# Extensions 1→N→G→Q→1 with N=C23 and Q=C2×F5

Direct product G=N×Q with N=C23 and Q=C2×F5
dρLabelID
C24×F580C2^4xF5320,1638

Semidirect products G=N:Q with N=C23 and Q=C2×F5
extensionφ:Q→Aut NdρLabelID
C231(C2×F5) = (C2×D4)⋊7F5φ: C2×F5/D5C4 ⊆ Aut C23408+C2^3:1(C2xF5)320,1108
C232(C2×F5) = (C2×F5)⋊D4φ: C2×F5/D5C22 ⊆ Aut C2340C2^3:2(C2xF5)320,1117
C233(C2×F5) = D10.C24φ: C2×F5/D5C22 ⊆ Aut C23408+C2^3:3(C2xF5)320,1596
C234(C2×F5) = C2×C23⋊F5φ: C2×F5/C10C4 ⊆ Aut C2380C2^3:4(C2xF5)320,1134
C235(C2×F5) = C2×D4×F5φ: C2×F5/F5C2 ⊆ Aut C2340C2^3:5(C2xF5)320,1595
C236(C2×F5) = C22×C22⋊F5φ: C2×F5/D10C2 ⊆ Aut C2380C2^3:6(C2xF5)320,1607

Non-split extensions G=N.Q with N=C23 and Q=C2×F5
extensionφ:Q→Aut NdρLabelID
C23.1(C2×F5) = C5⋊C2≀C4φ: C2×F5/D5C4 ⊆ Aut C23408+C2^3.1(C2xF5)320,202
C23.2(C2×F5) = C22⋊C4⋊F5φ: C2×F5/D5C4 ⊆ Aut C23808-C2^3.2(C2xF5)320,203
C23.3(C2×F5) = (C2×D4)⋊8F5φ: C2×F5/D5C4 ⊆ Aut C23808-C2^3.3(C2xF5)320,1109
C23.4(C2×F5) = D5⋊(C4.D4)φ: C2×F5/D5C4 ⊆ Aut C23408+C2^3.4(C2xF5)320,1116
C23.5(C2×F5) = (C22×F5)⋊C4φ: C2×F5/D5C22 ⊆ Aut C23408+C2^3.5(C2xF5)320,204
C23.6(C2×F5) = C22⋊C4.F5φ: C2×F5/D5C22 ⊆ Aut C23808-C2^3.6(C2xF5)320,205
C23.7(C2×F5) = D10⋊M4(2)φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.7(C2xF5)320,1032
C23.8(C2×F5) = Dic5⋊M4(2)φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.8(C2xF5)320,1033
C23.9(C2×F5) = C23.(C2×F5)φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.9(C2xF5)320,1035
C23.10(C2×F5) = C10.(C4×D4)φ: C2×F5/D5C22 ⊆ Aut C2380C2^3.10(C2xF5)320,1038
C23.11(C2×F5) = C5⋊C87D4φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.11(C2xF5)320,1111
C23.12(C2×F5) = C202M4(2)φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.12(C2xF5)320,1112
C23.13(C2×F5) = (C2×D4).7F5φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.13(C2xF5)320,1113
C23.14(C2×F5) = (C2×D4).8F5φ: C2×F5/D5C22 ⊆ Aut C23160C2^3.14(C2xF5)320,1114
C23.15(C2×F5) = (C2×D4).9F5φ: C2×F5/D5C22 ⊆ Aut C23808-C2^3.15(C2xF5)320,1115
C23.16(C2×F5) = C2.(D4×F5)φ: C2×F5/D5C22 ⊆ Aut C2380C2^3.16(C2xF5)320,1118
C23.17(C2×F5) = Dic5.C24φ: C2×F5/D5C22 ⊆ Aut C23808-C2^3.17(C2xF5)320,1594
C23.18(C2×F5) = (C22×C4)⋊F5φ: C2×F5/C10C4 ⊆ Aut C23804C2^3.18(C2xF5)320,254
C23.19(C2×F5) = C242F5φ: C2×F5/C10C4 ⊆ Aut C23404C2^3.19(C2xF5)320,272
C23.20(C2×F5) = C23⋊F55C2φ: C2×F5/C10C4 ⊆ Aut C23804C2^3.20(C2xF5)320,1083
C23.21(C2×F5) = (C4×D5).D4φ: C2×F5/C10C4 ⊆ Aut C23804C2^3.21(C2xF5)320,1099
C23.22(C2×F5) = C2×C23.F5φ: C2×F5/C10C4 ⊆ Aut C2380C2^3.22(C2xF5)320,1137
C23.23(C2×F5) = Dic5.C42φ: C2×F5/F5C2 ⊆ Aut C23160C2^3.23(C2xF5)320,1029
C23.24(C2×F5) = C5⋊C88D4φ: C2×F5/F5C2 ⊆ Aut C23160C2^3.24(C2xF5)320,1030
C23.25(C2×F5) = C5⋊C8⋊D4φ: C2×F5/F5C2 ⊆ Aut C23160C2^3.25(C2xF5)320,1031
C23.26(C2×F5) = C20⋊C8⋊C2φ: C2×F5/F5C2 ⊆ Aut C23160C2^3.26(C2xF5)320,1034
C23.27(C2×F5) = C22⋊C4×F5φ: C2×F5/F5C2 ⊆ Aut C2340C2^3.27(C2xF5)320,1036
C23.28(C2×F5) = D10⋊(C4⋊C4)φ: C2×F5/F5C2 ⊆ Aut C2340C2^3.28(C2xF5)320,1037
C23.29(C2×F5) = D4×C5⋊C8φ: C2×F5/F5C2 ⊆ Aut C23160C2^3.29(C2xF5)320,1110
C23.30(C2×F5) = C2×D4.F5φ: C2×F5/F5C2 ⊆ Aut C23160C2^3.30(C2xF5)320,1593
C23.31(C2×F5) = (C2×C20)⋊1C8φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.31(C2xF5)320,251
C23.32(C2×F5) = (C22×C4).F5φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.32(C2xF5)320,252
C23.33(C2×F5) = C5⋊(C23⋊C8)φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.33(C2xF5)320,253
C23.34(C2×F5) = C22⋊F5⋊C4φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.34(C2xF5)320,255
C23.35(C2×F5) = C22.F5⋊C4φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.35(C2xF5)320,257
C23.36(C2×F5) = C24.F5φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.36(C2xF5)320,271
C23.37(C2×F5) = C2×D10.D4φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.37(C2xF5)320,1082
C23.38(C2×F5) = Dic5.12M4(2)φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.38(C2xF5)320,1086
C23.39(C2×F5) = C4×C22.F5φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.39(C2xF5)320,1088
C23.40(C2×F5) = D10.11M4(2)φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.40(C2xF5)320,1091
C23.41(C2×F5) = C20.34M4(2)φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.41(C2xF5)320,1092
C23.42(C2×F5) = D109M4(2)φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.42(C2xF5)320,1093
C23.43(C2×F5) = D1010M4(2)φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.43(C2xF5)320,1094
C23.44(C2×F5) = Dic5.13M4(2)φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.44(C2xF5)320,1095
C23.45(C2×F5) = C208M4(2)φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.45(C2xF5)320,1096
C23.46(C2×F5) = C20.30M4(2)φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.46(C2xF5)320,1097
C23.47(C2×F5) = C2×Dic5.D4φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.47(C2xF5)320,1098
C23.48(C2×F5) = C4×C22⋊F5φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.48(C2xF5)320,1101
C23.49(C2×F5) = (C22×C4)⋊7F5φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.49(C2xF5)320,1102
C23.50(C2×F5) = D106(C4⋊C4)φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.50(C2xF5)320,1103
C23.51(C2×F5) = C24.4F5φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.51(C2xF5)320,1136
C23.52(C2×F5) = C244F5φ: C2×F5/D10C2 ⊆ Aut C2340C2^3.52(C2xF5)320,1138
C23.53(C2×F5) = C2×D5⋊M4(2)φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.53(C2xF5)320,1589
C23.54(C2×F5) = C2×D10.C23φ: C2×F5/D10C2 ⊆ Aut C2380C2^3.54(C2xF5)320,1592
C23.55(C2×F5) = C22×C22.F5φ: C2×F5/D10C2 ⊆ Aut C23160C2^3.55(C2xF5)320,1606
C23.56(C2×F5) = C10.(C4⋊C8)central extension (φ=1)320C2^3.56(C2xF5)320,256
C23.57(C2×F5) = C2×C4×C5⋊C8central extension (φ=1)320C2^3.57(C2xF5)320,1084
C23.58(C2×F5) = C2×C20⋊C8central extension (φ=1)320C2^3.58(C2xF5)320,1085
C23.59(C2×F5) = C2×C10.C42central extension (φ=1)320C2^3.59(C2xF5)320,1087
C23.60(C2×F5) = C2×D10⋊C8central extension (φ=1)160C2^3.60(C2xF5)320,1089
C23.61(C2×F5) = C2×Dic5⋊C8central extension (φ=1)320C2^3.61(C2xF5)320,1090
C23.62(C2×F5) = C2×D10.3Q8central extension (φ=1)80C2^3.62(C2xF5)320,1100
C23.63(C2×F5) = C2×C23.2F5central extension (φ=1)160C2^3.63(C2xF5)320,1135
C23.64(C2×F5) = C22×D5⋊C8central extension (φ=1)160C2^3.64(C2xF5)320,1587
C23.65(C2×F5) = C22×C4.F5central extension (φ=1)160C2^3.65(C2xF5)320,1588
C23.66(C2×F5) = C22×C4×F5central extension (φ=1)80C2^3.66(C2xF5)320,1590
C23.67(C2×F5) = C22×C4⋊F5central extension (φ=1)80C2^3.67(C2xF5)320,1591
C23.68(C2×F5) = C23×C5⋊C8central extension (φ=1)320C2^3.68(C2xF5)320,1605

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