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Math Help - Find subgroup of an external direct product

  1. #1
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    Find subgroup of an external direct product

    Problem: Find a subgroup of order 280 from
    a. Z_{2} \oplus Z_{2} \oplus Z_{2} \oplus Z_{2} \oplus Z_{5} \oplus Z_{5} \oplus Z_{7}

    b. Z_{2^{4}} \oplus Z_{5} \oplus Z_{5} \oplus Z_{7}

    My solution:

    a. <2> \oplus <2> \oplus <2> \oplus <0> \oplus <1> \oplus <0> \oplus <1>

    b. I can't find subgroup with orders that can multiply into 280, any help?

    Thanks.
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    2^3 \times 5 \times 1 \times 7
    Or
    2^3 \times 1 \times 5 \times 7
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