← #13032332
Subgroups — #13032332
Order 1280.
726 conjugacy classes of subgroups.
The subgroup lattice has 394 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10617227 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10612428 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10604794 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10604696 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#170⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10604481 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10604065 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10603945 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10603944 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#4131 | — | 2 | 2 | no | — |
| 11 | #65930 | C22 | 1 | 2 | yes | — |
| 12 | #65775 | — | 2 | 2 | no | — |
| 13 | #65774 | C22 | 1 | 2 | yes | — |
| 14 | D4×#170 | C22 | 1 | 2 | yes | — |
| 15 | #65758 | C22 | 1 | 2 | yes | — |
| 16 | C2×C4×#170 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×#170 | C22 | 1 | 1 | yes | characteristic |
| 18 | #65705 | C22 | 1 | 2 | yes | — |
| 19 | #65702 | C22 | 1 | 2 | yes | — |
| 20 | #65695 | — | 2 | 2 | no | — |
| 21 | #65692 | — | 2 | 2 | no | — |
| 22 | C5×#466 | C4 | 1 | 1 | yes | characteristic |
| 23 | #65440 | C4 | 1 | 1 | yes | characteristic |
| 24 | D8×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 25 | #65404 | C4 | 1 | 1 | yes | characteristic |
| 26 | C2×C8×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 27 | #65327 | C4 | 1 | 2 | yes | — |
| 28 | #65163 | C4 | 1 | 1 | yes | characteristic |
| 29 | #65161 | C22 | 1 | 1 | yes | characteristic |
| 30 | #65049 | C4 | 1 | 2 | yes | — |
| 31 | #65045 | C22 | 1 | 2 | yes | — |
| 32 | D4⋊#170 | C22 | 1 | 2 | yes | — |
| 33 | D4⋊#170 | C22 | 1 | 2 | yes | — |
| 34 | #64883 | C22 | 1 | 2 | yes | — |
| 35 | #64881 | C22 | 1 | 1 | yes | characteristic |
| 36 | #64881 | C22 | 1 | 1 | yes | characteristic |
| 37 | #170⋊C8 | C22 | 1 | 2 | yes | — |
| 38 | #170⋊C8 | C22 | 1 | 2 | yes | — |
| 39 | #64871 | C22 | 1 | 2 | yes | — |
| 40 | #64871 | C22 | 1 | 2 | yes | — |
| 41 | #17981 | — | 5 | 1 | no | maximal, Sylow |
| 42 | C2×#711 | — | 2 | 2 | no | — |
| 43 | C2×#704 | — | 2 | 2 | no | — |
| 44 | C2×#704 | — | 2 | 2 | no | — |
| 45 | C22×#170 | — | 2 | 1 | no | — |
| 46 | C22×#170 | — | 2 | 2 | no | — |
| 47 | C22×#170 | D4 | 1 | 2 | yes | — |
| 48 | #4131 | — | 4 | 8 | no | — |
| 49 | C2×#700 | — | 2 | 2 | no | — |
| 50 | C2×D5⋊C8 | — | 2 | 2 | no | — |
| 51 | C2×C5×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C22×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C5×#121 | C2×C4 | 1 | 2 | yes | — |
| 54 | #4086 | C2×C4 | 1 | 2 | yes | — |
| 55 | #4085 | — | 2 | 2 | no | — |
| 56 | D4×Dic5 | C23 | 1 | 2 | yes | — |
| 57 | C2×#686 | C2×C4 | 1 | 2 | yes | — |
| 58 | #4076 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×D40 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | #4039 | C23 | 1 | 2 | yes | — |
| 63 | #4034 | C2×C4 | 1 | 2 | yes | — |
| 64 | #4031 | — | 2 | 2 | no | — |
| 65 | #4027 | — | 2 | 2 | no | — |
| 66 | C22⋊#170 | — | 2 | 2 | no | — |
| 67 | C22⋊#170 | — | 2 | 2 | no | — |
| 68 | #4004 | — | 2 | 2 | no | — |
| 69 | #4003 | — | 2 | 2 | no | — |
| 70 | #4003 | — | 2 | 2 | no | — |
| 71 | C4⋊#170 | C23 | 1 | 2 | yes | — |
| 72 | C4⋊#170 | C23 | 1 | 2 | yes | — |
| 73 | C4×#170 | — | 2 | 1 | no | — |
| 74 | C4×#170 | D4 | 1 | 1 | yes | characteristic |
| 75 | C4×#170 | D4 | 1 | 1 | yes | characteristic |
| 76 | C4×#170 | C23 | 1 | 2 | yes | — |
| 77 | C4×#170 | C23 | 1 | 2 | yes | — |
| 78 | C5×#107 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C5×#102 | C2×C4 | 1 | 2 | yes | — |
| 80 | #3964 | C2×C4 | 1 | 2 | yes | — |
| 81 | #3953 | C2×C4 | 1 | 2 | yes | — |
| 82 | #3950 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C8×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C8×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C8×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 86 | C8×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 87 | #3941 | C2×C4 | 1 | 2 | yes | — |
| 88 | #3939 | C2×C4 | 1 | 2 | yes | — |
| 89 | #3169 | — | 5 | 1 | no | — |
| 90 | #2931 | — | 5 | 2 | no | — |
| 91 | #1586 | — | 5 | 2 | no | — |
| 92 | #1586 | — | 5 | 2 | no | — |
| 93 | #1586 | — | 5 | 2 | no | — |
| 94 | #1586 | — | 5 | 2 | no | — |
| 95 | #1566 | — | 5 | 1 | no | — |
| 96 | #1492 | — | 5 | 2 | no | — |
| 97 | C2×#322 | — | 5 | 1 | no | — |
| 98 | C2×C5×D4 | — | 2 | 2 | no | — |
| 99 | C2×C5×D4 | C22×C4 | 1 | 2 | yes | — |
| 100 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 102 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 103 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 104 | C22×Dic5 | — | 2 | 2 | no | — |
| 105 | C22×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C22×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 107 | #711 | — | 4 | 4 | no | — |
| 108 | #711 | — | 4 | 4 | no | — |
| 109 | C2×D20 | C22×C4 | 1 | 2 | yes | — |
| 110 | C2×C4×D5 | — | 2 | 2 | no | — |
| 111 | C2×Dic10 | — | 2 | 2 | no | — |
| 112 | #704 | — | 4 | 4 | no | — |
| 113 | #704 | — | 4 | 4 | no | — |
| 114 | C2×#170 | — | 2 | 4 | no | — |
| 115 | C2×#170 | — | 2 | 4 | no | — |
| 116 | C2×#170 | — | 2 | 2 | no | — |
| 117 | C2×#170 | — | 2 | 2 | no | — |
| 118 | C2×#170 | — | 2 | 2 | no | — |
| 119 | C2×#170 | — | 4 | 4 | no | — |
| 120 | C2×#170 | C2×D4 | 1 | 2 | yes | — |
| 121 | C2×#170 | C2×D4 | 1 | 2 | yes | — |
| 122 | #700 | — | 4 | 4 | no | — |
| 123 | D5⋊C8 | — | 4 | 4 | no | — |
| 124 | C5×D8 | — | 4 | 1 | no | — |
| 125 | C2×C5×C8 | — | 4 | 1 | no | — |
| 126 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 128 | C5×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 129 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 130 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 131 | #686 | — | 4 | 2 | no | — |
| 132 | #685 | — | 2 | 2 | no | — |
| 133 | #685 | — | 2 | 2 | no | — |
| 134 | C4⋊Dic5 | C22×C4 | 1 | 2 | yes | — |
| 135 | #683 | — | 2 | 2 | no | — |
| 136 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 137 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C4×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 139 | C4×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 140 | C2×#168 | — | 4 | 1 | no | — |
| 141 | C2×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 142 | C2×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | D40 | — | 4 | 1 | no | — |
| 144 | C2×#131 | — | 10 | 2 | no | — |
| 145 | #532 | — | 5 | 2 | no | — |
| 146 | #500 | — | 5 | 1 | no | — |
| 147 | #493 | — | 5 | 1 | no | — |
| 148 | #486 | — | 5 | 2 | no | — |
| 149 | #466 | — | 5 | 1 | no | — |
| 150 | #466 | — | 5 | 2 | no | — |
| 151 | #466 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 152 | C4×D8 | — | 5 | 1 | no | — |
| 153 | C4×D8 | — | 5 | 1 | no | — |
| 154 | C4×D8 | — | 5 | 2 | no | — |
| 155 | #436 | — | 5 | 2 | no | — |
| 156 | #436 | — | 5 | 2 | no | — |
| 157 | #436 | — | 10 | 2 | no | — |
| 158 | C8×D4 | — | 5 | 2 | no | — |
| 159 | C8×D4 | — | 5 | 2 | no | — |
| 160 | C8×D4 | — | 10 | 2 | no | — |
| 161 | #423 | — | 5 | 2 | no | — |
| 162 | #408 | — | 10 | 2 | no | — |
| 163 | C2×C4×C8 | — | 5 | 1 | no | — |
| 164 | C2×C4×C8 | — | 5 | 1 | no | — |
| 165 | C2×C4×C8 | — | 5 | 1 | no | — |
| 166 | #334 | — | 5 | 1 | no | — |
| 167 | #334 | — | 5 | 1 | no | — |
| 168 | #334 | — | 5 | 2 | no | — |
| 169 | D4⋊C8 | — | 5 | 2 | no | — |
| 170 | D4⋊C8 | — | 5 | 2 | no | — |
| 171 | D4⋊C8 | — | 5 | 2 | no | — |
| 172 | D4⋊C8 | — | 5 | 2 | no | — |
| 173 | #322 | — | 5 | 2 | no | — |
| 174 | #322 | — | 5 | 2 | no | — |
| 175 | C23×C5 | — | 2 | 2 | no | — |
| 176 | C23×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 177 | C22×D5 | — | 2 | 2 | no | — |
| 178 | C5×D4 | — | 2 | 2 | no | — |
| 179 | C5×D4 | — | 2 | 2 | no | — |
| 180 | C5×D4 | — | 4 | 4 | no | — |
| 181 | C2×C4×C5 | — | 2 | 1 | no | — |
| 182 | C2×C4×C5 | — | 2 | 1 | no | — |
| 183 | C2×C4×C5 | — | 2 | 2 | no | — |
| 184 | C2×C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 186 | C22⋊D5 | — | 4 | 4 | no | — |
| 187 | C22⋊D5 | — | 4 | 4 | no | — |
| 188 | C22⋊D5 | — | 4 | 4 | no | — |
| 189 | C2×Dic5 | — | 2 | 2 | no | — |
| 190 | C2×Dic5 | — | 2 | 2 | no | — |
| 191 | C2×Dic5 | — | 4 | 2 | no | — |
| 192 | C2×Dic5 | — | 4 | 2 | no | — |
| 193 | C2×Dic5 | C4×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×Dic5 | C4×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×Dic5 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 196 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×Dic5 | C2×#41 | 1 | 1 | yes | characteristic |
| 198 | D20 | — | 2 | 2 | no | — |
| 199 | D20 | — | 2 | 2 | no | — |
| 200 | C4×D5 | — | 4 | 2 | no | — |
| 201 | C4×D5 | — | 4 | 2 | no | — |
| 202 | Dic10 | — | 4 | 4 | no | — |
| 203 | #170 | — | 2 | 4 | no | — |
| 204 | #170 | — | 2 | 2 | no | — |
| 205 | #170 | — | 2 | 2 | no | — |
| 206 | #170 | — | 4 | 2 | no | — |
| 207 | #170 | — | 4 | 2 | no | — |
| 208 | C5×C8 | — | 2 | 1 | no | — |
| 209 | C5×C8 | — | 2 | 1 | no | — |
| 210 | #168 | — | 2 | 1 | no | — |
| 211 | #168 | — | 2 | 1 | no | — |
| 212 | C2×#41 | — | 10 | 2 | no | — |
| 213 | C2×D8 | — | 5 | 2 | no | — |
| 214 | C2×D8 | — | 5 | 1 | no | — |
| 215 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 216 | #131 | — | 20 | 8 | no | — |
| 217 | C2×M16 | — | 10 | 2 | no | — |
| 218 | C2×M16 | — | 10 | 2 | no | — |
| 219 | C2×M16 | — | 10 | 2 | no | — |
| 220 | C22×C8 | — | 5 | 2 | no | — |
| 221 | C22×C8 | — | 5 | 1 | no | — |
| 222 | C22×C8 | — | 10 | 2 | no | — |
| 223 | C22×C8 | — | 10 | 2 | no | — |
| 224 | C22×C8 | — | 10 | 1 | no | — |
| 225 | C22×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 226 | C4⋊Q8 | — | 5 | 2 | no | — |
| 227 | #127 | — | 5 | 2 | no | — |
| 228 | #124 | — | 10 | 2 | no | — |
| 229 | #121 | — | 5 | 2 | no | — |
| 230 | #121 | — | 10 | 2 | no | — |
| 231 | #121 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 232 | C4×D4 | — | 5 | 2 | no | — |
| 233 | C4×D4 | — | 5 | 2 | no | — |
| 234 | C4×D4 | — | 10 | 2 | no | — |
| 235 | C2×C42 | — | 5 | 1 | no | — |
| 236 | #107 | — | 5 | 1 | no | — |
| 237 | #107 | — | 5 | 2 | no | — |
| 238 | #107 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 239 | C4⋊C8 | — | 5 | 2 | no | — |
| 240 | C4⋊C8 | — | 5 | 2 | no | — |
| 241 | C4⋊C8 | — | 10 | 2 | no | — |
| 242 | #102 | — | 5 | 2 | no | — |
| 243 | #102 | — | 5 | 2 | no | — |
| 244 | #102 | — | 5 | 2 | no | — |
| 245 | #102 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 246 | C22⋊C8 | — | 10 | 2 | no | — |
| 247 | C22⋊C8 | — | 10 | 2 | no | — |
| 248 | C22⋊C8 | — | 10 | 2 | no | — |
| 249 | C22⋊C8 | — | 10 | 2 | no | — |
| 250 | C4×C8 | — | 5 | 2 | no | — |
| 251 | C4×C8 | — | 5 | 1 | no | — |
| 252 | C4×C8 | — | 5 | 1 | no | — |
| 253 | C4×C8 | — | 5 | 1 | no | — |
| 254 | C4×C8 | — | 5 | 1 | no | — |
| 255 | C4×C8 | — | 5 | 1 | no | — |
| 256 | C4×C8 | — | 5 | 1 | no | — |
| 257 | C4×C8 | — | 5 | 2 | no | — |
| 258 | C4×C8 | — | 10 | 1 | no | — |
| 259 | C22×C5 | — | 2 | 1 | no | — |
| 260 | C22×C5 | — | 2 | 1 | no | — |
| 261 | C22×C5 | — | 4 | 2 | no | — |
| 262 | C22×C5 | — | 4 | 2 | no | — |
| 263 | C22×C5 | — | 4 | 2 | no | — |
| 264 | C22×C5 | #442 | 1 | 2 | yes | — |
| 265 | C22×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×D5 | — | 4 | 2 | no | — |
| 267 | C2×D5 | — | 4 | 2 | no | — |
| 268 | C2×D5 | — | 4 | 2 | no | — |
| 269 | C4×C5 | — | 2 | 1 | no | — |
| 270 | C4×C5 | — | 4 | 2 | no | — |
| 271 | C4×C5 | #568 | 1 | 1 | yes | characteristic |
| 272 | C4×C5 | #568 | 1 | 1 | yes | characteristic |
| 273 | Dic5 | — | 2 | 1 | no | — |
| 274 | Dic5 | — | 4 | 2 | no | — |
| 275 | Dic5 | #442 | 1 | 2 | yes | — |
| 276 | Dic5 | #443 | 1 | 2 | yes | — |
| 277 | Dic5 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 278 | #41 | — | 20 | 4 | no | — |
| 279 | #41 | — | 20 | 4 | no | — |
| 280 | C2×Q8 | — | 10 | 2 | no | — |
| 281 | C2×D4 | — | 2 | 2 | no | — |
| 282 | C2×D4 | — | 5 | 2 | no | — |
| 283 | C2×D4 | — | 10 | 2 | no | — |
| 284 | C2×D4 | — | 10 | 2 | no | — |
| 285 | C2×D4 | — | 10 | 2 | no | — |
| 286 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 287 | C22×C4 | — | 5 | 1 | no | — |
| 288 | C22×C4 | — | 5 | 1 | no | — |
| 289 | C22×C4 | — | 10 | 2 | no | — |
| 290 | C22×C4 | — | 10 | 2 | no | — |
| 291 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 292 | D8 | — | 4 | 1 | no | — |
| 293 | D8 | — | 20 | 1 | no | — |
| 294 | D8 | — | 20 | 2 | no | — |
| 295 | M16 | — | 20 | 4 | no | — |
| 296 | M16 | — | 20 | 4 | no | — |
| 297 | M16 | — | 20 | 4 | no | — |
| 298 | C2×C8 | — | 4 | 1 | no | — |
| 299 | C2×C8 | — | 5 | 2 | no | — |
| 300 | C2×C8 | — | 5 | 2 | no | — |
| 301 | C2×C8 | — | 5 | 1 | no | — |
| 302 | C2×C8 | — | 5 | 1 | no | — |
| 303 | C2×C8 | — | 10 | 2 | no | — |
| 304 | C2×C8 | — | 10 | 4 | no | — |
| 305 | C2×C8 | — | 10 | 4 | no | — |
| 306 | C2×C8 | — | 10 | 2 | no | — |
| 307 | C2×C8 | — | 10 | 2 | no | — |
| 308 | C2×C8 | — | 20 | 1 | no | — |
| 309 | C2×C8 | — | 20 | 4 | no | — |
| 310 | C2×C8 | — | 20 | 4 | no | — |
| 311 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 312 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 313 | C4⋊C4 | — | 5 | 2 | no | — |
| 314 | C4⋊C4 | — | 10 | 2 | no | — |
| 315 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 316 | C22⋊C4 | — | 2 | 2 | no | — |
| 317 | C22⋊C4 | — | 10 | 2 | no | — |
| 318 | C22⋊C4 | — | 10 | 2 | no | — |
| 319 | C22⋊C4 | — | 10 | 2 | no | — |
| 320 | C42 | — | 5 | 1 | no | — |
| 321 | C42 | — | 5 | 1 | no | — |
| 322 | C42 | — | 5 | 1 | no | — |
| 323 | C42 | — | 5 | 1 | no | — |
| 324 | C2×C5 | — | 2 | 2 | no | — |
| 325 | C2×C5 | — | 8 | 2 | no | — |
| 326 | C2×C5 | #2932 | 1 | 1 | yes | characteristic |
| 327 | C2×C5 | C2×#442 | 1 | 1 | yes | characteristic |
| 328 | C2×C5 | C2×#443 | 1 | 1 | yes | characteristic |
| 329 | D5 | — | 8 | 2 | no | — |
| 330 | C23 | — | 2 | 2 | no | — |
| 331 | C23 | — | 10 | 2 | no | — |
| 332 | C23 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 333 | Q8 | — | 20 | 4 | no | — |
| 334 | D4 | — | 2 | 2 | no | — |
| 335 | D4 | — | 2 | 2 | no | — |
| 336 | D4 | — | 4 | 4 | no | — |
| 337 | D4 | — | 10 | 2 | no | — |
| 338 | D4 | — | 10 | 2 | no | — |
| 339 | D4 | — | 20 | 4 | no | — |
| 340 | D4 | — | 20 | 4 | no | — |
| 341 | D4 | — | 20 | 4 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 2 | 1 | no | — |
| 344 | C2×C4 | — | 2 | 2 | no | — |
| 345 | C2×C4 | — | 5 | 4 | no | — |
| 346 | C2×C4 | — | 5 | 1 | no | — |
| 347 | C2×C4 | — | 5 | 1 | no | — |
| 348 | C2×C4 | — | 5 | 1 | no | — |
| 349 | C2×C4 | — | 5 | 1 | no | — |
| 350 | C2×C4 | — | 10 | 2 | no | — |
| 351 | C2×C4 | — | 10 | 2 | no | — |
| 352 | C2×C4 | — | 20 | 2 | no | — |
| 353 | C2×C4 | — | 20 | 2 | no | — |
| 354 | C2×C4 | — | 20 | 2 | no | — |
| 355 | C2×C4 | — | 20 | 2 | no | — |
| 356 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 358 | C8 | — | 2 | 1 | no | — |
| 359 | C8 | — | 2 | 1 | no | — |
| 360 | C8 | — | 10 | 2 | no | — |
| 361 | C8 | — | 10 | 2 | no | — |
| 362 | C8 | — | 10 | 4 | no | — |
| 363 | C8 | — | 10 | 1 | no | — |
| 364 | C8 | — | 10 | 1 | no | — |
| 365 | C8 | — | 20 | 2 | no | — |
| 366 | C8 | — | 20 | 2 | no | — |
| 367 | C5 | #17981 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 368 | C22 | — | 2 | 1 | no | — |
| 369 | C22 | — | 2 | 1 | no | — |
| 370 | C22 | — | 4 | 2 | no | — |
| 371 | C22 | — | 4 | 2 | no | — |
| 372 | C22 | — | 4 | 2 | no | — |
| 373 | C22 | — | 20 | 2 | no | — |
| 374 | C22 | — | 20 | 2 | no | — |
| 375 | C22 | — | 20 | 2 | no | — |
| 376 | C22 | #65731 | 1 | 2 | yes | — |
| 377 | C22 | C2×D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 378 | C4 | — | 2 | 1 | no | — |
| 379 | C4 | — | 4 | 2 | no | — |
| 380 | C4 | — | 5 | 2 | no | — |
| 381 | C4 | — | 5 | 2 | no | — |
| 382 | C4 | — | 5 | 2 | no | — |
| 383 | C4 | — | 10 | 1 | no | — |
| 384 | C4 | — | 20 | 2 | no | — |
| 385 | C4 | #66256 | 1 | 1 | yes | characteristic |
| 386 | C4 | #66264 | 1 | 1 | yes | characteristic |
| 387 | C2 | — | 2 | 2 | no | — |
| 388 | C2 | — | 8 | 2 | no | — |
| 389 | C2 | — | 40 | 2 | no | — |
| 390 | C2 | #10617228 | 1 | 1 | yes | characteristic |
| 391 | C2 | C2×#65731 | 1 | 1 | yes | characteristic |
| 392 | C2 | D5⋊#443 | 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