65764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D5 | 2 |
| C22×C22⋊AGL(1,𝔽5) | 2 |
| #65764 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C2×#381 | 5 |