15阶以下群的结构
| 群的阶数 | Abel群 | 非Abel群 |
| 1 | $\{1\}$ | |
| 2 | $\mathbb Z_{2}$ | |
| 3 | $\mathbb Z_{3}$ | |
| 4 | $\mathbb Z_{2}^{2},\mathbb Z_{4}$ | |
| 5 | $\mathbb Z_{5}$ | |
| 6 | $\mathbb Z_{6}$ | $S_{3}$ |
| 7 | $\mathbb Z_{7}$ | |
| 8 | $\mathbb Z_{2}^{3},\mathbb Z_{2}\oplus\mathbb Z_{4},\mathbb Z_{8}$ | $D_{4},\mathbb Q_{8}$ |
| 9 | $\mathbb Z_{9},\mathbb Z_{3}^{2}$ | |
| 10 | $\mathbb Z_{10}$ | $D_{5}$ |
| 11 | $\mathbb Z_{11}$ | |
| 12 | $\mathbb Z_{12},\mathbb Z_{2}^2\oplus\mathbb Z_{3}$ | $D_{6},A_{4},T$ |
| 13 | $\mathbb Z_{13}$ | |
| 14 | $\mathbb Z_{14}$ | $D_{7}$ |
| 15 | $\mathbb Z_{15}$ |
