Math 2.0

Group theory and generalizations Theorem

Extension of Lagrange's theorem

Statement

If HH is a subgroup of GG and KK is a subgroup of HH, then

[G:K]=[G:H] [H:K].[G:K] = [G:H]\,[H:K].

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first. The path takes the proof Proof of Extension of Lagrange's theorem.

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Proof of Extension of Lagrange's theorem, proof, no evidence levelProof of Extension of…proofExtension of Lagrange's theorem, statement, no evidence levelExtension of Lagrange…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Proof of Extension of Lagrange's theorem proof
  2. Extension of Lagrange's theorem statement

Further reading

  1. Wikipedia, page 31150, revision 1321322691, Lagrange's theorem (group theory), section Extension. adopted
About this page
TagVAF6B01Q8W
URIm2://VAF6B01Q8W
Kindstatement, theorem
WritingW0 stub
MSC20D60
StatusThis copy of the site has no build data. Run m2 status VAF6B01Q8W.
Changed3 November 2026

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  • edge uses out: each definition that the statement needs (0 of 1)

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Proofs