  In this paper, we list all cyclic automorphisms subgroups $H$ for which there
exists a smooth projective non-hyperelliptic sextic curve $C$ with $H\preceq
Aut(C)$. Furthermore, we attach to each group a defining equation of a plane
sextic curve having exactly this group as cyclic automorphisms subgroup. These
equations cover up to isomorphism all plane non-singular sextic curves having
some non-trivial automorphism.
