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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
360.1 | $C_9:C_{40}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $120$ | $C_{20}$ | Solvable - 2 |
360.2 | $C_5:C_{72}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $144$ | $C_{36}$ | Solvable - 2 |
360.3 | $C_{45}:C_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $96$ | $C_4$ | Solvable - 2 |
360.5 | $C_5:C_{72}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $90$ | $C_{18}$ | Solvable - 2 |
360.6 | $C_{45}:C_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $42$ | $C_2$ | Solvable - 2 |
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 |
360.14 | $Q_8:C_{45}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $105$ | $C_{30}$ | Solvable - 3 |
360.15 | $C_{45}:Q_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $117$ | $C_{18}$ | Solvable - 2 |
360.16 | $D_5\times C_{36}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $144$ | $C_{36}$ | Solvable - 2 |
360.17 | $C_9\times D_{20}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $117$ | $C_{18}$ | Solvable - 2 |
360.18 | $C_{10}:C_{36}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $144$ | $C_2\times C_{18}$ | 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 |
360.20 | $C_{45}:Q_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $105$ | $C_{10}$ | Solvable - 2 |
360.21 | $D_9\times C_{20}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $120$ | $C_{20}$ | Solvable - 2 |
360.22 | $C_5\times D_{36}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $105$ | $C_{10}$ | Solvable - 2 |
360.23 | $C_{18}:C_{20}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $120$ | $C_2\times C_{10}$ | 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 |
360.25 | $C_{45}:Q_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $93$ | $C_2$ | Solvable - 2 |
360.26 | $C_4\times D_{45}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $96$ | $C_4$ | Solvable - 2 |
360.27 | $D_{180}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $93$ | $C_2$ | Solvable - 2 |
360.28 | $C_{90}:C_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $96$ | $C_2^2$ | 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 |
360.33 | $C_{15}:C_{24}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $144$ | $C_3\times C_{12}$ | Solvable - 2 |
360.34 | $C_3:C_{120}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $180$ | $C_{60}$ | Solvable - 2 |
360.35 | $C_{15}:C_{24}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $108$ | $C_{12}$ | 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 |
360.40 | $C_{15}.S_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $45$ | $C_5$ | Solvable - 3 |
360.41 | $C_2^2:D_{45}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $33$ | $C_1$ | Solvable - 3 |
360.42 | $C_2^2:C_9\times D_5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | $48$ | $C_3$ | Solvable - 2 |
360.43 | $C_{18}\times F_5$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $90$ | $C_{18}$ | Solvable - 2 |
360.44 | $C_{90}:C_4$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3^{2} \cdot 5$ | $42$ | $C_2$ | 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 |
360.46 | $C_2^2:C_{90}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2 \cdot 3^{2} \cdot 5$ | $120$ | $C_{30}$ | 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 |
360.51 | $C_3\times \SL(2,5)$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $27$ | $C_6$ | Non-Solvable - 3 |
360.52 | $C_{15}:C_{24}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $90$ | $C_3\times C_6$ | Solvable - 2 |
360.53 | $C_{15}:C_{24}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $54$ | $C_6$ | 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 |
360.55 | $C_3^2:C_{40}$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $60$ | $C_{10}$ | Solvable - 2 |
360.56 | $(C_3\times C_{15}):C_8$ | $2^{3} \cdot 3^{2} \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $36$ | $C_2$ | Solvable - 2 |