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We characterize the magnetic order using NMR, Mössbauer spectroscopy, and neutron diffraction data for several compositions of CaK(Fe_1-xMn_x)₄As₄. The magnetic order is antiferromagnetic and consistent with the hedgehog spin vortex crystal (hSVC) magnetic moment motif which has previously been found for Ni-doped CaKFe₄As₄. The hSVC state is characterized by the stripe-type propagation vectors (π, 0) and (0, π) just as in the doped 122 compounds. The hSVC state preserves tetragonal symmetry about the Fe site, and only this SVC motif with simple AFM stacking along c is consistent with all our observations. The Mn-doped 1144 compound coexists with superconductivity, but unlike several 122 compounds the ordered magnetic moment is not observed to decrease as the superconducting order parameter develops. In addition, with measurements of T_N < T_C,  we infer a possible quantum phase transition into the AFM state at approximatively x=0.10.