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| Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
|---|---|---|---|---|---|---|
| 60.1 | $C_3:C_{20}$ | $2^{2} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | 30 | $C_{10}$ | Solvable - 2 |
| 60.2 | $C_5:C_{12}$ | $2^{2} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | 24 | $C_6$ | Solvable - 2 |
| 60.3 | $C_{15}:C_4$ | $2^{2} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | 18 | $C_2$ | Solvable - 2 |
| 60.6 | $C_3\times F_5$ | $2^{2} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | 15 | $C_3$ | Solvable - 2 |
| 60.7 | $C_{15}:C_4$ | $2^{2} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | 9 | $C_1$ | Solvable - 2 |
| 60.10 | $C_3\times D_{10}$ | $2^{2} \cdot 3 \cdot 5$ | $2 \cdot 3 \cdot 5$ | 24 | $C_6$ | Solvable - 2 |
| 60.11 | $S_3\times C_{10}$ | $2^{2} \cdot 3 \cdot 5$ | $2 \cdot 3 \cdot 5$ | 30 | $C_{10}$ | Solvable - 2 |
| 60.12 | $D_{30}$ | $2^{2} \cdot 3 \cdot 5$ | $2 \cdot 3 \cdot 5$ | 18 | $C_2$ | Solvable - 2 |
| 84.1 | $C_7:C_{12}$ | $2^{2} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | 14 | $C_2$ | Solvable - 2 |
| 84.2 | $C_7:C_{12}$ | $2^{2} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | 20 | $C_4$ | Solvable - 2 |
| 84.3 | $C_3:C_{28}$ | $2^{2} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | 42 | $C_{14}$ | Solvable - 2 |
| 84.4 | $C_7:C_{12}$ | $2^{2} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | 30 | $C_6$ | Solvable - 2 |
| 84.5 | $C_{21}:C_4$ | $2^{2} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | 24 | $C_2$ | Solvable - 2 |
| 84.7 | $C_2\times F_7$ | $2^{2} \cdot 3 \cdot 7$ | $2 \cdot 3 \cdot 7$ | 14 | $C_2$ | Solvable - 2 |
| 84.9 | $C_{14}:C_6$ | $2^{2} \cdot 3 \cdot 7$ | $2 \cdot 3 \cdot 7$ | 20 | $C_2^2$ | Solvable - 2 |
| 84.12 | $C_3\times D_{14}$ | $2^{2} \cdot 3 \cdot 7$ | $2 \cdot 3 \cdot 7$ | 30 | $C_6$ | Solvable - 2 |
| 84.13 | $S_3\times C_{14}$ | $2^{2} \cdot 3 \cdot 7$ | $2 \cdot 3 \cdot 7$ | 42 | $C_{14}$ | Solvable - 2 |
| 84.14 | $D_{42}$ | $2^{2} \cdot 3 \cdot 7$ | $2 \cdot 3 \cdot 7$ | 24 | $C_2$ | Solvable - 2 |
| 90.1 | $C_5\times D_9$ | $2 \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | 30 | $C_5$ | Solvable - 2 |
| 90.2 | $C_9\times D_5$ | $2 \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | 36 | $C_9$ | Solvable - 2 |
| 90.3 | $D_{45}$ | $2 \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | 24 | $C_1$ | Solvable - 2 |
| 90.5 | $C_3^2\times D_5$ | $2 \cdot 3^{2} \cdot 5$ | $2 \cdot 3 \cdot 5$ | 36 | $C_3^2$ | Solvable - 2 |
| 90.6 | $S_3\times C_{15}$ | $2 \cdot 3^{2} \cdot 5$ | $2 \cdot 3 \cdot 5$ | 45 | $C_{15}$ | Solvable - 2 |
| 90.7 | $C_3\times D_{15}$ | $2 \cdot 3^{2} \cdot 5$ | $2 \cdot 3 \cdot 5$ | 27 | $C_3$ | Solvable - 2 |
| 126.1 | $C_7:C_{18}$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3^{2} \cdot 7$ | 21 | $C_3$ | Solvable - 2 |
| 126.2 | $C_7:C_{18}$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3^{2} \cdot 7$ | 30 | $C_6$ | Solvable - 2 |
| 126.3 | $C_7\times D_9$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3^{2} \cdot 7$ | 42 | $C_7$ | Solvable - 2 |
| 126.4 | $C_9\times D_7$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3^{2} \cdot 7$ | 45 | $C_9$ | Solvable - 2 |
| 126.5 | $D_{63}$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3^{2} \cdot 7$ | 33 | $C_1$ | Solvable - 2 |
| 126.7 | $C_3\times F_7$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 21 | $C_3$ | Solvable - 2 |
| 126.8 | $C_{21}:C_6$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 15 | $C_1$ | Solvable - 2 |
| 126.9 | $C_{21}:C_6$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 12 | $C_1$ | Solvable - 2 |
| 126.10 | $C_{21}:C_6$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 30 | $C_6$ | Solvable - 2 |
| 126.11 | $C_3^2\times D_7$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 45 | $C_3^2$ | Solvable - 2 |
| 126.12 | $S_3\times C_{21}$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 63 | $C_{21}$ | Solvable - 2 |
| 126.13 | $C_3\times D_{21}$ | $2 \cdot 3^{2} \cdot 7$ | $2 \cdot 3 \cdot 7$ | 36 | $C_3$ | Solvable - 2 |
| 132.1 | $C_3:C_{44}$ | $2^{2} \cdot 3 \cdot 11$ | $2^{2} \cdot 3 \cdot 11$ | 66 | $C_{22}$ | Solvable - 2 |
| 132.2 | $C_{11}:C_{12}$ | $2^{2} \cdot 3 \cdot 11$ | $2^{2} \cdot 3 \cdot 11$ | 42 | $C_6$ | Solvable - 2 |
| 132.3 | $C_{33}:C_4$ | $2^{2} \cdot 3 \cdot 11$ | $2^{2} \cdot 3 \cdot 11$ | 36 | $C_2$ | Solvable - 2 |
| 132.7 | $C_3\times D_{22}$ | $2^{2} \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | 42 | $C_6$ | Solvable - 2 |
| 132.8 | $S_3\times C_{22}$ | $2^{2} \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | 66 | $C_{22}$ | Solvable - 2 |
| 132.9 | $D_{66}$ | $2^{2} \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | 36 | $C_2$ | Solvable - 2 |
| 140.1 | $C_5:C_{28}$ | $2^{2} \cdot 5 \cdot 7$ | $2^{2} \cdot 5 \cdot 7$ | 56 | $C_{14}$ | Solvable - 2 |
| 140.2 | $C_7:C_{20}$ | $2^{2} \cdot 5 \cdot 7$ | $2^{2} \cdot 5 \cdot 7$ | 50 | $C_{10}$ | Solvable - 2 |
| 140.3 | $C_{35}:C_4$ | $2^{2} \cdot 5 \cdot 7$ | $2^{2} \cdot 5 \cdot 7$ | 38 | $C_2$ | Solvable - 2 |
| 140.5 | $C_7\times F_5$ | $2^{2} \cdot 5 \cdot 7$ | $2^{2} \cdot 5 \cdot 7$ | 35 | $C_7$ | Solvable - 2 |
| 140.6 | $C_{35}:C_4$ | $2^{2} \cdot 5 \cdot 7$ | $2^{2} \cdot 5 \cdot 7$ | 17 | $C_1$ | Solvable - 2 |
| 140.8 | $C_5\times D_{14}$ | $2^{2} \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | 50 | $C_{10}$ | Solvable - 2 |
| 140.9 | $C_7\times D_{10}$ | $2^{2} \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | 56 | $C_{14}$ | Solvable - 2 |
| 140.10 | $D_{70}$ | $2^{2} \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | 38 | $C_2$ | Solvable - 2 |