An alteration of the uranyl oxide hydroxy-hydrate mineral schoepite [(UO2)8O2(OH)12](H2O)12 at mild hydrothermal conditions was studied. As the result, four different crystalline phases Cs[(UO2)(SO4)(OH)](H2O)0.25 (1), Cs3[(UO2)4(SO4)2O3(OH)](H2O)3 (2), Cs6[(UO2)2(SO4)5](H2O)3 (3), and Cs2[(UO2)(SO4)2] (4) were obtained, including three novel compounds. The obtained Cs uranyl sulfate compounds 1, 3, and 4 were analyzed using single-crystal XRD, EDX, as well as topological analysis and information-based structural complexity measures. The crystal structure of 3 was based on the 1D complex, the topology of which was unprecedented for the structural chemistry of inorganic oxysalts. Crystal chemical analysis performed herein suggested that the majority of the uranyl sulfates minerals were grown from heated solutions, and the temperature range could be assumed from the manner of interpolyhedral linkage. The presence of edge-sharing uranyl bipyramids most likely pointed to the temperatures of higher than 100 °C. The linkage of sulfate tetrahedra with uranyl polyhedra through the common edges involved elevated temperatures but of lower values (~70–100 °C). Complexity parameters of the synthetic compounds were generally lower than that of uranyl sulfate minerals, whose structures were based on the complexes with the same or genetically similar topologies. The topological complexity of the uranyl sulfate structural units contributed the major portion to the overall complexity of the synthesized compounds, while the complexity of the respective minerals was largely governed by the interstitial structure and H-bonding system.