Relativistic electrons (E > 1 MeV) cause internal charging on satellites and are an important space weather hazard. A key requirement in space weather research concerns extreme events and knowledge of the largest flux expected to be encountered over the lifetime of a satellite mission. This is interesting both from a scientific and practical point of view since satellite operators, engineers and the insurance industry need this information to better evaluate the effects of extreme events on their spacecraft. Here we conduct an extreme value analysis of daily averaged E > 2 MeV electron fluxes from the Geostationary Operational Environmental Satellites (GOES) during the 19.5 year period from 1 January 1995 to 30 June 2014. We find that the daily averaged flux measured at GOES West is typically a factor of ~2.5 higher than that measured at GOES East and we conduct independent analyses for these two locations. The 1 in 10, 1 in 50 and 1 in 100 year daily averaged E> 2 MeV electron fluxes at GOES West are 1.84x10^5, 5.00x10^5 and 7.68x10^5 cm^-2s^-1sr^-1 respectively. The corresponding fluxes at GOES East are 6.53x10^4, 1.98x10^5 and 3.25x10^5 cm^-2s^-1sr^-1 respectively. The largest fluxes seen during the 19.5 year period on 29 July 2004 were particularly extreme and were seen by satellites at GOES West and GOES East. The extreme value analysis suggests that this event was a 1 in 50 year event.