A major hallmark of Alzheimer's disease (AD) is the accumulation of extracellular aggregates of amyloid-β (Aβ). Structural polymorphism observed among Aβ fibrils in AD brains seem to correlate with the clinical subtypes suggesting a link between fibril polymorphism and pathology. Since fibrils emerge from a templated growth of low-molecular-weight oligomers, understanding the factors affecting oligomer generation is important. Membrane lipids are key factors to influence early stages of Aβ aggregation and oligomer generation, which cause membrane disruption. We have previously demonstrated that conformationally discrete Aβ oligomers can be generated by modulating the charge, composition, and chain length of lipids and surfactants. Here, we extend our studies into liposomal models by investigating Aβ oligomerization on large unilamellar vesicles (LUVs) of total brain extracts (TBE), reconstituted lipid rafts (LRs), or 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). Varying the vesicle composition by specifically increasing the amount of GM1 gangliosides as a constituent, we found that only GM1-enriched liposomes induce the formation of toxic, low-molecular-weight oligomers. Furthermore, we found that the aggregation on liposome surface and membrane disruption are highly cooperative and sensitive to membrane surface characteristics. Numerical simulations confirm such a cooperativity and reveal that GM1-enriched liposomes form twice as many pores as those formed in the absence GM1. Overall, this study uncovers mechanisms of cooperativity between oligomerization and membrane disruption under controlled lipid compositional bias, and refocuses the significance of the early stages of Aβ aggregation in polymorphism, propagation, and toxicity in AD.