To answer my own question. No state prohibits subletting. Maine law gives renters the right to sublet, New York limits the reasons landlords can refuse subletting, and all other states leave it up to the landlord (with differences in details, such as the default if the lease doesn't explicitly prohibit or allow it).

However, many states and/or cities do limit the number of unrelated individuals living together, and this applies whether they are all on the lease, subletted, or even in one's privately owned home. A brief search shows different areas have limits of no more than 2, 3, 4 or 5 unrelated individuals.

I've just happened to live in places that allow 4 or 5 unrelated individuals, and never rented a house with more than that many bedrooms/roomates.

It is crazy to me that in some parts of the country it is fine to have 7 family members living together (easy to do in a multigenerational home), but letting 3 friends live with me in the same size house that I own is illegal.

I wonder how they define "related".

It's obvious what they're trying to do but if you had 12 kids with 12 women would all of them living in the same house be illegal?