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.

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.

So C8 is cyclic group of order 8. What does that mean to you?
F=(C8)^10 and H=(C8)^3 . What does that mean to you?
H is a subgroup of G. What does that mean to you?
H∩F is C8 ...
LaGrange's theorem states that ......?

So C8 is cyclic group of order 8. What does that mean to you?
F=(C8)^10 and H=(C8)^3 . What does that mean to you?
H is a subgroup of G. What does that mean to you?
H∩F is C8 ...
LaGrange's theorem states that ......?