How many subgroups does d4 have

Prove N H is a normal subgroup of G, or give counterexample. Every group is a normal subgroup of itself. Similarly, the trivial group is a subgroup of every group. The most basic way to figure out subgroups is to take a subset of the elements, and then find all products of powers of those elements.

So, say you have two elements a,b in your group, then you need to consider all strings of a,b, yielding 1,a,b,a2,ab,ba,b2,a3,aba,ba2,a2b,ab2,bab,b3,…. The order of a group G is denoted by ord G or G , and the order of an element a is denoted by ord a or a.

In particular, the order a of any element is a divisor of G. Michael Albanese Michael Albanese Add a comment. Community Bot 1. Dietrich Burde Dietrich Burde k 7 7 gold badges 69 69 silver badges bronze badges. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches!

I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me. It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.

Note: Your answer helped me a lot, thanks! Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post.

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