Numbers of isomorphism types of finite groups of given order

The following table contains the numbers of isomorphism types of groups of a given order for most orders up to 50,000.

The vast majority of the data (44,142 orders) has been extracted from the Small Groups library, specifically the GAP version.
The entry of order 2304 is taken from this paper.
A few entries follow from the existing data plus Sylow theorems.
Most of the remaining entries have been calculated using the GrpConst package of the GAP computer algebra system.
The number of groups of order 3^9 is from David Burell, The number of p-groups of order 19,683 and new lists of p-groups, Comm. Alg. (2023)
The classification of finite simple groups (of order <= 50000) is used to determine the orders without non-solvable groups.
The rest are the result of various methods, see Bettina Eick, Max Horn, Alexander Hulpke, "Constructing groups of ‘small’ order: Recent results and open problems", (2017) PDF

For questions and feedback regarding this page, please contact its creator, Max Horn.

Last updated: Dec 11, 2023; 23:57 CET

Order	Factors	Total	Nilpotent	Solvable	Solvable, non-nilpotent	Non-solvable	Sources Solvable	Time Solvable	Sources Non-solvable	Time Non-solvable
Order	Factors	Total	Nilpotent	Solvable	Solvable, non-nilpotent	Non-solvable	Sources Solvable	Time Solvable	Sources Non-solvable	Time Non-solvable

Order is between	and
Order is a multiple of
Order is NOT a multiple of
	You may enter a comma separated list of simple expressions, e.g. "2304,3^8,73^437"
Number of primes factors is between	and
Number of distinct primes factors is between	and
Number of total classes ...	is unknown doesn't matter is between and
Number of solvable classes ...	is unknown doesn't matter is between and
Number of nonsolvable classes ...	is unknown doesn't matter is between and