Alzheimer's disease (AD) is caused by the assembly of amyloid-beta (Aβ) peptides into oligomers and fibrils. Endogenous Aβ aggregation may be assisted by cell membranes, which can accelerate the nucleation step enormously, but knowledge of membrane-assisted aggregation is still very limited. Here, we used extensive molecular dynamics (MD) simulations to structurally and energetically characterize key intermediates along the membrane-assisted aggregation pathways of Aβ40. Reinforcing experimental observations, the simulations reveal unique roles of GM1 ganglioside and cholesterol in stabilizing membrane-embedded β sheets and of Y10 and K28 in the ordered release of a small oligomeric seed into solution. The same seed leads to either an open-shaped or R-shaped fibril, with significant stabilization provided by inter- or intra-subunit interfaces between a straight β sheet (residues Q15-D23) and a bent β sheet (residues A30-V36). This work presents a comprehensive picture of membrane-assisted aggregation of Aβ40, with broad implications for developing AD therapies and rationalizing disease-specific polymorphisms of amyloidogenic proteins.