In various domains, many datasets exhibit both high variable dependency and group structures, which necessitates their simultaneous estimation. This package provides functions for two subgroup identification methods based on penalized functions, both of which utilize factor model structures to adapt to data with cross-sectional dependency. The first method is the Subgroup Identification with Latent Factor Structure Method (SILFSM) we proposed. By employing Center-Augmented Regularization and factor structures, the SILFSM effectively eliminates data dependencies while identifying subgroups within datasets. For this model, we offer optimization functions based on two different methods: Coordinate Descent and our newly developed Difference of Convex-Alternating Direction Method of Multipliers (DC-ADMM) algorithms; the latter can be applied to cases where the distance function in Center-Augmented Regularization takes L1 and L2 forms. The other method is the Factor-Adjusted Pairwise Fusion Penalty (FA-PFP) model, which incorporates factor augmentation into the Pairwise Fusion Penalty (PFP) developed by Ma, S. and Huang, J. (2017) <doi:10.1080/01621459.2016.1148039>. Additionally, we provide a function for the Standard CAR (S-CAR) method, which does not consider the dependency and is for comparative analysis with other approaches. Furthermore, functions based on the Bayesian Information Criterion (BIC) of the SILFSM and the FA-PFP method are also included in 'SILFS' for selecting tuning parameters. For more details of Subgroup Identification with Latent Factor Structure Method, please refer to He et al. (2024) <doi:10.48550/arXiv.2407.00882>.