Network slicing applied to a radio access network (RAN) offers the potential to enhance the satisfaction of service requirements and optimize resource utilization, particularly in scenarios where radio resources are limited. The dependence of RAN slice performance on the allocated bandwidth part (BWP) size has not been investigated. In this paper, we use the acquired knowledge of RAN slice performance dependence on the number of allocated resource blocks (RB) for automatic subslicing to improve slice performance on a fixed BWP size. Subslicing means that the slice user equipments (UE) are clustered, slice BWP is subpartitioned, and slice RBs are allocated to the UE groups. Based on six key performance indicators (KPI), it is decided for each subslice whether it should be split, merged, or not changed for its performance improvement. Performance improvement means that the slice utilization and block error ratio (BLER) are reduced and goodput (application-level throughput) per one resource block (RB) is increased. The monitor-analyze-plan-execute-knowledge (MAPE-K)-type management closed control loop (MCCL) was implemented for slice performance improvement by subslicing. A realistic 5G new radio (NR) band serving a set of UEs of different values of their BLER and requested rates was a setup of the RAN slice simulated using MATLAB R2021b. By automatic subslicing, the slice utilization can be reduced by up to 7%, goodput per one RB by up to 38%, and slice BLER by up to 60%. This effect was greater for the uplink. The best slice performance improvement is achieved by automatic subslicing if the UEs are clustered by their achieved BLER.