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G = SymmetricGroup(6); G

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subgroups = []
for P in G:
    U= G.subgroup([P])
    if U not in subgroups:
        subgroups.append(U)

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eins = []
zwei = []
drei = []
vier = []
fuenf = []
sechs = []
for P in G:
    U= G.subgroup([P])
    order = U.order()
    if order == 1:
        if U not in eins:
            eins.append(U)
    if order == 2:
        if U not in zwei:
            zwei.append(U)
    if order == 3:
        if U not in drei:
            drei.append(U)
    if order == 4:
        if U not in vier:
            vier.append(U)
    if order == 5:
        if U not in fuenf:
            fuenf.append(U)
    if order == 6:
        if U not in sechs:
            sechs.append(U)

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len(eins)
len(zwei)
len(drei)
len(vier)
len(fuenf)
len(sechs)

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1
75
40
90
36
120

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U.list()