Let C8 be the cyclic group of order eight. Let G=(C8)^10 and H=(C8)^3 and H is a subgroup of G.

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How many exist subgroups F in G such that F=(C8)^5 and H∩F is C8?

I yet understood that there are 2⋅8^(i−1)−4^(i−1) ways to choose C8 from (C8)^i. But I don't know what I can do next.