  We determine the automorphism groups of the cyclic orbifold vertex operator
algebras associated with coinvariant lattices of isometries of the Leech
lattice in the conjugacy classes $4C,6E,6G,8E$ and $10F$. As a consequence, we
have determined the automorphism groups of all the $10$ vertex operator
algebras in [H\"o], which are useful to analyze holomorphic vertex operator
algebras of central charge $24$.
