Quotient groups of D10

group-theory finite-groups

Solution 1:

The standard reference (on this site at least) for dihedral groups are the notes by K. Conrad. Theorem $2.3$ and its proof answers the question. All quotients $D_{10}/N$ are again dihedral groups. All normal subgroups of $D_{10}$ are listed in Theorem $3.8$.

Related

Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
find nonsingular matrices $B$ and $C$ that satisfy $BC+ CB= 0$
Independence of $\min(X,Y)$ and $|X-Y|$ when $(X,Y)$ are i.i.d. exponential
Probability that distance of two random points within a sphere is less than a constant
If and only if proof dealing with a function that is uniformly continuous.
Is there any closed form for the following series?
Distinct Sylow P subgroups
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
Not Complete Statistic in Normal Distribution
Lebesgue measure as $\sup$ of measures of contained compact sets
Let $p$ be an odd prime. Prove that if $a\equiv b\pmod{p}$, then $a^p\equiv b^p\pmod{p^2}$