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More precisely, we show that the Riesz potential $$ R_\\alpha(\\rho)(g) = \\int_{\\G} N(g^{-1} g')^{\\alpha-Q} \\rho(g') dg', \\qquad 0<\\alpha<Q, $$ of a nonnegative function $\\rho\\in C_0(\\G)$ on a group $\\G$ of Heisenberg type is necessarily either $p$-subharmonic or $p$-superharmonic, depending on $p$ and $\\alpha$. Here $N$ denotes the non-isotropic homogeneous norm on such groups, as introduced by Kaplan. 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