Deep subspace clustering uses latent features instead of raw images to construct the self-expression coefficient matrix. Existing methods primarily focus on optimizing the self-expression coefficient matrix, often neglecting the impact of latent features. However, better latent features are more in line with the self-representation assumption and results in a better self-expression coefficient matrix, which construct a chain relationship. Based on the chain relationship, this paper proposes a Class Relation Constraint (CRC) induced Deep Subspace Clustering (DSC) method to improve the representation ability of latent features. First, an intra- and inter-class weighted constraint is proposed to enhance latent data separability in subspaces. Then, to further remove negative samples inside a subspace, a contrastive loss function is introduced within the diagonal blocks of the self-expression coefficient matrix, i.e. the same subspace, under the guidance of spectral clustering results. Along with the enhanced representation ability on latent features and corresponding diagonal blocks, the self-expression coefficient matrix can provide more accurate data relationships for spectral clustering. Experimental results on multiple benchmark datasets have validated the effectiveness of the proposed DSCCRC method, particularly in handling small samples and complex datasets.