Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 75 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 | #10614722 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C5×#355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10602517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#64697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10600897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10600895 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C5×#124 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#4093 | C22 | 1 | 1 | yes | characteristic |
| 10 | #66146 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C5×#101 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×#101 | C22 | 1 | 1 | yes | characteristic |
| 13 | #65519 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#3968 | C22 | 1 | 1 | yes | characteristic |
| 15 | #65512 | — | 2 | 1 | no | — |
| 16 | #65504 | — | 2 | 1 | no | — |
| 17 | #65420 | — | 2 | 1 | no | — |
| 18 | #65410 | — | 2 | 1 | no | — |
| 19 | #65250 | — | 2 | 1 | no | — |
| 20 | #65249 | — | 2 | 1 | no | — |
| 21 | #65246 | — | 2 | 1 | no | — |
| 22 | #65233 | — | 2 | 1 | no | — |
| 23 | #65229 | — | 2 | 1 | no | — |
| 24 | C5×#355 | — | 2 | 2 | no | — |
| 25 | #64775 | — | 2 | 1 | no | — |
| 26 | #64775 | — | 2 | 1 | no | — |
| 27 | #64743 | — | 2 | 1 | no | — |
| 28 | #64697 | — | 2 | 2 | no | — |
| 29 | #13426 | — | 5 | 1 | no | maximal, Sylow |
| 30 | C22×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22×C5×D4 | D4 | 1 | 1 | yes | characteristic |
| 32 | C22×C22⋊D5 | — | 2 | 1 | no | — |
| 33 | C22×C22⋊D5 | — | 2 | 1 | no | — |
| 34 | C22×D20 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C5×M16 | — | 2 | 1 | no | — |
| 36 | C2×C5×M16 | — | 2 | 1 | no | — |
| 37 | C5×#124 | — | 2 | 1 | no | — |
| 38 | C5×#124 | — | 2 | 1 | no | — |
| 39 | C5×#124 | — | 2 | 1 | no | — |
| 40 | C5×#124 | — | 2 | 1 | no | — |
| 41 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 42 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 43 | C2×C42×C5 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×C22⋊Dic5 | — | 2 | 1 | no | — |
| 45 | C2×C22⋊Dic5 | — | 2 | 1 | no | — |
| 46 | #4093 | — | 2 | 1 | no | — |
| 47 | #4093 | — | 2 | 1 | no | — |
| 48 | #4093 | — | 2 | 1 | no | — |
| 49 | #4093 | — | 2 | 1 | no | — |
| 50 | Q8×Dic5 | — | 4 | 1 | no | — |
| 51 | Q8×Dic5 | — | 4 | 1 | no | — |
| 52 | C2×#685 | — | 2 | 1 | no | — |
| 53 | C2×#685 | — | 2 | 1 | no | — |
| 54 | C2×#685 | — | 2 | 1 | no | — |
| 55 | C2×#685 | — | 2 | 1 | no | — |
| 56 | #4072 | — | 2 | 1 | no | — |
| 57 | #4072 | — | 2 | 1 | no | — |
| 58 | #4072 | — | 2 | 1 | no | — |
| 59 | C2×C4⋊Dic5 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×#683 | — | 2 | 1 | no | — |
| 61 | C2×C4×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×C4×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×#681 | — | 2 | 1 | no | — |
| 64 | C5×#101 | — | 2 | 1 | no | — |
| 65 | C5×#101 | — | 2 | 1 | no | — |
| 66 | C5×#101 | — | 2 | 1 | no | — |
| 67 | C5×#101 | D4 | 1 | 2 | yes | complemented |
| 68 | #3968 | — | 2 | 1 | no | — |
| 69 | #3968 | — | 2 | 1 | no | — |
| 70 | #3964 | — | 4 | 1 | no | — |
| 71 | #3964 | — | 4 | 1 | no | — |
| 72 | #3963 | — | 2 | 1 | no | — |
| 73 | #3963 | — | 2 | 1 | no | — |
| 74 | #3963 | — | 2 | 1 | no | — |
| 75 | #3953 | — | 4 | 1 | no | — |
| 76 | #3953 | — | 4 | 1 | no | — |
| 77 | #3950 | — | 4 | 1 | no | — |
| 78 | #3949 | — | 4 | 1 | no | — |
| 79 | #2733 | — | 5 | 1 | no | — |
| 80 | C2×#355 | — | 5 | 1 | no | — |
| 81 | C2×#355 | D5 | 1 | 1 | yes | characteristic, complemented |
| 82 | #1888 | — | 5 | 1 | no | — |
| 83 | #1888 | — | 5 | 1 | no | — |
| 84 | #1857 | — | 5 | 1 | no | — |
| 85 | #1394 | — | 5 | 1 | no | — |
| 86 | C24×C5 | — | 2 | 1 | no | — |
| 87 | C23×D5 | — | 2 | 1 | no | — |
| 88 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 89 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 90 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C5×Q8 | #41 | 1 | 1 | yes | characteristic |
| 92 | C2×C5×Q8 | #41 | 1 | 1 | yes | characteristic |
| 93 | C2×C5×Q8 | #41 | 1 | 1 | yes | characteristic |
| 94 | C2×C5×D4 | — | 2 | 1 | no | — |
| 95 | C2×C5×D4 | — | 2 | 1 | no | — |
| 96 | C2×C5×D4 | — | 4 | 1 | no | — |
| 97 | C2×C5×D4 | — | 4 | 1 | no | — |
| 98 | C22×C4×C5 | — | 2 | 1 | no | — |
| 99 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 103 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 104 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 105 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 106 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 107 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 108 | C22×Dic5 | — | 2 | 1 | no | — |
| 109 | C22×Dic5 | — | 2 | 1 | no | — |
| 110 | C22×Dic5 | — | 2 | 1 | no | — |
| 111 | C2×D20 | — | 2 | 1 | no | — |
| 112 | C2×D20 | — | 2 | 1 | no | — |
| 113 | C2×D20 | — | 4 | 1 | no | — |
| 114 | C2×D20 | — | 4 | 1 | no | — |
| 115 | C5×M16 | — | 2 | 2 | no | — |
| 116 | C5×M16 | — | 4 | 1 | no | — |
| 117 | C5×M16 | — | 4 | 1 | no | — |
| 118 | C5×M16 | — | 4 | 1 | no | — |
| 119 | C2×C5×C8 | — | 4 | 1 | no | — |
| 120 | C2×C5×C8 | — | 4 | 1 | no | — |
| 121 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 122 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 123 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 124 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 125 | C42×C5 | — | 2 | 1 | no | — |
| 126 | C42×C5 | — | 2 | 1 | no | — |
| 127 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 128 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 129 | C22⋊Dic5 | — | 8 | 1 | no | — |
| 130 | #685 | — | 4 | 2 | no | — |
| 131 | #685 | — | 4 | 1 | no | — |
| 132 | #685 | — | 4 | 1 | no | — |
| 133 | #685 | — | 4 | 1 | no | — |
| 134 | #685 | — | 4 | 1 | no | — |
| 135 | #685 | — | 8 | 1 | no | — |
| 136 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 137 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 138 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 139 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 140 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 141 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 142 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 143 | #683 | — | 8 | 1 | no | — |
| 144 | C4×Dic5 | — | 2 | 1 | no | — |
| 145 | C4×Dic5 | — | 2 | 1 | no | — |
| 146 | C4×Dic5 | — | 4 | 1 | no | — |
| 147 | C4×Dic5 | — | 4 | 1 | no | — |
| 148 | C4×Dic5 | — | 4 | 1 | no | — |
| 149 | C4×Dic5 | — | 4 | 1 | no | — |
| 150 | #681 | — | 4 | 1 | no | — |
| 151 | #681 | — | 4 | 1 | no | — |
| 152 | C2×#168 | — | 4 | 1 | no | — |
| 153 | C2×#124 | — | 5 | 1 | no | — |
| 154 | C2×#124 | C2×D5 | 1 | 1 | yes | characteristic |
| 155 | #519 | — | 5 | 1 | no | — |
| 156 | #428 | — | 10 | 1 | no | — |
| 157 | #418 | — | 10 | 1 | no | — |
| 158 | #418 | — | 10 | 1 | no | — |
| 159 | C2×#101 | — | 5 | 1 | no | — |
| 160 | C2×#101 | C2×D5 | 1 | 1 | yes | characteristic |
| 161 | C2×#101 | C2×D5 | 1 | 1 | yes | characteristic |
| 162 | #394 | — | 10 | 1 | no | — |
| 163 | #392 | — | 10 | 1 | no | — |
| 164 | #392 | — | 10 | 1 | no | — |
| 165 | #391 | — | 5 | 1 | no | — |
| 166 | #390 | — | 10 | 1 | no | — |
| 167 | #388 | — | 10 | 1 | no | — |
| 168 | #388 | — | 10 | 1 | no | — |
| 169 | #355 | — | 2 | 2 | no | — |
| 170 | #355 | — | 10 | 2 | no | — |
| 171 | #339 | — | 10 | 1 | no | — |
| 172 | #339 | — | 10 | 1 | no | — |
| 173 | #339 | — | 10 | 1 | no | — |
| 174 | C23×C5 | — | 4 | 1 | no | — |
| 175 | C23×C5 | — | 4 | 1 | no | — |
| 176 | C23×C5 | — | 4 | 1 | no | — |
| 177 | C23×C5 | — | 4 | 1 | no | — |
| 178 | C23×C5 | — | 4 | 1 | no | — |
| 179 | C23×C5 | — | 4 | 1 | no | — |
| 180 | C23×C5 | — | 4 | 1 | no | — |
| 181 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 182 | C22×D5 | — | 4 | 1 | no | — |
| 183 | C22×D5 | — | 4 | 1 | no | — |
| 184 | C22×D5 | — | 4 | 1 | no | — |
| 185 | C22×D5 | — | 4 | 1 | no | — |
| 186 | C22×D5 | — | 4 | 1 | no | — |
| 187 | C22×D5 | — | 4 | 1 | no | — |
| 188 | C22×D5 | — | 4 | 1 | no | — |
| 189 | C5×Q8 | — | 4 | 1 | no | — |
| 190 | C5×Q8 | — | 4 | 1 | no | — |
| 191 | C5×Q8 | — | 4 | 1 | no | — |
| 192 | C5×Q8 | — | 4 | 1 | no | — |
| 193 | C5×D4 | — | 4 | 2 | no | — |
| 194 | C5×D4 | — | 8 | 1 | no | — |
| 195 | C2×C4×C5 | — | 2 | 1 | no | — |
| 196 | C2×C4×C5 | — | 2 | 1 | no | — |
| 197 | C2×C4×C5 | — | 2 | 1 | no | — |
| 198 | C2×C4×C5 | — | 2 | 1 | no | — |
| 199 | C2×C4×C5 | — | 2 | 1 | no | — |
| 200 | C2×C4×C5 | — | 2 | 1 | no | — |
| 201 | C2×C4×C5 | — | 4 | 1 | no | — |
| 202 | C2×C4×C5 | — | 4 | 1 | no | — |
| 203 | C2×C4×C5 | — | 4 | 1 | no | — |
| 204 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C5 | #123 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C5 | #123 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C5 | #124 | 1 | 1 | yes | characteristic |
| 210 | C22⋊D5 | — | 8 | 4 | no | — |
| 211 | C22⋊D5 | — | 8 | 4 | no | — |
| 212 | C2×Dic5 | — | 2 | 2 | no | — |
| 213 | C2×Dic5 | — | 4 | 1 | no | — |
| 214 | C2×Dic5 | — | 4 | 1 | no | — |
| 215 | C2×Dic5 | — | 4 | 1 | no | — |
| 216 | C2×Dic5 | — | 4 | 1 | no | — |
| 217 | C2×Dic5 | — | 4 | 1 | no | — |
| 218 | C2×Dic5 | — | 4 | 1 | no | — |
| 219 | C2×Dic5 | — | 4 | 1 | no | — |
| 220 | C2×Dic5 | — | 4 | 1 | no | — |
| 221 | C2×Dic5 | — | 4 | 1 | no | — |
| 222 | C2×Dic5 | — | 4 | 1 | no | — |
| 223 | D20 | — | 4 | 2 | no | — |
| 224 | D20 | — | 8 | 1 | no | — |
| 225 | C5×C8 | — | 4 | 2 | no | — |
| 226 | C5×C8 | — | 8 | 1 | no | — |
| 227 | #168 | — | 8 | 1 | no | — |
| 228 | C22×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 229 | C22×D4 | — | 5 | 1 | no | — |
| 230 | C22×D4 | — | 10 | 1 | no | — |
| 231 | C22×D4 | — | 10 | 1 | no | — |
| 232 | C22×D4 | D20 | 1 | 1 | yes | characteristic |
| 233 | C2×M16 | — | 2 | 1 | no | — |
| 234 | C2×M16 | — | 2 | 1 | no | — |
| 235 | C2×M16 | — | 10 | 1 | no | — |
| 236 | #124 | — | 2 | 1 | no | — |
| 237 | #124 | — | 2 | 1 | no | — |
| 238 | #124 | — | 2 | 1 | no | — |
| 239 | #124 | — | 2 | 1 | no | — |
| 240 | #124 | — | 10 | 1 | no | — |
| 241 | #124 | — | 10 | 1 | no | — |
| 242 | #124 | — | 10 | 1 | no | — |
| 243 | #124 | — | 10 | 1 | no | — |
| 244 | C4×Q8 | — | 20 | 1 | no | — |
| 245 | C4×Q8 | — | 20 | 1 | no | — |
| 246 | #117 | — | 10 | 1 | no | — |
| 247 | #117 | — | 10 | 1 | no | — |
| 248 | #117 | — | 10 | 1 | no | — |
| 249 | C2×C4⋊C4 | — | 5 | 1 | no | — |
| 250 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 251 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 252 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 253 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 254 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 255 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 256 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 257 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 258 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 259 | C2×C42 | — | 5 | 1 | no | — |
| 260 | C2×C42 | — | 5 | 1 | no | — |
| 261 | C2×C42 | D20 | 1 | 1 | yes | characteristic |
| 262 | #107 | — | 20 | 1 | no | — |
| 263 | #106 | — | 20 | 1 | no | — |
| 264 | #102 | — | 20 | 1 | no | — |
| 265 | #102 | — | 20 | 1 | no | — |
| 266 | #102 | — | 20 | 1 | no | — |
| 267 | #102 | — | 20 | 1 | no | — |
| 268 | #101 | — | 2 | 1 | no | — |
| 269 | #101 | — | 2 | 1 | no | — |
| 270 | #101 | — | 2 | 1 | no | — |
| 271 | #101 | — | 10 | 1 | no | — |
| 272 | #101 | — | 10 | 1 | no | — |
| 273 | #101 | C22⋊D5 | 1 | 2 | yes | complemented |
| 274 | #95 | — | 10 | 1 | no | — |
| 275 | #95 | — | 10 | 1 | no | — |
| 276 | #95 | — | 10 | 1 | no | — |
| 277 | C22×C5 | — | 2 | 1 | no | — |
| 278 | C22×C5 | — | 2 | 1 | no | — |
| 279 | C22×C5 | — | 8 | 1 | no | — |
| 280 | C22×C5 | — | 8 | 1 | no | — |
| 281 | C22×C5 | — | 8 | 1 | no | — |
| 282 | C22×C5 | — | 8 | 1 | no | — |
| 283 | C22×C5 | — | 8 | 1 | no | — |
| 284 | C22×C5 | — | 8 | 1 | no | — |
| 285 | C22×C5 | — | 8 | 1 | no | — |
| 286 | C22×C5 | #394 | 1 | 1 | yes | characteristic |
| 287 | C22×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 288 | C22×C5 | #458 | 1 | 1 | yes | characteristic |
| 289 | C2×D5 | — | 8 | 1 | no | — |
| 290 | C2×D5 | — | 8 | 1 | no | — |
| 291 | C2×D5 | — | 8 | 1 | no | — |
| 292 | C2×D5 | — | 8 | 1 | no | — |
| 293 | C2×D5 | — | 8 | 1 | no | — |
| 294 | C2×D5 | — | 8 | 1 | no | — |
| 295 | C2×D5 | — | 8 | 1 | no | — |
| 296 | C4×C5 | — | 2 | 1 | no | — |
| 297 | C4×C5 | — | 2 | 1 | no | — |
| 298 | C4×C5 | — | 2 | 1 | no | — |
| 299 | C4×C5 | — | 2 | 1 | no | — |
| 300 | C4×C5 | — | 2 | 1 | no | — |
| 301 | C4×C5 | — | 2 | 1 | no | — |
| 302 | C4×C5 | — | 8 | 1 | no | — |
| 303 | Dic5 | — | 4 | 2 | no | — |
| 304 | Dic5 | — | 8 | 1 | no | — |
| 305 | Dic5 | — | 8 | 1 | no | — |
| 306 | Dic5 | — | 8 | 1 | no | — |
| 307 | Dic5 | — | 8 | 1 | no | — |
| 308 | C24 | — | 2 | 1 | no | — |
| 309 | C24 | — | 10 | 1 | no | — |
| 310 | C2×Q8 | — | 4 | 1 | no | — |
| 311 | C2×Q8 | — | 4 | 1 | no | — |
| 312 | C2×Q8 | #709 | 1 | 1 | yes | characteristic |
| 313 | C2×Q8 | #711 | 1 | 1 | yes | characteristic |
| 314 | C2×Q8 | #711 | 1 | 1 | yes | characteristic |
| 315 | C2×Q8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 316 | C2×D4 | — | 2 | 1 | no | — |
| 317 | C2×D4 | — | 2 | 1 | no | — |
| 318 | C2×D4 | — | 4 | 1 | no | — |
| 319 | C2×D4 | — | 4 | 1 | no | — |
| 320 | C2×D4 | — | 10 | 1 | no | — |
| 321 | C2×D4 | — | 10 | 1 | no | — |
| 322 | C2×D4 | — | 20 | 1 | no | — |
| 323 | C2×D4 | — | 20 | 1 | no | — |
| 324 | C2×D4 | — | 20 | 2 | no | — |
| 325 | C2×D4 | — | 40 | 1 | no | — |
| 326 | C2×D4 | — | 40 | 1 | no | — |
| 327 | C2×D4 | — | 40 | 1 | no | — |
| 328 | C2×D4 | — | 40 | 1 | no | — |
| 329 | C2×D4 | — | 40 | 1 | no | — |
| 330 | C22×C4 | — | 2 | 1 | no | — |
| 331 | C22×C4 | — | 10 | 1 | no | — |
| 332 | C22×C4 | — | 10 | 1 | no | — |
| 333 | C22×C4 | — | 10 | 1 | no | — |
| 334 | C22×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 335 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 337 | M16 | — | 2 | 2 | no | — |
| 338 | M16 | — | 4 | 1 | no | — |
| 339 | M16 | — | 4 | 1 | no | — |
| 340 | M16 | — | 4 | 1 | no | — |
| 341 | M16 | — | 20 | 1 | no | — |
| 342 | M16 | — | 20 | 1 | no | — |
| 343 | C2×C8 | — | 4 | 1 | no | — |
| 344 | C2×C8 | — | 4 | 1 | no | — |
| 345 | C2×C8 | — | 20 | 1 | no | — |
| 346 | C4⋊C4 | — | 10 | 1 | no | — |
| 347 | C4⋊C4 | — | 10 | 1 | no | — |
| 348 | C4⋊C4 | — | 10 | 1 | no | — |
| 349 | C4⋊C4 | — | 10 | 1 | no | — |
| 350 | C4⋊C4 | — | 10 | 1 | no | — |
| 351 | C4⋊C4 | — | 10 | 1 | no | — |
| 352 | C4⋊C4 | — | 20 | 1 | no | — |
| 353 | C4⋊C4 | — | 40 | 1 | no | — |
| 354 | C22⋊C4 | — | 4 | 1 | no | — |
| 355 | C22⋊C4 | — | 4 | 1 | no | — |
| 356 | C22⋊C4 | — | 4 | 1 | no | — |
| 357 | C22⋊C4 | — | 4 | 1 | no | — |
| 358 | C22⋊C4 | — | 20 | 2 | no | — |
| 359 | C22⋊C4 | — | 20 | 2 | no | — |
| 360 | C22⋊C4 | — | 20 | 1 | no | — |
| 361 | C22⋊C4 | — | 20 | 1 | no | — |
| 362 | C22⋊C4 | — | 20 | 1 | no | — |
| 363 | C22⋊C4 | — | 20 | 1 | no | — |
| 364 | C22⋊C4 | — | 20 | 1 | no | — |
| 365 | C22⋊C4 | — | 40 | 1 | no | — |
| 366 | C22⋊C4 | — | 40 | 1 | no | — |
| 367 | C42 | — | 2 | 1 | no | — |
| 368 | C42 | — | 2 | 1 | no | — |
| 369 | C42 | — | 10 | 1 | no | — |
| 370 | C42 | — | 10 | 1 | no | — |
| 371 | C42 | — | 20 | 1 | no | — |
| 372 | C42 | — | 20 | 1 | no | — |
| 373 | C42 | — | 20 | 1 | no | — |
| 374 | C42 | — | 20 | 1 | no | — |
| 375 | C2×C5 | — | 2 | 1 | no | — |
| 376 | C2×C5 | — | 2 | 1 | no | — |
| 377 | C2×C5 | — | 16 | 1 | no | — |
| 378 | C2×C5 | #2044 | 1 | 1 | yes | characteristic |
| 379 | C2×C5 | #2202 | 1 | 1 | yes | characteristic |
| 380 | C2×C5 | #2204 | 1 | 1 | yes | characteristic |
| 381 | D5 | — | 16 | 1 | no | — |
| 382 | C23 | — | 4 | 1 | no | — |
| 383 | C23 | — | 4 | 1 | no | — |
| 384 | C23 | — | 4 | 1 | no | — |
| 385 | C23 | — | 4 | 1 | no | — |
| 386 | C23 | — | 4 | 1 | no | — |
| 387 | C23 | — | 4 | 1 | no | — |
| 388 | C23 | — | 4 | 1 | no | — |
| 389 | C23 | — | 20 | 1 | no | — |
| 390 | C23 | — | 20 | 1 | no | — |
| 391 | C23 | — | 20 | 1 | no | — |
| 392 | C23 | — | 20 | 1 | no | — |
| 393 | C23 | — | 20 | 1 | no | — |
| 394 | C23 | — | 20 | 1 | no | — |
| 395 | C23 | — | 20 | 1 | no | — |
| 396 | C23 | #4028 | 1 | 1 | yes | characteristic |
| 397 | Q8 | — | 4 | 1 | no | — |
| 398 | Q8 | — | 4 | 1 | no | — |
| 399 | Q8 | — | 4 | 1 | no | — |
| 400 | Q8 | — | 4 | 1 | no | — |
| 401 | D4 | — | 4 | 2 | no | — |
| 402 | D4 | — | 8 | 1 | no | — |
| 403 | D4 | — | 20 | 2 | no | — |
| 404 | D4 | — | 40 | 1 | no | — |
| 405 | D4 | — | 40 | 4 | no | — |
| 406 | D4 | — | 40 | 4 | no | — |
| 407 | C2×C4 | — | 2 | 1 | no | — |
| 408 | C2×C4 | — | 2 | 1 | no | — |
| 409 | C2×C4 | — | 2 | 1 | no | — |
| 410 | C2×C4 | — | 2 | 1 | no | — |
| 411 | C2×C4 | — | 2 | 1 | no | — |
| 412 | C2×C4 | — | 2 | 1 | no | — |
| 413 | C2×C4 | — | 4 | 1 | no | — |
| 414 | C2×C4 | — | 4 | 1 | no | — |
| 415 | C2×C4 | — | 4 | 1 | no | — |
| 416 | C2×C4 | — | 10 | 2 | no | — |
| 417 | C2×C4 | — | 20 | 1 | no | — |
| 418 | C2×C4 | — | 20 | 1 | no | — |
| 419 | C2×C4 | — | 20 | 1 | no | — |
| 420 | C2×C4 | — | 20 | 1 | no | — |
| 421 | C2×C4 | — | 20 | 1 | no | — |
| 422 | C2×C4 | — | 20 | 1 | no | — |
| 423 | C2×C4 | — | 20 | 1 | no | — |
| 424 | C2×C4 | — | 20 | 1 | no | — |
| 425 | C2×C4 | — | 20 | 1 | no | — |
| 426 | C2×C4 | — | 20 | 1 | no | — |
| 427 | C2×C4 | #4029 | 1 | 1 | yes | characteristic |
| 428 | C2×C4 | #4031 | 1 | 1 | yes | characteristic |
| 429 | C2×C4 | #4032 | 1 | 1 | yes | characteristic |
| 430 | C2×C4 | #4076 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | #4084 | 1 | 1 | yes | characteristic |
| 432 | C2×C4 | #4085 | 1 | 1 | yes | characteristic |
| 433 | C8 | — | 4 | 2 | no | — |
| 434 | C8 | — | 8 | 1 | no | — |
| 435 | C8 | — | 40 | 1 | no | — |
| 436 | C5 | #13426 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 437 | C22 | — | 2 | 1 | no | — |
| 438 | C22 | — | 2 | 1 | no | — |
| 439 | C22 | — | 8 | 1 | no | — |
| 440 | C22 | — | 8 | 1 | no | — |
| 441 | C22 | — | 8 | 1 | no | — |
| 442 | C22 | — | 8 | 1 | no | — |
| 443 | C22 | — | 8 | 1 | no | — |
| 444 | C22 | — | 8 | 1 | no | — |
| 445 | C22 | — | 8 | 1 | no | — |
| 446 | C22 | — | 40 | 1 | no | — |
| 447 | C22 | — | 40 | 1 | no | — |
| 448 | C22 | — | 40 | 1 | no | — |
| 449 | C22 | — | 40 | 1 | no | — |
| 450 | C22 | — | 40 | 1 | no | — |
| 451 | C22 | — | 40 | 1 | no | — |
| 452 | C22 | — | 40 | 1 | no | — |
| 453 | C22 | #65030 | 1 | 1 | yes | characteristic |
| 454 | C22 | #65031 | 1 | 1 | yes | characteristic |
| 455 | C22 | #65250 | 1 | 1 | yes | characteristic |
| 456 | C4 | — | 2 | 1 | no | — |
| 457 | C4 | — | 2 | 1 | no | — |
| 458 | C4 | — | 2 | 1 | no | — |
| 459 | C4 | — | 2 | 1 | no | — |
| 460 | C4 | — | 2 | 1 | no | — |
| 461 | C4 | — | 2 | 1 | no | — |
| 462 | C4 | — | 8 | 1 | no | — |
| 463 | C4 | — | 20 | 2 | no | — |
| 464 | C4 | — | 40 | 1 | no | — |
| 465 | C4 | — | 40 | 1 | no | — |
| 466 | C4 | — | 40 | 1 | no | — |
| 467 | C4 | — | 40 | 1 | no | — |
| 468 | C2 | — | 2 | 1 | no | — |
| 469 | C2 | — | 2 | 1 | no | — |
| 470 | C2 | — | 16 | 1 | no | — |
| 471 | C2 | — | 80 | 1 | no | — |
| 472 | C2 | #10599953 | 1 | 1 | yes | characteristic |
| 473 | C2 | #10599954 | 1 | 1 | yes | characteristic |
| 474 | C2 | #10600825 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#355 | C2 | semidirect |
| 3. #10602517 | C2 | semidirect |
| 4. C2×#64697 | C2 | semidirect |
| 5. #10600897 | C2 | semidirect |
| 6. #10600895 | C2 | semidirect |
| 7. #10598190 | C2 | semidirect |
| 67. C5×#101 | D4 | semidirect |
| 81. C2×#355 | D5 | semidirect |
| 273. #101 | C22⋊D5 | semidirect |
| 436. C5 | #13426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614722 | 2 |
| C2×C5×#355 | 2 |
| #10602517 | 2 |
| C2×#64697 | 2 |
| #10600897 | 2 |
| #10600895 | 2 |
| #10598190 | 2 |
| #13426 | 5 |