ABSTRACT
We shall take the lists of certain subgroups of various classical groups from the article from O.H. King [162], also see [47].
The subgroups of PSL(2; q), for q = pr, p a prime, are as follows: (a) a single class of q + 1 conjugate Abelian groups of order q; (b) a single class of q+1 conjugate cyclic groups of order d for each
divisor d of q 1 for q even and (q 1)=2 for q odd; (c) a single class of q(q1)=2 conjugate cyclic groups of order d for
each divisor d of q + 1, for q even and (q + 1)=2, for q odd; (d) for q odd, a single class of q(q2 1)=4d dihedral groups of order
2d, for each divisor d of (q 10)=2 with (q 1)=(2d) odd; (e) for q odd, two classes each of q(q2 1)=(8d) dihedral groups of
order 2d for each divisor d > 2 of (q 1)=2 with (q 1)=(2d) even; (f) for q even, a single class of q(q2 1)=(2d) dihedral groups of
order 2d, for each divisor d of q 1; (g) for q odd, a single class of q(q2 1)=(2d) dihedral groups of
order 2d, for each divisor d of (q + 1)=2 with (q + 1)=(2d) odd; (h) for q odd, two classes each of q(q2 1)=(2d) dihedral groups of
order 2d, for each divisor d of (q + 1)=2 with (q + 1)=(2d) even; (i) for q even, a single class of q(q2 1)=(2d) dihedral groups of
order 2d, for each divisor d of (q + 1); (j) a single class of q(q2 1)=24 conjugate four-groups when q
3 mod 8; (k) two classes each of q(q2 1)=48 conjugate four-groups when
q 1 mod 8; (l) a number of classes of conjugate Abelian groups of order q0, for
each divisor q0 of q; (m) a number of classes of conjugate groups of order q0d, for each
divisor q0 of q and for certain d depending on q0, all lying inside a group of order q(q 1)=2 for q odd and q(q 1) for q even; (n) two classes each of [q(q2 1)]=[2q0(q20 1)] groups PSL(2; q0),
where q is an even power of q0, for q odd;
(o) a single class of [q(q21)]=[q0(q201)] groups PSL(2; q0), where q is an odd power of q0, for q odd; (p) a single class of [q(q21)]=[q0(q201)] groups PSL(2; q0), where
q is a power of q0, for q even; (q) two classes each of [q(q2 1)]=[2q0(q20 1)] groups PGL(2; q0),
where q is a even power of q0, for q odd; (r) two classes each of q(q21)=48 conjugate S4, when q 1 mod 8; (s) two classes each of q(q21)=48 conjugateA4, when q 1 mod 8; (t) a single class of q(q2 1)=24 conjugate A4, when q 3 mod 8; (u) a single class of q(q2 1)=12 conjugate A4, when q is an even
power of 2; (v) two classes each of q(q2 1)=120 conjugate A5, when q
3 mod 10.
