Recent failures translating preclinical behavioral treatment effects to positive clinical trial results in humans with Fragile X Syndrome (FXS) support refocusing attention on biological pathways and associated measures, such as electroencephalography (EEG), with strong translational potential and small molecule target engagement. This study utilized guided machine learning to test promising translational EEG measures (resting power and auditory chirp oscillatory variables) in a large heterogeneous sample of individuals with FXS to identify best performing EEG variables for reliably separating individuals with FXS, and genetically-mediated subgroups within FXS, from typically developing controls. Best performing variables included resting relative frontal theta power, all combined posterior-head resting power bands, posterior peak alpha frequency (PAF), combined PAF across all measured regions, combined theta, alpha, and gamma power during the chirp, and all combined chirp oscillatory variables. Sub-group analyses for resting EEG best discriminated non-mosaic FXS males via frontal theta resting relative power (AUC = 0.8759), even with data reduced to a 20-channel clinical montage (AUC = 0.9062). In the chirp task, FXS females and non-mosaic males were nearly perfectly discriminated by combined theta, alpha, and gamma power (AUC = 0.9444) and a combination of all variables (AUC = 0.9610), respectively. Results support use of resting and auditory oscillatory tasks to reliably identify neural deficit in FXS, and to identify specific translational targets for genetically-mediated sub-groups, supporting potential points for stratification.