Left: distribution of RLAGNs with or without an associated cluster in L_150 MHz–M_* space. Red contours denote the distribution of in-cluster RLAGNs, while the blue contours denote the not-in-cluster RLAGNs (defined in Sect. 3.4). The grey lines (“Box 1”) and black dashed lines (“Box 2”) mark the L_150 MHz and M_* constraints and bins used in the control sample analysis in Sect. 3.4. The grey lines are for the low-power sample, while the black dashed lines are for the high-power sample. Middle and right: example of the q distributions of in-cluster RLAGNs (red shaded histograms) and the not-in-cluster control sample (blue histograms). The null hypothesis p-value from a K–S test (median value from 1000 tests) is noted.