This work proposes RaNNC (Rapid Neural Network Connector) as middleware for automatic hybrid parallelism. In recent deep learning research, as exemplified by T5 and GPT-3, the size of neural network models continues to grow. Since such models do not fit into the memory of accelerator devices, they need to be partitioned by model parallelism techniques. Moreover, to accelerate training for huge training data, we need a combination of model and data parallelisms, i.e., hybrid parallelism. Given a model description for PyTorch without any specification for model parallelism, RaNNC automatically partitions the model into a set of subcomponents so that (1) each subcomponent fits a device memory and (2) a high training throughput for pipeline parallelism is achieved by balancing the computation times of the subcomponents. In our experiments, we compared RaNNC with two popular frameworks, Megatron-LM (hybrid parallelism) and GPipe (originally proposed for model parallelism, but a version allowing hybrid parallelism also exists), for training models with increasingly greater numbers of parameters. In the pre-training of enlarged BERT models, RaNNC successfully trained models five times larger than those Megatron-LM could, and RaNNC's training throughputs were comparable to Megatron-LM's when pre-training the same models. RaNNC also achieved better training throughputs than GPipe on both the enlarged BERT model pre-training (GPipe with hybrid parallelism) and the enlarged ResNet models (GPipe with model parallelism) in all of the settings we tried. These results are remarkable, since RaNNC automatically partitions models without any modification to their descriptions; Megatron-LM and GPipe require users to manually rewrite the models' descriptions.