%N The orders, with repetition, of the non-cyclic finite simple groups that are subquotients of the sporadic finite simple groups.
%C By the classification theorem for finite simple groups, there are exactly 26 sporadic finite simple groups, whose orders form A001228. The online ATLAS includes lists of the maximal subgroups of these groups, and entries for their simple subquotients.
%C Subsequence of A083207. - _Ivan N. Ianakiev_, Jan 02 2020
%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.
%H Hal M. Switkay, <a href="/A330585/b330585.txt">Table of n, a(n) for n = 1..82</a>
%H Ivan N. Ianakiev, <a href="/A330585/a330585.txt">Subsequence of A083207, Proof</a>
%H David A. Madore, <a href="http://www.madore.org/~david/math/simplegroups.html">Orders of non-abelian simple groups</a>
%H R. A. Wilson et al., <a href="http://brauer.maths.qmul.ac.uk/Atlas/v3/">ATLAS of Finite Group Representations - Version 3</a>
%e This list includes the orders of all non-cyclic simple groups of order less than 9828. L2(27), of order 9828, does not appear as a subquotient of any of the sporadic finite simple groups.
%Y Cf. A109379, A001228, A083207.
%A _Hal M. Switkay_, Dec 18 2019