Only purebred dogs are traditionally accepted by the American Kennel Club (AKC), so the Jug dog, as a hybrid dog breed, doesn’t get in there, even though both of its parent breeds — the Jack Russell Terrier and the Pug — are part of the AKC registry.However, the Jug is a part of the American Canine Hybrid Club (ACHC), which is the country’s finest registry of mixed-breed dogs.