[FOM] Query on alternating groups

[joeshipman@aol.com]

I am looking for results on the orders (or, equivalently, the indexes) 
of maximal subgroups of the alternating groups An.

An example of the kind of result I am looking for would be something 
like

"for sufficiently large n, the maximal subgroups of An have indexes n, 
n(n-1)/2, n(n-1)(n-2)/6, .... down to the middle binomial coefficient, 
dividing the last term by an extra factor of 2 when n is even"

Examination of cases suggests that a set of "degree axioms" 
D(i1),D(i2),...,D(i_j) entails the degree axiom D(n) when it includes 
all the primes dividing n as well as any number expressible as a sum of 
indexes of maximal subgroups of An.

-- JS