Question

16

Step 1

It is known that in the group Z_{n} , if *d* divides *n* , then Z_{n} has a unique subgroup of order *d* and that subgroup is <*n*/*d*> .

Step 2

Since, the divisors of 240 are {1,2,3,4,5,6,……80,120,240},

Therefore, collection of subgroups of Z240 will be:

<0> = <0>

<120> is a subgroup of order 2.

<80> is a subgroup of order 3.

<60> is a subgroup of order 4.

…. ...

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