Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
1074 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #14577392 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14564099 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14564096 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14563930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14561994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14561971 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C19×#1471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#10597430 | C4 | 1 | 2 | yes | — |
| 9 | C22×#64520 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11927195 | — | 2 | 1 | no | — |
| 11 | #11927194 | — | 2 | 1 | no | — |
| 12 | #11927184 | — | 2 | 2 | no | — |
| 13 | #11927183 | — | 2 | 2 | no | — |
| 14 | #11927178 | — | 2 | 1 | no | — |
| 15 | D4×C22⋊D19 | — | 2 | 1 | no | — |
| 16 | #11927121 | — | 2 | 1 | no | — |
| 17 | #11927103 | C4 | 1 | 2 | yes | — |
| 18 | #11927102 | — | 2 | 1 | no | — |
| 19 | #11927089 | — | 2 | 1 | no | — |
| 20 | C2×#10597376 | C22 | 1 | 1 | yes | characteristic |
| 21 | #121×D19 | — | 2 | 1 | no | — |
| 22 | C2×C4×C22⋊D19 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#10597290 | — | 2 | 1 | no | — |
| 24 | C2×#10597280 | — | 2 | 1 | no | — |
| 25 | #11926508 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×(C2×D19)⋊C8 | — | 2 | 1 | no | — |
| 27 | #11926313 | — | 2 | 1 | no | — |
| 28 | #11926312 | — | 2 | 1 | no | — |
| 29 | #11926298 | — | 2 | 1 | no | — |
| 30 | #11926269 | — | 2 | 1 | no | — |
| 31 | #11926267 | — | 2 | 1 | no | — |
| 32 | #11926267 | — | 2 | 2 | no | — |
| 33 | C2×C19×#121 | C22 | 1 | 1 | yes | characteristic |
| 34 | C19×#407 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×C19×C22⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C19×#323 | — | 2 | 2 | no | — |
| 37 | C22×D4×C19 | C2×C4 | 1 | 2 | yes | — |
| 38 | C22×D4×C19 | D4 | 1 | 1 | yes | characteristic |
| 39 | C23×C4×C19 | C23 | 1 | 1 | yes | characteristic |
| 40 | C22×C22⋊D19 | — | 2 | 2 | no | — |
| 41 | C22×C22⋊D19 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C22×C22⋊D19 | C2×C4 | 1 | 2 | yes | — |
| 43 | #10597430 | — | 4 | 4 | no | — |
| 44 | #10597430 | — | 4 | 4 | no | — |
| 45 | C2×#64543 | — | 2 | 2 | no | — |
| 46 | C2×#64543 | — | 2 | 2 | no | — |
| 47 | C2×D4×D19 | — | 2 | 2 | no | — |
| 48 | C2×D4×D19 | — | 2 | 2 | no | — |
| 49 | C2×D4×D19 | — | 2 | 1 | no | — |
| 50 | C2×#64541 | — | 2 | 2 | no | — |
| 51 | C22×D76 | D4 | 1 | 1 | yes | characteristic |
| 52 | C22×C4×D19 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×M16×C19 | — | 2 | 1 | no | — |
| 54 | C22×C8×C19 | — | 2 | 1 | no | — |
| 55 | C19×#121 | — | 2 | 1 | no | — |
| 56 | C19×#121 | — | 2 | 1 | no | — |
| 57 | C19×#121 | — | 2 | 1 | no | — |
| 58 | C19×#121 | — | 2 | 1 | no | — |
| 59 | C2×C4⋊C4×C19 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C22⋊C4×C19 | D4 | 1 | 2 | yes | — |
| 61 | #10597399 | — | 2 | 2 | no | — |
| 62 | C2×C22⋊Dic19 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | #10597386 | — | 2 | 1 | no | — |
| 64 | #10597385 | — | 2 | 2 | no | — |
| 65 | #10597385 | — | 2 | 2 | no | — |
| 66 | #10597385 | — | 2 | 2 | no | — |
| 67 | #10597384 | — | 2 | 1 | no | — |
| 68 | #10597383 | — | 2 | 2 | no | — |
| 69 | #10597383 | — | 2 | 2 | no | — |
| 70 | #10597381 | — | 2 | 2 | no | — |
| 71 | D4×Dic19 | — | 2 | 1 | no | — |
| 72 | #10597376 | — | 2 | 1 | no | — |
| 73 | #10597376 | — | 2 | 1 | no | — |
| 74 | #10597376 | — | 2 | 1 | no | — |
| 75 | #10597376 | — | 2 | 1 | no | — |
| 76 | #10597375 | — | 2 | 2 | no | — |
| 77 | C4×C22⋊D19 | — | 2 | 1 | no | — |
| 78 | C4×C22⋊D19 | — | 2 | 1 | no | — |
| 79 | C4×C22⋊D19 | — | 2 | 1 | no | — |
| 80 | C4×C22⋊D19 | — | 2 | 1 | no | — |
| 81 | C2×(C2×D19)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 82 | C2×(C2×D19)⋊C4 | D4 | 1 | 2 | yes | — |
| 83 | C2×C4⋊Dic19 | D4 | 1 | 1 | yes | characteristic |
| 84 | C2×Dic19⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×Dic19 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×#64520 | — | 2 | 1 | no | — |
| 87 | C2×#64520 | — | 2 | 1 | no | — |
| 88 | C2×#64520 | — | 2 | 1 | no | — |
| 89 | C2×#64520 | — | 4 | 2 | no | — |
| 90 | C22×C19⋊C8 | — | 2 | 1 | no | — |
| 91 | #10597342 | — | 2 | 2 | no | — |
| 92 | #10597341 | — | 2 | 1 | no | — |
| 93 | #10597340 | — | 2 | 2 | no | — |
| 94 | #10597339 | — | 2 | 1 | no | — |
| 95 | C4⋊C4×D19 | — | 2 | 1 | no | — |
| 96 | #10597334 | — | 2 | 1 | no | — |
| 97 | #10597331 | — | 2 | 2 | no | — |
| 98 | #10597330 | — | 2 | 2 | no | — |
| 99 | #10597330 | — | 2 | 2 | no | — |
| 100 | #10597329 | — | 2 | 2 | no | — |
| 101 | #10597328 | — | 2 | 2 | no | — |
| 102 | (C22⋊D19)⋊C4 | — | 2 | 2 | no | — |
| 103 | C22⋊C4×D19 | — | 2 | 2 | no | — |
| 104 | #10597324 | — | 2 | 2 | no | — |
| 105 | C19×C22⋊C8 | — | 2 | 1 | no | — |
| 106 | C19×C22⋊C8 | — | 2 | 1 | no | — |
| 107 | C19×C22⋊C8 | — | 2 | 1 | no | — |
| 108 | C19×C22⋊C8 | — | 2 | 1 | no | — |
| 109 | #10597290 | — | 4 | 2 | no | — |
| 110 | C22⋊(C19⋊C8) | — | 2 | 1 | no | — |
| 111 | C22⋊(C19⋊C8) | — | 2 | 1 | no | — |
| 112 | #10597280 | — | 4 | 2 | no | — |
| 113 | (C2×D19)⋊C8 | — | 4 | 2 | no | — |
| 114 | C24×C19 | C22⋊C4 | 1 | 2 | yes | — |
| 115 | C24×C19 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C23×D19 | — | 2 | 2 | no | — |
| 117 | C23×D19 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C23×D19 | C22⋊C4 | 1 | 2 | yes | — |
| 119 | C2×D4×C19 | — | 2 | 2 | no | — |
| 120 | C2×D4×C19 | — | 2 | 2 | no | — |
| 121 | C2×D4×C19 | — | 2 | 1 | no | — |
| 122 | C2×D4×C19 | — | 2 | 1 | no | — |
| 123 | C2×D4×C19 | — | 4 | 1 | no | — |
| 124 | C2×D4×C19 | — | 4 | 1 | no | — |
| 125 | C2×D4×C19 | — | 4 | 2 | no | — |
| 126 | C2×D4×C19 | — | 4 | 2 | no | — |
| 127 | C22×C4×C19 | — | 4 | 1 | no | — |
| 128 | C22×C4×C19 | — | 4 | 1 | no | — |
| 129 | C22×C4×C19 | C22⋊C4 | 1 | 2 | yes | — |
| 130 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C22⋊D19 | — | 2 | 1 | no | — |
| 137 | C2×C22⋊D19 | — | 2 | 1 | no | — |
| 138 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 139 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 140 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 141 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 142 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 144 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 145 | C2×C22⋊D19 | — | 2 | 2 | no | — |
| 146 | C2×C22⋊D19 | — | 4 | 8 | no | — |
| 147 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 148 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 149 | C22×Dic19 | — | 2 | 2 | no | — |
| 150 | C22×Dic19 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C22×Dic19 | C22⋊C4 | 1 | 2 | yes | — |
| 152 | C22×Dic19 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 153 | C22×Dic19 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 154 | #64543 | — | 4 | 4 | no | — |
| 155 | #64543 | — | 4 | 8 | no | — |
| 156 | #64543 | — | 4 | 4 | no | — |
| 157 | D4×D19 | — | 4 | 8 | no | — |
| 158 | D4×D19 | — | 4 | 4 | no | — |
| 159 | D4×D19 | — | 4 | 4 | no | — |
| 160 | D4×D19 | — | 8 | 1 | no | — |
| 161 | D4×D19 | — | 8 | 1 | no | — |
| 162 | #64541 | — | 4 | 8 | no | — |
| 163 | C2×D76 | — | 2 | 2 | no | — |
| 164 | C2×D76 | — | 2 | 1 | no | — |
| 165 | C2×D76 | — | 2 | 1 | no | — |
| 166 | C2×D76 | — | 4 | 1 | no | — |
| 167 | C2×D76 | — | 4 | 1 | no | — |
| 168 | C2×C4×D19 | — | 2 | 2 | no | — |
| 169 | C2×C4×D19 | — | 2 | 2 | no | — |
| 170 | C2×C4×D19 | — | 2 | 1 | no | — |
| 171 | C2×C4×D19 | — | 2 | 1 | no | — |
| 172 | C2×C4×D19 | — | 4 | 1 | no | — |
| 173 | C2×C4×D19 | — | 4 | 1 | no | — |
| 174 | C2×Dic38 | — | 2 | 2 | no | — |
| 175 | M16×C19 | — | 4 | 1 | no | — |
| 176 | M16×C19 | — | 4 | 1 | no | — |
| 177 | C2×C8×C19 | — | 4 | 1 | no | — |
| 178 | C2×C8×C19 | — | 4 | 1 | no | — |
| 179 | C2×C8×C19 | — | 4 | 1 | no | — |
| 180 | C2×C8×C19 | — | 4 | 1 | no | — |
| 181 | C4⋊C4×C19 | — | 2 | 1 | no | — |
| 182 | C4⋊C4×C19 | — | 2 | 1 | no | — |
| 183 | C22⋊C4×C19 | — | 2 | 2 | no | — |
| 184 | C22⋊C4×C19 | — | 2 | 2 | no | — |
| 185 | C22⋊Dic19 | — | 2 | 2 | no | — |
| 186 | C22⋊Dic19 | — | 2 | 2 | no | — |
| 187 | C22⋊Dic19 | — | 2 | 1 | no | — |
| 188 | C22⋊Dic19 | — | 2 | 1 | no | — |
| 189 | (C2×D19)⋊C4 | — | 2 | 2 | no | — |
| 190 | (C2×D19)⋊C4 | — | 2 | 2 | no | — |
| 191 | (C2×D19)⋊C4 | — | 2 | 2 | no | — |
| 192 | (C2×D19)⋊C4 | — | 2 | 2 | no | — |
| 193 | (C2×D19)⋊C4 | — | 2 | 1 | no | — |
| 194 | (C2×D19)⋊C4 | — | 2 | 1 | no | — |
| 195 | C4⋊Dic19 | — | 2 | 1 | no | — |
| 196 | C4⋊Dic19 | — | 2 | 1 | no | — |
| 197 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 198 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 199 | Dic19⋊C4 | — | 2 | 1 | no | — |
| 200 | Dic19⋊C4 | — | 2 | 1 | no | — |
| 201 | C4×Dic19 | — | 2 | 1 | no | — |
| 202 | C4×Dic19 | — | 2 | 1 | no | — |
| 203 | #64520 | — | 2 | 2 | no | — |
| 204 | #64520 | — | 2 | 2 | no | — |
| 205 | #64520 | — | 4 | 1 | no | — |
| 206 | #64520 | — | 4 | 1 | no | — |
| 207 | #64520 | — | 4 | 1 | no | — |
| 208 | #64520 | — | 4 | 1 | no | — |
| 209 | C2×C19⋊C8 | — | 2 | 2 | no | — |
| 210 | C2×C19⋊C8 | — | 4 | 1 | no | — |
| 211 | C2×C19⋊C8 | — | 4 | 1 | no | — |
| 212 | C2×C19⋊C8 | — | 4 | 1 | no | — |
| 213 | #8536 | — | 19 | 1 | no | maximal, Sylow |
| 214 | C23×C19 | — | 2 | 1 | no | — |
| 215 | C23×C19 | — | 2 | 1 | no | — |
| 216 | C23×C19 | — | 2 | 2 | no | — |
| 217 | C23×C19 | — | 4 | 1 | no | — |
| 218 | C23×C19 | — | 4 | 1 | no | — |
| 219 | C23×C19 | — | 4 | 2 | no | — |
| 220 | C23×C19 | — | 4 | 2 | no | — |
| 221 | C23×C19 | — | 4 | 2 | no | — |
| 222 | C23×C19 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 223 | C23×C19 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 224 | C23×C19 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 225 | C22×D19 | — | 2 | 1 | no | — |
| 226 | C22×D19 | — | 2 | 1 | no | — |
| 227 | C22×D19 | — | 2 | 2 | no | — |
| 228 | C22×D19 | — | 4 | 4 | no | — |
| 229 | C22×D19 | — | 4 | 1 | no | — |
| 230 | C22×D19 | — | 4 | 1 | no | — |
| 231 | C22×D19 | — | 4 | 2 | no | — |
| 232 | C22×D19 | — | 4 | 2 | no | — |
| 233 | C22×D19 | — | 4 | 2 | no | — |
| 234 | C22×D19 | — | 8 | 2 | no | — |
| 235 | C22×D19 | — | 8 | 2 | no | — |
| 236 | C22×D19 | #100 | 1 | 2 | yes | complemented |
| 237 | D4×C19 | — | 4 | 4 | no | — |
| 238 | D4×C19 | — | 4 | 2 | no | — |
| 239 | D4×C19 | — | 4 | 2 | no | — |
| 240 | D4×C19 | — | 4 | 1 | no | — |
| 241 | D4×C19 | — | 4 | 1 | no | — |
| 242 | D4×C19 | — | 8 | 1 | no | — |
| 243 | C2×C4×C19 | — | 2 | 1 | no | — |
| 244 | C2×C4×C19 | — | 2 | 1 | no | — |
| 245 | C2×C4×C19 | — | 2 | 1 | no | — |
| 246 | C2×C4×C19 | — | 2 | 1 | no | — |
| 247 | C2×C4×C19 | — | 2 | 1 | no | — |
| 248 | C2×C4×C19 | — | 2 | 1 | no | — |
| 249 | C2×C4×C19 | — | 2 | 2 | no | — |
| 250 | C2×C4×C19 | — | 4 | 1 | no | — |
| 251 | C2×C4×C19 | — | 4 | 1 | no | — |
| 252 | C2×C4×C19 | — | 4 | 1 | no | — |
| 253 | C2×C4×C19 | — | 4 | 2 | no | — |
| 254 | C2×C4×C19 | #120 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C19 | #120 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C19 | #120 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C19 | #120 | 1 | 1 | yes | characteristic |
| 258 | C22⋊D19 | — | 2 | 4 | no | — |
| 259 | C22⋊D19 | — | 2 | 4 | no | — |
| 260 | C22⋊D19 | — | 4 | 4 | no | — |
| 261 | C22⋊D19 | — | 4 | 4 | no | — |
| 262 | C22⋊D19 | — | 4 | 4 | no | — |
| 263 | C22⋊D19 | — | 4 | 2 | no | — |
| 264 | C22⋊D19 | — | 4 | 2 | no | — |
| 265 | C22⋊D19 | — | 8 | 2 | no | — |
| 266 | C22⋊D19 | — | 8 | 2 | no | — |
| 267 | C2×Dic19 | — | 2 | 1 | no | — |
| 268 | C2×Dic19 | — | 2 | 1 | no | — |
| 269 | C2×Dic19 | — | 2 | 1 | no | — |
| 270 | C2×Dic19 | — | 2 | 1 | no | — |
| 271 | C2×Dic19 | — | 2 | 2 | no | — |
| 272 | C2×Dic19 | — | 4 | 4 | no | — |
| 273 | C2×Dic19 | — | 4 | 1 | no | — |
| 274 | C2×Dic19 | — | 4 | 2 | no | — |
| 275 | C2×Dic19 | — | 4 | 1 | no | — |
| 276 | C2×Dic19 | #100 | 1 | 2 | yes | complemented |
| 277 | D76 | — | 4 | 4 | no | — |
| 278 | D76 | — | 4 | 1 | no | — |
| 279 | D76 | — | 4 | 1 | no | — |
| 280 | D76 | — | 8 | 1 | no | — |
| 281 | C4×D19 | — | 4 | 4 | no | — |
| 282 | C4×D19 | — | 4 | 4 | no | — |
| 283 | C4×D19 | — | 4 | 1 | no | — |
| 284 | C4×D19 | — | 4 | 1 | no | — |
| 285 | C4×D19 | — | 8 | 1 | no | — |
| 286 | Dic38 | — | 4 | 4 | no | — |
| 287 | C8×C19 | — | 8 | 1 | no | — |
| 288 | C8×C19 | — | 8 | 1 | no | — |
| 289 | C19⋊C8 | — | 4 | 2 | no | — |
| 290 | C19⋊C8 | — | 8 | 1 | no | — |
| 291 | #3496 | — | 19 | 1 | no | — |
| 292 | #1900 | — | 19 | 1 | no | — |
| 293 | #1900 | — | 19 | 1 | no | — |
| 294 | #1870 | — | 19 | 1 | no | — |
| 295 | #1471 | — | 19 | 1 | no | — |
| 296 | #1471 | D19 | 1 | 1 | yes | characteristic, complemented |
| 297 | #1465 | — | 19 | 1 | no | — |
| 298 | C22×C19 | — | 2 | 1 | no | — |
| 299 | C22×C19 | — | 2 | 1 | no | — |
| 300 | C22×C19 | — | 2 | 1 | no | — |
| 301 | C22×C19 | — | 2 | 1 | no | — |
| 302 | C22×C19 | — | 2 | 1 | no | — |
| 303 | C22×C19 | — | 2 | 1 | no | — |
| 304 | C22×C19 | — | 2 | 1 | no | — |
| 305 | C22×C19 | — | 2 | 1 | no | — |
| 306 | C22×C19 | — | 4 | 2 | no | — |
| 307 | C22×C19 | — | 4 | 2 | no | — |
| 308 | C22×C19 | — | 4 | 2 | no | — |
| 309 | C22×C19 | — | 8 | 1 | no | — |
| 310 | C22×C19 | — | 8 | 1 | no | — |
| 311 | C22×C19 | — | 16 | 2 | no | — |
| 312 | C22×C19 | #379 | 1 | 1 | yes | characteristic |
| 313 | C22×C19 | C2×#100 | 1 | 1 | yes | characteristic |
| 314 | C22×C19 | C2×#100 | 1 | 1 | yes | characteristic |
| 315 | C2×D19 | — | 2 | 2 | no | — |
| 316 | C2×D19 | — | 4 | 1 | no | — |
| 317 | C2×D19 | — | 4 | 1 | no | — |
| 318 | C2×D19 | — | 4 | 2 | no | — |
| 319 | C2×D19 | — | 4 | 2 | no | — |
| 320 | C2×D19 | — | 4 | 2 | no | — |
| 321 | C2×D19 | — | 4 | 2 | no | — |
| 322 | C2×D19 | — | 8 | 1 | no | — |
| 323 | C2×D19 | — | 16 | 4 | no | — |
| 324 | C2×D19 | — | 16 | 2 | no | — |
| 325 | C4×C19 | — | 2 | 1 | no | — |
| 326 | C4×C19 | — | 2 | 1 | no | — |
| 327 | C4×C19 | — | 2 | 1 | no | — |
| 328 | C4×C19 | — | 4 | 2 | no | — |
| 329 | C4×C19 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 330 | C4×C19 | #458 | 1 | 1 | yes | characteristic |
| 331 | Dic19 | — | 2 | 2 | no | — |
| 332 | Dic19 | — | 4 | 2 | no | — |
| 333 | Dic19 | — | 4 | 1 | no | — |
| 334 | Dic19 | — | 4 | 1 | no | — |
| 335 | C2×H(5,𝔽2) | — | 19 | 2 | no | — |
| 336 | C22×M16 | — | 19 | 1 | no | — |
| 337 | #547 | — | 38 | 1 | no | — |
| 338 | #547 | — | 38 | 1 | no | — |
| 339 | #546 | — | 38 | 2 | no | — |
| 340 | #546 | — | 38 | 2 | no | — |
| 341 | D42 | — | 38 | 1 | no | — |
| 342 | D42 | — | 38 | 1 | no | — |
| 343 | #537 | — | 38 | 1 | no | — |
| 344 | #534 | — | 19 | 2 | no | — |
| 345 | #534 | — | 38 | 1 | no | — |
| 346 | #532 | — | 38 | 1 | no | — |
| 347 | C2×#121 | — | 19 | 1 | no | — |
| 348 | C2×#121 | — | 38 | 1 | no | — |
| 349 | C2×#121 | C2×D19 | 1 | 1 | yes | characteristic |
| 350 | C2×C4×D4 | — | 19 | 1 | no | — |
| 351 | C2×#100 | — | 38 | 1 | no | — |
| 352 | C2×#100 | — | 38 | 1 | no | — |
| 353 | #407 | — | 19 | 1 | no | — |
| 354 | #407 | C2×D19 | 1 | 1 | yes | characteristic, complemented |
| 355 | C2×C22⋊C8 | — | 38 | 1 | no | — |
| 356 | C2×C22⋊C8 | C2×D19 | 1 | 1 | yes | characteristic, complemented |
| 357 | #343 | — | 38 | 1 | no | — |
| 358 | #343 | — | 38 | 1 | no | — |
| 359 | #336 | — | 38 | 1 | no | — |
| 360 | #324 | — | 38 | 1 | no | — |
| 361 | #323 | — | 2 | 2 | no | — |
| 362 | #323 | — | 38 | 1 | no | — |
| 363 | #323 | — | 38 | 2 | no | — |
| 364 | C2×C19 | — | 2 | 1 | no | — |
| 365 | C2×C19 | — | 2 | 1 | no | — |
| 366 | C2×C19 | — | 4 | 1 | no | — |
| 367 | C2×C19 | — | 4 | 1 | no | — |
| 368 | C2×C19 | — | 8 | 2 | no | — |
| 369 | C2×C19 | #1783 | 1 | 1 | yes | characteristic |
| 370 | C2×C19 | #1790 | 1 | 1 | yes | characteristic |
| 371 | C2×C19 | #1791 | 1 | 1 | yes | characteristic |
| 372 | D19 | — | 4 | 2 | no | — |
| 373 | D19 | — | 8 | 2 | no | — |
| 374 | H(5,𝔽2) | — | 76 | 4 | no | — |
| 375 | H(5,𝔽2) | — | 76 | 4 | no | — |
| 376 | C2×#41 | — | 38 | 2 | no | — |
| 377 | C2×#41 | — | 38 | 2 | no | — |
| 378 | C2×#41 | — | 38 | 2 | no | — |
| 379 | C22×D4 | — | 19 | 1 | no | — |
| 380 | C22×D4 | — | 19 | 2 | no | — |
| 381 | C22×D4 | — | 19 | 1 | no | — |
| 382 | C22×D4 | — | 38 | 2 | no | — |
| 383 | C22×D4 | — | 38 | 2 | no | — |
| 384 | C22×D4 | — | 38 | 1 | no | — |
| 385 | C22×D4 | — | 38 | 2 | no | — |
| 386 | C22×D4 | C4×D19 | 1 | 2 | yes | — |
| 387 | C22×D4 | D76 | 1 | 1 | yes | characteristic |
| 388 | C23×C4 | — | 19 | 1 | no | — |
| 389 | C23×C4 | C22×D19 | 1 | 1 | yes | characteristic |
| 390 | C2×M16 | — | 2 | 1 | no | — |
| 391 | C2×M16 | — | 38 | 1 | no | — |
| 392 | C2×M16 | — | 38 | 1 | no | — |
| 393 | C2×M16 | — | 38 | 1 | no | — |
| 394 | C2×M16 | — | 76 | 2 | no | — |
| 395 | C22×C8 | — | 2 | 1 | no | — |
| 396 | C22×C8 | — | 38 | 1 | no | — |
| 397 | C4⋊Q8 | — | 38 | 1 | no | — |
| 398 | #127 | — | 38 | 1 | no | — |
| 399 | #124 | — | 38 | 2 | no | — |
| 400 | #123 | — | 38 | 2 | no | — |
| 401 | #123 | — | 38 | 2 | no | — |
| 402 | #123 | — | 38 | 2 | no | — |
| 403 | #123 | — | 38 | 2 | no | — |
| 404 | C22⋊Q8 | — | 38 | 2 | no | — |
| 405 | C22⋊Q8 | — | 38 | 2 | no | — |
| 406 | #121 | — | 2 | 1 | no | — |
| 407 | #121 | — | 2 | 1 | no | — |
| 408 | #121 | — | 2 | 1 | no | — |
| 409 | #121 | — | 2 | 1 | no | — |
| 410 | #121 | — | 38 | 2 | no | — |
| 411 | #121 | — | 38 | 2 | no | — |
| 412 | #121 | — | 38 | 1 | no | — |
| 413 | #121 | — | 38 | 2 | no | — |
| 414 | #121 | — | 38 | 2 | no | — |
| 415 | #121 | — | 38 | 1 | no | — |
| 416 | #121 | — | 38 | 2 | no | — |
| 417 | #121 | — | 38 | 1 | no | — |
| 418 | #121 | — | 38 | 1 | no | — |
| 419 | #121 | — | 38 | 1 | no | — |
| 420 | #121 | — | 38 | 1 | no | — |
| 421 | #120 | — | 38 | 2 | no | — |
| 422 | #120 | — | 38 | 2 | no | — |
| 423 | #120 | — | 38 | 2 | no | — |
| 424 | #120 | — | 38 | 2 | no | — |
| 425 | C4×D4 | — | 38 | 2 | no | — |
| 426 | C4×D4 | — | 38 | 1 | no | — |
| 427 | C4×D4 | — | 38 | 1 | no | — |
| 428 | C4×D4 | — | 38 | 1 | no | — |
| 429 | C4×D4 | — | 38 | 1 | no | — |
| 430 | C4×D4 | — | 38 | 1 | no | — |
| 431 | C4×D4 | — | 38 | 1 | no | — |
| 432 | C2×C4⋊C4 | — | 19 | 1 | no | — |
| 433 | C2×C4⋊C4 | — | 19 | 1 | no | — |
| 434 | C2×C4⋊C4 | — | 38 | 1 | no | — |
| 435 | C2×C4⋊C4 | D76 | 1 | 1 | yes | characteristic |
| 436 | C2×C22⋊C4 | — | 19 | 1 | no | — |
| 437 | C2×C22⋊C4 | — | 19 | 1 | no | — |
| 438 | C2×C22⋊C4 | — | 19 | 2 | no | — |
| 439 | C2×C22⋊C4 | — | 38 | 2 | no | — |
| 440 | C2×C22⋊C4 | C22⋊D19 | 1 | 2 | yes | — |
| 441 | C2×C42 | — | 19 | 1 | no | — |
| 442 | #100 | — | 76 | 2 | no | — |
| 443 | #100 | — | 76 | 2 | no | — |
| 444 | C22⋊C8 | — | 2 | 1 | no | — |
| 445 | C22⋊C8 | — | 2 | 1 | no | — |
| 446 | C22⋊C8 | — | 2 | 1 | no | — |
| 447 | C22⋊C8 | — | 2 | 1 | no | — |
| 448 | C22⋊C8 | — | 38 | 1 | no | — |
| 449 | C22⋊C8 | — | 38 | 1 | no | — |
| 450 | C22⋊C8 | — | 76 | 2 | no | — |
| 451 | C19 | #8536 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 452 | C24 | — | 19 | 1 | no | — |
| 453 | C24 | — | 19 | 2 | no | — |
| 454 | C24 | — | 38 | 2 | no | — |
| 455 | C24 | (C2×D19)⋊C4 | 1 | 2 | yes | — |
| 456 | C24 | C2×C4×D19 | 1 | 1 | yes | characteristic |
| 457 | #41 | — | 76 | 8 | no | — |
| 458 | #41 | — | 76 | 4 | no | — |
| 459 | #41 | — | 76 | 4 | no | — |
| 460 | #41 | — | 76 | 8 | no | — |
| 461 | C2×Q8 | — | 38 | 2 | no | — |
| 462 | C2×D4 | — | 2 | 2 | no | — |
| 463 | C2×D4 | — | 2 | 2 | no | — |
| 464 | C2×D4 | — | 2 | 1 | no | — |
| 465 | C2×D4 | — | 2 | 1 | no | — |
| 466 | C2×D4 | — | 4 | 1 | no | — |
| 467 | C2×D4 | — | 4 | 1 | no | — |
| 468 | C2×D4 | — | 4 | 2 | no | — |
| 469 | C2×D4 | — | 4 | 2 | no | — |
| 470 | C2×D4 | — | 38 | 2 | no | — |
| 471 | C2×D4 | — | 38 | 2 | no | — |
| 472 | C2×D4 | — | 38 | 2 | no | — |
| 473 | C2×D4 | — | 38 | 1 | no | — |
| 474 | C2×D4 | — | 38 | 1 | no | — |
| 475 | C2×D4 | — | 38 | 2 | no | — |
| 476 | C2×D4 | — | 38 | 2 | no | — |
| 477 | C2×D4 | — | 38 | 2 | no | — |
| 478 | C2×D4 | — | 38 | 2 | no | — |
| 479 | C2×D4 | — | 38 | 2 | no | — |
| 480 | C2×D4 | — | 38 | 2 | no | — |
| 481 | C2×D4 | — | 38 | 1 | no | — |
| 482 | C2×D4 | — | 38 | 1 | no | — |
| 483 | C2×D4 | — | 76 | 1 | no | — |
| 484 | C2×D4 | — | 76 | 1 | no | — |
| 485 | C2×D4 | — | 76 | 8 | no | — |
| 486 | C2×D4 | — | 76 | 4 | no | — |
| 487 | C2×D4 | — | 76 | 4 | no | — |
| 488 | C2×D4 | — | 76 | 8 | no | — |
| 489 | C2×D4 | — | 76 | 2 | no | — |
| 490 | C2×D4 | — | 76 | 2 | no | — |
| 491 | C2×D4 | — | 152 | 1 | no | — |
| 492 | C2×D4 | — | 152 | 1 | no | — |
| 493 | C22×C4 | — | 4 | 1 | no | — |
| 494 | C22×C4 | — | 4 | 1 | no | — |
| 495 | C22×C4 | — | 19 | 1 | no | — |
| 496 | C22×C4 | — | 19 | 1 | no | — |
| 497 | C22×C4 | — | 19 | 1 | no | — |
| 498 | C22×C4 | — | 19 | 2 | no | — |
| 499 | C22×C4 | — | 38 | 2 | no | — |
| 500 | C22×C4 | — | 38 | 2 | no | — |
| 501 | C22×C4 | — | 38 | 2 | no | — |
| 502 | C22×C4 | — | 38 | 1 | no | — |
| 503 | C22×C4 | — | 38 | 1 | no | — |
| 504 | C22×C4 | — | 76 | 1 | no | — |
| 505 | C22×C4 | — | 76 | 1 | no | — |
| 506 | C22×C4 | (C2×D19)⋊C4 | 1 | 2 | yes | — |
| 507 | C22×C4 | C2×D76 | 1 | 1 | yes | characteristic |
| 508 | C22×C4 | D4×D19 | 1 | 1 | yes | characteristic |
| 509 | C22×C4 | D4×D19 | 1 | 1 | yes | characteristic |
| 510 | C22×C4 | D4×D19 | 1 | 1 | yes | characteristic |
| 511 | C22×C4 | D4×D19 | 1 | 1 | yes | characteristic |
| 512 | C22×C4 | C2×C22⋊D19 | 1 | 1 | yes | characteristic |
| 513 | M16 | — | 4 | 1 | no | — |
| 514 | M16 | — | 4 | 1 | no | — |
| 515 | M16 | — | 38 | 2 | no | — |
| 516 | M16 | — | 38 | 2 | no | — |
| 517 | M16 | — | 76 | 1 | no | — |
| 518 | M16 | — | 76 | 1 | no | — |
| 519 | M16 | — | 76 | 1 | no | — |
| 520 | M16 | — | 76 | 1 | no | — |
| 521 | C2×C8 | — | 4 | 1 | no | — |
| 522 | C2×C8 | — | 4 | 1 | no | — |
| 523 | C2×C8 | — | 4 | 1 | no | — |
| 524 | C2×C8 | — | 4 | 1 | no | — |
| 525 | C2×C8 | — | 38 | 2 | no | — |
| 526 | C2×C8 | — | 76 | 1 | no | — |
| 527 | C2×C8 | — | 76 | 1 | no | — |
| 528 | C2×C8 | — | 76 | 1 | no | — |
| 529 | C4⋊C4 | — | 2 | 1 | no | — |
| 530 | C4⋊C4 | — | 2 | 1 | no | — |
| 531 | C4⋊C4 | — | 38 | 2 | no | — |
| 532 | C4⋊C4 | — | 38 | 2 | no | — |
| 533 | C4⋊C4 | — | 38 | 1 | no | — |
| 534 | C4⋊C4 | — | 38 | 1 | no | — |
| 535 | C4⋊C4 | — | 38 | 1 | no | — |
| 536 | C4⋊C4 | — | 38 | 1 | no | — |
| 537 | C22⋊C4 | — | 2 | 2 | no | — |
| 538 | C22⋊C4 | — | 2 | 2 | no | — |
| 539 | C22⋊C4 | — | 38 | 2 | no | — |
| 540 | C22⋊C4 | — | 38 | 2 | no | — |
| 541 | C22⋊C4 | — | 38 | 2 | no | — |
| 542 | C22⋊C4 | — | 38 | 2 | no | — |
| 543 | C22⋊C4 | — | 38 | 1 | no | — |
| 544 | C22⋊C4 | — | 38 | 1 | no | — |
| 545 | C22⋊C4 | — | 38 | 2 | no | — |
| 546 | C22⋊C4 | — | 38 | 1 | no | — |
| 547 | C22⋊C4 | — | 38 | 1 | no | — |
| 548 | C22⋊C4 | — | 38 | 2 | no | — |
| 549 | C42 | — | 38 | 1 | no | — |
| 550 | C42 | — | 38 | 1 | no | — |
| 551 | C23 | — | 2 | 1 | no | — |
| 552 | C23 | — | 2 | 1 | no | — |
| 553 | C23 | — | 2 | 2 | no | — |
| 554 | C23 | — | 4 | 1 | no | — |
| 555 | C23 | — | 4 | 1 | no | — |
| 556 | C23 | — | 4 | 2 | no | — |
| 557 | C23 | — | 4 | 2 | no | — |
| 558 | C23 | — | 4 | 2 | no | — |
| 559 | C23 | — | 19 | 2 | no | — |
| 560 | C23 | — | 38 | 1 | no | — |
| 561 | C23 | — | 38 | 1 | no | — |
| 562 | C23 | — | 38 | 2 | no | — |
| 563 | C23 | — | 76 | 2 | no | — |
| 564 | C23 | — | 76 | 2 | no | — |
| 565 | C23 | — | 76 | 2 | no | — |
| 566 | C23 | — | 76 | 1 | no | — |
| 567 | C23 | — | 76 | 1 | no | — |
| 568 | C23 | — | 76 | 4 | no | — |
| 569 | C23 | — | 152 | 2 | no | — |
| 570 | C23 | — | 152 | 2 | no | — |
| 571 | C23 | C22⋊C4×D19 | 1 | 1 | yes | characteristic |
| 572 | C23 | C22⋊C4×D19 | 1 | 1 | yes | characteristic |
| 573 | C23 | C2×(C2×D19)⋊C4 | 1 | 1 | yes | characteristic |
| 574 | Q8 | — | 76 | 4 | no | — |
| 575 | D4 | — | 4 | 4 | no | — |
| 576 | D4 | — | 4 | 2 | no | — |
| 577 | D4 | — | 4 | 2 | no | — |
| 578 | D4 | — | 4 | 1 | no | — |
| 579 | D4 | — | 4 | 1 | no | — |
| 580 | D4 | — | 8 | 1 | no | — |
| 581 | D4 | — | 38 | 4 | no | — |
| 582 | D4 | — | 38 | 4 | no | — |
| 583 | D4 | — | 76 | 4 | no | — |
| 584 | D4 | — | 76 | 4 | no | — |
| 585 | D4 | — | 76 | 4 | no | — |
| 586 | D4 | — | 76 | 4 | no | — |
| 587 | D4 | — | 76 | 2 | no | — |
| 588 | D4 | — | 76 | 2 | no | — |
| 589 | D4 | — | 76 | 1 | no | — |
| 590 | D4 | — | 76 | 1 | no | — |
| 591 | D4 | — | 152 | 1 | no | — |
| 592 | D4 | — | 152 | 2 | no | — |
| 593 | D4 | — | 152 | 2 | no | — |
| 594 | C2×C4 | — | 2 | 1 | no | — |
| 595 | C2×C4 | — | 2 | 1 | no | — |
| 596 | C2×C4 | — | 2 | 1 | no | — |
| 597 | C2×C4 | — | 2 | 1 | no | — |
| 598 | C2×C4 | — | 2 | 1 | no | — |
| 599 | C2×C4 | — | 2 | 1 | no | — |
| 600 | C2×C4 | — | 2 | 2 | no | — |
| 601 | C2×C4 | — | 4 | 1 | no | — |
| 602 | C2×C4 | — | 4 | 1 | no | — |
| 603 | C2×C4 | — | 4 | 1 | no | — |
| 604 | C2×C4 | — | 4 | 2 | no | — |
| 605 | C2×C4 | — | 19 | 2 | no | — |
| 606 | C2×C4 | — | 38 | 1 | no | — |
| 607 | C2×C4 | — | 38 | 1 | no | — |
| 608 | C2×C4 | — | 38 | 1 | no | — |
| 609 | C2×C4 | — | 38 | 1 | no | — |
| 610 | C2×C4 | — | 38 | 2 | no | — |
| 611 | C2×C4 | — | 76 | 4 | no | — |
| 612 | C2×C4 | — | 76 | 4 | no | — |
| 613 | C2×C4 | — | 76 | 4 | no | — |
| 614 | C2×C4 | — | 76 | 1 | no | — |
| 615 | C2×C4 | — | 76 | 1 | no | — |
| 616 | C2×C4 | — | 76 | 1 | no | — |
| 617 | C2×C4 | — | 76 | 2 | no | — |
| 618 | C2×C4 | — | 76 | 1 | no | — |
| 619 | C2×C4 | — | 152 | 1 | no | — |
| 620 | C2×C4 | #10597328 | 1 | 1 | yes | characteristic |
| 621 | C2×C4 | #10597328 | 1 | 1 | yes | characteristic |
| 622 | C2×C4 | #10597383 | 1 | 1 | yes | characteristic |
| 623 | C2×C4 | #10597383 | 1 | 1 | yes | characteristic |
| 624 | C8 | — | 8 | 1 | no | — |
| 625 | C8 | — | 8 | 1 | no | — |
| 626 | C8 | — | 76 | 2 | no | — |
| 627 | C8 | — | 152 | 1 | no | — |
| 628 | C22 | — | 2 | 1 | no | — |
| 629 | C22 | — | 2 | 1 | no | — |
| 630 | C22 | — | 2 | 1 | no | — |
| 631 | C22 | — | 2 | 1 | no | — |
| 632 | C22 | — | 2 | 1 | no | — |
| 633 | C22 | — | 2 | 1 | no | — |
| 634 | C22 | — | 2 | 1 | no | — |
| 635 | C22 | — | 2 | 1 | no | — |
| 636 | C22 | — | 4 | 2 | no | — |
| 637 | C22 | — | 4 | 2 | no | — |
| 638 | C22 | — | 4 | 2 | no | — |
| 639 | C22 | — | 8 | 1 | no | — |
| 640 | C22 | — | 8 | 1 | no | — |
| 641 | C22 | — | 16 | 2 | no | — |
| 642 | C22 | — | 38 | 2 | no | — |
| 643 | C22 | — | 304 | 2 | no | — |
| 644 | C22 | — | 304 | 4 | no | — |
| 645 | C22 | — | 76 | 2 | no | — |
| 646 | C22 | — | 76 | 1 | no | — |
| 647 | C22 | — | 76 | 1 | no | — |
| 648 | C22 | — | 76 | 2 | no | — |
| 649 | C22 | — | 76 | 2 | no | — |
| 650 | C22 | — | 76 | 2 | no | — |
| 651 | C22 | — | 152 | 1 | no | — |
| 652 | C22 | #11926399 | 1 | 1 | yes | characteristic |
| 653 | C22 | #100×D19 | 1 | 1 | yes | characteristic |
| 654 | C22 | #100×D19 | 1 | 1 | yes | characteristic |
| 655 | C4 | — | 2 | 1 | no | — |
| 656 | C4 | — | 2 | 1 | no | — |
| 657 | C4 | — | 2 | 1 | no | — |
| 658 | C4 | — | 4 | 2 | no | — |
| 659 | C4 | — | 38 | 2 | no | — |
| 660 | C4 | — | 76 | 1 | no | — |
| 661 | C4 | — | 76 | 2 | no | — |
| 662 | C4 | — | 76 | 1 | no | — |
| 663 | C4 | #11926732 | 1 | 1 | yes | characteristic |
| 664 | C4 | #11926735 | 1 | 1 | yes | characteristic |
| 665 | C2 | — | 2 | 1 | no | — |
| 666 | C2 | — | 2 | 1 | no | — |
| 667 | C2 | — | 4 | 1 | no | — |
| 668 | C2 | — | 4 | 1 | no | — |
| 669 | C2 | — | 8 | 2 | no | — |
| 670 | C2 | — | 76 | 2 | no | — |
| 671 | C2 | — | 152 | 2 | no | — |
| 672 | C2 | #14563554 | 1 | 1 | yes | characteristic |
| 673 | C2 | #14563581 | 1 | 1 | yes | characteristic |
| 674 | C2 | #14563585 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14564099 | C2 | semidirect |
| 3. #14564096 | C2 | semidirect |
| 4. #14563930 | C2 | semidirect |
| 5. #14561994 | C2 | semidirect |
| 6. #14561971 | C2 | semidirect |
| 7. C19×#1471 | C2 | semidirect |
| 9. C22×#64520 | C22 | semidirect |
| 25. #11926508 | C22 | semidirect |
| 34. C19×#407 | C22 | semidirect |
| 35. C2×C19×C22⋊C8 | C22 | semidirect |
| 236. C22×D19 | #100 | semidirect |
| 276. C2×Dic19 | #100 | semidirect |
| 296. #1471 | D19 | semidirect |
| 354. #407 | C2×D19 | semidirect |
| 356. C2×C22⋊C8 | C2×D19 | semidirect |
| 451. C19 | #8536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14577392 | 2 |
| #14564099 | 2 |
| #14564096 | 2 |
| #14563930 | 2 |
| #14561994 | 2 |
| #14561971 | 2 |
| C19×#1471 | 2 |
| #8536 | 19 |