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Extensions 1→N→G→Q→1 with N=C10 and Q=C22×C4

Direct product G=N×Q with N=C10 and Q=C22×C4
dρLabelID
C23×C20160C2^3xC20160,228

Semidirect products G=N:Q with N=C10 and Q=C22×C4
extensionφ:Q→Aut NdρLabelID
C10⋊(C22×C4) = C23×F5φ: C22×C4/C22 → C4 ⊆ Aut C1040C10:(C2^2xC4)160,236
C10⋊2(C22×C4) = D5×C22×C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10:2(C2^2xC4)160,214
C10⋊3(C22×C4) = C23×Dic5φ: C22×C4/C23 → C2 ⊆ Aut C10160C10:3(C2^2xC4)160,226

Non-split extensions G=N.Q with N=C10 and Q=C22×C4
extensionφ:Q→Aut NdρLabelID
C10.1(C22×C4) = C2×D5⋊C8φ: C22×C4/C22 → C4 ⊆ Aut C1080C10.1(C2^2xC4)160,200
C10.2(C22×C4) = C2×C4.F5φ: C22×C4/C22 → C4 ⊆ Aut C1080C10.2(C2^2xC4)160,201
C10.3(C22×C4) = D5⋊M4(2)φ: C22×C4/C22 → C4 ⊆ Aut C10404C10.3(C2^2xC4)160,202
C10.4(C22×C4) = C2×C4×F5φ: C22×C4/C22 → C4 ⊆ Aut C1040C10.4(C2^2xC4)160,203
C10.5(C22×C4) = C2×C4⋊F5φ: C22×C4/C22 → C4 ⊆ Aut C1040C10.5(C2^2xC4)160,204
C10.6(C22×C4) = D10.C23φ: C22×C4/C22 → C4 ⊆ Aut C10404C10.6(C2^2xC4)160,205
C10.7(C22×C4) = D4.F5φ: C22×C4/C22 → C4 ⊆ Aut C10808-C10.7(C2^2xC4)160,206
C10.8(C22×C4) = D4×F5φ: C22×C4/C22 → C4 ⊆ Aut C10208+C10.8(C2^2xC4)160,207
C10.9(C22×C4) = Q8.F5φ: C22×C4/C22 → C4 ⊆ Aut C10808+C10.9(C2^2xC4)160,208
C10.10(C22×C4) = Q8×F5φ: C22×C4/C22 → C4 ⊆ Aut C10408-C10.10(C2^2xC4)160,209
C10.11(C22×C4) = C22×C5⋊C8φ: C22×C4/C22 → C4 ⊆ Aut C10160C10.11(C2^2xC4)160,210
C10.12(C22×C4) = C2×C22.F5φ: C22×C4/C22 → C4 ⊆ Aut C1080C10.12(C2^2xC4)160,211
C10.13(C22×C4) = C2×C22⋊F5φ: C22×C4/C22 → C4 ⊆ Aut C1040C10.13(C2^2xC4)160,212
C10.14(C22×C4) = C4×Dic10φ: C22×C4/C2×C4 → C2 ⊆ Aut C10160C10.14(C2^2xC4)160,89
C10.15(C22×C4) = D5×C42φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.15(C2^2xC4)160,92
C10.16(C22×C4) = C42⋊D5φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.16(C2^2xC4)160,93
C10.17(C22×C4) = C4×D20φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.17(C2^2xC4)160,94
C10.18(C22×C4) = C23.11D10φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.18(C2^2xC4)160,98
C10.19(C22×C4) = D5×C22⋊C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1040C10.19(C2^2xC4)160,101
C10.20(C22×C4) = Dic5⋊4D4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.20(C2^2xC4)160,102
C10.21(C22×C4) = Dic5⋊3Q8φ: C22×C4/C2×C4 → C2 ⊆ Aut C10160C10.21(C2^2xC4)160,108
C10.22(C22×C4) = D5×C4⋊C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.22(C2^2xC4)160,112
C10.23(C22×C4) = C4⋊C4⋊7D5φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.23(C2^2xC4)160,113
C10.24(C22×C4) = D20⋊8C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.24(C2^2xC4)160,114
C10.25(C22×C4) = D5×C2×C8φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.25(C2^2xC4)160,120
C10.26(C22×C4) = C2×C8⋊D5φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.26(C2^2xC4)160,121
C10.27(C22×C4) = D20.3C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C10802C10.27(C2^2xC4)160,122
C10.28(C22×C4) = D5×M4(2)φ: C22×C4/C2×C4 → C2 ⊆ Aut C10404C10.28(C2^2xC4)160,127
C10.29(C22×C4) = D20.2C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C10804C10.29(C2^2xC4)160,128
C10.30(C22×C4) = C2×C10.D4φ: C22×C4/C2×C4 → C2 ⊆ Aut C10160C10.30(C2^2xC4)160,144
C10.31(C22×C4) = C2×D10⋊C4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.31(C2^2xC4)160,148
C10.32(C22×C4) = C4×C5⋊D4φ: C22×C4/C2×C4 → C2 ⊆ Aut C1080C10.32(C2^2xC4)160,149
C10.33(C22×C4) = C22×C5⋊2C8φ: C22×C4/C23 → C2 ⊆ Aut C10160C10.33(C2^2xC4)160,141
C10.34(C22×C4) = C2×C4.Dic5φ: C22×C4/C23 → C2 ⊆ Aut C1080C10.34(C2^2xC4)160,142
C10.35(C22×C4) = C2×C4×Dic5φ: C22×C4/C23 → C2 ⊆ Aut C10160C10.35(C2^2xC4)160,143
C10.36(C22×C4) = C2×C4⋊Dic5φ: C22×C4/C23 → C2 ⊆ Aut C10160C10.36(C2^2xC4)160,146
C10.37(C22×C4) = C23.21D10φ: C22×C4/C23 → C2 ⊆ Aut C1080C10.37(C2^2xC4)160,147
C10.38(C22×C4) = D4×Dic5φ: C22×C4/C23 → C2 ⊆ Aut C1080C10.38(C2^2xC4)160,155
C10.39(C22×C4) = Q8×Dic5φ: C22×C4/C23 → C2 ⊆ Aut C10160C10.39(C2^2xC4)160,166
C10.40(C22×C4) = D4.Dic5φ: C22×C4/C23 → C2 ⊆ Aut C10804C10.40(C2^2xC4)160,169
C10.41(C22×C4) = C2×C23.D5φ: C22×C4/C23 → C2 ⊆ Aut C1080C10.41(C2^2xC4)160,173
C10.42(C22×C4) = C10×C22⋊C4central extension (φ=1)80C10.42(C2^2xC4)160,176
C10.43(C22×C4) = C10×C4⋊C4central extension (φ=1)160C10.43(C2^2xC4)160,177
C10.44(C22×C4) = C5×C42⋊C2central extension (φ=1)80C10.44(C2^2xC4)160,178
C10.45(C22×C4) = D4×C20central extension (φ=1)80C10.45(C2^2xC4)160,179
C10.46(C22×C4) = Q8×C20central extension (φ=1)160C10.46(C2^2xC4)160,180
C10.47(C22×C4) = C10×M4(2)central extension (φ=1)80C10.47(C2^2xC4)160,191
C10.48(C22×C4) = C5×C8○D4central extension (φ=1)802C10.48(C2^2xC4)160,192

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