Extensions 1→N→G→Q→1 with N=C10 and Q=C2×F5

Direct product G=N×Q with N=C10 and Q=C2×F5
dρLabelID
F5×C2×C1080F5xC2xC10400,214

Semidirect products G=N:Q with N=C10 and Q=C2×F5
extensionφ:Q→Aut NdρLabelID
C101(C2×F5) = C2×D5⋊F5φ: C2×F5/D5C4 ⊆ Aut C10208+C10:1(C2xF5)400,210
C102(C2×F5) = C22×C5⋊F5φ: C2×F5/C10C4 ⊆ Aut C10100C10:2(C2xF5)400,216
C103(C2×F5) = C22×C52⋊C4φ: C2×F5/C10C4 ⊆ Aut C1040C10:3(C2xF5)400,217
C104(C2×F5) = C2×D5×F5φ: C2×F5/F5C2 ⊆ Aut C10408+C10:4(C2xF5)400,209
C105(C2×F5) = C22×D5.D5φ: C2×F5/D10C2 ⊆ Aut C1080C10:5(C2xF5)400,215

Non-split extensions G=N.Q with N=C10 and Q=C2×F5
extensionφ:Q→Aut NdρLabelID
C10.1(C2×F5) = C523C42φ: C2×F5/D5C4 ⊆ Aut C10208+C10.1(C2xF5)400,124
C10.2(C2×F5) = D10⋊F5φ: C2×F5/D5C4 ⊆ Aut C10208+C10.2(C2xF5)400,125
C10.3(C2×F5) = Dic5⋊F5φ: C2×F5/D5C4 ⊆ Aut C10208+C10.3(C2xF5)400,126
C10.4(C2×F5) = D10.2F5φ: C2×F5/D5C4 ⊆ Aut C10808-C10.4(C2xF5)400,127
C10.5(C2×F5) = C524M4(2)φ: C2×F5/D5C4 ⊆ Aut C10808-C10.5(C2xF5)400,128
C10.6(C2×F5) = D25⋊C8φ: C2×F5/C10C4 ⊆ Aut C102004C10.6(C2xF5)400,28
C10.7(C2×F5) = C100.C4φ: C2×F5/C10C4 ⊆ Aut C102004C10.7(C2xF5)400,29
C10.8(C2×F5) = C4×C25⋊C4φ: C2×F5/C10C4 ⊆ Aut C101004C10.8(C2xF5)400,30
C10.9(C2×F5) = C100⋊C4φ: C2×F5/C10C4 ⊆ Aut C101004C10.9(C2xF5)400,31
C10.10(C2×F5) = C2×C25⋊C8φ: C2×F5/C10C4 ⊆ Aut C10400C10.10(C2xF5)400,32
C10.11(C2×F5) = C25⋊M4(2)φ: C2×F5/C10C4 ⊆ Aut C102004-C10.11(C2xF5)400,33
C10.12(C2×F5) = D25.D4φ: C2×F5/C10C4 ⊆ Aut C101004+C10.12(C2xF5)400,34
C10.13(C2×F5) = C22×C25⋊C4φ: C2×F5/C10C4 ⊆ Aut C10100C10.13(C2xF5)400,53
C10.14(C2×F5) = C20.F5φ: C2×F5/C10C4 ⊆ Aut C10200C10.14(C2xF5)400,149
C10.15(C2×F5) = C527M4(2)φ: C2×F5/C10C4 ⊆ Aut C10200C10.15(C2xF5)400,150
C10.16(C2×F5) = C4×C5⋊F5φ: C2×F5/C10C4 ⊆ Aut C10100C10.16(C2xF5)400,151
C10.17(C2×F5) = C20⋊F5φ: C2×F5/C10C4 ⊆ Aut C10100C10.17(C2xF5)400,152
C10.18(C2×F5) = C2×C524C8φ: C2×F5/C10C4 ⊆ Aut C10400C10.18(C2xF5)400,153
C10.19(C2×F5) = C5213M4(2)φ: C2×F5/C10C4 ⊆ Aut C10200C10.19(C2xF5)400,154
C10.20(C2×F5) = C102⋊C4φ: C2×F5/C10C4 ⊆ Aut C10100C10.20(C2xF5)400,155
C10.21(C2×F5) = C20.11F5φ: C2×F5/C10C4 ⊆ Aut C10404C10.21(C2xF5)400,156
C10.22(C2×F5) = C528M4(2)φ: C2×F5/C10C4 ⊆ Aut C10404C10.22(C2xF5)400,157
C10.23(C2×F5) = C4×C52⋊C4φ: C2×F5/C10C4 ⊆ Aut C10404C10.23(C2xF5)400,158
C10.24(C2×F5) = C202F5φ: C2×F5/C10C4 ⊆ Aut C10404C10.24(C2xF5)400,159
C10.25(C2×F5) = C2×C525C8φ: C2×F5/C10C4 ⊆ Aut C1080C10.25(C2xF5)400,160
C10.26(C2×F5) = C5214M4(2)φ: C2×F5/C10C4 ⊆ Aut C10404-C10.26(C2xF5)400,161
C10.27(C2×F5) = C1024C4φ: C2×F5/C10C4 ⊆ Aut C10204+C10.27(C2xF5)400,162
C10.28(C2×F5) = Dic5×F5φ: C2×F5/F5C2 ⊆ Aut C10808-C10.28(C2xF5)400,117
C10.29(C2×F5) = D5.D20φ: C2×F5/F5C2 ⊆ Aut C10408+C10.29(C2xF5)400,118
C10.30(C2×F5) = D5.Dic10φ: C2×F5/F5C2 ⊆ Aut C10808-C10.30(C2xF5)400,119
C10.31(C2×F5) = D5×C5⋊C8φ: C2×F5/F5C2 ⊆ Aut C10808-C10.31(C2xF5)400,120
C10.32(C2×F5) = Dic5.4F5φ: C2×F5/F5C2 ⊆ Aut C10408+C10.32(C2xF5)400,121
C10.33(C2×F5) = D10.F5φ: C2×F5/F5C2 ⊆ Aut C10808-C10.33(C2xF5)400,122
C10.34(C2×F5) = Dic5.F5φ: C2×F5/F5C2 ⊆ Aut C10408+C10.34(C2xF5)400,123
C10.35(C2×F5) = C20.14F5φ: C2×F5/D10C2 ⊆ Aut C10804C10.35(C2xF5)400,142
C10.36(C2×F5) = C20.12F5φ: C2×F5/D10C2 ⊆ Aut C10804C10.36(C2xF5)400,143
C10.37(C2×F5) = C4×D5.D5φ: C2×F5/D10C2 ⊆ Aut C10804C10.37(C2xF5)400,144
C10.38(C2×F5) = C205F5φ: C2×F5/D10C2 ⊆ Aut C10804C10.38(C2xF5)400,145
C10.39(C2×F5) = C2×C523C8φ: C2×F5/D10C2 ⊆ Aut C1080C10.39(C2xF5)400,146
C10.40(C2×F5) = C102.C4φ: C2×F5/D10C2 ⊆ Aut C10404C10.40(C2xF5)400,147
C10.41(C2×F5) = D10.D10φ: C2×F5/D10C2 ⊆ Aut C10404C10.41(C2xF5)400,148
C10.42(C2×F5) = C5×D5⋊C8central extension (φ=1)804C10.42(C2xF5)400,135
C10.43(C2×F5) = C5×C4.F5central extension (φ=1)804C10.43(C2xF5)400,136
C10.44(C2×F5) = C20×F5central extension (φ=1)804C10.44(C2xF5)400,137
C10.45(C2×F5) = C5×C4⋊F5central extension (φ=1)804C10.45(C2xF5)400,138
C10.46(C2×F5) = C10×C5⋊C8central extension (φ=1)80C10.46(C2xF5)400,139
C10.47(C2×F5) = C5×C22.F5central extension (φ=1)404C10.47(C2xF5)400,140
C10.48(C2×F5) = C5×C22⋊F5central extension (φ=1)404C10.48(C2xF5)400,141

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