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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
360.7 | $C_{45}:Q_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.8 | $C_{10}.D_{18}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.9 | $D_{45}:C_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.10 | $C_5:D_{36}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.11 | $C_{10}.D_{18}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.12 | $C_{45}:D_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.13 | $C_9:D_{20}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.19 | $C_{45}:D_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $117$ | $C_{18}$ | Solvable - 2 |
360.24 | $C_{45}:D_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $105$ | $C_{10}$ | Solvable - 2 |
360.29 | $C_{45}:D_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $93$ | $C_2$ | Solvable - 2 |
360.36 | $C_3^2:C_{40}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $120$ | $C_{20}$ | Solvable - 2 |
360.37 | $C_{12}.D_{15}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $96$ | $C_4$ | Solvable - 2 |
360.39 | $D_9\times F_5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $30$ | $C_1$ | Solvable - 2 |
360.45 | $D_5\times D_{18}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.47 | $C_{18}\times D_{10}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | $144$ | $C_2\times C_{18}$ | Solvable - 2 |
360.48 | $C_{10}\times D_{18}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | $120$ | $C_2\times C_{10}$ | Solvable - 2 |
360.49 | $C_2\times D_{90}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | $96$ | $C_2^2$ | Solvable - 2 |
360.54 | $(C_3\times C_{15}):C_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $42$ | $C_2$ | Solvable - 2 |
360.58 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $72$ | $C_6$ | Solvable - 2 |
360.59 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $72$ | $C_6$ | Solvable - 2 |
360.60 | $D_{15}:C_{12}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $72$ | $C_6$ | Solvable - 2 |
360.61 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $63$ | $C_6$ | Solvable - 2 |
360.62 | $D_{30}:C_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $63$ | $C_6$ | Solvable - 2 |
360.63 | $C_{15}:D_{12}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $63$ | $C_6$ | Solvable - 2 |
360.64 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $63$ | $C_6$ | Solvable - 2 |
360.65 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.66 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.67 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $48$ | $C_2$ | Solvable - 2 |
360.68 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.69 | $C_3^2:D_{20}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.70 | $C_{15}:D_{12}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.71 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_2$ | Solvable - 2 |
360.72 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $90$ | $C_{10}$ | Solvable - 2 |
360.73 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $90$ | $C_{10}$ | Solvable - 2 |
360.74 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $75$ | $C_{10}$ | Solvable - 2 |
360.75 | $C_{15}:D_{12}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $75$ | $C_{10}$ | Solvable - 2 |
360.76 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $75$ | $C_{10}$ | Solvable - 2 |
360.77 | $C_6.D_{30}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $54$ | $C_2$ | Solvable - 2 |
360.78 | $C_6.D_{30}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $54$ | $C_2$ | Solvable - 2 |
360.79 | $C_6.D_{30}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $54$ | $C_2$ | Solvable - 2 |
360.80 | $D_6:D_{15}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $51$ | $C_2$ | Solvable - 2 |
360.81 | $C_3:D_{60}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $51$ | $C_2$ | Solvable - 2 |
360.82 | $C_{15}:D_{12}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $51$ | $C_2$ | Solvable - 2 |
360.83 | $C_6.D_{30}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $51$ | $C_2$ | Solvable - 2 |
360.84 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $42$ | $C_2$ | Solvable - 2 |
360.85 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $42$ | $C_2$ | Solvable - 2 |
360.86 | $C_{15}:D_{12}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $39$ | $C_2$ | Solvable - 2 |
360.87 | $D_{30}:S_3$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $39$ | $C_2$ | Solvable - 2 |
360.88 | $C_{30}.D_6$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $39$ | $C_2$ | Solvable - 2 |
360.94 | $C_6^2:D_5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $117$ | $C_3\times C_6$ | Solvable - 2 |