# Extensions 1→N→G→Q→1 with N=C10 and Q=C22×Q8

Direct product G=N×Q with N=C10 and Q=C22×Q8
dρLabelID
Q8×C22×C10320Q8xC2^2xC10320,1630

Semidirect products G=N:Q with N=C10 and Q=C22×Q8
extensionφ:Q→Aut NdρLabelID
C101(C22×Q8) = C23×Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10:1(C2^2xQ8)320,1608
C102(C22×Q8) = C22×Q8×D5φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10:2(C2^2xQ8)320,1615

Non-split extensions G=N.Q with N=C10 and Q=C22×Q8
extensionφ:Q→Aut NdρLabelID
C10.1(C22×Q8) = C2×C4×Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.1(C2^2xQ8)320,1139
C10.2(C22×Q8) = C2×C202Q8φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.2(C2^2xQ8)320,1140
C10.3(C22×Q8) = C2×C20.6Q8φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.3(C2^2xQ8)320,1141
C10.4(C22×Q8) = C42.274D10φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.4(C2^2xQ8)320,1142
C10.5(C22×Q8) = C2×Dic5.14D4φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.5(C2^2xQ8)320,1153
C10.6(C22×Q8) = C232Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C1080C10.6(C2^2xQ8)320,1155
C10.7(C22×Q8) = C2×C20⋊Q8φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.7(C2^2xQ8)320,1169
C10.8(C22×Q8) = C2×C4.Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.8(C2^2xQ8)320,1171
C10.9(C22×Q8) = C10.12- 1+4φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.9(C2^2xQ8)320,1172
C10.10(C22×Q8) = C42.88D10φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.10(C2^2xQ8)320,1189
C10.11(C22×Q8) = C42.90D10φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.11(C2^2xQ8)320,1191
C10.12(C22×Q8) = D4×Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.12(C2^2xQ8)320,1209
C10.13(C22×Q8) = D45Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.13(C2^2xQ8)320,1211
C10.14(C22×Q8) = D46Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.14(C2^2xQ8)320,1215
C10.15(C22×Q8) = Q8×Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.15(C2^2xQ8)320,1238
C10.16(C22×Q8) = Q85Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.16(C2^2xQ8)320,1241
C10.17(C22×Q8) = Q86Dic10φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.17(C2^2xQ8)320,1242
C10.18(C22×Q8) = C22×C10.D4φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.18(C2^2xQ8)320,1455
C10.19(C22×Q8) = C2×C20.48D4φ: C22×Q8/C22×C4C2 ⊆ Aut C10160C10.19(C2^2xQ8)320,1456
C10.20(C22×Q8) = C22×C4⋊Dic5φ: C22×Q8/C22×C4C2 ⊆ Aut C10320C10.20(C2^2xQ8)320,1457
C10.21(C22×Q8) = C2×Dic53Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.21(C2^2xQ8)320,1168
C10.22(C22×Q8) = C2×Dic5.Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.22(C2^2xQ8)320,1170
C10.23(C22×Q8) = C2×D5×C4⋊C4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.23(C2^2xQ8)320,1173
C10.24(C22×Q8) = C2×D10⋊Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.24(C2^2xQ8)320,1180
C10.25(C22×Q8) = C2×D102Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.25(C2^2xQ8)320,1181
C10.26(C22×Q8) = C10.102+ 1+4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.26(C2^2xQ8)320,1183
C10.27(C22×Q8) = Dic1010Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.27(C2^2xQ8)320,1239
C10.28(C22×Q8) = C4×Q8×D5φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.28(C2^2xQ8)320,1243
C10.29(C22×Q8) = Q8×D20φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.29(C2^2xQ8)320,1247
C10.30(C22×Q8) = C42.232D10φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.30(C2^2xQ8)320,1250
C10.31(C22×Q8) = D2010Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.31(C2^2xQ8)320,1251
C10.32(C22×Q8) = (Q8×Dic5)⋊C2φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.32(C2^2xQ8)320,1294
C10.33(C22×Q8) = C10.502+ 1+4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.33(C2^2xQ8)320,1295
C10.34(C22×Q8) = D5×C22⋊Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C1080C10.34(C2^2xQ8)320,1298
C10.35(C22×Q8) = Dic1021D4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.35(C2^2xQ8)320,1304
C10.36(C22×Q8) = C10.512+ 1+4φ: C22×Q8/C2×Q8C2 ⊆ Aut C1080C10.36(C2^2xQ8)320,1306
C10.37(C22×Q8) = C10.1182+ 1+4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.37(C2^2xQ8)320,1307
C10.38(C22×Q8) = C10.522+ 1+4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.38(C2^2xQ8)320,1308
C10.39(C22×Q8) = Dic107Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.39(C2^2xQ8)320,1357
C10.40(C22×Q8) = D5×C42.C2φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.40(C2^2xQ8)320,1359
C10.41(C22×Q8) = C42.236D10φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.41(C2^2xQ8)320,1360
C10.42(C22×Q8) = C42.148D10φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.42(C2^2xQ8)320,1361
C10.43(C22×Q8) = D207Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.43(C2^2xQ8)320,1362
C10.44(C22×Q8) = Dic108Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.44(C2^2xQ8)320,1393
C10.45(C22×Q8) = Dic109Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.45(C2^2xQ8)320,1394
C10.46(C22×Q8) = D5×C4⋊Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.46(C2^2xQ8)320,1395
C10.47(C22×Q8) = D208Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.47(C2^2xQ8)320,1399
C10.48(C22×Q8) = C42.241D10φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.48(C2^2xQ8)320,1400
C10.49(C22×Q8) = C42.174D10φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.49(C2^2xQ8)320,1401
C10.50(C22×Q8) = D209Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.50(C2^2xQ8)320,1402
C10.51(C22×Q8) = C2×Dic5⋊Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.51(C2^2xQ8)320,1482
C10.52(C22×Q8) = C2×Q8×Dic5φ: C22×Q8/C2×Q8C2 ⊆ Aut C10320C10.52(C2^2xQ8)320,1483
C10.53(C22×Q8) = C2×D103Q8φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.53(C2^2xQ8)320,1485
C10.54(C22×Q8) = Q8×C5⋊D4φ: C22×Q8/C2×Q8C2 ⊆ Aut C10160C10.54(C2^2xQ8)320,1487
C10.55(C22×Q8) = C4⋊C4×C2×C10central extension (φ=1)320C10.55(C2^2xQ8)320,1515
C10.56(C22×Q8) = Q8×C2×C20central extension (φ=1)320C10.56(C2^2xQ8)320,1518
C10.57(C22×Q8) = C10×C22⋊Q8central extension (φ=1)160C10.57(C2^2xQ8)320,1525
C10.58(C22×Q8) = C10×C42.C2central extension (φ=1)320C10.58(C2^2xQ8)320,1529
C10.59(C22×Q8) = C10×C4⋊Q8central extension (φ=1)320C10.59(C2^2xQ8)320,1533
C10.60(C22×Q8) = C5×C23.37C23central extension (φ=1)160C10.60(C2^2xQ8)320,1535
C10.61(C22×Q8) = C5×C232Q8central extension (φ=1)80C10.61(C2^2xQ8)320,1545
C10.62(C22×Q8) = C5×C23.41C23central extension (φ=1)160C10.62(C2^2xQ8)320,1546
C10.63(C22×Q8) = C5×D4×Q8central extension (φ=1)160C10.63(C2^2xQ8)320,1551
C10.64(C22×Q8) = C5×D43Q8central extension (φ=1)160C10.64(C2^2xQ8)320,1556
C10.65(C22×Q8) = C5×Q83Q8central extension (φ=1)320C10.65(C2^2xQ8)320,1559
C10.66(C22×Q8) = C5×Q82central extension (φ=1)320C10.66(C2^2xQ8)320,1560

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