Aims. The aim of this study is to explore the magnetic and flow properties of fully convective M dwarfs as a function of rotation period Prot and magnetic Reynolds ReM and Prandlt numbers PrM. Methods.We performed three-dimensional simulations of fully convective stars using a star-in-a-box set-up. This set-up allows global dynamo simulations in a sphere embedded in a Cartesian cube. The equations of non-ideal magnetohydrodynamics were solved with the Pencil Code. We used the stellar parameters of an M5 dwarf with 0.21 M⊙ at three rotation rates corresponding to rotation periods (Prot) of 43, 61, and 90 days, and varied the magnetic Prandtl number in the range from 0.1 to 10. Results. We found systematic differences in the behaviour of the large-scale magnetic field as functions of rotation and PrM. For the simulations with Prot = 43 days and PrM ≤ 2, we found cyclic large-scale magnetic fields. For PrM > 2, the cycles vanish and the field shows irregular reversals. In the simulations with Prot = 61 days for PrM ≤ 2, the cycles are less clear and the reversal are less periodic. In the higher PrM cases, the axisymmetric mean field shows irregular variations. For the slowest rotation case with Prot = 90 days, the field has an important dipolar component for PrM ≤ 5. For the highest PrM the large-scale magnetic field is predominantly irregular at mid-latitudes, with quasi-stationary fields near the poles. For the simulations with cycles, the cycle period length slightly increases with increasing ReM.