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 A277566 Irregular table by rows: Orders of subgroups of the symmetric group S_n. 2
 1, 1, 2, 1, 2, 3, 6, 1, 2, 3, 4, 6, 8, 12, 24, 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 36, 48, 60, 72, 120, 360, 720, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 36, 40, 42, 48, 60, 72, 120, 144, 168, 240, 360, 720, 2520, 5040, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 30, 32, 36, 40, 42, 48, 56, 60, 64, 72, 96, 120, 128, 144, 168, 180, 192, 240, 288, 336, 360, 384, 576, 720, 1152, 1344, 1440, 2520, 5040, 20160, 40320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Each row begins with 1 (the order of the trivial group) and ends with n! (the order of S_n itself). LINKS Charles R Greathouse IV, Rows n = 1..12 of table, flattened Götz Pfeiffer, Numbers of subgroups of various families of groups EXAMPLE 1; 1, 2; 1, 2, 3, 6; 1, 2, 3, 4, 6, 8, 12, 24; 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120; 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 36, 48, 60, 72, 120, 360, 720; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 36, 40, 42, 48, 60, 72, 120, 144, 168, 240, 360, 720, 2520, 5040; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 30, 32, 36, 40, 42, 48, 56, 60, 64, 72, 96, 120, 128, 144, 168, 180, 192, 240, 288, 336, 360, 384, 576, 720, 1152, 1344, 1440, 2520, 5040, 20160, 40320; PROG (GAP) LoadPackage("sonata"); a := function(n)   return Length(Unique(Apply(Subgroups(SymmetricGroup(n)), Size))); end;; # Charles R Greathouse IV, Nov 28 2016 CROSSREFS Row lengths are given by A218913. See A243748 for a closely related sequence. Sequence in context: A135938 A079210 A070861 * A261144 A106524 A323641 Adjacent sequences:  A277563 A277564 A277565 * A277567 A277568 A277569 KEYWORD nonn,tabf AUTHOR Charles R Greathouse IV, Nov 28 2016 STATUS approved

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Last modified January 21 10:25 EST 2022. Contains 350477 sequences. (Running on oeis4.)