The n-th dihedral group Dn is the group of symmetries on a regular n-gon. The group of symmetries on a square D4 has 8 elements. There are the 4 rotations {Po = 1, P1, P2, P3} the horizontal and vertical reflections {µ1, µ2} the two diagonals 81,82. Give the table defining the group operation for D4 and give the tree of subgroups of D4 and identify which subgroup are normal.

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