← #14439867
Subgroups — #14439867
Order 1920.
712 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C5×#5517 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11754616 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11751099 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#65287 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11748469 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11748458 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C2×Dic3×#168 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11747149 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11747148 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11747147 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11747146 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10615070 | — | 3 | 1 | no | maximal, Hall |
| 13 | C3×C5×#117 | C22 | 1 | 1 | yes | characteristic |
| 14 | #91815 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C3⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 16 | C5×#926 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×C5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#890 | C22 | 1 | 2 | yes | — |
| 19 | C5×#888 | C22 | 1 | 2 | yes | — |
| 20 | C5×#878 | — | 2 | 2 | no | — |
| 21 | C4×C5×Dic6 | — | 2 | 2 | no | — |
| 22 | C3×#4072 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×C3×#168 | C22 | 1 | 1 | yes | characteristic |
| 24 | #91575 | — | 2 | 2 | no | — |
| 25 | #91469 | C22 | 1 | 2 | yes | — |
| 26 | C4×#1204 | — | 2 | 2 | no | — |
| 27 | #91381 | C22 | 1 | 2 | yes | — |
| 28 | #91092 | C22 | 1 | 2 | yes | — |
| 29 | #91091 | C22 | 1 | 2 | yes | — |
| 30 | C3×#3940 | C22 | 1 | 2 | yes | — |
| 31 | C3×#3939 | C22 | 1 | 2 | yes | — |
| 32 | #90989 | C22 | 1 | 2 | yes | — |
| 33 | #90988 | C22 | 1 | 2 | yes | — |
| 34 | #90986 | C22 | 1 | 2 | yes | — |
| 35 | #90985 | C22 | 1 | 2 | yes | — |
| 36 | Dic3×#168 | C22 | 1 | 1 | yes | characteristic |
| 37 | Dic3×#168 | C22 | 1 | 1 | yes | characteristic |
| 38 | Dic3×#168 | C22 | 1 | 1 | yes | characteristic |
| 39 | Dic3×#168 | C22 | 1 | 1 | yes | characteristic |
| 40 | #79170 | — | 5 | 1 | no | maximal, Hall |
| 41 | C5×#533 | — | 3 | 1 | no | — |
| 42 | #65804 | — | 3 | 1 | no | — |
| 43 | #65368 | — | 3 | 2 | no | — |
| 44 | #65367 | — | 3 | 2 | no | — |
| 45 | #65353 | — | 3 | 2 | no | — |
| 46 | #65353 | — | 3 | 2 | no | — |
| 47 | #65287 | — | 3 | 1 | no | — |
| 48 | #65287 | — | 3 | 1 | no | — |
| 49 | #65287 | — | 3 | 1 | no | — |
| 50 | #65287 | D3 | 1 | 1 | yes | characteristic |
| 51 | C2×C4×#168 | — | 3 | 1 | no | — |
| 52 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C5×Dic3 | D4 | 1 | 2 | yes | — |
| 54 | C2×C5×Dic6 | — | 2 | 2 | no | — |
| 55 | C2×#1204 | — | 2 | 2 | no | — |
| 56 | C3×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 57 | C3×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 58 | C3×C42×C5 | — | 2 | 1 | no | — |
| 59 | #6719 | — | 2 | 1 | no | — |
| 60 | C4⋊Dic15 | C23 | 1 | 2 | yes | — |
| 61 | C4×Dic15 | — | 2 | 1 | no | — |
| 62 | C2×C3⋊#168 | Q8 | 1 | 4 | yes | complemented |
| 63 | C2×C3⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C3⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 65 | C5×#217 | — | 2 | 1 | no | — |
| 66 | C5×C4⋊Dic3 | — | 2 | 2 | no | — |
| 67 | C5×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 68 | C5×Dic3⋊C4 | — | 2 | 2 | no | — |
| 69 | C5×Dic3⋊C4 | — | 2 | 2 | no | — |
| 70 | C4×C5×Dic3 | — | 2 | 1 | no | — |
| 71 | C4×C5×Dic3 | D4 | 1 | 2 | yes | — |
| 72 | C4×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 73 | C4×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 74 | C3×C22⋊Dic5 | — | 2 | 1 | no | — |
| 75 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 76 | C3×C4×Dic5 | — | 2 | 1 | no | — |
| 77 | C2×C3×#168 | Q8 | 1 | 4 | yes | complemented |
| 78 | C2×C3×#168 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×C3×#168 | C23 | 1 | 1 | yes | characteristic |
| 80 | Dic3⋊Dic5 | — | 2 | 2 | no | — |
| 81 | #6669 | — | 2 | 2 | no | — |
| 82 | #6668 | — | 2 | 2 | no | — |
| 83 | #5517 | — | 5 | 1 | no | — |
| 84 | #5517 | D5 | 1 | 1 | yes | characteristic |
| 85 | C3×#427 | — | 5 | 1 | no | — |
| 86 | #5106 | — | 5 | 1 | no | — |
| 87 | C2×C8×Dic3 | — | 5 | 1 | no | — |
| 88 | #4998 | — | 5 | 1 | no | — |
| 89 | #4998 | — | 5 | 1 | no | — |
| 90 | #4878 | — | 5 | 2 | no | — |
| 91 | #4874 | — | 5 | 2 | no | — |
| 92 | #4858 | — | 5 | 2 | no | — |
| 93 | #4855 | — | 5 | 2 | no | — |
| 94 | C5×C4⋊Q8 | — | 3 | 2 | no | — |
| 95 | C5×#125 | — | 3 | 2 | no | — |
| 96 | C5×C22⋊Q8 | — | 6 | 2 | no | — |
| 97 | C4×C5×Q8 | — | 6 | 2 | no | — |
| 98 | C5×#117 | — | 3 | 1 | no | — |
| 99 | C5×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | C2×C42×C5 | — | 3 | 1 | no | — |
| 101 | #4072 | — | 3 | 1 | no | — |
| 102 | #4072 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | #4070 | — | 6 | 2 | no | — |
| 104 | C22×#168 | — | 3 | 1 | no | — |
| 105 | C22×#168 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | #4016 | — | 3 | 2 | no | — |
| 107 | #4015 | — | 3 | 2 | no | — |
| 108 | C4×Dic10 | — | 6 | 2 | no | — |
| 109 | #3940 | — | 3 | 2 | no | — |
| 110 | #3940 | — | 3 | 2 | no | — |
| 111 | #3940 | — | 3 | 2 | no | — |
| 112 | #3940 | C2×D3 | 1 | 2 | yes | — |
| 113 | #3939 | — | 3 | 2 | no | — |
| 114 | #3939 | — | 3 | 2 | no | — |
| 115 | #3939 | — | 3 | 2 | no | — |
| 116 | #3939 | C2×D3 | 1 | 2 | yes | — |
| 117 | C4×#168 | — | 3 | 1 | no | — |
| 118 | C4×#168 | — | 3 | 1 | no | — |
| 119 | C4×#168 | — | 3 | 1 | no | — |
| 120 | C4×#168 | — | 3 | 1 | no | — |
| 121 | #3160 | — | 15 | 1 | no | Sylow |
| 122 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 124 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C3×C4×C5 | C2×Q8 | 1 | 2 | yes | — |
| 126 | C2×C3×C4×C5 | C2×Q8 | 1 | 2 | yes | — |
| 127 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 128 | C2×Dic15 | — | 2 | 2 | no | — |
| 129 | C2×C5×Dic3 | — | 2 | 4 | no | — |
| 130 | C2×C5×Dic3 | — | 2 | 2 | no | — |
| 131 | C2×C5×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 132 | C2×C5×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 133 | C5×Dic6 | — | 4 | 4 | no | — |
| 134 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 135 | #1204 | — | 4 | 4 | no | — |
| 136 | C3⋊#168 | C2×Q8 | 1 | 2 | yes | — |
| 137 | C3⋊#168 | C2×Q8 | 1 | 2 | yes | — |
| 138 | C3×#168 | C2×Q8 | 1 | 2 | yes | — |
| 139 | C3×#168 | C2×Q8 | 1 | 2 | yes | — |
| 140 | C22×C3×C8 | — | 5 | 1 | no | — |
| 141 | C3×#117 | — | 5 | 1 | no | — |
| 142 | C3×#117 | C2×D5 | 1 | 1 | yes | characteristic |
| 143 | #926 | — | 5 | 1 | no | — |
| 144 | #926 | C2×D5 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 146 | C22×C3⋊C8 | — | 5 | 1 | no | — |
| 147 | #890 | — | 5 | 2 | no | — |
| 148 | #890 | C2×D5 | 1 | 2 | yes | — |
| 149 | #888 | — | 5 | 2 | no | — |
| 150 | #888 | C2×D5 | 1 | 2 | yes | — |
| 151 | #878 | — | 2 | 2 | no | — |
| 152 | #878 | — | 10 | 2 | no | — |
| 153 | C4×Dic6 | — | 2 | 2 | no | — |
| 154 | C4×Dic6 | — | 10 | 2 | no | — |
| 155 | C3×#107 | — | 5 | 2 | no | — |
| 156 | C3×#106 | — | 5 | 2 | no | — |
| 157 | #818 | — | 5 | 2 | no | — |
| 158 | #817 | — | 5 | 2 | no | — |
| 159 | C8×Dic3 | — | 5 | 1 | no | — |
| 160 | C8×Dic3 | — | 5 | 1 | no | — |
| 161 | C8×Dic3 | — | 5 | 1 | no | — |
| 162 | C8×Dic3 | — | 5 | 1 | no | — |
| 163 | #808 | — | 5 | 2 | no | — |
| 164 | #808 | — | 5 | 2 | no | — |
| 165 | #807 | — | 5 | 2 | no | — |
| 166 | #807 | — | 5 | 2 | no | — |
| 167 | C2×C5×Q8 | — | 6 | 2 | no | — |
| 168 | C22×C4×C5 | — | 3 | 2 | no | — |
| 169 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 170 | C2×Dic10 | — | 6 | 2 | no | — |
| 171 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 172 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 173 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 174 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 175 | C5×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 176 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 177 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 178 | C42×C5 | — | 2 | 1 | no | — |
| 179 | C42×C5 | — | 3 | 2 | no | — |
| 180 | C42×C5 | — | 3 | 1 | no | — |
| 181 | C42×C5 | — | 3 | 1 | no | — |
| 182 | C42×C5 | — | 6 | 1 | no | — |
| 183 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 184 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 185 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 186 | C4⋊Dic5 | — | 6 | 2 | no | — |
| 187 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 188 | #683 | — | 6 | 2 | no | — |
| 189 | #683 | — | 6 | 2 | no | — |
| 190 | C4×Dic5 | — | 2 | 1 | no | — |
| 191 | C4×Dic5 | — | 6 | 1 | no | — |
| 192 | C2×#168 | — | 3 | 4 | no | — |
| 193 | C2×#168 | — | 3 | 1 | no | — |
| 194 | C2×#168 | — | 3 | 1 | no | — |
| 195 | C2×#168 | Dic6 | 1 | 4 | yes | complemented |
| 196 | C2×#168 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | C2×#168 | C22×D3 | 1 | 1 | yes | characteristic |
| 198 | #533 | — | 3 | 1 | no | — |
| 199 | #533 | — | 15 | 1 | no | — |
| 200 | #500 | — | 15 | 2 | no | — |
| 201 | #499 | — | 15 | 2 | no | — |
| 202 | #499 | — | 15 | 2 | no | — |
| 203 | #498 | — | 15 | 2 | no | — |
| 204 | #427 | — | 5 | 1 | no | — |
| 205 | #427 | — | 15 | 1 | no | — |
| 206 | #427 | — | 15 | 1 | no | — |
| 207 | #427 | — | 15 | 1 | no | — |
| 208 | C2×C4×C8 | — | 15 | 1 | no | — |
| 209 | C22×C3×C5 | — | 2 | 2 | no | — |
| 210 | C22×C3×C5 | C4⋊Q8 | 1 | 2 | yes | — |
| 211 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 212 | C3×C4×C5 | — | 4 | 2 | no | — |
| 213 | C3×C4×C5 | C4⋊Q8 | 1 | 2 | yes | — |
| 214 | C3×C4×C5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 215 | C3×C4×C5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 216 | Dic15 | — | 4 | 2 | no | — |
| 217 | C3×Dic5 | — | 4 | 2 | no | — |
| 218 | C5×Dic3 | — | 2 | 2 | no | — |
| 219 | C5×Dic3 | — | 4 | 2 | no | — |
| 220 | C5×Dic3 | #135 | 1 | 4 | yes | — |
| 221 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 222 | C22×Dic3 | C22⋊D5 | 1 | 2 | yes | — |
| 223 | C2×Dic6 | — | 2 | 2 | no | — |
| 224 | C2×Dic6 | — | 10 | 2 | no | — |
| 225 | C2×C3×C8 | — | 5 | 4 | no | — |
| 226 | C2×C3×C8 | — | 5 | 1 | no | — |
| 227 | C2×C3×C8 | — | 5 | 1 | no | — |
| 228 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 229 | C3×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 230 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 231 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 232 | C3×C42 | — | 2 | 1 | no | — |
| 233 | C3×C42 | — | 10 | 1 | no | — |
| 234 | #217 | — | 2 | 1 | no | — |
| 235 | #217 | — | 10 | 1 | no | — |
| 236 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 237 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 238 | C4⋊Dic3 | — | 10 | 2 | no | — |
| 239 | C4⋊Dic3 | C22×D5 | 1 | 2 | yes | — |
| 240 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 241 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 242 | Dic3⋊C4 | — | 10 | 2 | no | — |
| 243 | Dic3⋊C4 | — | 10 | 2 | no | — |
| 244 | C4×Dic3 | — | 2 | 1 | no | — |
| 245 | C4×Dic3 | — | 10 | 1 | no | — |
| 246 | C4×Dic3 | C22⋊D5 | 1 | 2 | yes | — |
| 247 | C4×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 248 | C4×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 249 | C2×C3⋊C8 | — | 5 | 4 | no | — |
| 250 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 251 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 252 | C23×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 253 | C5×Q8 | — | 12 | 4 | no | — |
| 254 | C2×C4×C5 | — | 2 | 2 | no | — |
| 255 | C2×C4×C5 | — | 3 | 2 | no | — |
| 256 | C2×C4×C5 | — | 3 | 2 | no | — |
| 257 | C2×C4×C5 | — | 6 | 4 | no | — |
| 258 | C2×C4×C5 | — | 6 | 2 | no | — |
| 259 | C2×C4×C5 | C2×Dic6 | 1 | 2 | yes | — |
| 260 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C5 | D3×Q8 | 1 | 2 | yes | — |
| 262 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 263 | C2×Dic5 | — | 2 | 2 | no | — |
| 264 | C2×Dic5 | — | 6 | 2 | no | — |
| 265 | Dic10 | — | 12 | 4 | no | — |
| 266 | #168 | — | 3 | 2 | no | — |
| 267 | #168 | — | 3 | 2 | no | — |
| 268 | #168 | C2×Dic6 | 1 | 2 | yes | — |
| 269 | #168 | C2×Dic6 | 1 | 2 | yes | — |
| 270 | C22×C8 | — | 5 | 1 | no | — |
| 271 | C22×C8 | — | 15 | 1 | no | — |
| 272 | C4⋊Q8 | — | 3 | 2 | no | — |
| 273 | C4⋊Q8 | — | 15 | 2 | no | — |
| 274 | #125 | — | 3 | 2 | no | — |
| 275 | #125 | — | 15 | 2 | no | — |
| 276 | C22⋊Q8 | — | 6 | 2 | no | — |
| 277 | C22⋊Q8 | — | 30 | 2 | no | — |
| 278 | C4×Q8 | — | 6 | 2 | no | — |
| 279 | C4×Q8 | — | 30 | 2 | no | — |
| 280 | #117 | — | 3 | 1 | no | — |
| 281 | #117 | — | 5 | 1 | no | — |
| 282 | #117 | — | 15 | 1 | no | — |
| 283 | #117 | D3×D5 | 1 | 1 | yes | characteristic |
| 284 | C2×C42 | — | 3 | 1 | no | — |
| 285 | #107 | — | 5 | 2 | no | — |
| 286 | #107 | — | 15 | 2 | no | — |
| 287 | #107 | — | 15 | 2 | no | — |
| 288 | #107 | — | 15 | 2 | no | — |
| 289 | #106 | — | 5 | 2 | no | — |
| 290 | #106 | — | 15 | 2 | no | — |
| 291 | #106 | — | 15 | 2 | no | — |
| 292 | #106 | — | 15 | 2 | no | — |
| 293 | C4×C8 | — | 15 | 1 | no | — |
| 294 | C4×C8 | — | 15 | 1 | no | — |
| 295 | C4×C8 | — | 15 | 1 | no | — |
| 296 | C4×C8 | — | 15 | 1 | no | — |
| 297 | C2×C3×C5 | — | 2 | 2 | no | — |
| 298 | C2×C3×C5 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 299 | C2×C3×C5 | C2×#135 | 1 | 2 | yes | — |
| 300 | C23×C3 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 301 | C2×C3×C4 | — | 2 | 2 | no | — |
| 302 | C2×C3×C4 | — | 10 | 2 | no | — |
| 303 | C2×C3×C4 | Q8×D5 | 1 | 2 | yes | — |
| 304 | C2×C3×C4 | Q8×D5 | 1 | 2 | yes | — |
| 305 | C2×C3×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 306 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 307 | C2×Dic3 | — | 2 | 4 | no | — |
| 308 | C2×Dic3 | — | 2 | 2 | no | — |
| 309 | C2×Dic3 | — | 10 | 2 | no | — |
| 310 | C2×Dic3 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 311 | C2×Dic3 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 312 | Dic6 | — | 4 | 4 | no | — |
| 313 | Dic6 | — | 20 | 4 | no | — |
| 314 | C3×C8 | — | 5 | 2 | no | — |
| 315 | C3×C8 | — | 5 | 2 | no | — |
| 316 | C3⋊C8 | — | 5 | 2 | no | — |
| 317 | C3⋊C8 | — | 5 | 2 | no | — |
| 318 | C22×C5 | — | 2 | 2 | no | — |
| 319 | C22×C5 | #888 | 1 | 2 | yes | — |
| 320 | C22×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 321 | C4×C5 | — | 3 | 4 | no | — |
| 322 | C4×C5 | — | 4 | 2 | no | — |
| 323 | C4×C5 | — | 6 | 2 | no | — |
| 324 | C4×C5 | — | 12 | 2 | no | — |
| 325 | C4×C5 | #888 | 1 | 2 | yes | — |
| 326 | C4×C5 | C22×Dic6 | 1 | 1 | yes | characteristic |
| 327 | C4×C5 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 328 | Dic5 | — | 4 | 2 | no | — |
| 329 | Dic5 | — | 12 | 2 | no | — |
| 330 | C2×Q8 | — | 6 | 2 | no | — |
| 331 | C2×Q8 | — | 30 | 2 | no | — |
| 332 | C22×C4 | — | 3 | 2 | no | — |
| 333 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 334 | C2×C8 | — | 5 | 4 | no | — |
| 335 | C2×C8 | — | 5 | 1 | no | — |
| 336 | C2×C8 | — | 5 | 1 | no | — |
| 337 | C2×C8 | — | 15 | 4 | no | — |
| 338 | C2×C8 | — | 15 | 1 | no | — |
| 339 | C2×C8 | — | 15 | 1 | no | — |
| 340 | C4⋊C4 | — | 3 | 2 | no | — |
| 341 | C4⋊C4 | — | 5 | 2 | no | — |
| 342 | C4⋊C4 | — | 6 | 2 | no | — |
| 343 | C4⋊C4 | — | 6 | 2 | no | — |
| 344 | C4⋊C4 | — | 6 | 2 | no | — |
| 345 | C4⋊C4 | — | 15 | 2 | no | — |
| 346 | C4⋊C4 | — | 30 | 2 | no | — |
| 347 | C4⋊C4 | — | 30 | 2 | no | — |
| 348 | C4⋊C4 | — | 30 | 2 | no | — |
| 349 | C4⋊C4 | C2×D3×D5 | 1 | 2 | yes | — |
| 350 | C22⋊C4 | — | 2 | 1 | no | — |
| 351 | C22⋊C4 | — | 6 | 1 | no | — |
| 352 | C22⋊C4 | — | 10 | 1 | no | — |
| 353 | C22⋊C4 | — | 30 | 1 | no | — |
| 354 | C42 | — | 2 | 1 | no | — |
| 355 | C42 | — | 3 | 2 | no | — |
| 356 | C42 | — | 3 | 1 | no | — |
| 357 | C42 | — | 3 | 1 | no | — |
| 358 | C42 | — | 6 | 1 | no | — |
| 359 | C42 | — | 10 | 1 | no | — |
| 360 | C42 | — | 30 | 1 | no | — |
| 361 | C3×C5 | #3160 | 1 | 1 | yes | characteristic, complemented, Hall |
| 362 | C22×C3 | — | 2 | 2 | no | — |
| 363 | C22×C3 | #4090 | 1 | 2 | yes | — |
| 364 | C22×C3 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 365 | C3×C4 | — | 4 | 2 | no | — |
| 366 | C3×C4 | — | 20 | 2 | no | — |
| 367 | C3×C4 | #4090 | 1 | 2 | yes | — |
| 368 | C3×C4 | C2×Q8×D5 | 1 | 1 | yes | characteristic |
| 369 | C3×C4 | C2×Q8×D5 | 1 | 1 | yes | characteristic |
| 370 | Dic3 | — | 2 | 2 | no | — |
| 371 | Dic3 | — | 4 | 2 | no | — |
| 372 | Dic3 | — | 20 | 2 | no | — |
| 373 | Dic3 | #4096 | 1 | 4 | yes | — |
| 374 | C2×C5 | — | 2 | 2 | no | — |
| 375 | C2×C5 | C2×#888 | 1 | 1 | yes | characteristic |
| 376 | C2×C5 | D3×#135 | 1 | 2 | yes | — |
| 377 | C23 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 378 | Q8 | — | 12 | 4 | no | — |
| 379 | Q8 | — | 60 | 4 | no | — |
| 380 | C2×C4 | — | 2 | 2 | no | — |
| 381 | C2×C4 | — | 3 | 2 | no | — |
| 382 | C2×C4 | — | 3 | 2 | no | — |
| 383 | C2×C4 | — | 6 | 4 | no | — |
| 384 | C2×C4 | — | 6 | 2 | no | — |
| 385 | C2×C4 | — | 10 | 2 | no | — |
| 386 | C2×C4 | — | 30 | 2 | no | — |
| 387 | C2×C4 | D5×Dic6 | 1 | 2 | yes | — |
| 388 | C2×C4 | D15⋊Q8 | 1 | 2 | yes | — |
| 389 | C2×C4 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 391 | C8 | — | 5 | 2 | no | — |
| 392 | C8 | — | 5 | 2 | no | — |
| 393 | C8 | — | 15 | 2 | no | — |
| 394 | C8 | — | 15 | 2 | no | — |
| 395 | C2×C3 | — | 2 | 2 | no | — |
| 396 | C2×C3 | C2×#4090 | 1 | 1 | yes | characteristic |
| 397 | C2×C3 | C2×#4096 | 1 | 2 | yes | — |
| 398 | C5 | #79170 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 399 | C22 | — | 2 | 2 | no | — |
| 400 | C22 | #91329 | 1 | 2 | yes | — |
| 401 | C22 | C2×D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 402 | C4 | — | 3 | 4 | no | — |
| 403 | C4 | — | 4 | 2 | no | — |
| 404 | C4 | — | 6 | 2 | no | — |
| 405 | C4 | — | 12 | 2 | no | — |
| 406 | C4 | — | 20 | 2 | no | — |
| 407 | C4 | — | 60 | 2 | no | — |
| 408 | C4 | #91329 | 1 | 2 | yes | — |
| 409 | C4 | C2×D5×Dic6 | 1 | 1 | yes | characteristic |
| 410 | C4 | C2×D15⋊Q8 | 1 | 1 | yes | characteristic |
| 411 | C3 | #10615070 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 412 | C2 | — | 2 | 2 | no | — |
| 413 | C2 | C2×#91329 | 1 | 1 | yes | characteristic |
| 414 | C2 | D3×#4096 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta