Large-Eddy Simulations (LES) based on scale-selective implicit filtering are carried out in order to study the effect of nozzle pressure ratios on the characteristics of highly underexpanded jets. Pressure ratios ranging from 3 to 9 with Reynolds numbers of the order 70000 to 150000 are considered. The studied configuration agrees well with the classical picture of the structure of highly underexpanded jets. The coherent structures of the jet are investigated using Proper Orthogonal Decomposition (POD). The statistics of scalar dissipation rate are investigated in detail. Using the first POD modes, we reconstruct the scalar fields and provide the link between the dominant modes and the dissipative structures.