Order

Abelian Groups

Non-Abelian Groups

1

${\text{Z}}_1$

2

${\text{Z}}_2$

3

${\text{Z}}_3$

4

${\text{Z}}_4,{\text{Z}}_2\oplus {\text{Z}}_2$

5

${\text{Z}}_5$

6

${\text{Z}}_6$

$D_3$

7

${\text{Z}}_7$

8

${\text{Z}}_8,{\text{Z}}_4\oplus {\text{Z}}_2,{\text{Z}}_2\oplus {\text{Z}}_2\oplus {\text{Z}}_2$

$D_4,Q_4$

9

${\text{Z}}_9,{\text{Z}}_3\oplus {\text{Z}}_3$

10

${\text{Z}}_{10}$

$D_5$

11

${\text{Z}}_{11}$

12

${\text{Z}}_{12},{\text{Z}}_6\oplus {\text{Z}}_2$

$D_6,A_4,Q_6$

13

${\text{Z}}_{13}$

14

${\text{Z}}_{14}$

$D_7$

15

${\text{Z}}_{15}$