The Community of Inquiry (CoI) framework has gained widespread recognition as a theoretical model for understanding student learning in online environments. Despite its prevalence, CoI has been critiqued for its limited emphasis on learners' proactive roles in self-regulating their own learning. To address this, researchers have suggested integrating self-regulated learning (SRL) into the CoI framework. This integration calls for empirical research to explore the relationship between SRL and the three established CoI presences: teaching, social, and cognitive. Using a person-centered approach, this study examines how varying SRL skills among 750 undergraduate students in an online introductory mathematics course are related to the three CoI components. Latent profile analyses identified five distinct SRL profiles: "minimal regulators," "low regulators with limited social skills," "low regulators," "moderate regulators," and "competent regulators." We found that students in higher SRL profiles demonstrated higher perception of CoI, whereas those in relatively lower SRL profiles showed lower levels of perceived CoI. Our findings underscore the importance of incorporating self-regulation in the CoI framework for a more comprehensive understanding of online learning.