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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{40}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 5P | ||||||
| $D_{10}.(C_4\times D_4)$ | 1A | $1$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2A | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2A | $ \left(\begin{array}{rr} 21 & 0 \\ 0 & 21 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2B | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2B | $ \left(\begin{array}{rr} 11 & 20 \\ 0 & 11 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2C | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2C | $ \left(\begin{array}{rr} 31 & 20 \\ 0 & 31 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2D | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2D | $ \left(\begin{array}{rr} 1 & 20 \\ 0 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2E | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2E | $ \left(\begin{array}{rr} 21 & 20 \\ 0 & 21 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2F | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2F | $ \left(\begin{array}{rr} 31 & 0 \\ 0 & 31 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2G | $2$ | $1$ | $D_{10}.(C_4\times D_4)$ | 1A | 2G | $ \left(\begin{array}{rr} 11 & 0 \\ 0 & 11 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2H | $2$ | $4$ | $C_2^3\times D_{10}$ | 1A | 2H | $ \left(\begin{array}{rr} 31 & 25 \\ 0 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2I | $2$ | $4$ | $C_2^3\times D_{10}$ | 1A | 2I | $ \left(\begin{array}{rr} 31 & 5 \\ 0 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2J | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2J | $ \left(\begin{array}{rr} 1 & 36 \\ 0 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2K | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2K | $ \left(\begin{array}{rr} 11 & 20 \\ 0 & 19 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2L | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2L | $ \left(\begin{array}{rr} 21 & 20 \\ 0 & 29 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2M | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2M | $ \left(\begin{array}{rr} 31 & 16 \\ 0 & 39 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2N | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2N | $ \left(\begin{array}{rr} 11 & 0 \\ 0 & 19 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2O | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2O | $ \left(\begin{array}{rr} 1 & 16 \\ 0 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2P | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2P | $ \left(\begin{array}{rr} 21 & 24 \\ 0 & 29 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2Q | $2$ | $5$ | $C_2^3.C_2^4$ | 1A | 2Q | $ \left(\begin{array}{rr} 31 & 12 \\ 0 & 39 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2R | $2$ | $20$ | $C_2^5$ | 1A | 2R | $ \left(\begin{array}{rr} 31 & 1 \\ 0 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 2S | $2$ | $20$ | $C_2^5$ | 1A | 2S | $ \left(\begin{array}{rr} 31 & 21 \\ 0 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4A1 | $4$ | $2$ | $D_{10}:C_4^2$ | 2A | 4A1 | $ \left(\begin{array}{rr} 11 & 30 \\ 30 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4A-1 | $4$ | $2$ | $D_{10}:C_4^2$ | 2A | 4A-1 | $ \left(\begin{array}{rr} 31 & 30 \\ 30 & 21 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4B1 | $4$ | $2$ | $D_{10}:C_4^2$ | 2A | 4B1 | $ \left(\begin{array}{rr} 11 & 10 \\ 30 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4B-1 | $4$ | $2$ | $D_{10}:C_4^2$ | 2A | 4B-1 | $ \left(\begin{array}{rr} 31 & 10 \\ 30 & 21 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4C | $4$ | $4$ | $C_{20}:C_2^3$ | 2B | 4C | $ \left(\begin{array}{rr} 11 & 35 \\ 30 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4D | $4$ | $4$ | $C_{20}:C_2^3$ | 2B | 4D | $ \left(\begin{array}{rr} 11 & 15 \\ 30 & 1 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4E1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4E1 | $ \left(\begin{array}{rr} 11 & 4 \\ 20 & 23 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4E-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4E-1 | $ \left(\begin{array}{rr} 11 & 12 \\ 20 & 7 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4F1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2A | 4F1 | $ \left(\begin{array}{rr} 11 & 38 \\ 30 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4F-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2A | 4F-1 | $ \left(\begin{array}{rr} 31 & 22 \\ 30 & 29 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4G1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4G1 | $ \left(\begin{array}{rr} 1 & 6 \\ 30 & 23 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4G-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4G-1 | $ \left(\begin{array}{rr} 21 & 38 \\ 30 & 27 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4H1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4H1 | $ \left(\begin{array}{rr} 21 & 24 \\ 20 & 33 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4H-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4H-1 | $ \left(\begin{array}{rr} 21 & 32 \\ 20 & 17 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4I1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4I1 | $ \left(\begin{array}{rr} 11 & 24 \\ 20 & 23 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4I-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4I-1 | $ \left(\begin{array}{rr} 11 & 32 \\ 20 & 7 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4J1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4J1 | $ \left(\begin{array}{rr} 21 & 30 \\ 30 & 3 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4J-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4J-1 | $ \left(\begin{array}{rr} 1 & 14 \\ 30 & 7 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4K1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2A | 4K1 | $ \left(\begin{array}{rr} 11 & 18 \\ 30 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4K-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2A | 4K-1 | $ \left(\begin{array}{rr} 31 & 2 \\ 30 & 29 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4L1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4L1 | $ \left(\begin{array}{rr} 1 & 26 \\ 30 & 23 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4L-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4L-1 | $ \left(\begin{array}{rr} 21 & 18 \\ 30 & 27 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4M1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4M1 | $ \left(\begin{array}{rr} 21 & 4 \\ 20 & 33 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4M-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2O | 4M-1 | $ \left(\begin{array}{rr} 21 & 12 \\ 20 & 17 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4N1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4N1 | $ \left(\begin{array}{rr} 21 & 10 \\ 30 & 3 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4N-1 | $4$ | $10$ | $C_2^2\times C_4^2$ | 2P | 4N-1 | $ \left(\begin{array}{rr} 1 & 34 \\ 30 & 7 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4O | $4$ | $20$ | $C_2^3\times C_4$ | 2B | 4O | $ \left(\begin{array}{rr} 11 & 3 \\ 30 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4P | $4$ | $20$ | $C_2^3\times C_4$ | 2B | 4P | $ \left(\begin{array}{rr} 11 & 23 \\ 30 & 9 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4Q1 | $4$ | $20$ | $C_2^3\times C_4$ | 2P | 4Q1 | $ \left(\begin{array}{rr} 1 & 27 \\ 20 & 7 \end{array}\right) $ |
| $D_{10}.(C_4\times D_4)$ | 4Q-1 | $4$ | $20$ | $C_2^3\times C_4$ | 2P | 4Q-1 | $ \left(\begin{array}{rr} 1 & 19 \\ 20 & 23 \end{array}\right) $ |