Objectives Cercopithicine primates tend to have nepotistic hierarchies characterized by predictable, kinship‐based dominance. Although aggression is typically directed down the hierarchy, insubordinate aggression does occur. Insubordination is important to understand because it can precipitate social upheaval and undermine group stability; however, the factors underlying it are not well understood. We test whether key social and demographic variables predict insubordination among captive female rhesus macaques. Materials and Methods To identify factors influencing insubordination, multivariate analyses of 10,821 dyadic conflicts among rhesus macaque females were conducted, using data from six captive groups. A segmented regression analysis was used to identify dyads with insubordination. Negative binomial regression analyses and an information theoretic approach were used to assess predictors of insubordination among dyads. Results In the best models, weight difference (w = 1.0; IRR = 0.930), age (dominant: w = 1.0, IRR = 0.681; subordinate: w = 1.0, IRR = 1.069), the subordinate's total number of allies (w = 0.727, IRR = 1.060) or non‐kin allies (w = 0.273, IRR = 1.165), the interaction of the dominant's kin allies and weight difference (w = 0.938, IRR = 1.046), violation of youngest ascendancy (w = 1.0; IRR = 2.727), and the subordinate's maternal support (w = 1.0; IRR = 2.928), are important predictors of insubordination. Discussion These results show that both intrinsic and social factors influence insubordinate behavior. This adds to evidence of the importance of intrinsic factors and flexibility in a social structure thought to be rigid and predetermined by external factors. Further, because insubordination can precipitate social overthrow, determining predictors of insubordination will shed light on mechanisms underlying stability in nepotistic societies.