Maximal subgroup has prime power index in finite solvable group

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Let G be a finite solvable group and M be a maximal subgroup of G. Then, the index [G:M] is a power of a prime.

Facts used

  1. Primitive implies Fitting-free or elementary Abelian Fitting subgroup


Textbook references

  • Finite Groups by Daniel Gorenstein, ISBN 0821843427, More info, Page 219, Theorem 1.5 (Section 6.1)
  • Abstract Algebra by David S. Dummit and Richard M. Foote, 10-digit ISBN 0471433349, 13-digit ISBN 978-0471433347, More info, Page 200, Exercise 32, Section 6.1 (p-groups, nilpotent groups and solvable groups)