Houghton's groups of those permutations of rays of natural numbers that act as translation far down each ray long ago provided wonderful illustrations of the geometric finiteness conditions of being of type FP_n. The nth Houghton group is of type FP_n but not of type FP_{n+1} for each n. This lovely fact proved by Brown in his classic paper from 1987 has been generalised in many ways. Here, in joint work with Armando Martino, we'll see that this behaviour applies not only to the Houghton groups themselves but also many of their subgroups.