Python: shuffle within a for loop shuffles the same way every time

I have a list of numbers [1,2,3,4,5]. I would like to make a list, containing different permutations of [1,2,3,4,5] (i.e it would be a list of lists).

For example, I want something like [[1,4,5,3,2], [3,1,4,5,2],[ 5,1,2,4,3]].

import random
from random import shuffle

superlist = []
littlelist = [1,2,3,4,5]

for i in range(1, 4):
    random.shuffle(little_list)
    superlist.append(little_list)
print(superlist)

This outputs

[[2, 5, 4, 3, 1], [2, 5, 4, 3, 1], [2, 5, 4, 3, 1]]

So within my for loop, the 'random shuffle' produces the same thing. I tried time seeding it, but there was the same problem.