Do I have to find out every element in D5 and draw a table to find out subgroups?
I know how to find out every single element in D5,
but can't think of how to find proper nontrivial subgroups
$\endgroup$1 Answer
$\begingroup$There are five subgroups of order 2 consisting of $R_0$(rotation by zero degrees) and a flip $F_i\,\,(i\in \{1,2,3,4,5\}$).
Note that there is a subgroup of rotations (of order $5$) and hence generated by each non-identity rotation.
Claim There is no other non-trivial subgroup. (why?)
Hint
(1) What happens to a subgroup containing two flips(flips along different axes)?
(2) What happens to a subgroup containing a non-trivial (hence all) rotation and a flip?
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