Can one prove that a group of order 150 is not simple using element counting?
1360
Every group of order $150$ has a normal subgroup of order $25$
18881
Number of elements of order $7$ in a group
83178
Matrix Group induction proof and order of elements question
5089
An element of a group has the same order as its inverse
113413
How do I show that two groups are not isomorphic?
67554
In a group, the number of non-self-inverse elements is even
124224
How many groups of order $n$ with center {e} exist?
92968
how many element of order 2 and 5 are there
33912
Group with 380 elements is not simple.
24212
proving how many permutations exist.
62255
Notation question: Subroup generated by two elements?
26398
Group of even order contains an element of order 2
63725
No group of order 200 is simple
136848
Find the number of nonzero elements
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
84132
Number of preimages of a group element under a homomorphism.
79380
How to find the order of a group generated by two elements?