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Extensions 1→N→G→Q→1 with N=C6 and Q=C22⋊F5

Direct product G=N×Q with N=C6 and Q=C22⋊F5
dρLabelID
C6×C22⋊F5120C6xC2^2:F5480,1059

Semidirect products G=N:Q with N=C6 and Q=C22⋊F5
extensionφ:Q→Aut NdρLabelID
C6⋊1(C22⋊F5) = C2×D6⋊F5φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C6120C6:1(C2^2:F5)480,1000
C6⋊2(C22⋊F5) = C2×D10.D6φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C6120C6:2(C2^2:F5)480,1072

Non-split extensions G=N.Q with N=C6 and Q=C22⋊F5
extensionφ:Q→Aut NdρLabelID
C6.1(C22⋊F5) = D60⋊C4φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208+C6.1(C2^2:F5)480,227
C6.2(C22⋊F5) = D12⋊F5φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208+C6.2(C2^2:F5)480,228
C6.3(C22⋊F5) = Dic6⋊F5φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208-C6.3(C2^2:F5)480,229
C6.4(C22⋊F5) = Dic30⋊C4φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208-C6.4(C2^2:F5)480,230
C6.5(C22⋊F5) = D12⋊4F5φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208-C6.5(C2^2:F5)480,231
C6.6(C22⋊F5) = D12⋊2F5φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208-C6.6(C2^2:F5)480,232
C6.7(C22⋊F5) = D60⋊2C4φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208+C6.7(C2^2:F5)480,233
C6.8(C22⋊F5) = D60⋊5C4φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208+C6.8(C2^2:F5)480,234
C6.9(C22⋊F5) = D10.20D12φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C6120C6.9(C2^2:F5)480,243
C6.10(C22⋊F5) = Dic5.22D12φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C6240C6.10(C2^2:F5)480,246
C6.11(C22⋊F5) = D30⋊C8φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C6240C6.11(C2^2:F5)480,247
C6.12(C22⋊F5) = D10.D12φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208-C6.12(C2^2:F5)480,248
C6.13(C22⋊F5) = D10.4D12φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208+C6.13(C2^2:F5)480,249
C6.14(C22⋊F5) = Dic5.D12φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C61208+C6.14(C2^2:F5)480,250
C6.15(C22⋊F5) = Dic5.4D12φ: C22⋊F5/C2×F5 → C2 ⊆ Aut C62408-C6.15(C2^2:F5)480,251
C6.16(C22⋊F5) = (C2×C60)⋊C4φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61204C6.16(C2^2:F5)480,304
C6.17(C22⋊F5) = C30.7M4(2)φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C6240C6.17(C2^2:F5)480,308
C6.18(C22⋊F5) = (C2×C60).C4φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C62404C6.18(C2^2:F5)480,310
C6.19(C22⋊F5) = D10.10D12φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C6120C6.19(C2^2:F5)480,311
C6.20(C22⋊F5) = D20⋊Dic3φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61208C6.20(C2^2:F5)480,312
C6.21(C22⋊F5) = Dic10⋊Dic3φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61208C6.21(C2^2:F5)480,313
C6.22(C22⋊F5) = Dic10⋊2Dic3φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61208C6.22(C2^2:F5)480,314
C6.23(C22⋊F5) = D20⋊2Dic3φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61208C6.23(C2^2:F5)480,315
C6.24(C22⋊F5) = C3⋊(C23⋊F5)φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61204C6.24(C2^2:F5)480,316
C6.25(C22⋊F5) = C30.22M4(2)φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C6240C6.25(C2^2:F5)480,317
C6.26(C22⋊F5) = C5⋊(C12.D4)φ: C22⋊F5/C22×D5 → C2 ⊆ Aut C61204C6.26(C2^2:F5)480,318
C6.27(C22⋊F5) = C3×D10.D4central extension (φ=1)1204C6.27(C2^2:F5)480,279
C6.28(C22⋊F5) = C3×D10⋊C8central extension (φ=1)240C6.28(C2^2:F5)480,283
C6.29(C22⋊F5) = C3×Dic5.D4central extension (φ=1)2404C6.29(C2^2:F5)480,285
C6.30(C22⋊F5) = C3×D10.3Q8central extension (φ=1)120C6.30(C2^2:F5)480,286
C6.31(C22⋊F5) = C3×D20⋊C4central extension (φ=1)1208C6.31(C2^2:F5)480,287
C6.32(C22⋊F5) = C3×D4⋊F5central extension (φ=1)1208C6.32(C2^2:F5)480,288
C6.33(C22⋊F5) = C3×Q8⋊F5central extension (φ=1)1208C6.33(C2^2:F5)480,289
C6.34(C22⋊F5) = C3×Q8⋊2F5central extension (φ=1)1208C6.34(C2^2:F5)480,290
C6.35(C22⋊F5) = C3×C23⋊F5central extension (φ=1)1204C6.35(C2^2:F5)480,291
C6.36(C22⋊F5) = C3×C23.2F5central extension (φ=1)240C6.36(C2^2:F5)480,292
C6.37(C22⋊F5) = C3×C23.F5central extension (φ=1)1204C6.37(C2^2:F5)480,293

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