Patterns of cervical human papillomavirus (HPV) infection suggest that HPV genotypes are not independent of each other. This may be explained by risk factors common to all HPV infections, but type-specific biological factors may also play a role. This raises the question of whether widespread use of the quadrivalent vaccine (covering HPV6, 11, 16, 18) may indirectly affect the prevalence of any non-vaccine types. Routine screening samples from 5014 Danish women were tested for 35 HPV genotypes (including 13 high-risk) using the Genomica CLART® HPV2 kit, which is a low-density microarray based on PCR amplification. Simulation studies were performed both under independence between genotypes and under a common dependence structure as would arise from common risk factors, and simulation results were compared to observed coinfection patterns. Overall HPV prevalence was 37.4%, with multiple infections in 17.9%. For 15 HPV types of primary interest (13 high-risk plus HPV6, 11), almost all pairs occurred more often than expected under independence; 33/105 (31.4%) were statistically significant (p<0.05 after adjustment for multiple comparisons). The pairwise odds ratios showed significant heterogeneity (Woolf's test p<0.0001). For simulations based on common dependence, three pairs had observed to expected (O/E) ratios significantly different than 1 (31/68, O/E=4.20; 51/68, O/E=2.52; 33/58, O/E=3.27; all p<0.05 after adjustment for multiple comparisons). HPV68 occurred in multiple infections nearly four times as often as expected under common dependence (p<0.005 after adjustment for multiple comparisons). These results indicate some interaction between HPV types, and suggest that common risk factors do not entirely explain the observed HPV coinfection pattern, although no evidence is found that the prevalence of any types not targeted by the quadrivalent vaccine may be indirectly increased or decreased after widespread use of the vaccine.