The magnetic properties and the low-temperature magnetic structures of the orthorhombic perovskite HoMnO3 (space group Pnma) have been studied on polycrystalline samples by magnetization, specific heat, and neutron diffraction measurements. By cooling, HoMnO3 exhibits three singularities at TN = 41 K, T ≈ 26 K, and T ≈ 6.5 K, suggesting a rich magnetic phase diagram. The neutron diffraction data show that below TN = 41 K, the Mn3+ magnetic moments become ordered in an antiferromagnetic arrangement, adopting a modulated sinusoidal magnetic structure characterized by the wave vector k = (kx,0,0) (kx = 0.40 at 41 K) and defined by the magnetic mode (Cx,0,0). When the temperature is decreased, the propagation vector varies and at T ≈ 29 K a transition to a commensurate magnetic structure defined by k = (1/2,0,0) takes place. Below T ≈ 22 K, a small ordered magnetic moment appears on the Ho3+ cations, strongly increasing below 9 K and reaching 7.3(1) μB at T = 1.8 K. The magnetic structure of the Ho3+ moments ...