Motivated by the experimentally observed √ 5 × √ 5 iron vacancy order and a block spin antiferromagnetic phase with large magnetic moment in K0.8Fe1.6Se2, we study the magnetic phase diagram of an extended J1 − J2 model on a 1 5 -depleted square lattice with √ 5 × √ 5 vacancy order, using a classical Monte Carlo analysis. The magnetic phase diagram involves various antiferromagnetically ordered phases, and most of them have higher order commensuration. We find that the experimentally relevant block-spin state occupies a significant portion of the phase diagram, and we discuss the spin dynamics of this phase using a linear spinwave analysis. By comparing the calculated magnetization with the experimental values of magnetic moment, we determine the physical parameter regimes corresponding to the block spin antiferromagnetic phase. Based on our spin wave calculations in different parameter regimes, we show how spin-wave degeneracy along the high symmetry directions of the magnetic Brillouin zone can provide information regarding the underlying exchange couplings. We have also analyzed the magnetic phase diagram of a J1 − J2 model on two different modulated square lattices relevant for KyFe1.5Se2, which respectively exhibit 1 4 -depleted 2×2 and 4×2 vacancy ordering.