Extensions 1→N→G→Q→1 with N=C22 and Q=C22⋊F5

Direct product G=N×Q with N=C22 and Q=C22⋊F5
dρLabelID
C22×C22⋊F580C2^2xC2^2:F5320,1607

Semidirect products G=N:Q with N=C22 and Q=C22⋊F5
extensionφ:Q→Aut NdρLabelID
C221(C22⋊F5) = (C2×F5)⋊D4φ: C22⋊F5/C2×F5C2 ⊆ Aut C2240C2^2:1(C2^2:F5)320,1117
C222(C22⋊F5) = C244F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C2240C2^2:2(C2^2:F5)320,1138

Non-split extensions G=N.Q with N=C22 and Q=C22⋊F5
extensionφ:Q→Aut NdρLabelID
C22.1(C22⋊F5) = (C2×D4)⋊7F5φ: C22⋊F5/C2×F5C2 ⊆ Aut C22408+C2^2.1(C2^2:F5)320,1108
C22.2(C22⋊F5) = (C2×D4).7F5φ: C22⋊F5/C2×F5C2 ⊆ Aut C22160C2^2.2(C2^2:F5)320,1113
C22.3(C22⋊F5) = (C2×D4).9F5φ: C22⋊F5/C2×F5C2 ⊆ Aut C22808-C2^2.3(C2^2:F5)320,1115
C22.4(C22⋊F5) = D5⋊C4≀C2φ: C22⋊F5/C2×F5C2 ⊆ Aut C22408C2^2.4(C2^2:F5)320,1130
C22.5(C22⋊F5) = C4○D4⋊F5φ: C22⋊F5/C2×F5C2 ⊆ Aut C22408C2^2.5(C2^2:F5)320,1131
C22.6(C22⋊F5) = C4○D20⋊C4φ: C22⋊F5/C2×F5C2 ⊆ Aut C22808C2^2.6(C2^2:F5)320,1132
C22.7(C22⋊F5) = D4⋊F5⋊C2φ: C22⋊F5/C2×F5C2 ⊆ Aut C22808C2^2.7(C2^2:F5)320,1133
C22.8(C22⋊F5) = C42⋊F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22404+C2^2.8(C2^2:F5)320,191
C22.9(C22⋊F5) = C422F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22804C2^2.9(C2^2:F5)320,192
C22.10(C22⋊F5) = C42.F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22804-C2^2.10(C2^2:F5)320,193
C22.11(C22⋊F5) = C42.2F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22804C2^2.11(C2^2:F5)320,194
C22.12(C22⋊F5) = C426F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22404C2^2.12(C2^2:F5)320,200
C22.13(C22⋊F5) = C423F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22804C2^2.13(C2^2:F5)320,201
C22.14(C22⋊F5) = C5⋊C2≀C4φ: C22⋊F5/C22×D5C2 ⊆ Aut C22408+C2^2.14(C2^2:F5)320,202
C22.15(C22⋊F5) = C22⋊C4⋊F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808-C2^2.15(C2^2:F5)320,203
C22.16(C22⋊F5) = (C22×F5)⋊C4φ: C22⋊F5/C22×D5C2 ⊆ Aut C22408+C2^2.16(C2^2:F5)320,204
C22.17(C22⋊F5) = C22⋊C4.F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808-C2^2.17(C2^2:F5)320,205
C22.18(C22⋊F5) = (C22×C4)⋊F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22804C2^2.18(C2^2:F5)320,254
C22.19(C22⋊F5) = (C2×D4)⋊F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22408+C2^2.19(C2^2:F5)320,260
C22.20(C22⋊F5) = (D4×C10).C4φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808-C2^2.20(C2^2:F5)320,261
C22.21(C22⋊F5) = (C2×Q8)⋊F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808+C2^2.21(C2^2:F5)320,266
C22.22(C22⋊F5) = (Q8×C10).C4φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808-C2^2.22(C2^2:F5)320,267
C22.23(C22⋊F5) = C242F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22404C2^2.23(C2^2:F5)320,272
C22.24(C22⋊F5) = D109M4(2)φ: C22⋊F5/C22×D5C2 ⊆ Aut C2280C2^2.24(C2^2:F5)320,1093
C22.25(C22⋊F5) = (C22×C4)⋊7F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C2280C2^2.25(C2^2:F5)320,1102
C22.26(C22⋊F5) = (D4×C10)⋊C4φ: C22⋊F5/C22×D5C2 ⊆ Aut C22408+C2^2.26(C2^2:F5)320,1105
C22.27(C22⋊F5) = (C2×D4)⋊6F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808-C2^2.27(C2^2:F5)320,1107
C22.28(C22⋊F5) = (C2×Q8)⋊4F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808-C2^2.28(C2^2:F5)320,1120
C22.29(C22⋊F5) = (C2×Q8)⋊6F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C22808+C2^2.29(C2^2:F5)320,1122
C22.30(C22⋊F5) = C24.4F5φ: C22⋊F5/C22×D5C2 ⊆ Aut C2280C2^2.30(C2^2:F5)320,1136
C22.31(C22⋊F5) = D20⋊C8central extension (φ=1)160C2^2.31(C2^2:F5)320,209
C22.32(C22⋊F5) = Dic101C8central extension (φ=1)320C2^2.32(C2^2:F5)320,210
C22.33(C22⋊F5) = D10.18D8central extension (φ=1)80C2^2.33(C2^2:F5)320,212
C22.34(C22⋊F5) = C20.C42central extension (φ=1)80C2^2.34(C2^2:F5)320,213
C22.35(C22⋊F5) = (C2×C20)⋊1C8central extension (φ=1)160C2^2.35(C2^2:F5)320,251
C22.36(C22⋊F5) = (C22×C4).F5central extension (φ=1)160C2^2.36(C2^2:F5)320,252
C22.37(C22⋊F5) = C5⋊(C23⋊C8)central extension (φ=1)80C2^2.37(C2^2:F5)320,253
C22.38(C22⋊F5) = C22⋊F5⋊C4central extension (φ=1)80C2^2.38(C2^2:F5)320,255
C22.39(C22⋊F5) = C10.(C4⋊C8)central extension (φ=1)320C2^2.39(C2^2:F5)320,256
C22.40(C22⋊F5) = C22.F5⋊C4central extension (φ=1)160C2^2.40(C2^2:F5)320,257
C22.41(C22⋊F5) = Dic5.23D8central extension (φ=1)160C2^2.41(C2^2:F5)320,262
C22.42(C22⋊F5) = Dic5.12Q16central extension (φ=1)320C2^2.42(C2^2:F5)320,268
C22.43(C22⋊F5) = C24.F5central extension (φ=1)80C2^2.43(C2^2:F5)320,271
C22.44(C22⋊F5) = C2×D10.D4central extension (φ=1)80C2^2.44(C2^2:F5)320,1082
C22.45(C22⋊F5) = C2×D10⋊C8central extension (φ=1)160C2^2.45(C2^2:F5)320,1089
C22.46(C22⋊F5) = C2×Dic5.D4central extension (φ=1)160C2^2.46(C2^2:F5)320,1098
C22.47(C22⋊F5) = C2×D10.3Q8central extension (φ=1)80C2^2.47(C2^2:F5)320,1100
C22.48(C22⋊F5) = C2×D20⋊C4central extension (φ=1)80C2^2.48(C2^2:F5)320,1104
C22.49(C22⋊F5) = C2×D4⋊F5central extension (φ=1)80C2^2.49(C2^2:F5)320,1106
C22.50(C22⋊F5) = C2×Q8⋊F5central extension (φ=1)80C2^2.50(C2^2:F5)320,1119
C22.51(C22⋊F5) = C2×Q82F5central extension (φ=1)80C2^2.51(C2^2:F5)320,1121
C22.52(C22⋊F5) = C2×C23⋊F5central extension (φ=1)80C2^2.52(C2^2:F5)320,1134
C22.53(C22⋊F5) = C2×C23.2F5central extension (φ=1)160C2^2.53(C2^2:F5)320,1135
C22.54(C22⋊F5) = C2×C23.F5central extension (φ=1)80C2^2.54(C2^2:F5)320,1137
C22.55(C22⋊F5) = D10.1D8central stem extension (φ=1)80C2^2.55(C2^2:F5)320,206
C22.56(C22⋊F5) = D10.1Q16central stem extension (φ=1)80C2^2.56(C2^2:F5)320,207
C22.57(C22⋊F5) = C10.C4≀C2central stem extension (φ=1)320C2^2.57(C2^2:F5)320,208
C22.58(C22⋊F5) = Dic5.D8central stem extension (φ=1)320C2^2.58(C2^2:F5)320,211
C22.59(C22⋊F5) = D10.SD16central stem extension (φ=1)80C2^2.59(C2^2:F5)320,258
C22.60(C22⋊F5) = (C2×D4).F5central stem extension (φ=1)160C2^2.60(C2^2:F5)320,259
C22.61(C22⋊F5) = Dic5.SD16central stem extension (φ=1)160C2^2.61(C2^2:F5)320,263
C22.62(C22⋊F5) = D10.Q16central stem extension (φ=1)80C2^2.62(C2^2:F5)320,264
C22.63(C22⋊F5) = (C2×Q8).F5central stem extension (φ=1)160C2^2.63(C2^2:F5)320,265
C22.64(C22⋊F5) = Dic5.Q16central stem extension (φ=1)320C2^2.64(C2^2:F5)320,269

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