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Give this one a try:

def find_common_lists(lists):
    common_lists = []
    for i in range(len(lists)):
        for j in range(i+1, len(lists)):
            if set(lists[i]) & set(lists[j]):
                common_lists.append(lists[i])
                common_lists.append(lists[j])
    return common_lists

def find_largest_common_lists(lists):
    largest_common_lists = []
    for i in range(len(lists)):
        for j in range(i+1, len(lists)):
            if set(lists[i]) & set(lists[j]):
                common_lists = [lists[i], lists[j]]
                for k in range(j+1, len(lists)):
                    if set(lists[k]) & set(common_lists[0]):
                        common_lists.append(lists[k])
                if len(common_lists) > len(largest_common_lists):
                    largest_common_lists = common_lists
    return largest_common_lists

# Test the find_common_lists function
lists = [ [1, 2, 3, 4], [1, 3, 1, 3], [4, 1, 4, 1], [1, 3, 2, 1], [4, 1, 2, 4] ]
print(find_common_lists(lists))

# Test the find_largest_common_lists function
lists = [ [1, 2, 3, 4], [1, 3, 1, 3], [4, 1, 4, 1], [1, 3, 2, 1], [4, 1, 2, 4] ]
print(find_largest_common_lists(lists))

Give this one a try:

def find_common_lists(lists):
    common_lists = []
    for i in range(len(lists)):
        for j in range(i+1, len(lists)):
            for k in range(len(lists[i])):
                if set(lists[i]) & set(lists[j]):
lists[i][k] == lists[j][k]:
                    common_lists.append(lists[i])
                 common_lists.append(lists[j])
                    break
    return common_lists

def find_largest_common_lists(lists):
    largest_common_lists = []
    for i in range(len(lists)):
        for j in range(i+1, len(lists)):
            for k in range(len(lists[i])):
                if set(lists[i]) & set(lists[j]):
lists[i][k] == lists[j][k]:
                    common_lists = [lists[i], lists[j]]
                for k     for l in range(j+1, len(lists)):
                        for m in range(len(lists[l])):
                            if set(lists[k]) & set(common_lists[0]):
                        common_lists.append(lists[k])
lists[l][m] == lists[i][m]:
                                common_lists.append(lists[l])
                                break
                    if len(common_lists) > len(largest_common_lists):
                     largest_common_lists = common_lists
    return largest_common_lists

# Test the find_common_lists function
lists = [ [1, 2, 3, 4], [1, 3, 1, 3], [4, 1, 4, 1], [1, 3, 2, 1], [4, 1, 2, 4] ]
print(find_common_lists(lists))

# Test the find_largest_common_lists function
lists = [lists = [ [1, 2, 3, 4], [1, 3, 1, 3], [4, 1, 4, 1], [1, 3, 2, 1], [4, 1, 2, 4] ]
print(find_largest_common_lists(lists))