import itertools


def list_all_symbols_for_element(name):
    """
    Creates list of all valid symbols for an element
    :param name: Element name
    :return: List of all valid symbols (unsorted)
    """

    if len(name) < 2:
        raise ValueError('Element name must be at least 2 chars long')

    result = set()
    for i, _ in enumerate(name, start=0):
        for pair in itertools.product(name[:i], name[i:]):
            result.add(''.join(pair).capitalize())
    return result