# Thread: Find subgroup of an external direct product

1. ## 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.

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