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Questions on Symmetric group of degree 5
I was told that $S_5$ has subgroups isomorphic to $D_5$ and $D_6$, however when I looked it up here I didn't see any mention of $D_6$? (I am presuming that $D_5$ is actually $D_10$ on this page, but there is no mention of a $D_12$). So does $S_5$ have subgroups isomorphic to $D_5$ and $D_6$?
And how would the generators of these subgroups relate to the elements of $S_5$?