The adoption of Software Defined Networking (SDN) has encountered resistance mainly due to its disruptivenature for current deployed networks. In order to allow a smoother transition of SDN into production networksand take advantage of SDN’s characteristics, a mix of SDN with traditional networks, or Hybrid SDN Networks,can be deployed, paving the path to fully SDN-capable networks. The introduction of SDN allows for new andmore efficient network optimization methods. This paper presents a Hybrid SDN Mobile Core Network for4G and Non-Standalone 5G, which integrates support for Wi-Fi access, traffic offloading capabilities from3GPP to non-3GPP Access and dynamic non-3GPP network slice instantiation, while still being flexible enoughto be used in Standalone 5G. Results showed that the virtualization of the Mobile Core Network and theintroduction of SDN in its architecture (making it a hybrid SDN solution) presented no significant impact inlatency, attachment time and throughput in the mobile network when compared with a traditional deployment,coupling it with all the flexibility that SDN provides. Furthermore, benefits of traffic offloading for both theend user and the network operator are also shown.