← #72223183
Subgroups — #72223183
Order 6400.
1052 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72223181 | C2 | 1 | 2 | yes | maximal |
| 2 | #72220909 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72220908 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C4×#11716860 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72220686 | C2 | 1 | 2 | yes | maximal |
| 6 | #13104853 | C22 | 1 | 2 | yes | — |
| 7 | C2×#11716860 | C4 | 1 | 1 | yes | characteristic |
| 8 | C2×#11716860 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×#11716860 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#11716860 | C22 | 1 | 1 | yes | characteristic |
| 11 | C42×#1043 | C4 | 1 | 1 | yes | characteristic |
| 12 | C4×#87855 | C4 | 1 | 1 | yes | characteristic |
| 13 | C4×C8×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 14 | #13100806 | C22 | 1 | 2 | yes | — |
| 15 | #13100361 | C4 | 1 | 2 | yes | complemented |
| 16 | #13100331 | C4 | 1 | 2 | yes | complemented |
| 17 | #13099852 | — | 2 | 2 | no | — |
| 18 | #13099851 | — | 2 | 2 | no | — |
| 19 | C5×#64683 | C4 | 1 | 2 | yes | complemented |
| 20 | #13099305 | C4 | 1 | 2 | yes | complemented |
| 21 | #13025974 | — | 5 | 2 | no | maximal |
| 22 | C2×C4×#1043 | — | 2 | 2 | no | — |
| 23 | C2×C4×#1043 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×#1043 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C2×#87855 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C2×#87855 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×C8×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×C8×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 29 | C42×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #11716891 | C2×C4 | 1 | 4 | yes | — |
| 31 | #11716883 | — | 2 | 2 | no | — |
| 32 | #11716882 | — | 2 | 2 | no | — |
| 33 | C4×#6033 | — | 2 | 2 | no | — |
| 34 | #11716860 | — | 2 | 2 | no | — |
| 35 | #11716860 | — | 2 | 2 | no | — |
| 36 | #11716860 | — | 2 | 1 | no | — |
| 37 | #11716860 | — | 2 | 1 | no | — |
| 38 | #11716860 | D4 | 1 | 2 | yes | — |
| 39 | #11716860 | Q8 | 1 | 2 | yes | — |
| 40 | C4×C52×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C8×#1039 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C8×#1039 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C4×#6029 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C5×#3944 | C2×C4 | 1 | 4 | yes | — |
| 45 | #11716585 | — | 2 | 2 | no | — |
| 46 | #11716583 | — | 2 | 2 | no | — |
| 47 | #10604114 | — | 5 | 4 | no | — |
| 48 | C4×#3992 | — | 5 | 2 | no | — |
| 49 | C4×#3992 | — | 10 | 2 | no | — |
| 50 | D5⋊#364 | — | 5 | 2 | no | — |
| 51 | D5×#364 | — | 5 | 2 | no | — |
| 52 | #10598671 | — | 5 | 4 | no | — |
| 53 | C22×#1043 | — | 2 | 1 | no | — |
| 54 | C22×#1043 | M16 | 1 | 2 | yes | — |
| 55 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 56 | C2×C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×#6033 | — | 2 | 1 | no | — |
| 58 | C2×#6033 | M16 | 1 | 2 | yes | — |
| 59 | C4×#1043 | — | 2 | 1 | no | — |
| 60 | C4×#1043 | — | 2 | 1 | no | — |
| 61 | C4×#1043 | — | 2 | 1 | no | — |
| 62 | C4×#1043 | — | 4 | 4 | no | — |
| 63 | C4×#1043 | C4⋊C4 | 1 | 2 | yes | — |
| 64 | #87855 | — | 2 | 1 | no | — |
| 65 | #87855 | — | 2 | 1 | no | — |
| 66 | #87855 | — | 2 | 1 | no | — |
| 67 | #87855 | C4⋊C4 | 1 | 2 | yes | — |
| 68 | C2×C52×C8 | C42 | 1 | 1 | yes | characteristic |
| 69 | C2×C52×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C42×C52 | C42 | 1 | 1 | yes | characteristic |
| 71 | C4×#1039 | — | 2 | 1 | no | — |
| 72 | C4×#1039 | C42 | 1 | 1 | yes | characteristic |
| 73 | C2×#6029 | C42 | 1 | 1 | yes | characteristic |
| 74 | C2×#6029 | C22×C4 | 1 | 1 | yes | characteristic |
| 75 | C8×C5⋊D5 | M16 | 1 | 2 | yes | — |
| 76 | C8×C5⋊D5 | M16 | 1 | 2 | yes | — |
| 77 | C8×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C8×C5⋊D5 | C2×Q8 | 1 | 1 | yes | characteristic |
| 79 | C8×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 80 | C8×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 81 | #87765 | — | 2 | 4 | no | — |
| 82 | C5×#672 | — | 2 | 4 | no | — |
| 83 | C2×#3992 | — | 5 | 2 | no | — |
| 84 | C2×#3992 | — | 5 | 2 | no | — |
| 85 | C2×#3992 | — | 5 | 2 | no | — |
| 86 | C2×#3992 | — | 5 | 2 | no | — |
| 87 | C2×#3992 | — | 10 | 2 | no | — |
| 88 | C2×#3992 | — | 10 | 2 | no | — |
| 89 | C2×#3992 | — | 10 | 2 | no | — |
| 90 | C2×#3992 | — | 10 | 2 | no | — |
| 91 | D5⋊M32 | — | 5 | 4 | no | — |
| 92 | C42×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 93 | C42×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 94 | C4×D5⋊C8 | — | 5 | 2 | no | — |
| 95 | C4×D5⋊C8 | — | 10 | 2 | no | — |
| 96 | D5×M32 | — | 5 | 4 | no | — |
| 97 | C4×C8×D5 | — | 5 | 2 | no | — |
| 98 | C4×C8×D5 | — | 10 | 2 | no | — |
| 99 | #64889 | — | 5 | 4 | no | — |
| 100 | #64861 | — | 5 | 4 | no | — |
| 101 | #64846 | — | 10 | 4 | no | — |
| 102 | #64845 | — | 10 | 4 | no | — |
| 103 | C5×#364 | — | 5 | 2 | no | — |
| 104 | #64731 | — | 5 | 4 | no | — |
| 105 | #64683 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 106 | #12659 | — | 25 | 1 | no | Sylow |
| 107 | C22×C5⋊D5 | C2×M16 | 1 | 1 | yes | characteristic |
| 108 | C2×#1043 | — | 2 | 2 | no | — |
| 109 | C2×#1043 | — | 2 | 2 | no | — |
| 110 | C2×#1043 | — | 4 | 2 | no | — |
| 111 | C2×#1043 | — | 4 | 2 | no | — |
| 112 | C2×C4×C52 | — | 2 | 1 | no | — |
| 113 | C2×C4×C52 | C2×C42 | 1 | 1 | yes | characteristic |
| 114 | C2×#1039 | — | 2 | 1 | no | — |
| 115 | C2×#1039 | C2×M16 | 1 | 1 | yes | characteristic |
| 116 | C4×C5⋊D5 | — | 2 | 4 | no | — |
| 117 | C4×C5⋊D5 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C4×C5⋊D5 | #117 | 1 | 1 | yes | characteristic |
| 119 | C4×C5⋊D5 | C2×M16 | 1 | 1 | yes | characteristic |
| 120 | C4×C5⋊D5 | C2×M16 | 1 | 1 | yes | characteristic |
| 121 | #6033 | — | 2 | 2 | no | — |
| 122 | #6033 | — | 2 | 2 | no | — |
| 123 | C52×C8 | #97 | 1 | 2 | yes | — |
| 124 | C52×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 125 | C52×C8 | C4×Q8 | 1 | 1 | yes | characteristic |
| 126 | #6029 | #97 | 1 | 2 | yes | — |
| 127 | #6029 | C4×D4 | 1 | 1 | yes | characteristic |
| 128 | #6029 | C4×Q8 | 1 | 1 | yes | characteristic |
| 129 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 130 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 131 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 132 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 133 | C2×C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 134 | C2×C4×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 135 | C2×D5⋊C8 | — | 5 | 2 | no | — |
| 136 | C2×D5⋊C8 | — | 5 | 2 | no | — |
| 137 | C2×D5⋊C8 | — | 10 | 2 | no | — |
| 138 | C2×D5⋊C8 | — | 10 | 2 | no | — |
| 139 | C2×C8×D5 | — | 5 | 2 | no | — |
| 140 | C2×C8×D5 | — | 5 | 2 | no | — |
| 141 | C2×C8×D5 | — | 10 | 2 | no | — |
| 142 | C2×C8×D5 | — | 10 | 2 | no | — |
| 143 | C42×D5 | — | 5 | 2 | no | — |
| 144 | C42×D5 | — | 10 | 2 | no | — |
| 145 | C4×#170 | — | 10 | 4 | no | — |
| 146 | C4×#170 | — | 10 | 8 | no | — |
| 147 | #3998 | — | 5 | 8 | no | — |
| 148 | #3992 | — | 5 | 4 | no | — |
| 149 | #3992 | — | 5 | 4 | no | — |
| 150 | #3992 | — | 10 | 4 | no | — |
| 151 | #3992 | — | 10 | 4 | no | — |
| 152 | #3992 | — | 10 | 2 | no | — |
| 153 | #3992 | — | 10 | 2 | no | — |
| 154 | #3992 | — | 10 | 4 | no | — |
| 155 | #3992 | — | 10 | 4 | no | — |
| 156 | #3992 | — | 10 | 8 | no | — |
| 157 | #3992 | — | 10 | 8 | no | — |
| 158 | #3992 | — | 10 | 4 | no | — |
| 159 | #3992 | — | 10 | 4 | no | — |
| 160 | #3990 | — | 10 | 4 | no | — |
| 161 | D5⋊C16 | — | 10 | 4 | no | — |
| 162 | C5×M32 | — | 5 | 4 | no | — |
| 163 | C4×C5×C8 | — | 2 | 2 | no | — |
| 164 | C4×C5×C8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 165 | C8×Dic5 | — | 5 | 2 | no | — |
| 166 | C8×Dic5 | — | 5 | 2 | no | — |
| 167 | C8×Dic5 | — | 10 | 2 | no | — |
| 168 | C8×Dic5 | — | 10 | 2 | no | — |
| 169 | #3944 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 170 | C4×#168 | — | 5 | 2 | no | — |
| 171 | C4×#168 | — | 10 | 2 | no | — |
| 172 | #3930 | — | 10 | 4 | no | — |
| 173 | D5×C16 | — | 10 | 4 | no | — |
| 174 | C2×#364 | — | 25 | 1 | no | — |
| 175 | C2×#364 | — | 25 | 1 | no | — |
| 176 | C2×#347 | — | 25 | 2 | no | — |
| 177 | C4×#97 | — | 25 | 1 | no | — |
| 178 | #1377 | — | 25 | 2 | no | — |
| 179 | C22×C52 | C4×M16 | 1 | 1 | yes | characteristic |
| 180 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 181 | C2×C5⋊D5 | #423 | 1 | 1 | yes | characteristic |
| 182 | C2×C5⋊D5 | #432 | 1 | 1 | yes | characteristic |
| 183 | #1043 | — | 4 | 2 | no | — |
| 184 | #1043 | — | 4 | 2 | no | — |
| 185 | C4×C52 | — | 2 | 2 | no | — |
| 186 | C4×C52 | C4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 187 | C4×C52 | C2×#97 | 1 | 1 | yes | characteristic |
| 188 | #1039 | — | 2 | 2 | no | — |
| 189 | #1039 | #423 | 1 | 1 | yes | characteristic |
| 190 | #1039 | #432 | 1 | 1 | yes | characteristic |
| 191 | C22×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 192 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 193 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 194 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 195 | C2×C4×D5 | — | 5 | 2 | no | — |
| 196 | C2×C4×D5 | — | 10 | 2 | no | — |
| 197 | C2×C4×D5 | — | 10 | 2 | no | — |
| 198 | C2×C4×D5 | — | 10 | 4 | no | — |
| 199 | C2×#170 | — | 5 | 4 | no | — |
| 200 | C2×#170 | — | 10 | 4 | no | — |
| 201 | C2×#170 | — | 10 | 2 | no | — |
| 202 | C2×#170 | — | 10 | 4 | no | — |
| 203 | C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 204 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 205 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 206 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 207 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 208 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 209 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 210 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 211 | C4×AGL(1,𝔽5) | — | 20 | 16 | no | — |
| 212 | C4×AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 213 | D5⋊C8 | — | 5 | 4 | no | — |
| 214 | D5⋊C8 | — | 10 | 4 | no | — |
| 215 | D5⋊C8 | — | 10 | 2 | no | — |
| 216 | D5⋊C8 | — | 10 | 2 | no | — |
| 217 | D5⋊C8 | — | 10 | 2 | no | — |
| 218 | D5⋊C8 | — | 10 | 4 | no | — |
| 219 | D5⋊C8 | — | 10 | 4 | no | — |
| 220 | D5⋊C8 | — | 10 | 4 | no | — |
| 221 | C2×C5×C8 | — | 2 | 2 | no | — |
| 222 | C2×C5×C8 | — | 2 | 2 | no | — |
| 223 | C2×C5×C8 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 224 | C2×C5×C8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 225 | C42×C5 | — | 2 | 2 | no | — |
| 226 | C42×C5 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 227 | C4×Dic5 | — | 5 | 2 | no | — |
| 228 | C4×Dic5 | — | 10 | 2 | no | — |
| 229 | C4×Dic5 | — | 10 | 2 | no | — |
| 230 | C4×Dic5 | — | 10 | 4 | no | — |
| 231 | C2×#168 | — | 5 | 2 | no | — |
| 232 | C2×#168 | — | 5 | 2 | no | — |
| 233 | C2×#168 | — | 10 | 2 | no | — |
| 234 | C2×#168 | — | 10 | 2 | no | — |
| 235 | C8×D5 | — | 5 | 2 | no | — |
| 236 | C8×D5 | — | 5 | 2 | no | — |
| 237 | C8×D5 | — | 5 | 2 | no | — |
| 238 | C8×D5 | — | 5 | 2 | no | — |
| 239 | C8×D5 | — | 5 | 4 | no | — |
| 240 | C8×D5 | — | 5 | 4 | no | — |
| 241 | C8×D5 | — | 10 | 4 | no | — |
| 242 | C8×D5 | — | 10 | 4 | no | — |
| 243 | C8×D5 | — | 10 | 2 | no | — |
| 244 | C8×D5 | — | 10 | 2 | no | — |
| 245 | C8×D5 | — | 10 | 2 | no | — |
| 246 | C8×D5 | — | 10 | 2 | no | — |
| 247 | #674 | — | 10 | 8 | no | — |
| 248 | C5×C16 | — | 10 | 4 | no | — |
| 249 | #672 | — | 2 | 4 | no | — |
| 250 | C2×M32 | — | 25 | 2 | no | — |
| 251 | C2×M32 | — | 25 | 2 | no | — |
| 252 | C2×#97 | — | 25 | 1 | no | — |
| 253 | C2×#97 | — | 25 | 1 | no | — |
| 254 | C2×#97 | — | 25 | 1 | no | — |
| 255 | C2×#97 | — | 25 | 1 | no | — |
| 256 | C2×C4×C8 | — | 25 | 1 | no | — |
| 257 | C2×C4×C8 | — | 25 | 1 | no | — |
| 258 | C43 | — | 25 | 1 | no | — |
| 259 | #364 | — | 5 | 2 | no | — |
| 260 | #364 | — | 25 | 2 | no | — |
| 261 | #364 | — | 25 | 2 | no | — |
| 262 | #364 | — | 25 | 2 | no | — |
| 263 | #347 | — | 50 | 2 | no | — |
| 264 | #347 | — | 50 | 2 | no | — |
| 265 | C2×C52 | — | 2 | 1 | no | — |
| 266 | C2×C52 | #1767 | 1 | 1 | yes | characteristic |
| 267 | C5⋊D5 | — | 2 | 1 | no | — |
| 268 | C5⋊D5 | #2165 | 1 | 2 | yes | — |
| 269 | C22×D5 | — | 5 | 2 | no | — |
| 270 | C22×D5 | — | 10 | 2 | no | — |
| 271 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 272 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 273 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 274 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 275 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 276 | C2×AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 277 | C2×AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 278 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 279 | C2×C4×C5 | — | 2 | 4 | no | — |
| 280 | C2×C4×C5 | — | 2 | 2 | no | — |
| 281 | C2×C4×C5 | — | 2 | 2 | no | — |
| 282 | C2×C4×C5 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 283 | C2×Dic5 | — | 5 | 2 | no | — |
| 284 | C2×Dic5 | — | 10 | 2 | no | — |
| 285 | C2×Dic5 | — | 10 | 4 | no | — |
| 286 | C2×Dic5 | — | 10 | 2 | no | — |
| 287 | C4×D5 | — | 5 | 2 | no | — |
| 288 | C4×D5 | — | 5 | 2 | no | — |
| 289 | C4×D5 | — | 5 | 2 | no | — |
| 290 | C4×D5 | — | 5 | 2 | no | — |
| 291 | C4×D5 | — | 10 | 2 | no | — |
| 292 | C4×D5 | — | 10 | 2 | no | — |
| 293 | C4×D5 | — | 10 | 2 | no | — |
| 294 | C4×D5 | — | 10 | 2 | no | — |
| 295 | C4×D5 | — | 10 | 8 | no | — |
| 296 | C4×D5 | — | 10 | 16 | no | — |
| 297 | #170 | — | 10 | 4 | no | — |
| 298 | #170 | — | 10 | 4 | no | — |
| 299 | #170 | — | 10 | 8 | no | — |
| 300 | #170 | — | 10 | 8 | no | — |
| 301 | C5×C8 | — | 2 | 4 | no | — |
| 302 | C5×C8 | — | 2 | 2 | no | — |
| 303 | C5×C8 | — | 2 | 2 | no | — |
| 304 | C5×C8 | #3992 | 1 | 4 | yes | — |
| 305 | C5×C8 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 306 | C5×C8 | Q8×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 307 | #168 | — | 5 | 2 | no | — |
| 308 | #168 | — | 5 | 2 | no | — |
| 309 | #168 | — | 5 | 4 | no | — |
| 310 | #168 | — | 10 | 4 | no | — |
| 311 | #168 | — | 10 | 2 | no | — |
| 312 | #168 | — | 10 | 2 | no | — |
| 313 | C22×C8 | — | 25 | 1 | no | — |
| 314 | C22×C8 | — | 25 | 1 | no | — |
| 315 | C22×C8 | — | 25 | 1 | no | — |
| 316 | C22×C8 | — | 25 | 1 | no | — |
| 317 | C2×C42 | — | 25 | 1 | no | — |
| 318 | C2×C42 | — | 25 | 1 | no | — |
| 319 | C2×C42 | — | 25 | 1 | no | — |
| 320 | C2×C42 | — | 50 | 2 | no | — |
| 321 | M32 | — | 5 | 4 | no | — |
| 322 | M32 | — | 25 | 4 | no | — |
| 323 | M32 | — | 50 | 2 | no | — |
| 324 | M32 | — | 50 | 2 | no | — |
| 325 | C2×C16 | — | 50 | 2 | no | — |
| 326 | C2×C16 | — | 50 | 2 | no | — |
| 327 | #97 | — | 25 | 2 | no | — |
| 328 | #97 | — | 25 | 2 | no | — |
| 329 | #97 | — | 50 | 2 | no | — |
| 330 | #97 | — | 50 | 2 | no | — |
| 331 | #97 | — | 50 | 1 | no | — |
| 332 | #97 | — | 50 | 1 | no | — |
| 333 | C4×C8 | — | 25 | 1 | no | — |
| 334 | C4×C8 | — | 25 | 1 | no | — |
| 335 | C4×C8 | — | 25 | 1 | no | — |
| 336 | C4×C8 | — | 50 | 2 | no | — |
| 337 | C4×C8 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 338 | C52 | #12659 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 339 | C22×C5 | — | 2 | 2 | no | — |
| 340 | C22×C5 | M16×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 341 | C2×D5 | — | 5 | 2 | no | — |
| 342 | C2×D5 | — | 5 | 2 | no | — |
| 343 | C2×D5 | — | 10 | 2 | no | — |
| 344 | C2×D5 | — | 10 | 2 | no | — |
| 345 | C2×D5 | — | 10 | 4 | no | — |
| 346 | C2×D5 | — | 10 | 8 | no | — |
| 347 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 348 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 349 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 350 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 351 | C4×C5 | — | 2 | 8 | no | — |
| 352 | C4×C5 | — | 2 | 4 | no | — |
| 353 | C4×C5 | — | 2 | 2 | no | — |
| 354 | C4×C5 | — | 2 | 2 | no | — |
| 355 | C4×C5 | C4⋊C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 356 | C4×C5 | C2×#3992 | 1 | 2 | yes | — |
| 357 | Dic5 | — | 5 | 2 | no | — |
| 358 | Dic5 | — | 5 | 2 | no | — |
| 359 | Dic5 | — | 10 | 2 | no | — |
| 360 | Dic5 | — | 10 | 2 | no | — |
| 361 | Dic5 | — | 10 | 8 | no | — |
| 362 | Dic5 | — | 10 | 4 | no | — |
| 363 | C22×C4 | — | 25 | 1 | no | — |
| 364 | C22×C4 | — | 25 | 2 | no | — |
| 365 | C22×C4 | — | 50 | 1 | no | — |
| 366 | C22×C4 | — | 50 | 1 | no | — |
| 367 | C2×C8 | — | 25 | 1 | no | — |
| 368 | C2×C8 | — | 25 | 1 | no | — |
| 369 | C2×C8 | — | 25 | 2 | no | — |
| 370 | C2×C8 | — | 25 | 2 | no | — |
| 371 | C2×C8 | — | 25 | 1 | no | — |
| 372 | C2×C8 | — | 25 | 1 | no | — |
| 373 | C2×C8 | — | 25 | 1 | no | — |
| 374 | C2×C8 | — | 25 | 1 | no | — |
| 375 | C2×C8 | — | 25 | 2 | no | — |
| 376 | C2×C8 | — | 25 | 2 | no | — |
| 377 | C2×C8 | — | 50 | 1 | no | — |
| 378 | C2×C8 | — | 50 | 1 | no | — |
| 379 | C2×C8 | — | 50 | 1 | no | — |
| 380 | C2×C8 | — | 50 | 1 | no | — |
| 381 | C2×C8 | #87830 | 1 | 1 | yes | characteristic |
| 382 | C2×C8 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 383 | C42 | — | 25 | 2 | no | — |
| 384 | C42 | — | 25 | 1 | no | — |
| 385 | C42 | — | 50 | 1 | no | — |
| 386 | C42 | — | 50 | 1 | no | — |
| 387 | C42 | — | 50 | 1 | no | — |
| 388 | C42 | — | 50 | 1 | no | — |
| 389 | C42 | — | 100 | 4 | no | — |
| 390 | C42 | #87830 | 1 | 1 | yes | characteristic |
| 391 | C16 | — | 10 | 4 | no | — |
| 392 | C16 | — | 50 | 4 | no | — |
| 393 | C2×C5 | — | 2 | 4 | no | — |
| 394 | C2×C5 | — | 2 | 2 | no | — |
| 395 | C2×C5 | — | 2 | 2 | no | — |
| 396 | C2×C5 | #10604028 | 1 | 2 | yes | — |
| 397 | D5 | — | 5 | 4 | no | — |
| 398 | D5 | — | 10 | 4 | no | — |
| 399 | D5 | — | 10 | 4 | no | — |
| 400 | D5 | — | 10 | 2 | no | — |
| 401 | C23 | — | 25 | 1 | no | — |
| 402 | C2×C4 | — | 2 | 1 | no | — |
| 403 | C2×C4 | — | 25 | 1 | no | — |
| 404 | C2×C4 | — | 25 | 1 | no | — |
| 405 | C2×C4 | — | 25 | 1 | no | — |
| 406 | C2×C4 | — | 25 | 1 | no | — |
| 407 | C2×C4 | — | 25 | 1 | no | — |
| 408 | C2×C4 | — | 50 | 4 | no | — |
| 409 | C2×C4 | — | 50 | 1 | no | — |
| 410 | C2×C4 | — | 50 | 2 | no | — |
| 411 | C2×C4 | — | 50 | 2 | no | — |
| 412 | C2×C4 | — | 100 | 2 | no | — |
| 413 | C2×C4 | — | 100 | 2 | no | — |
| 414 | C2×C4 | C2×#87830 | 1 | 1 | yes | characteristic |
| 415 | C8 | — | 25 | 2 | no | — |
| 416 | C8 | — | 25 | 1 | no | — |
| 417 | C8 | — | 25 | 1 | no | — |
| 418 | C8 | — | 50 | 2 | no | — |
| 419 | C8 | — | 50 | 2 | no | — |
| 420 | C8 | #11716763 | 1 | 2 | yes | — |
| 421 | C8 | #11717353 | 1 | 1 | yes | characteristic |
| 422 | C8 | #11717363 | 1 | 1 | yes | characteristic |
| 423 | C5 | — | 2 | 2 | no | — |
| 424 | C5 | #13025974 | 1 | 2 | yes | complemented |
| 425 | C22 | — | 25 | 1 | no | — |
| 426 | C22 | — | 25 | 1 | no | — |
| 427 | C22 | — | 50 | 2 | no | — |
| 428 | C22 | #13103905 | 1 | 1 | yes | characteristic |
| 429 | C4 | — | 2 | 2 | no | — |
| 430 | C4 | — | 25 | 1 | no | — |
| 431 | C4 | — | 25 | 1 | no | — |
| 432 | C4 | — | 50 | 2 | no | — |
| 433 | C4 | — | 100 | 2 | no | — |
| 434 | C4 | — | 100 | 2 | no | — |
| 435 | C4 | C2×#11716763 | 1 | 1 | yes | characteristic |
| 436 | C4 | #13103978 | 1 | 1 | yes | characteristic |
| 437 | C2 | — | 2 | 1 | no | — |
| 438 | C2 | — | 25 | 2 | no | — |
| 439 | C2 | — | 50 | 1 | no | — |
| 440 | C2 | #72223182 | 1 | 1 | yes | characteristic |
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