A066085 Orders of non-supersolvable groups.

12, 24, 36, 48, 56, 60, 72, 75, 80, 84, 96, 108, 112, 120, 132, 144, 150, 156, 160, 168, 180, 192, 196, 200, 204, 216, 224, 225, 228, 240, 252, 264, 276, 280, 288, 294, 300, 312, 320, 324, 336, 348, 351, 360, 363, 372, 375, 384, 392, 396, 400, 405, 408, 420

Offset: 1

Author

Reiner Martin, Dec 29 2001

Keywords

• nonn

Comments

A finite group is supersolvable if it has a normal series with cyclic factors. Huppert showed that a finite group is supersolvable iff the index of any maximal subgroup is prime.

All multiples of non-supersolvable orders are non-supersolvable orders. - Des MacHale, Dec 22 2003

Examples

			a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.
		

Links

• B. Huppert, Über das Produkt von paarweise vertauschbaren zyklischen Gruppen, Math. Z. 58 (1954).
• Des MacHale and J. Manning, Converse Lagrange Theorem Orders and Supersolvable Orders, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.

Crossrefs

Cf. A000001, A066083, A340511.

For primitive terms see A340517.

Extensions

More terms from Des MacHale, Dec 22 2003