Taking nuclear deformation and relativistic effects into account, an analysis of single-particle levels predicts new magic numbers for superheavy nuclei at Z = 126, 138, 154, and 164 and N = 228, 308, and 318. Therefore, in addition to the island of stability centered at Cn, Cn, and Fl, further islands of stability may exist around the doubly magic 126 as well as 164 or 164. These nuclei are predicted to be beta-stable and decay by alpha emission or spontaneous fission with relatively long half-lives, and confer additional stability on neighboring N = 228 isotones and elements 152–168, respectively. On the other hand, the same analysis suggests that proton shell closures may be relatively weak or even nonexistent in some cases such as 126, meaning that such nuclei might not be doubly magic and stability will instead be primarily determined by strong neutron shell closures. Additionally, due to the enormously greater forces of electromagnetic repulsion that must be overcome by the strong force at the second island (Z = 164), it is possible that nuclei around this region only exist as resonances and cannot stay together for a meaningful amount of time. It is also possible that some of the superactinides between these series may not actually exist because they are too far from both islands, in which case the periodic table might end around Z = 130. Interestingly, the area of elements 121–156 where periodicity is in abeyance is quite similar to the gap between the two islands.