Is there any relation with the meaning of word "simple" with what "there are groups $G$ in which the only normal subgroups are the trivial ones: $1$ and $G$. Such groups are called simple groups"$_1$ describes?
This might allow eliminating memory to know what the word "Simple group" describes, from the knowing of relation with word simple.
$_1$ Abstract Algebra, David S. Dummit, Richard M.Foote
On
The mathematical meaning of "simple" is not restricted to groups. It also applies to, say, Lie algebras (which are called simple if they do not have a proper nontrivial ideal). Also a ring is called simple, if it has no proper nontrivial two-sided ideal. An algebraic group over a field $K$ is called simple if it is non-commutative and has no closed connected normal subgroups other than itself and the trivial group. Furthermore, an object $X$ in a category $C$ with a zero object $0$ is simple if there are precisely two quotient objects of $X$ , namely $0$ and $X$.
In all cases, simple means that we cannot decompose anymore in a natural way.
One dictionary entry for simple is
One common way of decomposing groups is into a normal subgroup and the corresponding quotient group. Simple groups are simple because they cannot be decomposed like this in any meaningful way. Much the same way prime numbers cannot be factored in any meaningful way.