Personality factors as defined by the "five-factor model" are some of the most investigated characteristics that underlie various types of complex behavior. These are, however, often investigated as isolated traits that are conceptually independent, yet empirically are typically strongly related to each other. We apply Independent Component Analysis to these personality factors as measured by the NEO-FFI in 471 healthy subjects from the Human Connectome Project to investigate independent personality profiles that incorporate all five original factors. Subsequently we examine how these profiles are related to patterns of resting-state brain activity in specific networks-of-interest related to cognition and emotion. We find that a personality profile of contrasting openness and agreeableness is associated with engagement of a subcortical-medial prefrontal network and the dorsolateral prefrontal cortex. Likewise, a profile of contrasting extraversion and conscientiousness is associated with activity in the precuneus. This study shows a novel approach to investigating personality and how it is related to patterns of activity in the resting brain.