A thorough understanding of sex-independent and sex-specific neurobiological features that underlie cognitive abilities in healthy individuals is essential for the study of neurological illnesses in which males and females differentially experience and exhibit cognitive impairment. Here, we evaluate sex-independent and sex-specific relationships between functional connectivity and individual cognitive abilities in 392 healthy young adults (196 males) from the Human Connectome Project. First, we establish that sex-independent models comparably predict crystallised abilities in males and females, but more accurately predict fluid abilities in males. Second, we demonstrate sex-specific models comparably predict crystallised abilities within and between sexes, and generally fail to predict fluid abilities in either sex. Third, we reveal that largely overlapping connections between visual, dorsal attention, ventral attention, and default mode networks are associated with better performance on crystallised and fluid cognitive tests in males and females, while connections within visual, somatomotor, and default mode networks are associated with poorer performance. Together, our findings suggest that shared neurobiological features of the functional connectome underlie crystallised and fluid abilities across the sexes.