Update Profile - are all mailing lists public?

Update Profile - are all mailing lists public?

I would like some more clarity on what the subscriber can see when they click "update profile".

Do they see all mailing lists that they are subscribed to?

The reason being that I use some mailing lists to separate my subscribers based on search criteria or people who often read the newsletter email to make certain people easier to find. These mailing lists do not have a sign up option.

If the "update profile" option shows the subscriber every list they are signed up to (including those without sign up forms) this would appear quite confusing. The subscriber would see the mailing list that they would expect "newsletter mailing list" yet they would see they are signed up to other lists "newsletter readers" "follow up" etc.

Is there an option to set mailing lists to public or private?