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Given two structures $\mathcal{M}$ and $\mathcal{N}$ on the same domain, wesay that $\mathcal{N}$ is a reduct of $\mathcal{M}$ if all$\emptyset$-definable relations of $\mathcal{N}$ are $\emptyset$-definable in$\mathcal{M}$. In this article the reducts of the Henson digraphs areclassified. Henson digraphs are homogeneous countable digraphs that omit someset of finite tournaments. As the Henson digraphs are $\aleph_0$-categorical,determining their reducts is equivalent to determining all closed supergroups$G<$ Sym$(\mathbb{N})$ of their automorphism groups.  A consequence of the classification is that there are $2^{\aleph_0}$ pairwisenon-isomorphic Henson digraphs which have no proper non-trivial reducts. Takingtheir automorphisms groups gives a positive answer to a question of Macphersonthat asked if there are $2^{\aleph_0}$ pairwise non-conjugate maximal-closedsubgroups of Sym$(\mathbb{N})$. By the reconstruction results of Rubin, thesegroups are also non-isomorphic as abstract groups.

$2^{\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of Sym$(\mathbb{N})$ via the classification of the reducts of the Henson digraphs