Prove that the dihedral groups $D_n$ are all Lagrangian

Question

I was reading a book on group theory and there was problem in the book that states:

Prove that the dihedral groups $D_n$ are all Lagrangian for $n\geq3$.

Apologies the previous hint was not for this question.

If anyone could answer this question is would be hugely appreciated.

Answer 1

All dihedral groups are supersolvable and hence Lagrangian, i.e., the converse of Lagrange's theorem holds.

References:

Dihedral group is supersolvable

Complete classification of the groups for which converse of Lagrange's Theorem holds