Cubic unit cell has four 3-fold and three-4-fold elements of symmetry
It has all 3 edges of equal length and all 3 equal angles.
3
Ortho-rhombic
4
End centered
Tetragonal unit cell has two edges of equal length.
2
Monoclinic unit cell has all unequal edge lengths.
2
End centered
It has One 2-fold elements of symmetry
Triclinic has all unequal edge lengths.
1
Rhombohedral
1
Hexagonal
1