← AGL(1,𝔽5)×#3797 #72230305
Order 2880.
1300 conjugacy classes of subgroups.
The subgroup lattice has 598 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5×#3797 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13088733 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13088693 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C4×C3⋊D3×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×AGL(1,𝔽5)×Dic6 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13088420 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | AGL(1,𝔽5)×#627 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13088407 | C2 | 1 | 2 | yes | maximal |
| 9 | AGL(1,𝔽5)×#624 | C2 | 1 | 2 | yes | maximal |
| 10 | D3×Q8×AGL(1,𝔽5) | — | 3 | 2 | no | maximal |
| 11 | C2×ΓL(1,𝔽16)⋊D3 | C22 | 1 | 2 | yes | — |
| 12 | C2×C3⋊D3×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3⋊D3×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 14 | #10624222 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #10624198 | C4 | 1 | 2 | yes | complemented |
| 16 | C5×#3797 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C4×D5×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×D5×Dic6 | C22 | 1 | 2 | yes | — |
| 19 | C4×C3⋊ΓL(1,𝔽16) | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×C4⋊ΓL(1,𝔽16) | C22 | 1 | 2 | yes | — |
| 21 | C32×C4×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 22 | #10624040 | C4 | 1 | 2 | yes | complemented |
| 23 | #10624039 | C4 | 1 | 2 | yes | complemented |
| 24 | D5×#627 | C22 | 1 | 2 | yes | — |
| 25 | D5×#624 | C22 | 1 | 2 | yes | — |
| 26 | #10623979 | C22 | 1 | 2 | yes | — |
| 27 | Dic3⋊ΓL(1,𝔽16) | C22 | 1 | 4 | yes | — |
| 28 | Dic3×ΓL(1,𝔽16) | C22 | 1 | 4 | yes | — |
| 29 | AGL(1,𝔽5)×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 30 | AGL(1,𝔽5)×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 31 | C3×Dic3⋊AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 32 | C3×Dic3×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 33 | C4×#3797 | — | 5 | 1 | no | maximal, Hall |
| 34 | D3×Q8×D5 | — | 3 | 2 | no | — |
| 35 | Q8×ΓL(1,𝔽16) | — | 3 | 2 | no | — |
| 36 | C3×Q8×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 37 | D3×C4⋊AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 38 | D3×C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 39 | C4×D3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 40 | C4×D3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 41 | C4×D3×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 42 | ΓL(1,𝔽16)⋊Q8 | — | 3 | 2 | no | — |
| 43 | ΓL(1,𝔽16)⋊Q8 | — | 3 | 4 | no | — |
| 44 | AGL(1,𝔽5)×Dic6 | — | 3 | 4 | no | — |
| 45 | AGL(1,𝔽5)×Dic6 | D3 | 1 | 2 | yes | complemented |
| 46 | C2×D5×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C3⋊ΓL(1,𝔽16) | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C3⋊ΓL(1,𝔽16) | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×ΓL(1,𝔽16) | C23 | 1 | 4 | yes | — |
| 50 | C2×C32×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×C32×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 52 | ΓL(1,𝔽16)⋊D3 | — | 2 | 4 | no | — |
| 53 | C3⋊D3×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 54 | C3⋊D3×AGL(1,𝔽5) | Q8 | 1 | 4 | yes | complemented |
| 55 | C4×C3⋊D15 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C4×C5×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C3×Dic30 | C2×C4 | 1 | 2 | yes | complemented |
| 58 | C3×C5×Dic6 | C2×C4 | 1 | 2 | yes | complemented |
| 59 | C32×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 60 | #67158 | C2×C4 | 1 | 2 | yes | complemented |
| 61 | #67155 | C2×C4 | 1 | 2 | yes | — |
| 62 | #67153 | C2×C4 | 1 | 4 | yes | complemented |
| 63 | #67149 | C2×C4 | 1 | 4 | yes | — |
| 64 | C5×#627 | C2×C4 | 1 | 2 | yes | complemented |
| 65 | C5×#624 | C2×C4 | 1 | 2 | yes | — |
| 66 | #67137 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C3⋊D3×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | D5×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 69 | C3×#1204 | C2×C4 | 1 | 4 | yes | complemented |
| 70 | C3×D5×Dic3 | C23 | 1 | 4 | yes | — |
| 71 | C2×Q8×AGL(1,𝔽5) | — | 9 | 1 | no | Hall |
| 72 | C2×#3797 | — | 5 | 1 | no | — |
| 73 | C42×C3⋊D3 | — | 5 | 1 | no | — |
| 74 | C3×C4×Dic6 | — | 5 | 2 | no | — |
| 75 | C4×#627 | — | 5 | 2 | no | — |
| 76 | #63900 | — | 5 | 1 | no | — |
| 77 | #63883 | — | 5 | 2 | no | — |
| 78 | C4×#624 | — | 5 | 2 | no | — |
| 79 | #63843 | — | 5 | 2 | no | — |
| 80 | #63838 | — | 5 | 2 | no | — |
| 81 | C2×D3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 82 | C2×D3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 83 | C2×D3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 84 | C2×D3×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 85 | C2×D3×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 86 | Q8×D15 | — | 3 | 2 | no | — |
| 87 | C5×D3×Q8 | — | 3 | 2 | no | — |
| 88 | C3×Q8×D5 | — | 3 | 2 | no | — |
| 89 | C4×D3×D5 | — | 3 | 2 | no | — |
| 90 | C4×D3×D5 | — | 3 | 4 | no | — |
| 91 | C4×D3×D5 | — | 6 | 1 | no | — |
| 92 | D15⋊Q8 | — | 3 | 2 | no | — |
| 93 | D15⋊Q8 | — | 3 | 4 | no | — |
| 94 | D3×Dic10 | — | 3 | 2 | no | — |
| 95 | D3×Dic10 | — | 3 | 4 | no | — |
| 96 | D5×Dic6 | — | 3 | 4 | no | — |
| 97 | D5×Dic6 | C2×D3 | 1 | 2 | yes | — |
| 98 | C4⋊ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 99 | C4⋊ΓL(1,𝔽16) | C2×D3 | 1 | 2 | yes | — |
| 100 | C4×ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 101 | C4×ΓL(1,𝔽16) | — | 3 | 2 | no | — |
| 102 | C4×ΓL(1,𝔽16) | — | 6 | 1 | no | — |
| 103 | C3×C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 104 | C3×C4⋊AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 105 | C3×C4×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 106 | C3×C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 107 | C3×C4×AGL(1,𝔽5) | C2×D3 | 1 | 2 | yes | — |
| 108 | Dic3⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 109 | Dic3⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 110 | Dic3⋊AGL(1,𝔽5) | C2×D3 | 1 | 4 | yes | — |
| 111 | Dic3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 112 | Dic3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 113 | Dic3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 114 | Dic3×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 115 | Dic3×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 116 | Dic3×AGL(1,𝔽5) | C2×D3 | 1 | 4 | yes | — |
| 117 | C4×D3×Q8 | — | 15 | 2 | no | — |
| 118 | C2×C3⋊D15 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C2×C5×C3⋊D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C2×C32×D5 | C24 | 1 | 1 | yes | characteristic |
| 121 | D5×C3⋊D3 | C2×Q8 | 1 | 2 | yes | — |
| 122 | D5×C3⋊D3 | #41 | 1 | 2 | yes | — |
| 123 | C3⋊ΓL(1,𝔽16) | — | 2 | 1 | no | — |
| 124 | C3⋊ΓL(1,𝔽16) | C2×Q8 | 1 | 2 | yes | complemented |
| 125 | C3×ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 126 | C32×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 127 | C32×AGL(1,𝔽5) | C2×Q8 | 1 | 2 | yes | complemented |
| 128 | C32×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C3⋊Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C5×C3⋊Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C3×Dic15 | C22×C4 | 1 | 4 | yes | — |
| 132 | C3×C5×Dic3 | C22×C4 | 1 | 4 | yes | — |
| 133 | C32×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | C2×Q8×D5 | — | 9 | 1 | no | — |
| 135 | Q8×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 136 | Q8×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 137 | Q8×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 138 | Q8×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 139 | C2×C4⋊AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 140 | C2×C4⋊AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 141 | C2×C4×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 142 | C2×C4×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 143 | C2×C4×C3⋊D3 | — | 5 | 1 | no | — |
| 144 | C2×C4×C3⋊D3 | — | 5 | 1 | no | — |
| 145 | C2×C4×C3⋊D3 | — | 5 | 1 | no | — |
| 146 | C2×C3×Dic6 | — | 5 | 2 | no | — |
| 147 | C2×#627 | — | 5 | 2 | no | — |
| 148 | C2×#624 | — | 5 | 2 | no | — |
| 149 | C2×#624 | — | 5 | 2 | no | — |
| 150 | #3797 | — | 5 | 1 | no | — |
| 151 | #3797 | — | 5 | 2 | no | — |
| 152 | #3797 | — | 5 | 2 | no | — |
| 153 | #3797 | — | 5 | 2 | no | — |
| 154 | #3797 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 155 | C32×C42 | — | 5 | 1 | no | — |
| 156 | C4×C3⋊Dic3 | — | 5 | 1 | no | — |
| 157 | C4×C3⋊Dic3 | — | 5 | 1 | no | — |
| 158 | C4×C3⋊Dic3 | — | 5 | 1 | no | — |
| 159 | C3×C4⋊Dic3 | — | 5 | 2 | no | — |
| 160 | C3×Dic3⋊C4 | — | 5 | 4 | no | — |
| 161 | C3×C4×Dic3 | — | 5 | 4 | no | — |
| 162 | #3724 | — | 5 | 2 | no | — |
| 163 | Dic3⋊Dic3 | — | 5 | 4 | no | — |
| 164 | Dic32 | — | 5 | 4 | no | — |
| 165 | C2×D3×D5 | — | 3 | 2 | no | — |
| 166 | C2×D3×D5 | — | 6 | 1 | no | — |
| 167 | C2×ΓL(1,𝔽16) | — | 3 | 2 | no | — |
| 168 | C2×ΓL(1,𝔽16) | — | 3 | 2 | no | — |
| 169 | C2×ΓL(1,𝔽16) | — | 6 | 1 | no | — |
| 170 | C2×ΓL(1,𝔽16) | — | 6 | 1 | no | — |
| 171 | C2×ΓL(1,𝔽16) | C22×D3 | 1 | 4 | yes | — |
| 172 | C2×C3×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 173 | C2×C3×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 174 | C2×C3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 175 | C2×C3×AGL(1,𝔽5) | C22×D3 | 1 | 2 | yes | — |
| 176 | C2×C3×AGL(1,𝔽5) | C22×D3 | 1 | 2 | yes | — |
| 177 | D3×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 178 | D3×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 179 | D3×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 180 | D3×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 181 | D3×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 182 | D3×AGL(1,𝔽5) | — | 6 | 8 | no | — |
| 183 | C3×C5×Q8 | — | 3 | 2 | no | — |
| 184 | C4×D15 | — | 3 | 2 | no | — |
| 185 | C4×D15 | — | 3 | 4 | no | — |
| 186 | C4×D15 | — | 6 | 1 | no | — |
| 187 | Dic30 | — | 3 | 4 | no | — |
| 188 | Dic30 | C4×D3 | 1 | 2 | yes | complemented |
| 189 | C4×C5×D3 | — | 3 | 2 | no | — |
| 190 | C4×C5×D3 | — | 3 | 4 | no | — |
| 191 | C4×C5×D3 | — | 6 | 1 | no | — |
| 192 | C5×Dic6 | — | 3 | 4 | no | — |
| 193 | C5×Dic6 | C4×D3 | 1 | 2 | yes | complemented |
| 194 | C3×C4×D5 | — | 2 | 1 | no | — |
| 195 | C3×C4×D5 | — | 3 | 4 | no | — |
| 196 | C3×C4×D5 | C22×D3 | 1 | 2 | yes | — |
| 197 | C3×Dic10 | — | 3 | 2 | no | — |
| 198 | C3×Dic10 | — | 3 | 4 | no | — |
| 199 | #1204 | — | 3 | 4 | no | — |
| 200 | #1204 | — | 3 | 4 | no | — |
| 201 | #1204 | C4×D3 | 1 | 4 | yes | complemented |
| 202 | #1200 | — | 3 | 2 | no | — |
| 203 | #1200 | — | 3 | 4 | no | — |
| 204 | #1200 | — | 6 | 1 | no | — |
| 205 | D3×Dic5 | — | 3 | 4 | no | — |
| 206 | D3×Dic5 | — | 3 | 2 | no | — |
| 207 | D3×Dic5 | — | 6 | 1 | no | — |
| 208 | D5×Dic3 | — | 3 | 2 | no | — |
| 209 | D5×Dic3 | — | 6 | 1 | no | — |
| 210 | D5×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 211 | C2×D3×Q8 | — | 15 | 2 | no | — |
| 212 | C3×C4×Q8 | — | 15 | 2 | no | — |
| 213 | Q8×Dic3 | — | 15 | 2 | no | — |
| 214 | D3×C4⋊C4 | — | 15 | 4 | no | — |
| 215 | D3×C4⋊C4 | — | 15 | 2 | no | — |
| 216 | #887 | — | 15 | 4 | no | — |
| 217 | #887 | — | 15 | 2 | no | — |
| 218 | C42×D3 | — | 15 | 4 | no | — |
| 219 | C42×D3 | — | 15 | 2 | no | — |
| 220 | C42×D3 | — | 30 | 1 | no | — |
| 221 | C4×Dic6 | — | 5 | 2 | no | — |
| 222 | C4×Dic6 | — | 15 | 4 | no | — |
| 223 | C2×C32×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 224 | C3⋊D15 | C4×Q8 | 1 | 2 | yes | complemented |
| 225 | C5×C3⋊D3 | C4×Q8 | 1 | 2 | yes | complemented |
| 226 | C32×D5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 227 | C32×D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 228 | C22×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 229 | C22×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 230 | C22×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 231 | C2×C5×Q8 | — | 9 | 1 | no | — |
| 232 | Q8×D5 | — | 3 | 2 | no | — |
| 233 | Q8×D5 | — | 9 | 2 | no | — |
| 234 | Q8×D5 | — | 9 | 2 | no | — |
| 235 | Q8×D5 | — | 9 | 2 | no | — |
| 236 | C2×C4×D5 | — | 9 | 2 | no | — |
| 237 | C2×C4×D5 | — | 9 | 1 | no | — |
| 238 | C2×Dic10 | — | 9 | 1 | no | — |
| 239 | C2×Dic10 | — | 9 | 2 | no | — |
| 240 | C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 241 | C4⋊AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 242 | C4⋊AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 243 | C4⋊AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 244 | C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 245 | C4×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 246 | C4×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 247 | C4×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 248 | C4×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 249 | C4×AGL(1,𝔽5) | D32 | 1 | 1 | yes | characteristic |
| 250 | C22×C3⋊D3 | — | 5 | 1 | no | — |
| 251 | C2×C32×C4 | — | 5 | 1 | no | — |
| 252 | C2×C32×C4 | — | 5 | 1 | no | — |
| 253 | C2×C32×C4 | — | 5 | 1 | no | — |
| 254 | C2×C3⋊Dic3 | — | 5 | 1 | no | — |
| 255 | C2×C3⋊Dic3 | — | 5 | 1 | no | — |
| 256 | C2×C3⋊Dic3 | — | 5 | 1 | no | — |
| 257 | C4×C3⋊D3 | — | 5 | 4 | no | — |
| 258 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 259 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 260 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 261 | C4×C3⋊D3 | — | 10 | 2 | no | — |
| 262 | C4×C3⋊D3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 263 | C2×C3×Dic3 | — | 5 | 4 | no | — |
| 264 | C2×C3×Dic3 | — | 5 | 4 | no | — |
| 265 | C3×Dic6 | — | 5 | 2 | no | — |
| 266 | C3×Dic6 | — | 5 | 4 | no | — |
| 267 | C3×Dic6 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 268 | #627 | — | 5 | 2 | no | — |
| 269 | #627 | — | 5 | 4 | no | — |
| 270 | #627 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 271 | #624 | — | 5 | 2 | no | — |
| 272 | #624 | — | 5 | 4 | no | — |
| 273 | #624 | — | 10 | 4 | no | — |
| 274 | #624 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 275 | C2×C4×Q8 | — | 45 | 1 | no | Sylow |
| 276 | C2×D15 | — | 3 | 2 | no | — |
| 277 | C2×D15 | — | 6 | 1 | no | — |
| 278 | C2×C5×D3 | — | 3 | 2 | no | — |
| 279 | C2×C5×D3 | — | 6 | 1 | no | — |
| 280 | C2×C3×D5 | — | 2 | 1 | no | — |
| 281 | C2×C3×D5 | C23×D3 | 1 | 2 | yes | — |
| 282 | D3×D5 | — | 3 | 4 | no | — |
| 283 | D3×D5 | — | 3 | 4 | no | — |
| 284 | D3×D5 | — | 6 | 2 | no | — |
| 285 | D3×D5 | — | 6 | 2 | no | — |
| 286 | ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 287 | ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 288 | ΓL(1,𝔽16) | — | 6 | 2 | no | — |
| 289 | ΓL(1,𝔽16) | — | 6 | 1 | no | — |
| 290 | ΓL(1,𝔽16) | — | 6 | 1 | no | — |
| 291 | ΓL(1,𝔽16) | — | 6 | 2 | no | — |
| 292 | C3×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 293 | C3×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 294 | C3×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 295 | C3×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 296 | C3×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 297 | C3×AGL(1,𝔽5) | D3×Q8 | 1 | 4 | yes | complemented |
| 298 | C3×C4×C5 | — | 2 | 1 | no | — |
| 299 | C3×C4×C5 | — | 3 | 4 | no | — |
| 300 | C3×C4×C5 | C2×C4×D3 | 1 | 2 | yes | — |
| 301 | Dic15 | — | 3 | 2 | no | — |
| 302 | Dic15 | — | 6 | 1 | no | — |
| 303 | Dic15 | C2×C4×D3 | 1 | 4 | yes | — |
| 304 | C3×Dic5 | — | 2 | 1 | no | — |
| 305 | C3×Dic5 | — | 3 | 4 | no | — |
| 306 | C3×Dic5 | C2×C4×D3 | 1 | 2 | yes | — |
| 307 | C5×Dic3 | — | 3 | 2 | no | — |
| 308 | C5×Dic3 | — | 6 | 1 | no | — |
| 309 | C5×Dic3 | C2×C4×D3 | 1 | 4 | yes | — |
| 310 | C2×C3×Q8 | — | 15 | 2 | no | — |
| 311 | D3×Q8 | — | 3 | 2 | no | — |
| 312 | D3×Q8 | — | 15 | 4 | no | — |
| 313 | D3×Q8 | — | 15 | 2 | no | — |
| 314 | D3×Q8 | — | 15 | 4 | no | — |
| 315 | D3×Q8 | — | 15 | 2 | no | — |
| 316 | D3×Q8 | — | 15 | 2 | no | — |
| 317 | C2×C4×D3 | — | 15 | 4 | no | — |
| 318 | C2×C4×D3 | — | 15 | 2 | no | — |
| 319 | C2×C4×D3 | — | 15 | 2 | no | — |
| 320 | C2×C4×D3 | — | 15 | 4 | no | — |
| 321 | C2×C4×D3 | — | 15 | 2 | no | — |
| 322 | C2×C4×D3 | — | 30 | 1 | no | — |
| 323 | C2×C4×D3 | — | 30 | 1 | no | — |
| 324 | C2×C4×D3 | — | 30 | 1 | no | — |
| 325 | C2×Dic6 | — | 5 | 2 | no | — |
| 326 | C2×Dic6 | — | 15 | 4 | no | — |
| 327 | C3×C4⋊C4 | — | 15 | 4 | no | — |
| 328 | C3×C4⋊C4 | — | 15 | 2 | no | — |
| 329 | C3×C42 | — | 5 | 2 | no | — |
| 330 | C3×C42 | — | 10 | 1 | no | — |
| 331 | C3×C42 | — | 15 | 4 | no | — |
| 332 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 333 | C4⋊Dic3 | — | 15 | 4 | no | — |
| 334 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 335 | Dic3⋊C4 | — | 15 | 4 | no | — |
| 336 | Dic3⋊C4 | — | 15 | 4 | no | — |
| 337 | C4×Dic3 | — | 5 | 4 | no | — |
| 338 | C4×Dic3 | — | 15 | 4 | no | — |
| 339 | C4×Dic3 | — | 15 | 4 | no | — |
| 340 | C4×Dic3 | — | 15 | 2 | no | — |
| 341 | C4×Dic3 | — | 15 | 2 | no | — |
| 342 | C4×Dic3 | — | 15 | 2 | no | — |
| 343 | C4×Dic3 | — | 30 | 1 | no | — |
| 344 | C4×Dic3 | — | 30 | 1 | no | — |
| 345 | C4×Dic3 | — | 30 | 1 | no | — |
| 346 | C32×C5 | C2×C4×Q8 | 1 | 1 | yes | characteristic, complemented, Hall |
| 347 | C22×D5 | — | 9 | 1 | no | — |
| 348 | C2×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 349 | C2×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 350 | C2×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 351 | C2×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 352 | C2×AGL(1,𝔽5) | — | 18 | 2 | no | — |
| 353 | C2×AGL(1,𝔽5) | — | 18 | 4 | no | — |
| 354 | C2×AGL(1,𝔽5) | C2×D32 | 1 | 1 | yes | characteristic |
| 355 | C2×AGL(1,𝔽5) | C2×D32 | 1 | 1 | yes | characteristic |
| 356 | C5×Q8 | — | 3 | 2 | no | — |
| 357 | C5×Q8 | — | 9 | 2 | no | — |
| 358 | C2×C4×C5 | — | 9 | 2 | no | — |
| 359 | C2×C4×C5 | — | 9 | 1 | no | — |
| 360 | C2×Dic5 | — | 9 | 2 | no | — |
| 361 | C2×Dic5 | — | 9 | 1 | no | — |
| 362 | C4×D5 | — | 3 | 4 | no | — |
| 363 | C4×D5 | — | 9 | 4 | no | — |
| 364 | C4×D5 | — | 9 | 1 | no | — |
| 365 | C4×D5 | — | 9 | 1 | no | — |
| 366 | C4×D5 | — | 9 | 1 | no | — |
| 367 | C4×D5 | C2×D32 | 1 | 1 | yes | characteristic |
| 368 | Dic10 | — | 3 | 2 | no | — |
| 369 | Dic10 | — | 3 | 4 | no | — |
| 370 | Dic10 | — | 9 | 2 | no | — |
| 371 | Dic10 | — | 9 | 4 | no | — |
| 372 | C22×C32 | — | 5 | 1 | no | — |
| 373 | C2×C3⋊D3 | — | 5 | 1 | no | — |
| 374 | C2×C3⋊D3 | — | 5 | 2 | no | — |
| 375 | C2×C3⋊D3 | — | 5 | 2 | no | — |
| 376 | C2×C3⋊D3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 377 | C32×C4 | — | 5 | 2 | no | — |
| 378 | C32×C4 | — | 5 | 1 | no | — |
| 379 | C32×C4 | — | 10 | 1 | no | — |
| 380 | C32×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 381 | C3⋊Dic3 | — | 5 | 2 | no | — |
| 382 | C3⋊Dic3 | — | 5 | 1 | no | — |
| 383 | C3⋊Dic3 | — | 10 | 1 | no | — |
| 384 | C3⋊Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 385 | C3×Dic3 | — | 5 | 4 | no | — |
| 386 | C3×Dic3 | — | 10 | 4 | no | — |
| 387 | C3×Dic3 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 388 | C22×Q8 | — | 45 | 1 | no | — |
| 389 | C4×Q8 | — | 15 | 2 | no | — |
| 390 | C4×Q8 | — | 45 | 2 | no | — |
| 391 | C4×Q8 | — | 45 | 2 | no | — |
| 392 | C4×Q8 | — | 45 | 2 | no | — |
| 393 | C2×C4⋊C4 | — | 45 | 2 | no | — |
| 394 | C2×C4⋊C4 | — | 45 | 1 | no | — |
| 395 | C2×C42 | — | 45 | 1 | no | — |
| 396 | C2×C42 | — | 45 | 2 | no | — |
| 397 | C2×C3×C5 | — | 2 | 1 | no | — |
| 398 | C2×C3×C5 | C22×C4×D3 | 1 | 2 | yes | — |
| 399 | D15 | — | 3 | 4 | no | — |
| 400 | D15 | — | 6 | 2 | no | — |
| 401 | C3×D5 | — | 2 | 1 | no | — |
| 402 | C3×D5 | — | 2 | 1 | no | — |
| 403 | C3×D5 | C2×D3×Q8 | 1 | 2 | yes | — |
| 404 | C3×D5 | D3×#41 | 1 | 2 | yes | — |
| 405 | C5×D3 | — | 3 | 4 | no | — |
| 406 | C5×D3 | — | 6 | 2 | no | — |
| 407 | C22×D3 | — | 15 | 2 | no | — |
| 408 | C22×D3 | — | 30 | 1 | no | — |
| 409 | C3×Q8 | — | 3 | 2 | no | — |
| 410 | C3×Q8 | — | 15 | 4 | no | — |
| 411 | C3×Q8 | — | 15 | 2 | no | — |
| 412 | C2×C3×C4 | — | 5 | 2 | no | — |
| 413 | C2×C3×C4 | — | 5 | 2 | no | — |
| 414 | C2×C3×C4 | — | 5 | 2 | no | — |
| 415 | C2×C3×C4 | — | 10 | 1 | no | — |
| 416 | C2×C3×C4 | — | 10 | 1 | no | — |
| 417 | C2×C3×C4 | — | 10 | 1 | no | — |
| 418 | C2×C3×C4 | — | 15 | 4 | no | — |
| 419 | C2×C3×C4 | — | 15 | 4 | no | — |
| 420 | C2×Dic3 | — | 5 | 4 | no | — |
| 421 | C2×Dic3 | — | 5 | 4 | no | — |
| 422 | C2×Dic3 | — | 15 | 2 | no | — |
| 423 | C2×Dic3 | — | 15 | 2 | no | — |
| 424 | C2×Dic3 | — | 15 | 2 | no | — |
| 425 | C2×Dic3 | — | 30 | 1 | no | — |
| 426 | C2×Dic3 | — | 30 | 1 | no | — |
| 427 | C2×Dic3 | — | 30 | 1 | no | — |
| 428 | C4×D3 | — | 3 | 2 | no | — |
| 429 | C4×D3 | — | 3 | 4 | no | — |
| 430 | C4×D3 | — | 6 | 1 | no | — |
| 431 | C4×D3 | — | 15 | 2 | no | — |
| 432 | C4×D3 | — | 15 | 4 | no | — |
| 433 | C4×D3 | — | 15 | 4 | no | — |
| 434 | C4×D3 | — | 15 | 2 | no | — |
| 435 | C4×D3 | — | 15 | 8 | no | — |
| 436 | C4×D3 | — | 15 | 2 | no | — |
| 437 | C4×D3 | — | 15 | 4 | no | — |
| 438 | C4×D3 | — | 30 | 1 | no | — |
| 439 | C4×D3 | — | 30 | 1 | no | — |
| 440 | C4×D3 | — | 30 | 1 | no | — |
| 441 | C4×D3 | — | 30 | 4 | no | — |
| 442 | C4×D3 | — | 30 | 8 | no | — |
| 443 | C4×D3 | — | 30 | 4 | no | — |
| 444 | C4×D3 | — | 30 | 2 | no | — |
| 445 | C4×D3 | — | 30 | 2 | no | — |
| 446 | Dic6 | — | 3 | 4 | no | — |
| 447 | Dic6 | — | 5 | 2 | no | — |
| 448 | Dic6 | — | 5 | 4 | no | — |
| 449 | Dic6 | — | 15 | 4 | no | — |
| 450 | Dic6 | — | 15 | 4 | no | — |
| 451 | Dic6 | — | 15 | 4 | no | — |
| 452 | Dic6 | D3×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 453 | C22×C5 | — | 9 | 1 | no | — |
| 454 | C2×D5 | — | 9 | 1 | no | — |
| 455 | C2×D5 | — | 9 | 2 | no | — |
| 456 | C2×D5 | — | 9 | 2 | no | — |
| 457 | C2×D5 | C22×D32 | 1 | 1 | yes | characteristic |
| 458 | AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 459 | AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 460 | AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 461 | AGL(1,𝔽5) | — | 18 | 1 | no | — |
| 462 | AGL(1,𝔽5) | #3797 | 1 | 2 | yes | direct product factor |
| 463 | C4×C5 | — | 3 | 4 | no | — |
| 464 | C4×C5 | — | 9 | 1 | no | — |
| 465 | C4×C5 | C4×D32 | 1 | 1 | yes | characteristic |
| 466 | Dic5 | — | 3 | 4 | no | — |
| 467 | Dic5 | — | 9 | 1 | no | — |
| 468 | Dic5 | C4×D32 | 1 | 1 | yes | characteristic |
| 469 | C2×C32 | — | 5 | 1 | no | — |
| 470 | C2×C32 | — | 5 | 1 | no | — |
| 471 | C2×C32 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 472 | C3⋊D3 | — | 5 | 2 | no | — |
| 473 | C3⋊D3 | Q8×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 474 | C2×Q8 | — | 9 | 1 | no | — |
| 475 | C2×Q8 | — | 15 | 2 | no | — |
| 476 | C2×Q8 | — | 45 | 2 | no | — |
| 477 | C2×Q8 | — | 45 | 1 | no | — |
| 478 | C2×Q8 | — | 45 | 2 | no | — |
| 479 | C2×Q8 | — | 45 | 2 | no | — |
| 480 | C2×Q8 | — | 45 | 2 | no | — |
| 481 | C22×C4 | — | 45 | 1 | no | — |
| 482 | C22×C4 | — | 45 | 1 | no | — |
| 483 | C22×C4 | — | 45 | 1 | no | — |
| 484 | C22×C4 | — | 45 | 2 | no | — |
| 485 | C22×C4 | — | 45 | 2 | no | — |
| 486 | C4⋊C4 | — | 15 | 4 | no | — |
| 487 | C4⋊C4 | — | 15 | 2 | no | — |
| 488 | C4⋊C4 | — | 45 | 2 | no | — |
| 489 | C4⋊C4 | — | 45 | 4 | no | — |
| 490 | C42 | — | 5 | 1 | no | — |
| 491 | C42 | — | 15 | 4 | no | — |
| 492 | C42 | — | 45 | 1 | no | — |
| 493 | C42 | — | 45 | 1 | no | — |
| 494 | C42 | — | 45 | 1 | no | — |
| 495 | C42 | — | 45 | 4 | no | — |
| 496 | C3×C5 | — | 2 | 1 | no | — |
| 497 | C3×C5 | C4×D3×Q8 | 1 | 2 | yes | complemented |
| 498 | C22×C3 | — | 5 | 2 | no | — |
| 499 | C22×C3 | — | 10 | 1 | no | — |
| 500 | C2×D3 | — | 3 | 2 | no | — |
| 501 | C2×D3 | — | 6 | 1 | no | — |
| 502 | C2×D3 | — | 15 | 4 | no | — |
| 503 | C2×D3 | — | 15 | 4 | no | — |
| 504 | C2×D3 | — | 15 | 2 | no | — |
| 505 | C2×D3 | — | 30 | 2 | no | — |
| 506 | C2×D3 | — | 30 | 2 | no | — |
| 507 | C2×D3 | — | 30 | 1 | no | — |
| 508 | C3×C4 | — | 2 | 1 | no | — |
| 509 | C3×C4 | — | 3 | 4 | no | — |
| 510 | C3×C4 | — | 5 | 4 | no | — |
| 511 | C3×C4 | — | 5 | 2 | no | — |
| 512 | C3×C4 | — | 10 | 1 | no | — |
| 513 | C3×C4 | — | 10 | 2 | no | — |
| 514 | C3×C4 | — | 10 | 2 | no | — |
| 515 | C3×C4 | — | 10 | 1 | no | — |
| 516 | C3×C4 | — | 10 | 1 | no | — |
| 517 | C3×C4 | — | 15 | 4 | no | — |
| 518 | C3×C4 | — | 30 | 4 | no | — |
| 519 | C3×C4 | C2×D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 520 | Dic3 | — | 3 | 2 | no | — |
| 521 | Dic3 | — | 5 | 4 | no | — |
| 522 | Dic3 | — | 6 | 1 | no | — |
| 523 | Dic3 | — | 10 | 4 | no | — |
| 524 | Dic3 | — | 15 | 4 | no | — |
| 525 | Dic3 | — | 15 | 2 | no | — |
| 526 | Dic3 | — | 30 | 1 | no | — |
| 527 | Dic3 | — | 30 | 2 | no | — |
| 528 | Dic3 | — | 30 | 2 | no | — |
| 529 | Dic3 | — | 30 | 1 | no | — |
| 530 | Dic3 | — | 30 | 1 | no | — |
| 531 | Dic3 | C2×D3×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 532 | C2×C5 | — | 9 | 2 | no | — |
| 533 | C2×C5 | C2×C4×D32 | 1 | 1 | yes | characteristic |
| 534 | D5 | — | 9 | 2 | no | — |
| 535 | D5 | C2×#3797 | 1 | 1 | yes | characteristic |
| 536 | D5 | #64306 | 1 | 1 | yes | characteristic |
| 537 | C32 | C2×Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 538 | C23 | — | 45 | 1 | no | — |
| 539 | Q8 | — | 3 | 2 | no | — |
| 540 | Q8 | — | 9 | 2 | no | — |
| 541 | Q8 | — | 15 | 4 | no | — |
| 542 | Q8 | — | 15 | 2 | no | — |
| 543 | Q8 | — | 45 | 4 | no | — |
| 544 | Q8 | — | 45 | 2 | no | — |
| 545 | C2×C4 | — | 5 | 1 | no | — |
| 546 | C2×C4 | — | 5 | 1 | no | — |
| 547 | C2×C4 | — | 5 | 1 | no | — |
| 548 | C2×C4 | — | 9 | 2 | no | — |
| 549 | C2×C4 | — | 9 | 1 | no | — |
| 550 | C2×C4 | — | 15 | 4 | no | — |
| 551 | C2×C4 | — | 15 | 4 | no | — |
| 552 | C2×C4 | — | 45 | 4 | no | — |
| 553 | C2×C4 | — | 45 | 1 | no | — |
| 554 | C2×C4 | — | 45 | 1 | no | — |
| 555 | C2×C4 | — | 45 | 4 | no | — |
| 556 | C2×C4 | — | 45 | 1 | no | — |
| 557 | C2×C4 | — | 45 | 2 | no | — |
| 558 | C2×C4 | — | 45 | 1 | no | — |
| 559 | C2×C4 | — | 45 | 1 | no | — |
| 560 | C2×C4 | — | 45 | 1 | no | — |
| 561 | C2×C4 | — | 90 | 2 | no | — |
| 562 | C2×C4 | — | 90 | 4 | no | — |
| 563 | C2×C3 | — | 2 | 1 | no | — |
| 564 | C2×C3 | — | 5 | 2 | no | — |
| 565 | C2×C3 | — | 5 | 2 | no | — |
| 566 | C2×C3 | — | 10 | 1 | no | — |
| 567 | C2×C3 | — | 10 | 1 | no | — |
| 568 | C2×C3 | C22×D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 569 | D3 | — | 3 | 4 | no | — |
| 570 | D3 | — | 6 | 2 | no | — |
| 571 | D3 | — | 15 | 4 | no | — |
| 572 | D3 | — | 30 | 2 | no | — |
| 573 | C5 | C4×#3797 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 574 | C22 | — | 5 | 1 | no | — |
| 575 | C22 | — | 9 | 1 | no | — |
| 576 | C22 | — | 45 | 2 | no | — |
| 577 | C22 | — | 45 | 2 | no | — |
| 578 | C22 | — | 45 | 1 | no | — |
| 579 | C4 | — | 3 | 4 | no | — |
| 580 | C4 | — | 5 | 2 | no | — |
| 581 | C4 | — | 5 | 1 | no | — |
| 582 | C4 | — | 9 | 1 | no | — |
| 583 | C4 | — | 10 | 1 | no | — |
| 584 | C4 | — | 15 | 4 | no | — |
| 585 | C4 | — | 30 | 4 | no | — |
| 586 | C4 | — | 45 | 2 | no | — |
| 587 | C4 | — | 45 | 1 | no | — |
| 588 | C4 | — | 90 | 1 | no | — |
| 589 | C4 | D32×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 590 | C3 | — | 2 | 1 | no | — |
| 591 | C3 | D3×Q8×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 592 | C2 | — | 5 | 1 | no | — |
| 593 | C2 | — | 5 | 1 | no | — |
| 594 | C2 | — | 9 | 2 | no | — |
| 595 | C2 | — | 45 | 2 | no | — |
| 596 | C2 | C2×D32×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 3. #13088693 | C2 | semidirect |
| 5. C3×AGL(1,𝔽5)×Dic6 | C2 | semidirect |
| 6. #13088420 | C2 | semidirect |
| 7. AGL(1,𝔽5)×#627 | C2 | semidirect |
| 14. #10624222 | C4 | semidirect |
| 15. #10624198 | C4 | semidirect |
| 16. C5×#3797 | C4 | semidirect |
| 22. #10624040 | C4 | semidirect |
| 23. #10624039 | C4 | semidirect |
| 45. AGL(1,𝔽5)×Dic6 | D3 | semidirect |
| 54. C3⋊D3×AGL(1,𝔽5) | Q8 | semidirect |
| 57. C3×Dic30 | C2×C4 | semidirect |
| 58. C3×C5×Dic6 | C2×C4 | semidirect |
| 60. #67158 | C2×C4 | semidirect |
| 62. #67153 | C2×C4 | semidirect |
| 64. C5×#627 | C2×C4 | semidirect |
| 69. C3×#1204 | C2×C4 | semidirect |
| 124. C3⋊ΓL(1,𝔽16) | C2×Q8 | semidirect |
| 127. C32×AGL(1,𝔽5) | C2×Q8 | semidirect |
| 154. #3797 | AGL(1,𝔽5) | direct (N × H) |
| 188. Dic30 | C4×D3 | semidirect |
| 193. C5×Dic6 | C4×D3 | semidirect |
| 201. #1204 | C4×D3 | semidirect |
| 224. C3⋊D15 | C4×Q8 | semidirect |
| 225. C5×C3⋊D3 | C4×Q8 | semidirect |
| 267. C3×Dic6 | C2×AGL(1,𝔽5) | semidirect |
| 270. #627 | C2×AGL(1,𝔽5) | semidirect |
| 297. C3×AGL(1,𝔽5) | D3×Q8 | semidirect |
| 346. C32×C5 | C2×C4×Q8 | semidirect |
| 452. Dic6 | D3×AGL(1,𝔽5) | semidirect |
| 462. AGL(1,𝔽5) | #3797 | direct (N × H) |
| 473. C3⋊D3 | Q8×AGL(1,𝔽5) | semidirect |
| 497. C3×C5 | C4×D3×Q8 | semidirect |
| 537. C32 | C2×Q8×AGL(1,𝔽5) | semidirect |
| 573. C5 | C4×#3797 | semidirect |
| 591. C3 | D3×Q8×AGL(1,𝔽5) | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta