The dihedral group D20 has several normal subgroups, as seen below. Each of these is the kernel of a homomorphism with D20 as the domain. For each normal subgroup of D20 construct a homomorphism from D20 to D20 that has the normal subgroup as the kernel. Include in your work verifications that you are creating the desired kernels. There is a pattern to many of these, but the three of order 20 will be a challenge.
\begin{verbatim}
G = DihedralGroup(20)
[H.order() for H in G.normal_subgroups()]
[40, 20, 20, 20, 10, 4, 2, 5, 1]
\end{verbatim}