# Extensions 1→N→G→Q→1 with N=C10 and Q=C22×D5

Direct product G=N×Q with N=C10 and Q=C22×D5
dρLabelID
D5×C22×C1080D5xC2^2xC10400,219

Semidirect products G=N:Q with N=C10 and Q=C22×D5
extensionφ:Q→Aut NdρLabelID
C101(C22×D5) = C22×D52φ: C22×D5/D10C2 ⊆ Aut C1040C10:1(C2^2xD5)400,218
C102(C22×D5) = C23×C5⋊D5φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10:2(C2^2xD5)400,220

Non-split extensions G=N.Q with N=C10 and Q=C22×D5
extensionφ:Q→Aut NdρLabelID
C10.1(C22×D5) = D5×Dic10φ: C22×D5/D10C2 ⊆ Aut C10804-C10.1(C2^2xD5)400,163
C10.2(C22×D5) = D205D5φ: C22×D5/D10C2 ⊆ Aut C10804-C10.2(C2^2xD5)400,164
C10.3(C22×D5) = D20⋊D5φ: C22×D5/D10C2 ⊆ Aut C10404C10.3(C2^2xD5)400,165
C10.4(C22×D5) = Dic10⋊D5φ: C22×D5/D10C2 ⊆ Aut C10404C10.4(C2^2xD5)400,166
C10.5(C22×D5) = D10.9D10φ: C22×D5/D10C2 ⊆ Aut C10404C10.5(C2^2xD5)400,167
C10.6(C22×D5) = Dic105D5φ: C22×D5/D10C2 ⊆ Aut C10404+C10.6(C2^2xD5)400,168
C10.7(C22×D5) = C4×D52φ: C22×D5/D10C2 ⊆ Aut C10404C10.7(C2^2xD5)400,169
C10.8(C22×D5) = D5×D20φ: C22×D5/D10C2 ⊆ Aut C10404+C10.8(C2^2xD5)400,170
C10.9(C22×D5) = C20⋊D10φ: C22×D5/D10C2 ⊆ Aut C10404C10.9(C2^2xD5)400,171
C10.10(C22×D5) = C2×D5×Dic5φ: C22×D5/D10C2 ⊆ Aut C1080C10.10(C2^2xD5)400,172
C10.11(C22×D5) = Dic5.D10φ: C22×D5/D10C2 ⊆ Aut C10404C10.11(C2^2xD5)400,173
C10.12(C22×D5) = D10.4D10φ: C22×D5/D10C2 ⊆ Aut C10404-C10.12(C2^2xD5)400,174
C10.13(C22×D5) = C2×Dic52D5φ: C22×D5/D10C2 ⊆ Aut C1040C10.13(C2^2xD5)400,175
C10.14(C22×D5) = C2×C522D4φ: C22×D5/D10C2 ⊆ Aut C1080C10.14(C2^2xD5)400,176
C10.15(C22×D5) = C2×C5⋊D20φ: C22×D5/D10C2 ⊆ Aut C1040C10.15(C2^2xD5)400,177
C10.16(C22×D5) = C2×C522Q8φ: C22×D5/D10C2 ⊆ Aut C1080C10.16(C2^2xD5)400,178
C10.17(C22×D5) = D5×C5⋊D4φ: C22×D5/D10C2 ⊆ Aut C10404C10.17(C2^2xD5)400,179
C10.18(C22×D5) = D10⋊D10φ: C22×D5/D10C2 ⊆ Aut C10204+C10.18(C2^2xD5)400,180
C10.19(C22×D5) = C2×Dic50φ: C22×D5/C2×C10C2 ⊆ Aut C10400C10.19(C2^2xD5)400,35
C10.20(C22×D5) = C2×C4×D25φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.20(C2^2xD5)400,36
C10.21(C22×D5) = C2×D100φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.21(C2^2xD5)400,37
C10.22(C22×D5) = D1005C2φ: C22×D5/C2×C10C2 ⊆ Aut C102002C10.22(C2^2xD5)400,38
C10.23(C22×D5) = D4×D25φ: C22×D5/C2×C10C2 ⊆ Aut C101004+C10.23(C2^2xD5)400,39
C10.24(C22×D5) = D42D25φ: C22×D5/C2×C10C2 ⊆ Aut C102004-C10.24(C2^2xD5)400,40
C10.25(C22×D5) = Q8×D25φ: C22×D5/C2×C10C2 ⊆ Aut C102004-C10.25(C2^2xD5)400,41
C10.26(C22×D5) = Q82D25φ: C22×D5/C2×C10C2 ⊆ Aut C102004+C10.26(C2^2xD5)400,42
C10.27(C22×D5) = C22×Dic25φ: C22×D5/C2×C10C2 ⊆ Aut C10400C10.27(C2^2xD5)400,43
C10.28(C22×D5) = C2×C25⋊D4φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.28(C2^2xD5)400,44
C10.29(C22×D5) = C23×D25φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.29(C2^2xD5)400,54
C10.30(C22×D5) = C2×C524Q8φ: C22×D5/C2×C10C2 ⊆ Aut C10400C10.30(C2^2xD5)400,191
C10.31(C22×D5) = C2×C4×C5⋊D5φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.31(C2^2xD5)400,192
C10.32(C22×D5) = C2×C20⋊D5φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.32(C2^2xD5)400,193
C10.33(C22×D5) = C20.50D10φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.33(C2^2xD5)400,194
C10.34(C22×D5) = D4×C5⋊D5φ: C22×D5/C2×C10C2 ⊆ Aut C10100C10.34(C2^2xD5)400,195
C10.35(C22×D5) = C20.D10φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.35(C2^2xD5)400,196
C10.36(C22×D5) = Q8×C5⋊D5φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.36(C2^2xD5)400,197
C10.37(C22×D5) = C20.26D10φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.37(C2^2xD5)400,198
C10.38(C22×D5) = C22×C526C4φ: C22×D5/C2×C10C2 ⊆ Aut C10400C10.38(C2^2xD5)400,199
C10.39(C22×D5) = C2×C527D4φ: C22×D5/C2×C10C2 ⊆ Aut C10200C10.39(C2^2xD5)400,200
C10.40(C22×D5) = C10×Dic10central extension (φ=1)80C10.40(C2^2xD5)400,181
C10.41(C22×D5) = D5×C2×C20central extension (φ=1)80C10.41(C2^2xD5)400,182
C10.42(C22×D5) = C10×D20central extension (φ=1)80C10.42(C2^2xD5)400,183
C10.43(C22×D5) = C5×C4○D20central extension (φ=1)402C10.43(C2^2xD5)400,184
C10.44(C22×D5) = C5×D4×D5central extension (φ=1)404C10.44(C2^2xD5)400,185
C10.45(C22×D5) = C5×D42D5central extension (φ=1)404C10.45(C2^2xD5)400,186
C10.46(C22×D5) = C5×Q8×D5central extension (φ=1)804C10.46(C2^2xD5)400,187
C10.47(C22×D5) = C5×Q82D5central extension (φ=1)804C10.47(C2^2xD5)400,188
C10.48(C22×D5) = Dic5×C2×C10central extension (φ=1)80C10.48(C2^2xD5)400,189
C10.49(C22×D5) = C10×C5⋊D4central extension (φ=1)40C10.49(C2^2xD5)400,190

׿
×
𝔽