A dihedral group that is not an internal direct product

#group_theory

The dihedral group, $D_{8}$ , is the group of eight rigid symmetries of a square. Prove that $D_{8}$ is not the internal direct product of two of its proper subgroups.

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The dihedral group, $D_8$, is the group of eight rigid symmetries of a square. Prove that $D_8$ is not the internal direct product of two of its proper subgroups.