When the entire population of a state is not bound by a shared sense of nationalism but is split by several local primary allegiances, that state is said to suffer from cultural subnationalism.

The statement is true. Cultural nationalism is a form of nationalism in which the nation is defined on the basis of a common culture.

Despite that, there are cases where nations are so extensive that a cultural distinction develops between their different geographical sectors. This can be clearly seen in Canada, where the western part of the country has cultural features associated mostly with the United States and Great Britain, while the east is culturally mostly related to France. Between both zones, idiomatic, political, architectural and even social differences can be observed. This is an example of cultural subnationalisms within a nation.