The subiculum (SUB) plays an essential role in spatial navigation. Compared with the hippocampal CA1 area, the SUB uniquely encodes navigational information. However, the geometry of population activity in the SUB remains to be determined. This study investigated neural population activity recorded extracellularly from the CA1 and SUB of rats performing T-maze and open-field tasks. The population activity in both areas was confined to low-dimensional neural manifolds that were homeomorphic to the external space. The neural manifolds conveyed information about the rats' position, speed, and future path, with the SUB showing higher decoding accuracy than the CA1. The neural manifolds showed a common geometry across different rats and regions in the CA1 and the SUB, as well as across tasks in the SUB. During post-task ripples in slow-wave sleep, population activity in the SUB more frequently represented reward locations/events than that of CA1. Thus, during both wakefulness and sleep, the neural manifolds in the CA1 and SUB distinctly encode navigational information.