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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{10}=b^{280}=1, b^{a}=b^{279} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 5P | 7P | ||||||
| $C_5\times D_{280}$ | 1A | $1$ | $1$ | $C_5\times D_{280}$ | 1A | 1A | 1A | $1$ |
| $C_5\times D_{280}$ | 2A | $2$ | $1$ | $C_5\times D_{280}$ | 1A | 2A | 2A | $b^{140}$ |
| $C_5\times D_{280}$ | 2B | $2$ | $140$ | $C_2\times C_{10}$ | 1A | 2B | 2B | $a^{5}b^{279}$ |
| $C_5\times D_{280}$ | 2C | $2$ | $140$ | $C_2\times C_{10}$ | 1A | 2C | 2C | $a^{5}b^{216}$ |
| $C_5\times D_{280}$ | 4A | $4$ | $2$ | $C_5\times C_{280}$ | 2A | 4A | 4A | $b^{70}$ |
| $C_5\times D_{280}$ | 5A1 | $5$ | $1$ | $C_5\times D_{280}$ | 5A2 | 5A-2 | 1A | $a^{2}$ |
| $C_5\times D_{280}$ | 5A-1 | $5$ | $1$ | $C_5\times D_{280}$ | 5A-2 | 5A2 | 1A | $a^{8}$ |
| $C_5\times D_{280}$ | 5A2 | $5$ | $1$ | $C_5\times D_{280}$ | 5A-1 | 5A1 | 1A | $a^{4}$ |
| $C_5\times D_{280}$ | 5A-2 | $5$ | $1$ | $C_5\times D_{280}$ | 5A1 | 5A-1 | 1A | $a^{6}$ |
| $C_5\times D_{280}$ | 5B1 | $5$ | $2$ | $C_5\times C_{280}$ | 5B2 | 5B2 | 1A | $b^{56}$ |
| $C_5\times D_{280}$ | 5B2 | $5$ | $2$ | $C_5\times C_{280}$ | 5B1 | 5B1 | 1A | $b^{112}$ |
| $C_5\times D_{280}$ | 5C1 | $5$ | $2$ | $C_5\times C_{280}$ | 5C2 | 5C-2 | 1A | $a^{2}b^{56}$ |
| $C_5\times D_{280}$ | 5C-1 | $5$ | $2$ | $C_5\times C_{280}$ | 5C-2 | 5C2 | 1A | $a^{8}b^{224}$ |
| $C_5\times D_{280}$ | 5C2 | $5$ | $2$ | $C_5\times C_{280}$ | 5C-1 | 5C1 | 1A | $a^{4}b^{112}$ |
| $C_5\times D_{280}$ | 5C-2 | $5$ | $2$ | $C_5\times C_{280}$ | 5C1 | 5C-1 | 1A | $a^{6}b^{168}$ |
| $C_5\times D_{280}$ | 5D1 | $5$ | $2$ | $C_5\times C_{280}$ | 5D2 | 5D-2 | 1A | $a^{4}b^{56}$ |
| $C_5\times D_{280}$ | 5D-1 | $5$ | $2$ | $C_5\times C_{280}$ | 5D-2 | 5D2 | 1A | $a^{6}b^{224}$ |
| $C_5\times D_{280}$ | 5D2 | $5$ | $2$ | $C_5\times C_{280}$ | 5D-1 | 5D1 | 1A | $a^{8}b^{112}$ |
| $C_5\times D_{280}$ | 5D-2 | $5$ | $2$ | $C_5\times C_{280}$ | 5D1 | 5D-1 | 1A | $a^{2}b^{168}$ |
| $C_5\times D_{280}$ | 7A1 | $7$ | $2$ | $C_5\times C_{280}$ | 7A2 | 7A3 | 7A2 | $b^{40}$ |
| $C_5\times D_{280}$ | 7A2 | $7$ | $2$ | $C_5\times C_{280}$ | 7A3 | 7A1 | 7A3 | $b^{80}$ |
| $C_5\times D_{280}$ | 7A3 | $7$ | $2$ | $C_5\times C_{280}$ | 7A1 | 7A2 | 7A1 | $b^{120}$ |
| $C_5\times D_{280}$ | 8A1 | $8$ | $2$ | $C_5\times C_{280}$ | 4A | 8A3 | 8A3 | $b^{35}$ |
| $C_5\times D_{280}$ | 8A3 | $8$ | $2$ | $C_5\times C_{280}$ | 4A | 8A1 | 8A1 | $b^{105}$ |
| $C_5\times D_{280}$ | 10A1 | $10$ | $1$ | $C_5\times D_{280}$ | 5A1 | 10A3 | 2A | $a^{6}b^{140}$ |
| $C_5\times D_{280}$ | 10A-1 | $10$ | $1$ | $C_5\times D_{280}$ | 5A-1 | 10A-3 | 2A | $a^{4}b^{140}$ |
| $C_5\times D_{280}$ | 10A3 | $10$ | $1$ | $C_5\times D_{280}$ | 5A-2 | 10A-1 | 2A | $a^{8}b^{140}$ |
| $C_5\times D_{280}$ | 10A-3 | $10$ | $1$ | $C_5\times D_{280}$ | 5A2 | 10A1 | 2A | $a^{2}b^{140}$ |
| $C_5\times D_{280}$ | 10B1 | $10$ | $2$ | $C_5\times C_{280}$ | 5B1 | 10B3 | 2A | $b^{28}$ |
| $C_5\times D_{280}$ | 10B3 | $10$ | $2$ | $C_5\times C_{280}$ | 5B2 | 10B1 | 2A | $b^{84}$ |
| $C_5\times D_{280}$ | 10C1 | $10$ | $2$ | $C_5\times C_{280}$ | 5C1 | 10C3 | 2A | $a^{6}b^{28}$ |
| $C_5\times D_{280}$ | 10C-1 | $10$ | $2$ | $C_5\times C_{280}$ | 5C-1 | 10C-3 | 2A | $a^{4}b^{252}$ |
| $C_5\times D_{280}$ | 10C3 | $10$ | $2$ | $C_5\times C_{280}$ | 5C-2 | 10C-1 | 2A | $a^{8}b^{84}$ |
| $C_5\times D_{280}$ | 10C-3 | $10$ | $2$ | $C_5\times C_{280}$ | 5C2 | 10C1 | 2A | $a^{2}b^{196}$ |
| $C_5\times D_{280}$ | 10D1 | $10$ | $2$ | $C_5\times C_{280}$ | 5D1 | 10D3 | 2A | $a^{2}b^{28}$ |
| $C_5\times D_{280}$ | 10D-1 | $10$ | $2$ | $C_5\times C_{280}$ | 5D-1 | 10D-3 | 2A | $a^{8}b^{252}$ |
| $C_5\times D_{280}$ | 10D3 | $10$ | $2$ | $C_5\times C_{280}$ | 5D-2 | 10D-1 | 2A | $a^{6}b^{84}$ |
| $C_5\times D_{280}$ | 10D-3 | $10$ | $2$ | $C_5\times C_{280}$ | 5D2 | 10D1 | 2A | $a^{4}b^{196}$ |
| $C_5\times D_{280}$ | 10E1 | $10$ | $140$ | $C_2\times C_{10}$ | 5A1 | 10E3 | 2B | $ab^{279}$ |
| $C_5\times D_{280}$ | 10E-1 | $10$ | $140$ | $C_2\times C_{10}$ | 5A-1 | 10E-3 | 2B | $a^{9}b^{279}$ |
| $C_5\times D_{280}$ | 10E3 | $10$ | $140$ | $C_2\times C_{10}$ | 5A-2 | 10E-1 | 2B | $a^{3}b^{279}$ |
| $C_5\times D_{280}$ | 10E-3 | $10$ | $140$ | $C_2\times C_{10}$ | 5A2 | 10E1 | 2B | $a^{7}b^{279}$ |
| $C_5\times D_{280}$ | 10F1 | $10$ | $140$ | $C_2\times C_{10}$ | 5A-1 | 10F3 | 2C | $a^{9}b^{216}$ |
| $C_5\times D_{280}$ | 10F-1 | $10$ | $140$ | $C_2\times C_{10}$ | 5A1 | 10F-3 | 2C | $ab^{216}$ |
| $C_5\times D_{280}$ | 10F3 | $10$ | $140$ | $C_2\times C_{10}$ | 5A2 | 10F-1 | 2C | $a^{7}b^{216}$ |
| $C_5\times D_{280}$ | 10F-3 | $10$ | $140$ | $C_2\times C_{10}$ | 5A-2 | 10F1 | 2C | $a^{3}b^{216}$ |
| $C_5\times D_{280}$ | 14A1 | $14$ | $2$ | $C_5\times C_{280}$ | 7A1 | 14A3 | 14A5 | $b^{20}$ |
| $C_5\times D_{280}$ | 14A3 | $14$ | $2$ | $C_5\times C_{280}$ | 7A3 | 14A5 | 14A1 | $b^{60}$ |
| $C_5\times D_{280}$ | 14A5 | $14$ | $2$ | $C_5\times C_{280}$ | 7A2 | 14A1 | 14A3 | $b^{100}$ |
| $C_5\times D_{280}$ | 20A1 | $20$ | $2$ | $C_5\times C_{280}$ | 10B1 | 20A3 | 4A | $b^{14}$ |