I've been tasked with drawing a subgroup lattice of the dihedral group of order 10. I know from Lagrange's theorem that non-trivial subgroups must have order 2 or 5. Finding the subgroups of order 2 is straightforward, since there can be only one element besides the identity, but what about the groups of order 5? I could feasibly brute-force my way through this problem by going through the elements of $D_{10}$ one by one and trying to construct groups of order 5, but there must be a better way to solve this.
2026-03-28 06:40:57.1774680057
Drawing the subgroup lattice of D10
3.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in FINITE-GROUPS
- List Conjugacy Classes in GAP?
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- Assuming unitarity of arbitrary representations in proof of Schur's lemma
- existence of subgroups of finite abelian groups
- Online reference about semi-direct products in finite group theory?
- classify groups of order $p^2$ simple or not
- Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.
- The number of conjugacy classes of a finite group
- Properties of symmetric and alternating characters
- Finite group, How can I construct solution step-by-step.
Related Questions in DIHEDRAL-GROUPS
- Show that no group has $D_n$ as its derived subgroup.
- Number of congruences for given polyhedron
- Is there a non-trivial homomorphism from $D_4$ to $D_3$?
- Is there a dihedral graph in which the vertices have degree 4?
- Show that a dihedral group of order $4$ is isomorphic to $V$, the $4$ group.
- Find a topological space whose fundamental group is $D_4$
- Prove or disprove: If $H$ is normal in $G$ and $H$ and $G/H$ are abelian, then $G$ is abelian.
- Principled way to find a shape with symmetries given by a group
- How does the element $ ba^{n} $ become $a^{3n}b $ from the relation $ ab=ba^{3}$ of the group $ D_{4}$?
- What is Gal$_\mathbb{Q}(x^4 + 5x^3 + 10x + 5)$?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
As $5$ is a prime number, groups of order $5$ are cyclic. So you should find all the elements of order $5$ in $D_{10}$ and then determine what subgroups they generate.
Note that any non-identity element of a cyclic group of order $5$ generates that group. So if an element of order $5$ is contained in a subgroup that you have already found, then it generates that subgroup and you do not need to check it again.