Finite group having a subgroup series with prime indexes

Definition
A finite group having a subgroup series with prime indices is a finite group with a subgroup series starting at the trivial subgroup and terminating at the whole group, where each subgroup has prime index in its successor.

In other words, it is a finite group whose max-length equals the sum of exponents of its prime divisors in the prime factorization of its order.

The smallest finite group that does not have this property is the alternating group of degree six.

Stronger properties

 * Weaker than::Finite cyclic group
 * Weaker than::Finite abelian group
 * Weaker than::Finite nilpotent group
 * Weaker than::Finite supersolvable group
 * Weaker than::Finite solvable group