Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
712 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 4. #65689 | C2 | direct (N × H) |
| 10. C2×C42×C5 | C4 | semidirect |
| 11. C2×C4×Dic5 | C4 | semidirect |
| 12. C2×C4×Dic5 | C4 | semidirect |
| 13. C42×D5 | C4 | semidirect |
| 33. C42×C5 | C2×C4 | semidirect |
| 34. C4×Dic5 | C2×C4 | semidirect |
| 35. C4×Dic5 | C2×C4 | semidirect |
| 71. C2×C42 | AGL(1,𝔽5) | semidirect |
| 106. C42 | C2×AGL(1,𝔽5) | semidirect |
| 107. C2×C5 | #382 | semidirect |
| 110. D5 | #382 | semidirect |
| 135. C5 | C2×#382 | semidirect |
| 154. C2 | #65689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊AGL(1,𝔽5) | 2 |
| C2×C42×D5 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65689 | 2 |
| C2×#382 | 5 |