Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
572 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10615047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615037 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10605466 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#1980 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10600653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10600650 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598112 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C5×#532 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#4021 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C4×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C5×#104 | — | 2 | 2 | no | — |
| 12 | C4×C5×M16 | C22 | 1 | 1 | yes | characteristic |
| 13 | C4×C5×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 14 | #65380 | — | 2 | 1 | no | — |
| 15 | #65378 | — | 2 | 1 | no | — |
| 16 | #65364 | — | 2 | 1 | no | — |
| 17 | #65363 | — | 2 | 1 | no | — |
| 18 | #65329 | — | 2 | 1 | no | — |
| 19 | #65329 | — | 2 | 1 | no | — |
| 20 | #65325 | — | 2 | 1 | no | — |
| 21 | #65322 | — | 2 | 1 | no | — |
| 22 | #65307 | — | 2 | 2 | no | — |
| 23 | #65305 | — | 2 | 2 | no | — |
| 24 | #65277 | — | 2 | 1 | no | — |
| 25 | #65263 | — | 2 | 1 | no | — |
| 26 | #65229 | — | 2 | 2 | no | — |
| 27 | #65215 | C22 | 1 | 1 | yes | characteristic |
| 28 | #65215 | C22 | 1 | 1 | yes | characteristic |
| 29 | #64963 | — | 2 | 1 | no | — |
| 30 | #64962 | — | 2 | 1 | no | — |
| 31 | #64684 | — | 2 | 2 | no | — |
| 32 | #64676 | — | 2 | 2 | no | — |
| 33 | #10006 | — | 5 | 1 | no | maximal, Sylow |
| 34 | C2×C5×#41 | — | 2 | 1 | no | — |
| 35 | C22×D20 | D4 | 1 | 1 | yes | characteristic |
| 36 | C22×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 37 | C22×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×C5×M16 | — | 2 | 1 | no | — |
| 39 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 40 | C5×#127 | D4 | 1 | 1 | yes | characteristic |
| 41 | C5×#124 | — | 2 | 1 | no | — |
| 42 | C5×#121 | — | 2 | 1 | no | — |
| 43 | C5×#121 | — | 2 | 1 | no | — |
| 44 | C4×C5×D4 | — | 2 | 1 | no | — |
| 45 | C4×C5×D4 | — | 2 | 1 | no | — |
| 46 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 47 | C2×C42×C5 | D4 | 1 | 2 | yes | — |
| 48 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#687 | — | 2 | 2 | no | — |
| 50 | C2×#687 | — | 2 | 2 | no | — |
| 51 | C2×#686 | — | 2 | 2 | no | — |
| 52 | C2×#685 | — | 2 | 2 | no | — |
| 53 | C2×#685 | — | 2 | 1 | no | — |
| 54 | C2×#685 | — | 2 | 1 | no | — |
| 55 | C2×#685 | — | 2 | 2 | no | — |
| 56 | C2×C4⋊Dic5 | D4 | 1 | 1 | yes | characteristic |
| 57 | C2×#683 | — | 2 | 1 | no | — |
| 58 | C2×C4×Dic5 | — | 2 | 1 | no | — |
| 59 | #4021 | — | 2 | 1 | no | — |
| 60 | #4021 | — | 2 | 1 | no | — |
| 61 | #4021 | — | 2 | 1 | no | — |
| 62 | #4021 | — | 2 | 1 | no | — |
| 63 | C4×Dic10 | — | 2 | 1 | no | — |
| 64 | C4×Dic10 | — | 2 | 1 | no | — |
| 65 | C4×Dic10 | — | 2 | 1 | no | — |
| 66 | C4×Dic10 | — | 2 | 1 | no | — |
| 67 | C5×#104 | — | 4 | 4 | no | — |
| 68 | C5×#97 | — | 2 | 1 | no | — |
| 69 | C4×C5×C8 | — | 2 | 1 | no | — |
| 70 | C5×#95 | — | 2 | 1 | no | — |
| 71 | #3964 | — | 2 | 2 | no | — |
| 72 | #3963 | — | 2 | 2 | no | — |
| 73 | #3963 | — | 2 | 2 | no | — |
| 74 | C22⋊#168 | — | 2 | 1 | no | — |
| 75 | C22⋊#168 | — | 2 | 1 | no | — |
| 76 | #3942 | — | 2 | 2 | no | — |
| 77 | #3942 | — | 2 | 2 | no | — |
| 78 | #3941 | — | 2 | 2 | no | — |
| 79 | #3939 | — | 2 | 2 | no | — |
| 80 | C4⋊#168 | — | 2 | 1 | no | — |
| 81 | C4⋊#168 | D4 | 1 | 2 | yes | — |
| 82 | #3935 | — | 2 | 1 | no | — |
| 83 | #3935 | D4 | 1 | 2 | yes | — |
| 84 | #3213 | — | 5 | 1 | no | — |
| 85 | #3112 | — | 5 | 1 | no | — |
| 86 | #2592 | — | 5 | 1 | no | — |
| 87 | #1980 | D5 | 1 | 1 | yes | characteristic, complemented |
| 88 | #1527 | — | 5 | 1 | no | — |
| 89 | #1491 | — | 5 | 1 | no | — |
| 90 | #1285 | — | 5 | 1 | no | — |
| 91 | C23×D5 | — | 2 | 1 | no | — |
| 92 | C5×#41 | — | 4 | 2 | no | — |
| 93 | C5×#41 | — | 4 | 2 | no | — |
| 94 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 95 | C2×C5×D4 | — | 2 | 1 | no | — |
| 96 | C2×C5×D4 | — | 2 | 1 | no | — |
| 97 | C2×C5×D4 | — | 2 | 1 | no | — |
| 98 | C2×C5×D4 | — | 4 | 1 | no | — |
| 99 | C22×C4×C5 | — | 2 | 2 | no | — |
| 100 | C22×C4×C5 | — | 4 | 1 | no | — |
| 101 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C22×Dic5 | — | 2 | 1 | no | — |
| 105 | C22×Dic5 | — | 2 | 1 | no | — |
| 106 | C22×Dic5 | — | 2 | 1 | no | — |
| 107 | C2×D20 | — | 2 | 1 | no | — |
| 108 | C2×D20 | — | 2 | 1 | no | — |
| 109 | C2×D20 | — | 4 | 2 | no | — |
| 110 | C2×Dic10 | — | 2 | 1 | no | — |
| 111 | C2×Dic10 | — | 2 | 1 | no | — |
| 112 | C2×Dic10 | — | 2 | 1 | no | — |
| 113 | C2×Dic10 | — | 2 | 1 | no | — |
| 114 | C2×Dic10 | — | 4 | 2 | no | — |
| 115 | C2×Dic10 | — | 4 | 2 | no | — |
| 116 | C5×M16 | — | 2 | 2 | no | — |
| 117 | C5×M16 | — | 4 | 1 | no | — |
| 118 | C2×C5×C8 | — | 4 | 1 | no | — |
| 119 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 120 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 121 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 122 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 123 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 124 | C42×C5 | — | 4 | 2 | no | — |
| 125 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C42×C5 | #41 | 1 | 1 | yes | characteristic |
| 129 | #687 | — | 4 | 4 | no | — |
| 130 | #687 | — | 8 | 2 | no | — |
| 131 | #686 | — | 8 | 2 | no | — |
| 132 | #685 | — | 4 | 4 | no | — |
| 133 | #685 | — | 4 | 1 | no | — |
| 134 | #685 | — | 4 | 1 | no | — |
| 135 | #685 | — | 4 | 1 | no | — |
| 136 | #685 | — | 4 | 1 | no | — |
| 137 | #685 | — | 8 | 2 | no | — |
| 138 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 139 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 140 | #683 | — | 4 | 1 | no | — |
| 141 | #683 | — | 4 | 1 | no | — |
| 142 | C4×Dic5 | — | 4 | 1 | no | — |
| 143 | C4×Dic5 | — | 4 | 1 | no | — |
| 144 | C2×#168 | — | 2 | 2 | no | — |
| 145 | C2×#168 | — | 2 | 2 | no | — |
| 146 | #532 | C2×D5 | 1 | 1 | yes | characteristic |
| 147 | C2×#124 | — | 5 | 1 | no | — |
| 148 | C2×C4×Q8 | — | 5 | 1 | no | — |
| 149 | #496 | — | 10 | 1 | no | — |
| 150 | #489 | — | 10 | 1 | no | — |
| 151 | #480 | — | 10 | 1 | no | — |
| 152 | #477 | — | 10 | 1 | no | — |
| 153 | #463 | — | 10 | 2 | no | — |
| 154 | #460 | — | 10 | 1 | no | — |
| 155 | #448 | — | 10 | 1 | no | — |
| 156 | #448 | — | 10 | 1 | no | — |
| 157 | #447 | — | 10 | 1 | no | — |
| 158 | #440 | — | 10 | 2 | no | — |
| 159 | #432 | — | 5 | 1 | no | — |
| 160 | #432 | — | 5 | 1 | no | — |
| 161 | C2×#104 | — | 2 | 2 | no | — |
| 162 | C4×M16 | C2×D5 | 1 | 1 | yes | characteristic |
| 163 | #397 | — | 10 | 1 | no | — |
| 164 | #393 | — | 10 | 1 | no | — |
| 165 | #391 | — | 10 | 1 | no | — |
| 166 | #390 | — | 10 | 1 | no | — |
| 167 | #388 | — | 10 | 2 | no | — |
| 168 | C4×C4⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 169 | #329 | — | 10 | 2 | no | — |
| 170 | Q8⋊C8 | — | 10 | 2 | no | — |
| 171 | C23×C5 | — | 4 | 1 | no | — |
| 172 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 173 | C22×D5 | — | 4 | 2 | no | — |
| 174 | C22×D5 | — | 4 | 2 | no | — |
| 175 | C22×D5 | — | 4 | 1 | no | — |
| 176 | C22×D5 | — | 4 | 1 | no | — |
| 177 | C22×D5 | — | 4 | 1 | no | — |
| 178 | C5×Q8 | — | 4 | 2 | no | — |
| 179 | C5×D4 | — | 4 | 2 | no | — |
| 180 | C5×D4 | — | 4 | 2 | no | — |
| 181 | C5×D4 | — | 4 | 2 | no | — |
| 182 | C5×D4 | — | 8 | 1 | no | — |
| 183 | C5×D4 | — | 8 | 1 | no | — |
| 184 | C2×C4×C5 | — | 2 | 1 | no | — |
| 185 | C2×C4×C5 | — | 2 | 1 | no | — |
| 186 | C2×C4×C5 | — | 2 | 2 | no | — |
| 187 | C2×C4×C5 | — | 4 | 1 | no | — |
| 188 | C2×C4×C5 | — | 4 | 2 | no | — |
| 189 | C2×C4×C5 | — | 4 | 2 | no | — |
| 190 | C2×C4×C5 | — | 4 | 1 | no | — |
| 191 | C2×C4×C5 | — | 4 | 2 | no | — |
| 192 | C2×C4×C5 | — | 8 | 2 | no | — |
| 193 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 198 | C2×C4×C5 | #127 | 1 | 1 | yes | characteristic |
| 199 | C2×Dic5 | — | 2 | 2 | no | — |
| 200 | C2×Dic5 | — | 4 | 1 | no | — |
| 201 | C2×Dic5 | — | 4 | 1 | no | — |
| 202 | C2×Dic5 | — | 4 | 2 | no | — |
| 203 | C2×Dic5 | — | 4 | 1 | no | — |
| 204 | C2×Dic5 | — | 4 | 1 | no | — |
| 205 | C2×Dic5 | — | 4 | 1 | no | — |
| 206 | C2×Dic5 | — | 4 | 1 | no | — |
| 207 | D20 | — | 4 | 2 | no | — |
| 208 | D20 | — | 8 | 1 | no | — |
| 209 | Dic10 | — | 2 | 2 | no | — |
| 210 | Dic10 | — | 2 | 2 | no | — |
| 211 | Dic10 | — | 4 | 1 | no | — |
| 212 | Dic10 | — | 4 | 1 | no | — |
| 213 | Dic10 | — | 4 | 2 | no | — |
| 214 | Dic10 | — | 8 | 1 | no | — |
| 215 | C5×C8 | — | 4 | 2 | no | — |
| 216 | #168 | — | 4 | 2 | no | — |
| 217 | #168 | — | 4 | 2 | no | — |
| 218 | C2×#41 | — | 2 | 1 | no | — |
| 219 | C22×Q8 | — | 5 | 1 | no | — |
| 220 | C22×Q8 | — | 5 | 1 | no | — |
| 221 | C22×D4 | — | 5 | 1 | no | — |
| 222 | C2×SD16 | — | 10 | 2 | no | — |
| 223 | C2×SD16 | — | 10 | 2 | no | — |
| 224 | C2×D8 | — | 10 | 2 | no | — |
| 225 | C2×M16 | — | 2 | 1 | no | — |
| 226 | C4⋊Q8 | D20 | 1 | 1 | yes | characteristic |
| 227 | #127 | D20 | 1 | 1 | yes | characteristic |
| 228 | #124 | — | 2 | 1 | no | — |
| 229 | #124 | — | 10 | 1 | no | — |
| 230 | #124 | — | 10 | 1 | no | — |
| 231 | #124 | — | 10 | 1 | no | — |
| 232 | #124 | — | 10 | 1 | no | — |
| 233 | #121 | — | 2 | 1 | no | — |
| 234 | #121 | — | 2 | 1 | no | — |
| 235 | C4×Q8 | — | 10 | 1 | no | — |
| 236 | C4×Q8 | — | 10 | 1 | no | — |
| 237 | C4×Q8 | — | 10 | 1 | no | — |
| 238 | C4×Q8 | — | 10 | 1 | no | — |
| 239 | C4×D4 | — | 2 | 1 | no | — |
| 240 | C4×D4 | — | 2 | 1 | no | — |
| 241 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 242 | C2×C4⋊C4 | — | 5 | 1 | no | — |
| 243 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 244 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 245 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 246 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 247 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 248 | C2×C42 | — | 10 | 1 | no | — |
| 249 | C2×C42 | C22⋊D5 | 1 | 2 | yes | — |
| 250 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 251 | #107 | — | 10 | 2 | no | — |
| 252 | C4⋊C8 | — | 5 | 2 | no | — |
| 253 | C4⋊C8 | — | 10 | 1 | no | — |
| 254 | #104 | — | 4 | 4 | no | — |
| 255 | #103 | — | 10 | 2 | no | — |
| 256 | #103 | — | 10 | 2 | no | — |
| 257 | #102 | — | 10 | 2 | no | — |
| 258 | #102 | — | 10 | 2 | no | — |
| 259 | C22⋊C8 | — | 10 | 1 | no | — |
| 260 | C22⋊C8 | — | 10 | 1 | no | — |
| 261 | #97 | — | 2 | 1 | no | — |
| 262 | #97 | — | 5 | 2 | no | — |
| 263 | #97 | — | 10 | 1 | no | — |
| 264 | C4×C8 | — | 2 | 1 | no | — |
| 265 | #95 | — | 2 | 1 | no | — |
| 266 | #95 | — | 10 | 2 | no | — |
| 267 | #95 | — | 10 | 2 | no | — |
| 268 | C22×C5 | — | 2 | 1 | no | — |
| 269 | C22×C5 | — | 2 | 1 | no | — |
| 270 | C22×C5 | — | 8 | 1 | no | — |
| 271 | C22×C5 | — | 8 | 1 | no | — |
| 272 | C22×C5 | — | 8 | 1 | no | — |
| 273 | C22×C5 | #392 | 1 | 1 | yes | characteristic |
| 274 | C22×C5 | #453 | 1 | 1 | yes | characteristic |
| 275 | C22×C5 | #454 | 1 | 1 | yes | characteristic |
| 276 | C2×D5 | — | 8 | 2 | no | — |
| 277 | C2×D5 | — | 8 | 2 | no | — |
| 278 | C2×D5 | — | 8 | 1 | no | — |
| 279 | C2×D5 | — | 8 | 1 | no | — |
| 280 | C2×D5 | — | 8 | 1 | no | — |
| 281 | C4×C5 | — | 2 | 1 | no | — |
| 282 | C4×C5 | — | 2 | 1 | no | — |
| 283 | C4×C5 | — | 2 | 1 | no | — |
| 284 | C4×C5 | — | 2 | 1 | no | — |
| 285 | C4×C5 | — | 2 | 1 | no | — |
| 286 | C4×C5 | — | 8 | 2 | no | — |
| 287 | C4×C5 | — | 8 | 1 | no | — |
| 288 | C4×C5 | #455 | 1 | 2 | yes | — |
| 289 | Dic5 | — | 4 | 2 | no | — |
| 290 | Dic5 | — | 8 | 1 | no | — |
| 291 | Dic5 | — | 8 | 1 | no | — |
| 292 | C24 | — | 10 | 1 | no | — |
| 293 | #41 | — | 4 | 2 | no | — |
| 294 | #41 | — | 4 | 2 | no | — |
| 295 | C2×Q8 | — | 2 | 1 | no | — |
| 296 | C2×Q8 | — | 10 | 1 | no | — |
| 297 | C2×Q8 | — | 10 | 1 | no | — |
| 298 | C2×Q8 | — | 10 | 1 | no | — |
| 299 | C2×Q8 | — | 10 | 1 | no | — |
| 300 | C2×Q8 | — | 20 | 2 | no | — |
| 301 | C2×Q8 | — | 20 | 2 | no | — |
| 302 | C2×D4 | — | 2 | 1 | no | — |
| 303 | C2×D4 | — | 2 | 1 | no | — |
| 304 | C2×D4 | — | 2 | 1 | no | — |
| 305 | C2×D4 | — | 4 | 1 | no | — |
| 306 | C2×D4 | — | 10 | 1 | no | — |
| 307 | C2×D4 | — | 10 | 1 | no | — |
| 308 | C2×D4 | — | 20 | 2 | no | — |
| 309 | C22×C4 | — | 2 | 2 | no | — |
| 310 | C22×C4 | — | 4 | 1 | no | — |
| 311 | C22×C4 | — | 10 | 1 | no | — |
| 312 | C22×C4 | — | 10 | 1 | no | — |
| 313 | C22×C4 | — | 10 | 1 | no | — |
| 314 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 315 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 316 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 317 | SD16 | — | 20 | 4 | no | — |
| 318 | SD16 | — | 40 | 2 | no | — |
| 319 | D8 | — | 40 | 2 | no | — |
| 320 | M16 | — | 2 | 2 | no | — |
| 321 | M16 | — | 4 | 1 | no | — |
| 322 | C2×C8 | — | 4 | 1 | no | — |
| 323 | C2×C8 | — | 10 | 2 | no | — |
| 324 | C2×C8 | — | 10 | 2 | no | — |
| 325 | C4⋊C4 | — | 2 | 1 | no | — |
| 326 | C4⋊C4 | — | 2 | 1 | no | — |
| 327 | C4⋊C4 | — | 4 | 2 | no | — |
| 328 | C4⋊C4 | — | 10 | 1 | no | — |
| 329 | C4⋊C4 | — | 10 | 1 | no | — |
| 330 | C4⋊C4 | — | 20 | 1 | no | — |
| 331 | C4⋊C4 | — | 20 | 1 | no | — |
| 332 | C22⋊C4 | — | 4 | 1 | no | — |
| 333 | C22⋊C4 | — | 4 | 1 | no | — |
| 334 | C22⋊C4 | — | 20 | 4 | no | — |
| 335 | C22⋊C4 | — | 20 | 1 | no | — |
| 336 | C22⋊C4 | — | 20 | 1 | no | — |
| 337 | C22⋊C4 | — | 20 | 1 | no | — |
| 338 | C22⋊C4 | — | 20 | 1 | no | — |
| 339 | C22⋊C4 | — | 40 | 2 | no | — |
| 340 | C42 | — | 4 | 2 | no | — |
| 341 | C42 | — | 20 | 1 | no | — |
| 342 | C42 | — | 20 | 1 | no | — |
| 343 | C42 | C2×D20 | 1 | 1 | yes | characteristic |
| 344 | C42 | #709 | 1 | 1 | yes | characteristic |
| 345 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 346 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 347 | C2×C5 | — | 2 | 1 | no | — |
| 348 | C2×C5 | — | 2 | 1 | no | — |
| 349 | C2×C5 | — | 16 | 1 | no | — |
| 350 | C2×C5 | #2004 | 1 | 1 | yes | characteristic |
| 351 | C2×C5 | #2006 | 1 | 1 | yes | characteristic |
| 352 | C2×C5 | #2010 | 1 | 1 | yes | characteristic |
| 353 | D5 | — | 16 | 1 | no | — |
| 354 | C23 | — | 4 | 1 | no | — |
| 355 | C23 | — | 20 | 2 | no | — |
| 356 | C23 | — | 20 | 2 | no | — |
| 357 | C23 | — | 20 | 1 | no | — |
| 358 | C23 | — | 20 | 1 | no | — |
| 359 | C23 | — | 20 | 1 | no | — |
| 360 | C23 | #4083 | 1 | 1 | yes | characteristic |
| 361 | Q8 | — | 4 | 2 | no | — |
| 362 | Q8 | — | 10 | 2 | no | — |
| 363 | Q8 | — | 10 | 2 | no | — |
| 364 | Q8 | — | 20 | 1 | no | — |
| 365 | Q8 | — | 20 | 1 | no | — |
| 366 | Q8 | — | 20 | 2 | no | — |
| 367 | Q8 | — | 40 | 1 | no | — |
| 368 | D4 | — | 4 | 2 | no | — |
| 369 | D4 | — | 4 | 2 | no | — |
| 370 | D4 | — | 4 | 2 | no | — |
| 371 | D4 | — | 8 | 1 | no | — |
| 372 | D4 | — | 8 | 1 | no | — |
| 373 | D4 | — | 20 | 2 | no | — |
| 374 | D4 | — | 40 | 1 | no | — |
| 375 | C2×C4 | — | 2 | 1 | no | — |
| 376 | C2×C4 | — | 2 | 1 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 4 | 2 | no | — |
| 380 | C2×C4 | — | 4 | 2 | no | — |
| 381 | C2×C4 | — | 4 | 2 | no | — |
| 382 | C2×C4 | — | 4 | 1 | no | — |
| 383 | C2×C4 | — | 8 | 2 | no | — |
| 384 | C2×C4 | — | 10 | 2 | no | — |
| 385 | C2×C4 | — | 20 | 1 | no | — |
| 386 | C2×C4 | — | 20 | 1 | no | — |
| 387 | C2×C4 | — | 20 | 2 | no | — |
| 388 | C2×C4 | — | 20 | 1 | no | — |
| 389 | C2×C4 | — | 20 | 1 | no | — |
| 390 | C2×C4 | — | 20 | 1 | no | — |
| 391 | C2×C4 | — | 20 | 1 | no | — |
| 392 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | #4030 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | #4030 | 1 | 1 | yes | characteristic |
| 396 | C2×C4 | #4076 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | #4086 | 1 | 1 | yes | characteristic |
| 398 | C8 | — | 4 | 2 | no | — |
| 399 | C8 | — | 20 | 2 | no | — |
| 400 | C8 | — | 20 | 2 | no | — |
| 401 | C5 | #10006 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 402 | C22 | — | 2 | 1 | no | — |
| 403 | C22 | — | 2 | 1 | no | — |
| 404 | C22 | — | 8 | 1 | no | — |
| 405 | C22 | — | 8 | 1 | no | — |
| 406 | C22 | — | 8 | 1 | no | — |
| 407 | C22 | — | 40 | 2 | no | — |
| 408 | C22 | — | 40 | 2 | no | — |
| 409 | C22 | — | 40 | 1 | no | — |
| 410 | C22 | — | 40 | 1 | no | — |
| 411 | C22 | — | 40 | 1 | no | — |
| 412 | C22 | #65249 | 1 | 1 | yes | characteristic |
| 413 | C22 | #65351 | 1 | 1 | yes | characteristic |
| 414 | C22 | #65366 | 1 | 1 | yes | characteristic |
| 415 | C4 | — | 2 | 1 | no | — |
| 416 | C4 | — | 2 | 1 | no | — |
| 417 | C4 | — | 2 | 1 | no | — |
| 418 | C4 | — | 2 | 1 | no | — |
| 419 | C4 | — | 2 | 1 | no | — |
| 420 | C4 | — | 8 | 2 | no | — |
| 421 | C4 | — | 8 | 1 | no | — |
| 422 | C4 | — | 20 | 2 | no | — |
| 423 | C4 | — | 40 | 1 | no | — |
| 424 | C4 | — | 40 | 1 | no | — |
| 425 | C4 | #65114 | 1 | 2 | yes | — |
| 426 | C2 | — | 2 | 1 | no | — |
| 427 | C2 | — | 2 | 1 | no | — |
| 428 | C2 | — | 16 | 1 | no | — |
| 429 | C2 | — | 80 | 1 | no | — |
| 430 | C2 | #10600457 | 1 | 1 | yes | characteristic |
| 431 | C2 | #10601179 | 1 | 1 | yes | characteristic |
| 432 | C2 | #10601199 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10615047 | C2 | semidirect |
| 3. #10605466 | C2 | semidirect |
| 4. C5×#1980 | C2 | semidirect |
| 5. #10600653 | C2 | semidirect |
| 6. #10600650 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 87. #1980 | D5 | semidirect |
| 401. C5 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615047 | 2 |
| #10615037 | 2 |
| #10605466 | 2 |
| C5×#1980 | 2 |
| #10600653 | 2 |
| #10600650 | 2 |
| #10598112 | 2 |
| #10006 | 5 |