When animals reproduce in social groups, the potential for conflict and cooperation is shaped by the number of reproductive individuals (breeders), their relatedness to one another, and division of reproduction among them. These features comprise species’ “breeding systems.” Despite their importance, breeding systems are poorly characterized in most social animals, and detailed accounts for single species are rare. Here, we fully characterize the breeding systems in invasive populations of the fire ant Solenopsis invicta, a species in which a large genetic element (supergene) determines whether a colony has a single queen (monogyne social form) or multiple queens (polygyne form). Colonies of the monogyne form are simple families, and the breeding system is correspondingly straightforward. The breeding system of the polygyne form is complex, with many features still uncharacterized. We conducted a large longitudinal experiment tracking parentage, relatedness, and supergene genotype in semi-natural polygyne colonies. Along with reanalyzed data from previous studies, we show that colony queen number is highly variable, queens generally mate once, nestmate breeders (queens and their mates) are unrelated, and reproductive skew is pervasive, especially for sexual daughters. Uncommon instances of polyandry occur when a queen remates after initially mating with a male bearing the Sb supergene haplotype (associated with low sperm counts). Paternity skew is pronounced and stable, with Sb sperm contributing to a minority of offspring (particularly sexuals). Thus, the supergene not only determines colony queen number, it broadly affects the breeding system, with impacts on colony kin structure and opportunities for reproductive competition.