A clutch for a motor vehicle, preferably for engaging and disengaging a drive train for all-wheel drive vehicles, comprises a first shaft, a second shaft arranged coaxially to the first shaft, a clutch sleeve which is moveable in the axial direction relative to the first shaft and the second shaft for causing a form-fit coupling or decoupling of the first shaft and the second shaft, and a coil which can be powered, wherein a plurality of engagement bodies are connected rotationally fixedly to the first shaft, wherein the coil which can be powered is arranged coaxially to the axial direction, wherein by powering the coil, the clutch sleeve can be moved in the axial direction, wherein by moving the clutch sleeve in the axial direction, the engagement bodies can be pressed over part of their height into receivers, and wherein the receivers are connected rotationally fixedly to the second shaft.