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A prototype Dual Gain Multilayer Thick Gas Electron Multilyer (DG-M-THGEM) with an active area of 10 cm $\times$ 10 cm was manufactured aiming at the production of a large-volume active-target time projection chamber which can work under the condition of high-intensity heavy-ion beam injections. The DG-M-THGEM has a alternating structure of electrodes and insulators. Effective gas gains of two regions, which are called beam and recoil regions, are separately controlled. Performance of the prototype DG-M-THGEM in hydrogen gas at a pressure of 40 kPa was evaluated. Irradiating a $^{132}$Xe beam, an effective gas gain lower than 100 with a charge resolution of 3% was achieved in the beam region while the effective gas gain of 2000 was maintained in the recoil region. Position distributions of measured charges along the beam axis were investigated in order to evaluate gain uniformity in the high intensity beam injection. The gain shift was estimated by simulations considering space charges in the drift region. The gain shift was suppressed within 3% even at the beam intensity of 2.5 $\times$ 10$^{6}$ particles per second.