Invariant-based Contrastive Learning (ICL) methods have achieved impressive performance across various domains. However, the absence of latent space representation for distortion (augmentation)-related information in the latent space makes ICL sub-optimal regarding training efficiency and robustness in downstream tasks. Recent studies suggest that introducing equivariance into Contrastive Learning (CL) can improve overall performance. In this paper, we rethink the roles of augmentation strategies and equivariance in improving CL efficacy. We propose a novel Equivariant-based Contrastive Learning (ECL) framework, CLeVER (Contrastive Learning Via Equivariant Representation), compatible with augmentation strategies of arbitrary complexity for various mainstream CL methods and model frameworks. Experimental results demonstrate that CLeVER effectively extracts and incorporates equivariant information from data, thereby improving the training efficiency and robustness of baseline models in downstream tasks.