Note: Each and every type can belong to any Hogwarts house. What I've done here is, I've analysed the traits of each type, and deduced what combination of cognitive functions is best sorted into each house, divided evenly so there are 4 types for every house, along with a fictional character (Both from the Harry Potter series and other parts of popular culture) as a good example of both house and type.

Gryffindor (Courage and Honor): ISFP (Harry Potter), ESFP (Eren Yeager, Attack on Titan), INFP (Frodo Baggins, Lord of the Rings), ENFP (Ron Weasley)

Slytherin (Pride and Ambition): ENTJ (Light Yagami, Death Note), INTJ (Severus Snape), ESTP (Venom/Eddie Brock, Marvel Comics), ISTP (Bane, DC Comics)

Ravenclaw (Wisdom and Wit): INTP (Luna Lovegood), ENTP (Rick Sanchez, Rick and Morty), ISTJ (Sheldon Cooper, The Big Bang Theory), ESTJ (Olenna Tyrell, Game of Thrones)

Hufflepuff (Loyalty and Communication): ESFJ (Ned Flanders, The Simpsons), ISFJ (Samwise Gamgee, Lord of the Rings), ENFJ (Mary Poppins), INFJ (Charles Xavier, Marvel Comics)

This thread is open for discussion.