Edge-localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Despite beneficial aspects of ELMs, in a future device the size of the energy loss per ELM must be controlled, in order to avoid intolerable divertor power flux densities. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of ELMs. This publication presents a detailed analysis of the toroidal structure of dominant magnetic perturbations during type-I ELMs in TCV. These signatures of the instability can be observed most intensely in close temporal vicinity to the onset of enhanced D-alpha-radiation. In particular it is shown that dominant magnetic perturbations already have a rigid toroidal mode structure when they are detected with magnetic probes. This indicates that perturbations associated with this type of ELM at TCV cannot be observed in their linear phase. Furthermore it is demonstrated that the toroidal structure of dominant magnetic perturbations is most often dominated by the n = 1 component. This is in clear contrast to typical results of linear stability calculations, leading to the hypothesis that the dominant toroidal mode number from the linear to the non-linear phase has a transition from intermediate to low values. In general, the reported results show that non-linear coupling leads to a significant modification of the mode structure.