Let n≥1 be an integer, p,q be distinct odd primes. Let G,N be two groups of order pnq with their Sylow-p-subgroups being cyclic. We enumerate the Hopf-Galois structures on a Galois G-extension, with type N. This also computes the number of skew braces with additive group isomorphic to N and multiplicative group isomorphic to G. Further when q<p, we give a complete classification of the Hopf-Galois structures on Galois-G-extensions.