The magnetic and iron vacancy orders in superconducting (Tl,Rb)2Fe4Se5 single-crystals were investigated using a high-pressure neutron diffraction technique. Similar to the temperature effect, the block antiferromagnetic order gradually decreases upon increasing pressure while the Fe vacancy superstructural order remains intact before its precipitous disappearance at the critical pressure Pc =8.3 GPa. Combined with previously determined Pc for superconductivity, our phase diagram under pressure reveals the concurrence of the block AFM order, the √ 5 × √ 5 iron vacancy order and superconductivity for the 245 superconductor. A synthesis of current experimental data in a coherent physical picture is attempted.PACS numbers: 74.62. Fj, 25.40.Dn, 74.25.Ha, The recently discovered metal-intercalated iron selenide superconductors A 2 Fe 4 Se 5 (A=K, Cs, Tl-K, Rb, Tl-Rb) (245) compounds, with T c ∼ 30 K, have attracted much interest [1,2].A high transitiontemperature (T N ≈ 470-560 K) and large magnetic moment (3.3µ B /Fe) block antiferromagnetic (AFM) order exists in the superconducting samples [3][4][5]. And magnetic order-parameter experiences an anomaly when T c is approached [4,5]. The superconductors crystallize with a highly ordered √ 5 × √ 5 superstructure, in which the Fe1 site of the I4/m structure is only a few percent occupied and the Fe2 site fully occupied [4,6]. The nonsuperconducting samples at low-T also crystallize in the I4/m structure, but both Fe sites are fractionally occupied [7,8], since the numbers of the Fe vacancies in the samples and the vacant sites in the √ 5 × √ 5 pattern are mismatched. The partially ordered √ 5 × √ 5 vacancy order becomes one of three competing phases for temperature below the room temperature up to ∼ 500 K, namely, these samples are phase-separated and in the miscibility gap at ambient condition [8,9].Close to the miscibility gap, it is not surprising that the nonstoichiometric 245 superconductors often contain several phases of different space-group symmetry. It has been a complex and controversial issue to determine the sample composition of the superconductors. The KFe 1.5 Se 2 (234) of the orthorhombic Fe vacancy order has been proposed as the parent compound [10]. However, this phase is not even the ground state for KFe 1.5 Se 2 , and a partially ordered √ 5 × √ 5 vacancy superlattice is more stable at low temperature [8]. The KFe 2 Se 2 (122) of I4/mmm symmetry has also been proposed as the superconducting phase [11]. But its existence in films grown by molecular beam epitaxy method likely requires charge transfer with the substrate, and there is no trace of its existence in bulk superconducting samples [4,12]. Detected in the 245 superconductors is the alkaline metal deficient A x Fe 2 Se 2 (x ∼ 0.3-0.6) phase embedded in √ 5 × √ 5 iron vacancy ordered superstructure [12][13][14], forming various microstructure patterns in plane [15,16] High pressure adds an additional dimension to the complex composition phase-diagram of 245 superconductors [8], offering a "clea...