The emergence of antibiotic resistance is a defining challenge, and Escherichia coli is recognized as one of the leading species resistant to the antimicrobials used in human or veterinary medicine. Here, we analyse the distribution of 2172 antimicrobial-resistance (AMR) genes in 4022 E. coli to provide a population-level view of resistance in this species. By separating the resistance determinants into ‘core’ (those found in all strains) and ‘accessory’ (those variably present) determinants, we have found that, surprisingly, almost half of all E. coli do not encode any accessory resistance determinants. However, those strains that do encode accessory resistance are significantly more likely to be resistant to multiple antibiotic classes than would be expected by chance. Furthermore, by studying the available date of isolation for the E. coli genomes, we have visualized an expanding, highly interconnected network that describes how resistances to antimicrobials have co-associated within genomes over time. These data can be exploited to reveal antimicrobial combinations that are less likely to be found together, and so if used in combination may present an increased chance of suppressing the growth of bacteria and reduce the rate at which resistance factors are spread. Our study provides a complex picture of AMR in the E. coli population. Although the incidence of resistance to all studied antibiotic classes has increased dramatically over time, there exist combinations of antibiotics that could, in theory, attack the entirety of E. coli, effectively removing the possibility that discrete AMR genes will increase in frequency in the population.