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The Einstein radius (ER) of a gravitational lens encodes information aboutdecisive quantities such as halo mass, concentration, triaxiality, andorientation with respect to the observer. Thus, the largest Einstein radii canpotentially be utilised to test the predictions of the LCDM model. Hitherto,studies have focussed on the single largest observed ER. We extend thosestudies by employing order statistics to formulate exclusion criteria based onthe n largest Einstein radii and apply these criteria to the strong lensinganalysis of 12 MACS clusters at z>0.5. We obtain the order statistics ofEinstein radii by a MC approach, based on the semi-analytic modelling of thehalo population on the past lightcone. After sampling the order statistics, wefit a GEV distribution to the first-order distribution, which allows us toderive analytic relations for the order statistics of the Einstein radii. Wefind that the Einstein radii of the 12 MACS clusters are not in conflict withthe LCDM expectations. Our exclusion criteria indicate that, in order toexhibit tension with the concordance model, one would need to observeapproximately twenty Einstein radii >30", ten >35" or five >42" in the range of0.5<z<1.0 on the full sky. Furthermore, we find that, with increasing order,the haloes with the largest Einstein radii are on average less aligned alongthe line-of-sight and less triaxial. In general, the cumulative distributionfunctions steepen for higher orders, giving them better constraining power.(abridged)

The strongest gravitational lenses: III. The order statistics of the largest Einstein radii