To start, an overview to about Anabaptism or Plain People you will find in Wikipedia.
Here some hats of the different goups.
Prospect of Flying Cloud Hats owned by Kore Stoltzfuss, Ronks, Pensylvania
Amish Hats
© picture: Eliana Castanho
© picture: Eliana Castanho
© picture: Eliana Castanho
© picture: Eliana Castanho
This very common Amish hat has a 3 1/2" brim which is the the most popular size in the Amish communities.
The Amish Bishop wears this hat, but he has the distinction of having a 4 inch brim.
These hats with telecope top are the absolute highest quality black fur felt Amish hats. They are made for the Amish by the Amish and are what they wear for any formal occasion (church, weddings, funerals, etc). The hat has a 1 1/2" leather band on the inside. Dimensions: 4 1/2" high with 3 1/2" brim.
This hat is worn by the Pike Mennonites (or Stauffer Mennonites). The hats have a center groove and a 2 1/2" brim and are made of black fur felt.
These straw hats are woven in Amish homes and worn by Amishman working out in the field.
Hat worn by the Quakers