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. 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 rest are the result of various methods, to be described in an upcoming paper.

Note we use the classification of finite simple groups (of order <= 50000) to determine the orders without non-solvable groups.

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

Last updated: Oct 8, 2018; 23:57:07 CEST

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. "2304,3^8,7*3^4*37" | |

Number of primes factors is between | and |

Number of distinct primes factors is between | and |

Number of total classes ... | and |

Number of solvable classes ... | and |

Number of nonsolvable classes ... | and |

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