← #72242313
Subgroups — #72242313
Order 6400.
685 conjugacy classes of subgroups.
The subgroup lattice has 464 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72242305 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72242301 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72242231 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72242231 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72242181 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C4×#87862 | C4 | 1 | 1 | yes | characteristic |
| 7 | C4×#87855 | C4 | 1 | 1 | yes | characteristic |
| 8 | C2×#11716747 | C4 | 1 | 2 | yes | — |
| 9 | C2×#11716747 | C4 | 1 | 2 | yes | — |
| 10 | C4×#87767 | C22 | 1 | 1 | yes | characteristic |
| 11 | #13100142 | C4 | 1 | 1 | yes | characteristic |
| 12 | #13100142 | C4 | 1 | 1 | yes | characteristic |
| 13 | C5×#64859 | C4 | 1 | 1 | yes | characteristic |
| 14 | C5×#64859 | C4 | 1 | 1 | yes | characteristic |
| 15 | #13099875 | C4 | 1 | 1 | yes | characteristic |
| 16 | #13099875 | C4 | 1 | 1 | yes | characteristic |
| 17 | #13099875 | C22 | 1 | 1 | yes | characteristic |
| 18 | #13099875 | C22 | 1 | 1 | yes | characteristic |
| 19 | #13099805 | C22 | 1 | 2 | yes | — |
| 20 | #13099805 | C22 | 1 | 2 | yes | — |
| 21 | #13022991 | — | 5 | 1 | no | maximal |
| 22 | #13022987 | — | 5 | 1 | no | maximal |
| 23 | C2×#87862 | — | 2 | 1 | no | — |
| 24 | C2×#87855 | — | 2 | 1 | no | — |
| 25 | C42×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C2×#87767 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×#87767 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C4×#6034 | — | 2 | 1 | no | — |
| 29 | C4×#6034 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C4×#6034 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C4×#6033 | — | 2 | 1 | no | — |
| 32 | C4×#6033 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C4×#6033 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#87763 | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×#87763 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×C5×#674 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×C5×#674 | C2×C4 | 1 | 2 | yes | — |
| 38 | #11716747 | — | 2 | 4 | no | — |
| 39 | #11716747 | C8 | 1 | 8 | yes | complemented |
| 40 | C4×C5×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C4×C5×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #11716594 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #11716594 | C23 | 1 | 1 | yes | characteristic |
| 44 | #10603823 | — | 5 | 1 | no | — |
| 45 | #10603823 | — | 5 | 1 | no | — |
| 46 | #10603807 | — | 5 | 1 | no | — |
| 47 | #10603807 | — | 5 | 1 | no | — |
| 48 | D5×#346 | — | 5 | 1 | no | — |
| 49 | D5×#346 | — | 5 | 1 | no | — |
| 50 | #10598640 | — | 5 | 2 | no | — |
| 51 | #10598640 | — | 5 | 2 | no | — |
| 52 | #10598639 | — | 5 | 2 | no | — |
| 53 | #10598638 | — | 5 | 2 | no | — |
| 54 | C2×C4×C5⋊D5 | C42 | 1 | 1 | yes | characteristic |
| 55 | C2×C4×C5⋊D5 | M16 | 1 | 1 | yes | characteristic |
| 56 | C2×C4×C5⋊D5 | M16 | 1 | 1 | yes | characteristic |
| 57 | C2×#6034 | — | 2 | 1 | no | — |
| 58 | C2×#6034 | — | 2 | 1 | no | — |
| 59 | #87862 | — | 4 | 2 | no | — |
| 60 | C2×#6033 | — | 2 | 1 | no | — |
| 61 | C2×#6033 | — | 2 | 1 | no | — |
| 62 | #87855 | — | 4 | 2 | no | — |
| 63 | C42×C52 | C42 | 1 | 1 | yes | characteristic |
| 64 | C4×#1039 | M16 | 1 | 1 | yes | characteristic |
| 65 | C4×#1039 | M16 | 1 | 1 | yes | characteristic |
| 66 | C4×#1039 | C22×C4 | 1 | 1 | yes | characteristic |
| 67 | C2×C5×#168 | C42 | 1 | 1 | yes | characteristic |
| 68 | C2×C5×#168 | C42 | 1 | 1 | yes | characteristic |
| 69 | C2×C5×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×C5×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | #87767 | C2×C8 | 1 | 4 | yes | — |
| 72 | #87767 | M16 | 1 | 4 | yes | — |
| 73 | #87763 | — | 2 | 2 | no | — |
| 74 | #87763 | C2×C8 | 1 | 4 | yes | complemented |
| 75 | C5×#674 | — | 2 | 2 | no | — |
| 76 | C5×#674 | C2×C8 | 1 | 4 | yes | complemented |
| 77 | C2×D5⋊C16 | — | 5 | 2 | no | — |
| 78 | C2×D5⋊C16 | — | 5 | 2 | no | — |
| 79 | C4×D5⋊C8 | — | 5 | 1 | no | — |
| 80 | C4×D5⋊C8 | — | 5 | 1 | no | — |
| 81 | C4×D5⋊C8 | — | 5 | 1 | no | — |
| 82 | C4×D5⋊C8 | — | 5 | 1 | no | — |
| 83 | C4×D5⋊C8 | — | 20 | 1 | no | — |
| 84 | C2×D5×C16 | — | 5 | 2 | no | — |
| 85 | C2×D5×C16 | — | 5 | 2 | no | — |
| 86 | C4×C8×D5 | — | 5 | 1 | no | — |
| 87 | C4×C8×D5 | — | 5 | 1 | no | — |
| 88 | #64886 | — | 5 | 2 | no | — |
| 89 | #64886 | — | 5 | 2 | no | — |
| 90 | #64879 | — | 5 | 1 | no | — |
| 91 | #64879 | — | 5 | 1 | no | — |
| 92 | #64879 | — | 5 | 1 | no | — |
| 93 | #64879 | — | 5 | 1 | no | — |
| 94 | #64879 | — | 5 | 1 | no | — |
| 95 | #64879 | — | 5 | 1 | no | — |
| 96 | #64879 | — | 5 | 1 | no | — |
| 97 | #64879 | — | 5 | 1 | no | — |
| 98 | #64859 | — | 5 | 1 | no | — |
| 99 | #64859 | — | 5 | 1 | no | — |
| 100 | #64859 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 101 | #64859 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 102 | C5×#346 | — | 5 | 1 | no | — |
| 103 | C5×#346 | — | 5 | 1 | no | — |
| 104 | #64722 | — | 5 | 2 | no | — |
| 105 | #64722 | — | 5 | 2 | no | — |
| 106 | #64681 | — | 5 | 1 | no | — |
| 107 | #64681 | — | 5 | 1 | no | — |
| 108 | C2×#1313 | — | 25 | 1 | no | Sylow |
| 109 | C22×C5⋊D5 | #97 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C52 | #97 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C52 | #97 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C52 | C2×C42 | 1 | 1 | yes | characteristic |
| 113 | C2×#1039 | #97 | 1 | 1 | yes | characteristic |
| 114 | C2×#1039 | C2×M16 | 1 | 1 | yes | characteristic |
| 115 | C2×#1039 | C2×M16 | 1 | 1 | yes | characteristic |
| 116 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 117 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 118 | C4×C5⋊D5 | C4×C8 | 1 | 2 | yes | — |
| 119 | C4×C5⋊D5 | #97 | 1 | 2 | yes | — |
| 120 | #6034 | — | 4 | 1 | no | — |
| 121 | #6034 | — | 4 | 1 | no | — |
| 122 | #6033 | — | 4 | 1 | no | — |
| 123 | #6033 | — | 4 | 1 | no | — |
| 124 | C5×#168 | C4×C8 | 1 | 2 | yes | — |
| 125 | C5×#168 | #97 | 1 | 2 | yes | — |
| 126 | C5×#168 | C22×C8 | 1 | 2 | yes | — |
| 127 | C5×#168 | C2×M16 | 1 | 2 | yes | — |
| 128 | C2×D5⋊C8 | — | 10 | 1 | no | — |
| 129 | C2×D5⋊C8 | — | 10 | 1 | no | — |
| 130 | C2×D5⋊C8 | — | 10 | 1 | no | — |
| 131 | C2×D5⋊C8 | — | 10 | 1 | no | — |
| 132 | C2×D5⋊C8 | — | 20 | 1 | no | — |
| 133 | C2×D5⋊C8 | — | 20 | 1 | no | — |
| 134 | C2×C8×D5 | — | 5 | 1 | no | — |
| 135 | C2×C8×D5 | — | 5 | 1 | no | — |
| 136 | C2×C8×D5 | — | 5 | 1 | no | — |
| 137 | C2×C8×D5 | — | 5 | 1 | no | — |
| 138 | C42×D5 | — | 5 | 1 | no | — |
| 139 | C42×D5 | — | 5 | 1 | no | — |
| 140 | C42×D5 | — | 20 | 1 | no | — |
| 141 | C4×#170 | — | 5 | 1 | no | — |
| 142 | C4×#170 | — | 5 | 1 | no | — |
| 143 | C4×#170 | — | 5 | 1 | no | — |
| 144 | C4×#170 | — | 5 | 1 | no | — |
| 145 | C4×#170 | — | 5 | 1 | no | — |
| 146 | C4×#170 | — | 5 | 1 | no | — |
| 147 | C4×#170 | — | 5 | 1 | no | — |
| 148 | C4×#170 | — | 5 | 1 | no | — |
| 149 | C4×#170 | — | 10 | 1 | no | — |
| 150 | C4×#170 | — | 10 | 1 | no | — |
| 151 | C4×#170 | — | 10 | 1 | no | — |
| 152 | C4×#170 | — | 10 | 1 | no | — |
| 153 | C4×#170 | — | 20 | 1 | no | — |
| 154 | C4×#170 | — | 20 | 1 | no | — |
| 155 | C4×#170 | — | 20 | 1 | no | — |
| 156 | C4×#170 | — | 20 | 1 | no | — |
| 157 | C2×#674 | — | 5 | 2 | no | — |
| 158 | C2×#674 | — | 5 | 2 | no | — |
| 159 | C2×#674 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 160 | C2×#674 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 161 | D5⋊C16 | — | 5 | 8 | no | — |
| 162 | D5⋊C16 | — | 10 | 4 | no | — |
| 163 | C2×C5×C16 | — | 5 | 2 | no | — |
| 164 | C2×C5×C16 | — | 5 | 2 | no | — |
| 165 | C4×C5×C8 | — | 5 | 1 | no | — |
| 166 | C4×C5×C8 | — | 5 | 1 | no | — |
| 167 | C8×Dic5 | — | 5 | 1 | no | — |
| 168 | C8×Dic5 | — | 5 | 1 | no | — |
| 169 | C8×Dic5 | — | 5 | 1 | no | — |
| 170 | C8×Dic5 | — | 5 | 1 | no | — |
| 171 | C2×#672 | — | 5 | 2 | no | — |
| 172 | C2×#672 | — | 5 | 2 | no | — |
| 173 | C4×#168 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 174 | C4×#168 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 175 | D5×C16 | — | 5 | 8 | no | — |
| 176 | D5×C16 | — | 10 | 4 | no | — |
| 177 | C2×#346 | — | 25 | 1 | no | — |
| 178 | C2×#346 | — | 25 | 1 | no | — |
| 179 | C2×#322 | — | 25 | 1 | no | — |
| 180 | #1313 | — | 25 | 2 | no | — |
| 181 | #1313 | — | 25 | 2 | no | — |
| 182 | C22×C52 | C2×#97 | 1 | 1 | yes | characteristic |
| 183 | C2×C5⋊D5 | #322 | 1 | 2 | yes | — |
| 184 | C2×C5⋊D5 | #347 | 1 | 2 | yes | — |
| 185 | C2×C5⋊D5 | #347 | 1 | 2 | yes | — |
| 186 | C4×C52 | — | 2 | 1 | no | — |
| 187 | C4×C52 | — | 2 | 1 | no | — |
| 188 | C4×C52 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 189 | C4×C52 | C2×#97 | 1 | 1 | yes | characteristic |
| 190 | #1039 | — | 2 | 1 | no | — |
| 191 | #1039 | — | 2 | 1 | no | — |
| 192 | #1039 | #322 | 1 | 2 | yes | — |
| 193 | C2×C4×D5 | — | 5 | 1 | no | — |
| 194 | C2×C4×D5 | — | 5 | 1 | no | — |
| 195 | C2×C4×D5 | — | 5 | 1 | no | — |
| 196 | C2×C4×D5 | — | 5 | 1 | no | — |
| 197 | C2×C4×D5 | — | 5 | 1 | no | — |
| 198 | C2×C4×D5 | — | 5 | 1 | no | — |
| 199 | C2×C4×D5 | — | 20 | 1 | no | — |
| 200 | C2×C4×D5 | — | 20 | 1 | no | — |
| 201 | C2×C4×D5 | — | 20 | 1 | no | — |
| 202 | C2×#170 | — | 10 | 1 | no | — |
| 203 | C2×#170 | — | 10 | 1 | no | — |
| 204 | C2×#170 | — | 10 | 1 | no | — |
| 205 | C2×#170 | — | 10 | 1 | no | — |
| 206 | C2×#170 | — | 10 | 1 | no | — |
| 207 | C2×#170 | — | 10 | 1 | no | — |
| 208 | C2×#170 | — | 10 | 1 | no | — |
| 209 | C2×#170 | — | 10 | 1 | no | — |
| 210 | C2×#170 | — | 20 | 1 | no | — |
| 211 | C2×#170 | — | 20 | 1 | no | — |
| 212 | C2×#170 | — | 20 | 1 | no | — |
| 213 | C2×#170 | — | 20 | 1 | no | — |
| 214 | D5⋊C8 | — | 20 | 2 | no | — |
| 215 | D5⋊C8 | — | 20 | 2 | no | — |
| 216 | D5⋊C8 | — | 20 | 2 | no | — |
| 217 | D5⋊C8 | — | 20 | 2 | no | — |
| 218 | D5⋊C8 | — | 20 | 2 | no | — |
| 219 | D5⋊C8 | — | 20 | 2 | no | — |
| 220 | D5⋊C8 | — | 20 | 2 | no | — |
| 221 | D5⋊C8 | — | 20 | 2 | no | — |
| 222 | C2×C5×C8 | — | 5 | 1 | no | — |
| 223 | C2×C5×C8 | — | 5 | 1 | no | — |
| 224 | C2×C5×C8 | — | 5 | 1 | no | — |
| 225 | C2×C5×C8 | — | 5 | 1 | no | — |
| 226 | C42×C5 | — | 4 | 1 | no | — |
| 227 | C42×C5 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 228 | C42×C5 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 229 | C4×Dic5 | — | 5 | 1 | no | — |
| 230 | C4×Dic5 | — | 5 | 1 | no | — |
| 231 | C4×Dic5 | — | 5 | 1 | no | — |
| 232 | C4×Dic5 | — | 5 | 1 | no | — |
| 233 | C4×Dic5 | — | 5 | 1 | no | — |
| 234 | C4×Dic5 | — | 5 | 1 | no | — |
| 235 | C4×Dic5 | — | 20 | 1 | no | — |
| 236 | C4×Dic5 | — | 20 | 1 | no | — |
| 237 | C4×Dic5 | — | 20 | 1 | no | — |
| 238 | C2×#168 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 239 | C2×#168 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 240 | C2×#168 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 241 | C2×#168 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 242 | C8×D5 | — | 5 | 4 | no | — |
| 243 | C8×D5 | — | 5 | 4 | no | — |
| 244 | C8×D5 | — | 5 | 4 | no | — |
| 245 | C8×D5 | — | 5 | 4 | no | — |
| 246 | #674 | — | 2 | 2 | no | — |
| 247 | #674 | — | 5 | 4 | no | — |
| 248 | #674 | — | 10 | 2 | no | — |
| 249 | #674 | D5⋊C8 | 1 | 4 | yes | complemented |
| 250 | C5×C16 | — | 5 | 4 | no | — |
| 251 | C5×C16 | — | 10 | 2 | no | — |
| 252 | #672 | — | 5 | 4 | no | — |
| 253 | #672 | — | 10 | 2 | no | — |
| 254 | C22×C16 | — | 25 | 2 | no | — |
| 255 | C22×C16 | — | 25 | 2 | no | — |
| 256 | C2×C4×C8 | — | 25 | 1 | no | — |
| 257 | C2×C4×C8 | — | 25 | 1 | no | — |
| 258 | C2×C4×C8 | — | 25 | 1 | no | — |
| 259 | #346 | — | 5 | 1 | no | — |
| 260 | #346 | — | 5 | 1 | no | — |
| 261 | #346 | — | 25 | 1 | no | — |
| 262 | #346 | — | 25 | 1 | no | — |
| 263 | #346 | — | 25 | 2 | no | — |
| 264 | #346 | — | 25 | 2 | no | — |
| 265 | #322 | — | 25 | 1 | no | — |
| 266 | #322 | — | 25 | 1 | no | — |
| 267 | #322 | — | 25 | 1 | no | — |
| 268 | #322 | — | 25 | 1 | no | — |
| 269 | C2×C52 | C2×#322 | 1 | 1 | yes | characteristic |
| 270 | C2×C52 | C2×#347 | 1 | 1 | yes | characteristic |
| 271 | C2×C52 | C2×#347 | 1 | 1 | yes | characteristic |
| 272 | C5⋊D5 | #1313 | 1 | 4 | yes | complemented |
| 273 | C22×D5 | — | 5 | 1 | no | — |
| 274 | C22×D5 | — | 5 | 1 | no | — |
| 275 | C22×D5 | — | 20 | 1 | no | — |
| 276 | C2×C4×C5 | — | 4 | 1 | no | — |
| 277 | C2×C4×C5 | — | 4 | 1 | no | — |
| 278 | C2×C4×C5 | — | 4 | 1 | no | — |
| 279 | C2×C4×C5 | #3992 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×C5 | #3992 | 1 | 1 | yes | characteristic |
| 281 | C2×C4×C5 | #3992 | 1 | 1 | yes | characteristic |
| 282 | C2×C4×C5 | #3992 | 1 | 1 | yes | characteristic |
| 283 | C2×C4×C5 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 284 | C2×C4×C5 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 285 | C2×Dic5 | — | 5 | 1 | no | — |
| 286 | C2×Dic5 | — | 5 | 1 | no | — |
| 287 | C2×Dic5 | — | 5 | 1 | no | — |
| 288 | C2×Dic5 | — | 5 | 1 | no | — |
| 289 | C2×Dic5 | — | 5 | 1 | no | — |
| 290 | C2×Dic5 | — | 5 | 1 | no | — |
| 291 | C2×Dic5 | — | 20 | 1 | no | — |
| 292 | C2×Dic5 | — | 20 | 1 | no | — |
| 293 | C2×Dic5 | — | 20 | 1 | no | — |
| 294 | C4×D5 | — | 5 | 2 | no | — |
| 295 | C4×D5 | — | 5 | 2 | no | — |
| 296 | C4×D5 | — | 5 | 2 | no | — |
| 297 | C4×D5 | — | 5 | 2 | no | — |
| 298 | C4×D5 | — | 10 | 2 | no | — |
| 299 | C4×D5 | — | 10 | 2 | no | — |
| 300 | C4×D5 | — | 10 | 2 | no | — |
| 301 | C4×D5 | — | 10 | 2 | no | — |
| 302 | C4×D5 | — | 20 | 2 | no | — |
| 303 | C4×D5 | — | 20 | 2 | no | — |
| 304 | C4×D5 | — | 20 | 2 | no | — |
| 305 | C4×D5 | — | 20 | 2 | no | — |
| 306 | C4×D5 | — | 20 | 2 | no | — |
| 307 | C4×D5 | — | 20 | 2 | no | — |
| 308 | #170 | — | 20 | 1 | no | — |
| 309 | #170 | — | 20 | 1 | no | — |
| 310 | #170 | — | 20 | 1 | no | — |
| 311 | #170 | — | 20 | 1 | no | — |
| 312 | #170 | — | 20 | 1 | no | — |
| 313 | #170 | — | 20 | 1 | no | — |
| 314 | #170 | — | 20 | 1 | no | — |
| 315 | #170 | — | 20 | 1 | no | — |
| 316 | #170 | — | 20 | 1 | no | — |
| 317 | #170 | — | 20 | 1 | no | — |
| 318 | #170 | — | 20 | 1 | no | — |
| 319 | #170 | — | 20 | 1 | no | — |
| 320 | #170 | — | 20 | 1 | no | — |
| 321 | #170 | — | 20 | 1 | no | — |
| 322 | #170 | — | 20 | 1 | no | — |
| 323 | #170 | — | 20 | 1 | no | — |
| 324 | C5×C8 | — | 5 | 2 | no | — |
| 325 | C5×C8 | — | 5 | 2 | no | — |
| 326 | C5×C8 | — | 5 | 2 | no | — |
| 327 | C5×C8 | — | 5 | 2 | no | — |
| 328 | #168 | C8×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 329 | #168 | #3992 | 1 | 2 | yes | — |
| 330 | #168 | C2×D5⋊C8 | 1 | 2 | yes | — |
| 331 | #168 | D5⋊M16 | 1 | 2 | yes | — |
| 332 | C22×C8 | — | 25 | 1 | no | — |
| 333 | C22×C8 | — | 25 | 1 | no | — |
| 334 | C22×C8 | — | 50 | 1 | no | — |
| 335 | C22×C8 | — | 50 | 1 | no | — |
| 336 | C2×C42 | — | 25 | 1 | no | — |
| 337 | C2×C16 | — | 5 | 2 | no | — |
| 338 | C2×C16 | — | 5 | 2 | no | — |
| 339 | C2×C16 | — | 25 | 8 | no | — |
| 340 | C2×C16 | — | 25 | 2 | no | — |
| 341 | C2×C16 | — | 25 | 2 | no | — |
| 342 | C2×C16 | — | 50 | 4 | no | — |
| 343 | C4×C8 | — | 5 | 1 | no | — |
| 344 | C4×C8 | — | 5 | 1 | no | — |
| 345 | C4×C8 | — | 25 | 1 | no | — |
| 346 | C4×C8 | — | 25 | 1 | no | — |
| 347 | C4×C8 | — | 25 | 1 | no | — |
| 348 | C4×C8 | — | 25 | 1 | no | — |
| 349 | C4×C8 | — | 25 | 1 | no | — |
| 350 | C4×C8 | — | 25 | 1 | no | — |
| 351 | C4×C8 | — | 50 | 1 | no | — |
| 352 | C4×C8 | — | 50 | 1 | no | — |
| 353 | C52 | C2×#1313 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 354 | C22×C5 | — | 4 | 1 | no | — |
| 355 | C22×C5 | C2×#3992 | 1 | 1 | yes | characteristic |
| 356 | C22×C5 | C2×#3992 | 1 | 1 | yes | characteristic |
| 357 | C2×D5 | — | 5 | 2 | no | — |
| 358 | C2×D5 | — | 5 | 2 | no | — |
| 359 | C2×D5 | — | 5 | 2 | no | — |
| 360 | C2×D5 | — | 5 | 2 | no | — |
| 361 | C2×D5 | — | 5 | 2 | no | — |
| 362 | C2×D5 | — | 5 | 2 | no | — |
| 363 | C2×D5 | — | 20 | 2 | no | — |
| 364 | C2×D5 | — | 20 | 2 | no | — |
| 365 | C2×D5 | — | 20 | 2 | no | — |
| 366 | C4×C5 | — | 2 | 1 | no | — |
| 367 | C4×C5 | — | 2 | 1 | no | — |
| 368 | C4×C5 | — | 2 | 1 | no | — |
| 369 | C4×C5 | — | 2 | 1 | no | — |
| 370 | C4×C5 | — | 4 | 1 | no | — |
| 371 | C4×C5 | — | 4 | 1 | no | — |
| 372 | C4×C5 | — | 4 | 1 | no | — |
| 373 | C4×C5 | — | 4 | 1 | no | — |
| 374 | C4×C5 | — | 4 | 1 | no | — |
| 375 | C4×C5 | — | 4 | 1 | no | — |
| 376 | C4×C5 | C4×D5⋊C8 | 1 | 1 | yes | characteristic |
| 377 | C4×C5 | #65676 | 1 | 1 | yes | characteristic |
| 378 | C4×C5 | C2×C8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 379 | C4×C5 | C2×#3992 | 1 | 1 | yes | characteristic |
| 380 | Dic5 | — | 5 | 2 | no | — |
| 381 | Dic5 | — | 5 | 2 | no | — |
| 382 | Dic5 | — | 10 | 1 | no | — |
| 383 | Dic5 | — | 10 | 1 | no | — |
| 384 | Dic5 | — | 10 | 1 | no | — |
| 385 | Dic5 | — | 10 | 1 | no | — |
| 386 | Dic5 | — | 20 | 2 | no | — |
| 387 | Dic5 | — | 20 | 1 | no | — |
| 388 | Dic5 | — | 20 | 1 | no | — |
| 389 | Dic5 | — | 20 | 1 | no | — |
| 390 | Dic5 | — | 20 | 1 | no | — |
| 391 | C22×C4 | — | 25 | 1 | no | — |
| 392 | C22×C4 | — | 25 | 1 | no | — |
| 393 | C22×C4 | — | 25 | 1 | no | — |
| 394 | C2×C8 | — | 5 | 1 | no | — |
| 395 | C2×C8 | — | 5 | 1 | no | — |
| 396 | C2×C8 | — | 5 | 1 | no | — |
| 397 | C2×C8 | — | 5 | 1 | no | — |
| 398 | C2×C8 | — | 25 | 4 | no | — |
| 399 | C2×C8 | — | 25 | 4 | no | — |
| 400 | C2×C8 | — | 50 | 1 | no | — |
| 401 | C2×C8 | — | 50 | 1 | no | — |
| 402 | C2×C8 | — | 50 | 1 | no | — |
| 403 | C2×C8 | — | 50 | 1 | no | — |
| 404 | C2×C8 | — | 100 | 2 | no | — |
| 405 | C2×C8 | — | 100 | 2 | no | — |
| 406 | C42 | — | 25 | 1 | no | — |
| 407 | C42 | — | 25 | 1 | no | — |
| 408 | C42 | — | 25 | 1 | no | — |
| 409 | C42 | AGL(1,𝔽5)2 | 1 | 1 | yes | characteristic |
| 410 | C16 | — | 5 | 4 | no | — |
| 411 | C16 | — | 10 | 2 | no | — |
| 412 | C16 | — | 25 | 4 | no | — |
| 413 | C16 | — | 50 | 2 | no | — |
| 414 | C2×C5 | — | 4 | 1 | no | — |
| 415 | C2×C5 | — | 4 | 1 | no | — |
| 416 | C2×C5 | — | 4 | 1 | no | — |
| 417 | C2×C5 | #10603806 | 1 | 1 | yes | characteristic |
| 418 | C2×C5 | #10603807 | 1 | 1 | yes | characteristic |
| 419 | C2×C5 | #10604114 | 1 | 1 | yes | characteristic |
| 420 | C2×C5 | #10604114 | 1 | 1 | yes | characteristic |
| 421 | C2×C5 | #10604114 | 1 | 1 | yes | characteristic |
| 422 | C2×C5 | #10604114 | 1 | 1 | yes | characteristic |
| 423 | D5 | — | 5 | 4 | no | — |
| 424 | D5 | — | 5 | 4 | no | — |
| 425 | D5 | — | 20 | 4 | no | — |
| 426 | C23 | — | 25 | 1 | no | — |
| 427 | C2×C4 | — | 25 | 1 | no | — |
| 428 | C2×C4 | — | 25 | 2 | no | — |
| 429 | C2×C4 | — | 25 | 2 | no | — |
| 430 | C2×C4 | — | 25 | 1 | no | — |
| 431 | C2×C4 | — | 25 | 1 | no | — |
| 432 | C2×C4 | — | 50 | 2 | no | — |
| 433 | C2×C4 | — | 50 | 2 | no | — |
| 434 | C2×C4 | #11717302 | 1 | 1 | yes | characteristic |
| 435 | C2×C4 | #11717302 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | C2×AGL(1,𝔽5)2 | 1 | 1 | yes | characteristic |
| 437 | C8 | — | 5 | 2 | no | — |
| 438 | C8 | — | 5 | 2 | no | — |
| 439 | C8 | — | 5 | 2 | no | — |
| 440 | C8 | — | 5 | 2 | no | — |
| 441 | C8 | — | 100 | 1 | no | — |
| 442 | C8 | — | 100 | 1 | no | — |
| 443 | C8 | — | 100 | 1 | no | — |
| 444 | C8 | — | 100 | 1 | no | — |
| 445 | C5 | — | 4 | 1 | no | — |
| 446 | C5 | #13022987 | 1 | 1 | yes | characteristic, complemented |
| 447 | C5 | #13022991 | 1 | 1 | yes | characteristic, complemented |
| 448 | C22 | — | 25 | 2 | no | — |
| 449 | C22 | — | 25 | 2 | no | — |
| 450 | C22 | — | 25 | 2 | no | — |
| 451 | C22 | C2×#11717302 | 1 | 1 | yes | characteristic |
| 452 | C4 | — | 2 | 1 | no | — |
| 453 | C4 | — | 2 | 1 | no | — |
| 454 | C4 | — | 25 | 2 | no | — |
| 455 | C4 | — | 50 | 1 | no | — |
| 456 | C4 | — | 50 | 1 | no | — |
| 457 | C4 | AGL(1,𝔽5)×D5⋊C8 | 1 | 1 | yes | characteristic |
| 458 | C4 | #13107452 | 1 | 1 | yes | characteristic |
| 459 | C2 | — | 25 | 4 | no | — |
| 460 | C2 | #72220677 | 1 | 1 | yes | characteristic |
| 461 | C2 | #72242309 | 1 | 1 | yes | characteristic |
| 462 | C2 | #72242310 | 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