← #13044367
Subgroups — #13044367
Order 1280.
2488 conjugacy classes of subgroups.
The subgroup lattice has 400 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617328 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10617327 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #10617324 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | AGL(1,𝔽5)×#124 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10617223 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10617222 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C22×C22⋊AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 9 | C2×Q8×AGL(1,𝔽5) | C22 | 1 | 3 | yes | complemented |
| 10 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 11 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 12 | C5×H(3,𝔽4) | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #66017 | C4 | 1 | 3 | yes | complemented |
| 14 | #66017 | C4 | 1 | 6 | yes | complemented |
| 15 | D5×#124 | C22 | 1 | 3 | yes | — |
| 16 | D5×#124 | C22 | 1 | 6 | yes | — |
| 17 | #65928 | C4 | 1 | 6 | yes | complemented |
| 18 | D5×#120 | C22 | 1 | 6 | yes | — |
| 19 | #65800 | C22 | 1 | 2 | yes | complemented |
| 20 | (C2×AGL(1,𝔽5))⋊Q8 | C22 | 1 | 3 | yes | complemented |
| 21 | (C2×AGL(1,𝔽5))⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 22 | #65780 | C22 | 1 | 6 | yes | — |
| 23 | #65780 | C22 | 1 | 3 | yes | — |
| 24 | #65779 | C22 | 1 | 12 | yes | — |
| 25 | #65779 | C22 | 1 | 6 | yes | — |
| 26 | #65700 | C22 | 1 | 12 | yes | complemented |
| 27 | #65700 | C22 | 1 | 12 | yes | complemented |
| 28 | #65700 | C22 | 1 | 12 | yes | complemented |
| 29 | #65699 | C22 | 1 | 6 | yes | complemented |
| 30 | #65699 | C22 | 1 | 12 | yes | complemented |
| 31 | C22⋊C4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 32 | C22⋊C4×AGL(1,𝔽5) | C22 | 1 | 12 | yes | complemented |
| 33 | #65689 | C22 | 1 | 3 | yes | complemented |
| 34 | #65688 | C22 | 1 | 2 | yes | complemented |
| 35 | #65686 | C22 | 1 | 6 | yes | complemented |
| 36 | C42×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #34524 | — | 5 | 1 | no | maximal, Sylow |
| 38 | C24×D5 | C23 | 1 | 2 | yes | — |
| 39 | C23×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 40 | C23×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 41 | C2×Q8×D5 | C23 | 1 | 3 | yes | — |
| 42 | C2×D4×D5 | C23 | 1 | 3 | yes | — |
| 43 | C2×D4×D5 | C23 | 1 | 6 | yes | — |
| 44 | C2×C22⋊AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 45 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 12 | yes | — |
| 46 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 47 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 48 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 12 | yes | — |
| 49 | Q8×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 50 | D4×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 51 | D4×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 52 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 53 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 54 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 55 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 56 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 57 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 58 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 59 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 60 | C5×#124 | C2×C4 | 1 | 3 | yes | complemented |
| 61 | C5×#124 | C2×C4 | 1 | 6 | yes | complemented |
| 62 | C5×#120 | C2×C4 | 1 | 6 | yes | complemented |
| 63 | #4099 | C2×C4 | 1 | 6 | yes | complemented |
| 64 | #4093 | C2×C4 | 1 | 3 | yes | complemented |
| 65 | #4093 | C2×C4 | 1 | 6 | yes | complemented |
| 66 | #4083 | C2×C4 | 1 | 6 | yes | complemented |
| 67 | #4083 | C2×C4 | 1 | 12 | yes | complemented |
| 68 | #4082 | C2×C4 | 1 | 3 | yes | complemented |
| 69 | #4082 | C2×C4 | 1 | 6 | yes | complemented |
| 70 | #4031 | C2×C4 | 1 | 12 | yes | complemented |
| 71 | #4031 | C2×C4 | 1 | 12 | yes | complemented |
| 72 | #4031 | C2×C4 | 1 | 12 | yes | complemented |
| 73 | #4028 | C2×C4 | 1 | 12 | yes | complemented |
| 74 | #4028 | C2×C4 | 1 | 6 | yes | complemented |
| 75 | D5×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 76 | D5×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 77 | #4021 | C2×C4 | 1 | 3 | yes | complemented |
| 78 | #4021 | C2×C4 | 1 | 6 | yes | complemented |
| 79 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 80 | C42×D5 | C23 | 1 | 2 | yes | — |
| 81 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 82 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 83 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 12 | yes | — |
| 84 | C2×H(3,𝔽4) | — | 5 | 1 | no | — |
| 85 | #2379 | — | 5 | 3 | no | — |
| 86 | #2372 | — | 5 | 6 | no | — |
| 87 | #2358 | — | 5 | 6 | no | — |
| 88 | #2326 | — | 5 | 6 | no | — |
| 89 | #2321 | — | 5 | 6 | no | — |
| 90 | C4×#124 | — | 5 | 3 | no | — |
| 91 | C24×C5 | C22×C4 | 1 | 2 | yes | — |
| 92 | C23×D5 | — | 4 | 6 | no | — |
| 93 | C23×D5 | — | 4 | 6 | no | — |
| 94 | C23×D5 | C22×C4 | 1 | 6 | yes | — |
| 95 | C23×D5 | C24 | 1 | 6 | yes | — |
| 96 | C22×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 97 | C22×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 98 | C22×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 99 | C22×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 100 | C22×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 101 | C22×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 102 | C22×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 103 | C22×AGL(1,𝔽5) | C24 | 1 | 3 | yes | — |
| 104 | C2×C5×Q8 | C22×C4 | 1 | 3 | yes | — |
| 105 | C2×C5×D4 | C22×C4 | 1 | 3 | yes | — |
| 106 | C2×C5×D4 | C22×C4 | 1 | 6 | yes | — |
| 107 | C2×C22⋊D5 | C22×C4 | 1 | 6 | yes | — |
| 108 | C2×C22⋊D5 | C22×C4 | 1 | 12 | yes | — |
| 109 | Q8×D5 | — | 4 | 3 | no | — |
| 110 | Q8×D5 | — | 4 | 3 | no | — |
| 111 | D4×D5 | — | 4 | 6 | no | — |
| 112 | D4×D5 | — | 4 | 3 | no | — |
| 113 | D4×D5 | — | 4 | 3 | no | — |
| 114 | D4×D5 | — | 4 | 6 | no | — |
| 115 | C2×D20 | C22×C4 | 1 | 3 | yes | — |
| 116 | C2×D20 | C22×C4 | 1 | 6 | yes | — |
| 117 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 118 | C2×C4×D5 | C24 | 1 | 6 | yes | — |
| 119 | C2×Dic10 | C22×C4 | 1 | 3 | yes | — |
| 120 | C2×Dic10 | C22×C4 | 1 | 6 | yes | — |
| 121 | C22⋊AGL(1,𝔽5) | — | 2 | 24 | no | — |
| 122 | C22⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 123 | C22⋊AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 124 | C22⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 125 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 126 | C4⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 127 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 128 | C4⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 129 | C4×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 130 | C4×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 131 | C4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 132 | C4×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 133 | C5×C22⋊C4 | C22×C4 | 1 | 12 | yes | — |
| 134 | C5×C22⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 135 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 136 | C42×C5 | C22×C4 | 1 | 2 | yes | — |
| 137 | C22⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 138 | C22⋊Dic5 | C22×C4 | 1 | 12 | yes | — |
| 139 | #685 | C22×C4 | 1 | 12 | yes | — |
| 140 | #685 | C22×C4 | 1 | 12 | yes | — |
| 141 | #685 | C22×C4 | 1 | 12 | yes | — |
| 142 | C4×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 143 | C4×Dic5 | C22×C4 | 1 | 6 | yes | — |
| 144 | H(3,𝔽4) | — | 5 | 3 | no | — |
| 145 | H(3,𝔽4) | — | 5 | 6 | no | — |
| 146 | H(3,𝔽4) | — | 5 | 6 | no | — |
| 147 | H(3,𝔽4) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 148 | C2×#124 | — | 5 | 6 | no | — |
| 149 | C2×#124 | — | 5 | 3 | no | — |
| 150 | C2×#120 | — | 5 | 6 | no | — |
| 151 | C2×C4×Q8 | — | 5 | 3 | no | — |
| 152 | C2×C4×D4 | — | 5 | 3 | no | — |
| 153 | C2×C4×D4 | — | 5 | 6 | no | — |
| 154 | C22×C22⋊C4 | — | 5 | 6 | no | — |
| 155 | #391 | — | 5 | 6 | no | — |
| 156 | #391 | — | 5 | 3 | no | — |
| 157 | #390 | — | 5 | 6 | no | — |
| 158 | #390 | — | 5 | 3 | no | — |
| 159 | #388 | — | 5 | 12 | no | — |
| 160 | #388 | — | 5 | 12 | no | — |
| 161 | #388 | — | 5 | 12 | no | — |
| 162 | #386 | — | 5 | 12 | no | — |
| 163 | #386 | — | 5 | 6 | no | — |
| 164 | #385 | — | 5 | 6 | no | — |
| 165 | #385 | — | 5 | 12 | no | — |
| 166 | #384 | — | 5 | 2 | no | — |
| 167 | #382 | — | 5 | 3 | no | — |
| 168 | #379 | — | 5 | 2 | no | — |
| 169 | C4×C22⋊C4 | — | 5 | 6 | no | — |
| 170 | C4×C22⋊C4 | — | 5 | 12 | no | — |
| 171 | #376 | — | 5 | 6 | no | — |
| 172 | C43 | — | 5 | 1 | no | — |
| 173 | C23×C5 | — | 4 | 6 | no | — |
| 174 | C23×C5 | C23×C4 | 1 | 6 | yes | — |
| 175 | C22×D5 | — | 2 | 12 | no | — |
| 176 | C22×D5 | — | 2 | 6 | no | — |
| 177 | C22×D5 | — | 2 | 6 | no | — |
| 178 | C22×D5 | — | 2 | 12 | no | — |
| 179 | C22×D5 | — | 4 | 6 | no | — |
| 180 | C22×D5 | — | 4 | 12 | no | — |
| 181 | C22×D5 | — | 8 | 12 | no | — |
| 182 | C22×D5 | — | 8 | 4 | no | — |
| 183 | C22×D5 | C23×C4 | 1 | 6 | yes | — |
| 184 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 185 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 186 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 187 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 188 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 189 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 190 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 191 | C2×AGL(1,𝔽5) | — | 8 | 12 | no | — |
| 192 | C2×AGL(1,𝔽5) | — | 8 | 12 | no | — |
| 193 | C2×AGL(1,𝔽5) | H(5,𝔽2) | 1 | 6 | yes | — |
| 194 | C5×Q8 | — | 4 | 3 | no | — |
| 195 | C5×D4 | — | 4 | 6 | no | — |
| 196 | C5×D4 | — | 4 | 3 | no | — |
| 197 | C2×C4×C5 | C23×C4 | 1 | 3 | yes | — |
| 198 | C2×C4×C5 | C23×C4 | 1 | 6 | yes | — |
| 199 | C22⋊D5 | — | 4 | 12 | no | — |
| 200 | C22⋊D5 | — | 4 | 6 | no | — |
| 201 | C2×Dic5 | C23×C4 | 1 | 3 | yes | — |
| 202 | C2×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 203 | D20 | — | 4 | 6 | no | — |
| 204 | D20 | — | 4 | 3 | no | — |
| 205 | C4×D5 | — | 2 | 3 | no | — |
| 206 | C4×D5 | — | 2 | 6 | no | — |
| 207 | C4×D5 | — | 2 | 3 | no | — |
| 208 | C4×D5 | — | 2 | 6 | no | — |
| 209 | Dic10 | — | 4 | 3 | no | — |
| 210 | Dic10 | — | 4 | 6 | no | — |
| 211 | C25 | — | 5 | 2 | no | — |
| 212 | C22×Q8 | — | 5 | 3 | no | — |
| 213 | C22×D4 | — | 5 | 3 | no | — |
| 214 | C22×D4 | — | 5 | 6 | no | — |
| 215 | C23×C4 | — | 5 | 6 | no | — |
| 216 | C23×C4 | — | 5 | 6 | no | — |
| 217 | #124 | — | 5 | 6 | no | — |
| 218 | #124 | — | 5 | 3 | no | — |
| 219 | #124 | — | 5 | 6 | no | — |
| 220 | #124 | — | 5 | 3 | no | — |
| 221 | #124 | — | 5 | 12 | no | — |
| 222 | #124 | — | 5 | 12 | no | — |
| 223 | #124 | — | 5 | 12 | no | — |
| 224 | #124 | — | 5 | 6 | no | — |
| 225 | #124 | — | 5 | 3 | no | — |
| 226 | #124 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 227 | #124 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 228 | #120 | — | 5 | 6 | no | — |
| 229 | #120 | — | 5 | 6 | no | — |
| 230 | #120 | — | 5 | 12 | no | — |
| 231 | #120 | — | 5 | 12 | no | — |
| 232 | #120 | — | 5 | 6 | no | — |
| 233 | #120 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 234 | C4×Q8 | — | 20 | 6 | no | — |
| 235 | C4×D4 | — | 20 | 12 | no | — |
| 236 | C4×D4 | — | 20 | 6 | no | — |
| 237 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 238 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 239 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 240 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 241 | C2×C22⋊C4 | — | 5 | 6 | no | — |
| 242 | C2×C22⋊C4 | — | 5 | 12 | no | — |
| 243 | C2×C22⋊C4 | — | 5 | 12 | no | — |
| 244 | C2×C22⋊C4 | — | 5 | 12 | no | — |
| 245 | C2×C22⋊C4 | — | 5 | 6 | no | — |
| 246 | C2×C22⋊C4 | — | 5 | 6 | no | — |
| 247 | C2×C22⋊C4 | — | 20 | 12 | no | — |
| 248 | C2×C42 | — | 5 | 1 | no | — |
| 249 | C2×C42 | — | 5 | 2 | no | — |
| 250 | C2×C42 | — | 5 | 3 | no | — |
| 251 | C2×C42 | — | 5 | 6 | no | — |
| 252 | C2×C42 | — | 5 | 3 | no | — |
| 253 | C2×C42 | — | 5 | 6 | no | — |
| 254 | #95 | — | 5 | 12 | no | — |
| 255 | #95 | — | 5 | 12 | no | — |
| 256 | #95 | — | 5 | 12 | no | — |
| 257 | C22×C5 | — | 2 | 12 | no | — |
| 258 | C22×C5 | — | 2 | 6 | no | — |
| 259 | C22×C5 | — | 8 | 4 | no | — |
| 260 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 261 | C2×D5 | — | 2 | 12 | no | — |
| 262 | C2×D5 | — | 2 | 6 | no | — |
| 263 | C2×D5 | — | 4 | 6 | no | — |
| 264 | C2×D5 | — | 4 | 12 | no | — |
| 265 | C2×D5 | — | 4 | 6 | no | — |
| 266 | C2×D5 | — | 8 | 12 | no | — |
| 267 | C2×D5 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 268 | C2×D5 | #585 | 1 | 3 | yes | — |
| 269 | AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 270 | AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 271 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 272 | AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 273 | C4×C5 | — | 2 | 3 | no | — |
| 274 | C4×C5 | — | 2 | 6 | no | — |
| 275 | Dic5 | — | 2 | 3 | no | — |
| 276 | Dic5 | — | 2 | 6 | no | — |
| 277 | C24 | — | 5 | 6 | no | — |
| 278 | C24 | — | 5 | 6 | no | — |
| 279 | C24 | — | 20 | 6 | no | — |
| 280 | C24 | — | 20 | 6 | no | — |
| 281 | C24 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 282 | C2×Q8 | — | 5 | 6 | no | — |
| 283 | C2×Q8 | — | 5 | 3 | no | — |
| 284 | C2×Q8 | — | 20 | 3 | no | — |
| 285 | C2×Q8 | — | 20 | 3 | no | — |
| 286 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 287 | C2×D4 | — | 5 | 12 | no | — |
| 288 | C2×D4 | — | 5 | 6 | no | — |
| 289 | C2×D4 | — | 5 | 6 | no | — |
| 290 | C2×D4 | — | 5 | 3 | no | — |
| 291 | C2×D4 | — | 20 | 6 | no | — |
| 292 | C2×D4 | — | 20 | 3 | no | — |
| 293 | C2×D4 | — | 20 | 3 | no | — |
| 294 | C2×D4 | — | 20 | 6 | no | — |
| 295 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 296 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 297 | C22×C4 | — | 5 | 3 | no | — |
| 298 | C22×C4 | — | 5 | 6 | no | — |
| 299 | C22×C4 | — | 5 | 3 | no | — |
| 300 | C22×C4 | — | 5 | 6 | no | — |
| 301 | C22×C4 | — | 5 | 6 | no | — |
| 302 | C22×C4 | — | 5 | 1 | no | — |
| 303 | C22×C4 | — | 10 | 12 | no | — |
| 304 | C22×C4 | — | 20 | 6 | no | — |
| 305 | C22×C4 | — | 20 | 12 | no | — |
| 306 | C22×C4 | — | 20 | 12 | no | — |
| 307 | C4⋊C4 | — | 20 | 6 | no | — |
| 308 | C4⋊C4 | — | 20 | 3 | no | — |
| 309 | C4⋊C4 | — | 20 | 6 | no | — |
| 310 | C4⋊C4 | — | 20 | 3 | no | — |
| 311 | C22⋊C4 | — | 5 | 6 | no | — |
| 312 | C22⋊C4 | — | 5 | 12 | no | — |
| 313 | C22⋊C4 | — | 5 | 12 | no | — |
| 314 | C22⋊C4 | — | 5 | 12 | no | — |
| 315 | C22⋊C4 | — | 5 | 12 | no | — |
| 316 | C22⋊C4 | — | 10 | 24 | no | — |
| 317 | C22⋊C4 | — | 20 | 12 | no | — |
| 318 | C22⋊C4 | — | 20 | 6 | no | — |
| 319 | C22⋊C4 | — | 20 | 6 | no | — |
| 320 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 321 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 322 | C42 | — | 5 | 3 | no | — |
| 323 | C42 | — | 5 | 6 | no | — |
| 324 | C42 | — | 10 | 6 | no | — |
| 325 | C42 | — | 10 | 12 | no | — |
| 326 | C42 | — | 20 | 3 | no | — |
| 327 | C42 | — | 20 | 6 | no | — |
| 328 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 329 | C42 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 330 | C2×C5 | — | 4 | 6 | no | — |
| 331 | C2×C5 | C4×H(5,𝔽2) | 1 | 3 | yes | — |
| 332 | D5 | — | 4 | 6 | no | — |
| 333 | D5 | #3545 | 1 | 3 | yes | — |
| 334 | D5 | #3549 | 1 | 1 | yes | characteristic |
| 335 | C23 | — | 4 | 6 | no | — |
| 336 | C23 | — | 5 | 1 | no | — |
| 337 | C23 | — | 5 | 6 | no | — |
| 338 | C23 | — | 10 | 12 | no | — |
| 339 | C23 | — | 10 | 6 | no | — |
| 340 | C23 | — | 10 | 6 | no | — |
| 341 | C23 | — | 10 | 12 | no | — |
| 342 | C23 | — | 20 | 12 | no | — |
| 343 | C23 | — | 20 | 6 | no | — |
| 344 | C23 | — | 40 | 4 | no | — |
| 345 | C23 | — | 40 | 12 | no | — |
| 346 | C23 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 347 | Q8 | — | 4 | 3 | no | — |
| 348 | Q8 | — | 20 | 6 | no | — |
| 349 | Q8 | — | 20 | 3 | no | — |
| 350 | D4 | — | 4 | 6 | no | — |
| 351 | D4 | — | 4 | 3 | no | — |
| 352 | D4 | — | 20 | 6 | no | — |
| 353 | D4 | — | 20 | 3 | no | — |
| 354 | D4 | — | 20 | 12 | no | — |
| 355 | D4 | — | 20 | 6 | no | — |
| 356 | C2×C4 | — | 5 | 6 | no | — |
| 357 | C2×C4 | — | 5 | 3 | no | — |
| 358 | C2×C4 | — | 5 | 6 | no | — |
| 359 | C2×C4 | — | 10 | 3 | no | — |
| 360 | C2×C4 | — | 10 | 6 | no | — |
| 361 | C2×C4 | — | 10 | 3 | no | — |
| 362 | C2×C4 | — | 10 | 6 | no | — |
| 363 | C2×C4 | — | 10 | 6 | no | — |
| 364 | C2×C4 | — | 10 | 3 | no | — |
| 365 | C2×C4 | — | 10 | 6 | no | — |
| 366 | C2×C4 | — | 10 | 12 | no | — |
| 367 | C2×C4 | — | 10 | 12 | no | — |
| 368 | C2×C4 | — | 10 | 6 | no | — |
| 369 | C2×C4 | — | 40 | 12 | no | — |
| 370 | C2×C4 | — | 40 | 12 | no | — |
| 371 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 372 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 373 | C5 | #34524 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 374 | C22 | — | 2 | 12 | no | — |
| 375 | C22 | — | 2 | 6 | no | — |
| 376 | C22 | — | 5 | 3 | no | — |
| 377 | C22 | — | 5 | 3 | no | — |
| 378 | C22 | — | 8 | 4 | no | — |
| 379 | C22 | — | 10 | 12 | no | — |
| 380 | C22 | — | 10 | 6 | no | — |
| 381 | C22 | — | 20 | 6 | no | — |
| 382 | C22 | — | 20 | 6 | no | — |
| 383 | C22 | — | 20 | 12 | no | — |
| 384 | C22 | — | 40 | 12 | no | — |
| 385 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 386 | C4 | — | 2 | 3 | no | — |
| 387 | C4 | — | 2 | 6 | no | — |
| 388 | C4 | — | 10 | 6 | no | — |
| 389 | C4 | — | 10 | 3 | no | — |
| 390 | C4 | — | 10 | 6 | no | — |
| 391 | C4 | — | 20 | 6 | no | — |
| 392 | C4 | — | 20 | 6 | no | — |
| 393 | C4 | — | 20 | 1 | no | — |
| 394 | C2 | — | 4 | 6 | no | — |
| 395 | C2 | — | 5 | 3 | no | — |
| 396 | C2 | — | 5 | 1 | no | — |
| 397 | C2 | — | 20 | 6 | no | — |
| 398 | C2 | AGL(1,𝔽5)×H(5,𝔽2) | 1 | 3 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 2. #10617328 | C2 | semidirect |
| 3. #10617327 | C2 | semidirect |
| 4. #10617324 | C2 | semidirect |
| 5. AGL(1,𝔽5)×#124 | C2 | semidirect |
| 6. #10617223 | C2 | semidirect |
| 7. #10617222 | C2 | semidirect |
| 8. C22×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 9. C2×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 12. C5×H(3,𝔽4) | C4 | semidirect |
| 13. #66017 | C4 | semidirect |
| 14. #66017 | C4 | semidirect |
| 17. #65928 | C4 | semidirect |
| 19. #65800 | C22 | semidirect |
| 20. (C2×AGL(1,𝔽5))⋊Q8 | C22 | semidirect |
| 21. (C2×AGL(1,𝔽5))⋊Q8 | C22 | semidirect |
| 26. #65700 | C22 | semidirect |
| 27. #65700 | C22 | semidirect |
| 28. #65700 | C22 | semidirect |
| 29. #65699 | C22 | semidirect |
| 30. #65699 | C22 | semidirect |
| 31. C22⋊C4×AGL(1,𝔽5) | C22 | semidirect |
| 32. C22⋊C4×AGL(1,𝔽5) | C22 | semidirect |
| 33. #65689 | C22 | semidirect |
| 34. #65688 | C22 | semidirect |
| 35. #65686 | C22 | semidirect |
| 36. C42×AGL(1,𝔽5) | C22 | semidirect |
| 60. C5×#124 | C2×C4 | semidirect |
| 61. C5×#124 | C2×C4 | semidirect |
| 62. C5×#120 | C2×C4 | semidirect |
| 63. #4099 | C2×C4 | semidirect |
| 64. #4093 | C2×C4 | semidirect |
| 65. #4093 | C2×C4 | semidirect |
| 66. #4083 | C2×C4 | semidirect |
| 67. #4083 | C2×C4 | semidirect |
| 68. #4082 | C2×C4 | semidirect |
| 69. #4082 | C2×C4 | semidirect |
| 70. #4031 | C2×C4 | semidirect |
| 71. #4031 | C2×C4 | semidirect |
| 72. #4031 | C2×C4 | semidirect |
| 73. #4028 | C2×C4 | semidirect |
| 74. #4028 | C2×C4 | semidirect |
| 77. #4021 | C2×C4 | semidirect |
| 78. #4021 | C2×C4 | semidirect |
| 147. H(3,𝔽4) | AGL(1,𝔽5) | semidirect |
| 226. #124 | C2×AGL(1,𝔽5) | semidirect |
| 227. #124 | C2×AGL(1,𝔽5) | semidirect |
| 233. #120 | C2×AGL(1,𝔽5) | semidirect |
| 373. C5 | #34524 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta