Groups of order 130

This article gives information about, and links to more details on, groups of order 130
See pages on algebraic structures of order 130 | See pages on groups of a particular order

Statistics at a glance

The number 130 has prime factors 2, 5, and 13. The prime factorization is:

$130=2^{1}\cdot 5^{1}\cdot 13^{1}$

One such way to classify groups of order 130 is therefore by the classification of groups of order 2pq.

Square-free implies solvability-forcing, so all groups of order 130 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 130 are in fact metacyclic groups.

Quantity	Value	Explanation
Number of groups up to isomorphism	4

The list

There are 4 groups of order 66:

Group	Second part of GAP ID	Abelian	Direct Product
direct product of D10 and Z13	1	no	yes
direct product of D26 and Z5	2	no	yes
dihedral group:D130	3	no	no
cyclic group:Z130	4	yes	yes