The numbers of inequivalent Hadamard matrices of various orders are

<p> Orders 1, 2, 4, 8, 12 are unique.
<p> Order 16: 5 (Marshall Hall Jr)
<p> Order 20: 3 (Marshall Hall Jr)
<p> Order 24: 60 (Norburo Ito and others)
<p> Order 28: 487 (H. Kimura)
<p> Order 32: more than 3,578,006 see Will Orrick http://www.arxiv.org/abs/math.CO/0507515
<p> Order 36: more than 18,292,717 see Will Orrick http://www.arxiv.org/abs/math.CO/0507515
<p> Orders 40-100: see Christos Koukouvinos http://www.math.ntua.gr/people/ckoukouv/en_index.html

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This page, created, 14th December 2005, updated 23rd July 2014,  will be made more precise at a future date. Comment to j.seberry@uow.edu.au.