Large solar flares and eruptions may influence remote regions through perturbations in the outer-atmospheric magnetic field, leading to causally related events outside of the primary or triggering eruptions that are referred to as sympathetic events. We quantify the occurrence of sympathetic events using the full-disk observations by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory associated with all flares of GOES class M5 or larger from 01 May 2010 through 31 December 2014. Using a superposed-epoch analysis, we find an increase in the rate of flares, filament eruptions, and substantial sprays and surges more than 20 degrees away from the primary flares within the first four hours at a significance of 1.8 standard deviations. We also find that the rate of distant events drops by two standard deviations, or a factor of 1.2, when comparing intervals between 4 hours and 24 hours before and after the start times of the primary large flares. We discuss the evidence for the concluding hypothesis that the gradual evolution leading to the large flare and the impulsive release of the energy in that flare both contribute to the destabilization of magnetic configurations in distant active regions and quiet-Sun areas. These effects appear to leave distant regions, in an ensemble sense, in a more stable state, so that fewer energetic events happen for at least a day following large energetic events.
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