Subgroup structure of groups of order 13

This article gives specific information, namely, subgroup structure, about a family of groups, namely: groups of order 13.
View subgroup structure of group families | View subgroup structure of groups of a particular order |View other specific information about groups of order 13

This article gives information on the subgroup structure of groups of order 13. There is one group of this order, namely cyclic group:Z13, since 13 is a prime number. (More generally, a cyclicity-forcing number.)

By Lagrange's theorem, the order of subgroups of a group of order 13 must be 1 or 13. Also, the subgroup of a cyclic group is cyclic.

Thus, the only subgroups of cyclic group:Z13 are cyclic group:Z13 and trivial group.

Since cyclic group:Z13 is abelian, these are normal subgroups. Thus, cyclic group:Z13 is a simple group.

Subgroup-defining functions

Subgroup-defining function	What it means	Value as subgroup for cyclic group:Z13
center	elements that commute with every group element	whole group (cyclic group:Z13)