Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
876 conjugacy classes of subgroups.
The subgroup lattice has 454 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#66100 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#2141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#64785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10602235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602231 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10601458 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601449 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#4147 | — | 2 | 1 | no | — |
| 9 | C22×C5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#4088 | — | 2 | 1 | no | — |
| 11 | #66100 | — | 2 | 2 | no | — |
| 12 | #66100 | — | 2 | 2 | no | — |
| 13 | #66100 | — | 2 | 2 | no | — |
| 14 | #66100 | C4 | 1 | 4 | yes | complemented |
| 15 | C2×#4065 | — | 2 | 1 | no | — |
| 16 | C2×#4064 | — | 2 | 2 | no | — |
| 17 | C2×D5×Q16 | — | 2 | 1 | no | — |
| 18 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C5×M32 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#427 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#3951 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#3944 | C22 | 1 | 1 | yes | characteristic |
| 24 | #65294 | — | 2 | 1 | no | — |
| 25 | C5×#358 | — | 2 | 2 | no | — |
| 26 | #64785 | — | 2 | 2 | no | — |
| 27 | #64753 | — | 2 | 1 | no | — |
| 28 | #64737 | — | 2 | 1 | no | — |
| 29 | #64736 | — | 2 | 1 | no | — |
| 30 | #64735 | — | 2 | 2 | no | — |
| 31 | #64708 | — | 2 | 2 | no | — |
| 32 | #12751 | — | 5 | 1 | no | maximal, Sylow |
| 33 | C22×C5×Q8 | — | 2 | 1 | no | — |
| 34 | #4147 | — | 2 | 4 | no | — |
| 35 | #4147 | — | 2 | 4 | no | — |
| 36 | #4147 | — | 4 | 2 | no | — |
| 37 | #4147 | — | 4 | 2 | no | — |
| 38 | C2×#713 | — | 2 | 2 | no | — |
| 39 | C2×#713 | — | 4 | 1 | no | — |
| 40 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 41 | C2×Q8×D5 | — | 4 | 1 | no | — |
| 42 | C2×#709 | — | 2 | 1 | no | — |
| 43 | C2×#709 | — | 4 | 2 | no | — |
| 44 | C2×#709 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 46 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 47 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 48 | C2×C5×Q16 | C2×C4 | 1 | 2 | yes | — |
| 49 | C2×C5×Q16 | D4 | 1 | 2 | yes | — |
| 50 | C2×C5×Q16 | D4 | 1 | 2 | yes | — |
| 51 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 52 | C5×#117 | — | 2 | 1 | no | — |
| 53 | C2×#689 | — | 2 | 2 | no | — |
| 54 | #4088 | — | 2 | 4 | no | — |
| 55 | #4088 | — | 2 | 4 | no | — |
| 56 | C2×#688 | — | 2 | 2 | no | — |
| 57 | C2×#681 | — | 2 | 1 | no | — |
| 58 | C2×#681 | D4 | 1 | 1 | yes | characteristic |
| 59 | #4065 | — | 2 | 4 | no | — |
| 60 | #4065 | — | 2 | 4 | no | — |
| 61 | #4064 | — | 2 | 8 | no | — |
| 62 | #4064 | — | 2 | 8 | no | — |
| 63 | D5×Q16 | — | 2 | 4 | no | — |
| 64 | D5×Q16 | — | 2 | 4 | no | — |
| 65 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 66 | #4050 | — | 2 | 1 | no | — |
| 67 | #4050 | — | 2 | 1 | no | — |
| 68 | #4050 | C2×C4 | 1 | 2 | yes | — |
| 69 | #4050 | D4 | 1 | 2 | yes | — |
| 70 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×#677 | — | 2 | 1 | no | — |
| 72 | #4047 | — | 2 | 1 | no | — |
| 73 | #4047 | — | 2 | 1 | no | — |
| 74 | #4047 | C2×C4 | 1 | 2 | yes | — |
| 75 | #4047 | D4 | 1 | 2 | yes | — |
| 76 | C2×#676 | — | 2 | 1 | no | — |
| 77 | C2×C8×D5 | — | 2 | 1 | no | — |
| 78 | C5×M32 | — | 2 | 1 | no | — |
| 79 | C5×M32 | — | 2 | 1 | no | — |
| 80 | C2×C5×C16 | — | 2 | 1 | no | — |
| 81 | C5×#107 | — | 2 | 1 | no | — |
| 82 | C5×#106 | — | 2 | 1 | no | — |
| 83 | #3951 | — | 2 | 1 | no | — |
| 84 | #3951 | — | 2 | 1 | no | — |
| 85 | #3944 | — | 2 | 1 | no | — |
| 86 | #3944 | — | 2 | 1 | no | — |
| 87 | C2×#672 | — | 2 | 1 | no | — |
| 88 | #3937 | — | 4 | 2 | no | — |
| 89 | C2×#578 | — | 5 | 1 | no | — |
| 90 | #2148 | — | 5 | 1 | no | — |
| 91 | C2×#362 | — | 5 | 1 | no | — |
| 92 | #2145 | — | 5 | 1 | no | — |
| 93 | #2141 | D5 | 1 | 1 | yes | characteristic, complemented |
| 94 | #2117 | — | 5 | 1 | no | — |
| 95 | #1814 | — | 5 | 1 | no | — |
| 96 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 97 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 98 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 99 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 100 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 101 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 102 | C22×C4×C5 | — | 4 | 1 | no | — |
| 103 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 105 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 106 | #713 | — | 2 | 8 | no | — |
| 107 | #713 | — | 4 | 4 | no | — |
| 108 | #713 | — | 4 | 4 | no | — |
| 109 | #713 | — | 4 | 4 | no | — |
| 110 | Q8×D5 | — | 2 | 8 | no | — |
| 111 | Q8×D5 | — | 4 | 4 | no | — |
| 112 | Q8×D5 | — | 4 | 4 | no | — |
| 113 | Q8×D5 | — | 4 | 4 | no | — |
| 114 | #709 | — | 2 | 1 | no | — |
| 115 | #709 | — | 2 | 1 | no | — |
| 116 | #709 | — | 2 | 2 | no | — |
| 117 | #709 | — | 2 | 2 | no | — |
| 118 | #709 | — | 4 | 8 | no | — |
| 119 | #709 | — | 4 | 8 | no | — |
| 120 | #709 | — | 4 | 1 | no | — |
| 121 | #709 | — | 4 | 1 | no | — |
| 122 | #709 | C22⋊C4 | 1 | 2 | yes | — |
| 123 | #709 | D8 | 1 | 2 | yes | — |
| 124 | C2×D20 | — | 2 | 1 | no | — |
| 125 | C2×D20 | — | 4 | 2 | no | — |
| 126 | C2×D20 | SD16 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×D5 | — | 2 | 1 | no | — |
| 128 | C2×C4×D5 | — | 4 | 2 | no | — |
| 129 | C2×C4×D5 | — | 4 | 2 | no | — |
| 130 | C2×C4×D5 | — | 4 | 1 | no | — |
| 131 | C2×Dic10 | — | 2 | 1 | no | — |
| 132 | C2×Dic10 | — | 4 | 2 | no | — |
| 133 | C2×Dic10 | SD16 | 1 | 1 | yes | characteristic |
| 134 | C5×Q16 | — | 2 | 2 | no | — |
| 135 | C5×Q16 | — | 2 | 2 | no | — |
| 136 | C5×Q16 | — | 2 | 2 | no | — |
| 137 | C5×Q16 | C22⋊C4 | 1 | 4 | yes | — |
| 138 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 139 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 145 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 146 | C42×C5 | — | 4 | 1 | no | — |
| 147 | #689 | — | 2 | 8 | no | — |
| 148 | #688 | — | 2 | 8 | no | — |
| 149 | #681 | — | 2 | 1 | no | — |
| 150 | #681 | — | 4 | 1 | no | — |
| 151 | #681 | — | 4 | 1 | no | — |
| 152 | #681 | C22⋊C4 | 1 | 2 | yes | — |
| 153 | C2×#168 | — | 2 | 1 | no | — |
| 154 | C2×#168 | — | 4 | 1 | no | — |
| 155 | Dic20 | — | 2 | 1 | no | — |
| 156 | Dic20 | C22⋊C4 | 1 | 2 | yes | — |
| 157 | D40 | — | 2 | 1 | no | — |
| 158 | D40 | C22⋊C4 | 1 | 2 | yes | — |
| 159 | #677 | — | 2 | 2 | no | — |
| 160 | #677 | — | 2 | 2 | no | — |
| 161 | #676 | — | 2 | 2 | no | — |
| 162 | #676 | — | 2 | 2 | no | — |
| 163 | C8×D5 | — | 2 | 2 | no | — |
| 164 | C8×D5 | — | 2 | 2 | no | — |
| 165 | C5×C16 | — | 4 | 1 | no | — |
| 166 | #672 | — | 4 | 1 | no | — |
| 167 | C2×2−1+4 | — | 10 | 1 | no | — |
| 168 | #578 | — | 5 | 4 | no | — |
| 169 | #578 | — | 10 | 2 | no | — |
| 170 | #578 | — | 10 | 2 | no | — |
| 171 | #578 | — | 10 | 2 | no | — |
| 172 | C2×#137 | — | 10 | 1 | no | — |
| 173 | C2×#137 | — | 10 | 2 | no | — |
| 174 | C2×#135 | — | 5 | 1 | no | — |
| 175 | C2×#135 | — | 10 | 1 | no | — |
| 176 | C22×Q16 | — | 10 | 1 | no | — |
| 177 | C22×Q16 | C2×D5 | 1 | 1 | yes | characteristic |
| 178 | C2×#131 | — | 5 | 1 | no | — |
| 179 | C2×M32 | — | 5 | 1 | no | — |
| 180 | C2×M32 | C2×D5 | 1 | 1 | yes | characteristic |
| 181 | C2×#108 | — | 5 | 1 | no | — |
| 182 | #427 | C2×D5 | 1 | 1 | yes | characteristic |
| 183 | #421 | — | 10 | 1 | no | — |
| 184 | #362 | — | 10 | 1 | no | — |
| 185 | #362 | — | 10 | 2 | no | — |
| 186 | #361 | — | 10 | 1 | no | — |
| 187 | #360 | — | 10 | 2 | no | — |
| 188 | #358 | — | 2 | 2 | no | — |
| 189 | #350 | — | 10 | 2 | no | — |
| 190 | #344 | — | 10 | 1 | no | — |
| 191 | C23×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 192 | C22×D5 | — | 2 | 1 | no | — |
| 193 | C22×D5 | — | 4 | 1 | no | — |
| 194 | C5×Q8 | — | 2 | 4 | no | — |
| 195 | C5×Q8 | — | 4 | 2 | no | — |
| 196 | C5×Q8 | — | 4 | 2 | no | — |
| 197 | C5×Q8 | — | 4 | 2 | no | — |
| 198 | C2×C4×C5 | — | 4 | 2 | no | — |
| 199 | C2×C4×C5 | — | 4 | 2 | no | — |
| 200 | C2×C4×C5 | — | 4 | 2 | no | — |
| 201 | C2×C4×C5 | — | 8 | 1 | no | — |
| 202 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 208 | C22⋊D5 | — | 2 | 2 | no | — |
| 209 | C22⋊D5 | — | 2 | 2 | no | — |
| 210 | C22⋊D5 | — | 4 | 2 | no | — |
| 211 | C22⋊D5 | — | 4 | 2 | no | — |
| 212 | C2×Dic5 | — | 2 | 1 | no | — |
| 213 | C2×Dic5 | — | 4 | 1 | no | — |
| 214 | D20 | — | 2 | 2 | no | — |
| 215 | D20 | — | 2 | 1 | no | — |
| 216 | D20 | — | 4 | 8 | no | — |
| 217 | D20 | — | 4 | 1 | no | — |
| 218 | D20 | #102 | 1 | 2 | yes | — |
| 219 | C4×D5 | — | 2 | 2 | no | — |
| 220 | C4×D5 | — | 2 | 2 | no | — |
| 221 | C4×D5 | — | 4 | 8 | no | — |
| 222 | C4×D5 | — | 4 | 8 | no | — |
| 223 | C4×D5 | — | 4 | 2 | no | — |
| 224 | C4×D5 | — | 4 | 2 | no | — |
| 225 | Dic10 | — | 2 | 1 | no | — |
| 226 | Dic10 | — | 2 | 2 | no | — |
| 227 | Dic10 | — | 4 | 8 | no | — |
| 228 | Dic10 | — | 4 | 1 | no | — |
| 229 | Dic10 | #102 | 1 | 2 | yes | — |
| 230 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 231 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 232 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 233 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 234 | #168 | — | 2 | 2 | no | — |
| 235 | #168 | — | 8 | 1 | no | — |
| 236 | 2−1+4 | — | 10 | 4 | no | — |
| 237 | 2−1+4 | — | 10 | 4 | no | — |
| 238 | 2−1+4 | — | 20 | 2 | no | — |
| 239 | 2−1+4 | — | 20 | 2 | no | — |
| 240 | C2×#41 | — | 5 | 1 | no | — |
| 241 | C2×#41 | — | 10 | 2 | no | — |
| 242 | C2×#41 | — | 10 | 1 | no | — |
| 243 | C2×#41 | — | 20 | 2 | no | — |
| 244 | C2×#41 | — | 20 | 1 | no | — |
| 245 | C22×Q8 | — | 2 | 1 | no | — |
| 246 | C22×Q8 | — | 10 | 2 | no | — |
| 247 | C22×Q8 | — | 20 | 1 | no | — |
| 248 | #137 | — | 10 | 4 | no | — |
| 249 | #137 | — | 10 | 8 | no | — |
| 250 | #137 | — | 10 | 4 | no | — |
| 251 | #137 | — | 10 | 8 | no | — |
| 252 | #135 | — | 5 | 2 | no | — |
| 253 | #135 | — | 5 | 2 | no | — |
| 254 | #135 | — | 10 | 4 | no | — |
| 255 | #135 | — | 10 | 4 | no | — |
| 256 | #135 | — | 10 | 1 | no | — |
| 257 | #135 | — | 10 | 1 | no | — |
| 258 | C2×Q16 | — | 2 | 1 | no | — |
| 259 | C2×Q16 | — | 2 | 1 | no | — |
| 260 | C2×Q16 | — | 2 | 1 | no | — |
| 261 | C2×Q16 | — | 5 | 1 | no | — |
| 262 | C2×Q16 | — | 10 | 4 | no | — |
| 263 | C2×Q16 | — | 10 | 4 | no | — |
| 264 | C2×Q16 | — | 10 | 2 | no | — |
| 265 | C2×Q16 | C4×D5 | 1 | 2 | yes | — |
| 266 | C2×Q16 | D20 | 1 | 2 | yes | — |
| 267 | C2×Q16 | C22⋊D5 | 1 | 2 | yes | — |
| 268 | C2×SD16 | — | 10 | 2 | no | — |
| 269 | C2×SD16 | — | 10 | 1 | no | — |
| 270 | C2×D8 | — | 5 | 1 | no | — |
| 271 | #131 | — | 5 | 2 | no | — |
| 272 | #131 | — | 5 | 2 | no | — |
| 273 | #131 | — | 10 | 1 | no | — |
| 274 | #131 | — | 10 | 1 | no | — |
| 275 | C2×M16 | — | 5 | 1 | no | — |
| 276 | C2×M16 | — | 10 | 1 | no | — |
| 277 | C2×M16 | — | 10 | 1 | no | — |
| 278 | C22×C8 | — | 10 | 1 | no | — |
| 279 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 280 | #117 | — | 2 | 1 | no | — |
| 281 | M32 | — | 2 | 1 | no | — |
| 282 | M32 | — | 2 | 1 | no | — |
| 283 | M32 | — | 10 | 1 | no | — |
| 284 | M32 | — | 10 | 1 | no | — |
| 285 | C2×C16 | — | 2 | 1 | no | — |
| 286 | C2×C16 | — | 10 | 1 | no | — |
| 287 | #108 | — | 10 | 1 | no | — |
| 288 | #108 | — | 10 | 1 | no | — |
| 289 | #107 | — | 2 | 1 | no | — |
| 290 | #106 | — | 2 | 1 | no | — |
| 291 | #104 | — | 20 | 2 | no | — |
| 292 | C22×C5 | — | 4 | 1 | no | — |
| 293 | C22×C5 | #418 | 1 | 1 | yes | characteristic |
| 294 | C22×C5 | #447 | 1 | 1 | yes | characteristic |
| 295 | C22×C5 | #450 | 1 | 1 | yes | characteristic |
| 296 | C2×D5 | — | 2 | 2 | no | — |
| 297 | C2×D5 | — | 4 | 2 | no | — |
| 298 | C2×D5 | — | 4 | 2 | no | — |
| 299 | C2×D5 | — | 8 | 2 | no | — |
| 300 | C4×C5 | — | 4 | 4 | no | — |
| 301 | C4×C5 | — | 16 | 1 | no | — |
| 302 | C4×C5 | #379 | 1 | 1 | yes | characteristic |
| 303 | C4×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 304 | C4×C5 | #447 | 1 | 1 | yes | characteristic |
| 305 | C4×C5 | #450 | 1 | 1 | yes | characteristic |
| 306 | Dic5 | — | 2 | 2 | no | — |
| 307 | Dic5 | — | 4 | 2 | no | — |
| 308 | #41 | — | 5 | 2 | no | — |
| 309 | #41 | — | 5 | 2 | no | — |
| 310 | #41 | — | 10 | 1 | no | — |
| 311 | #41 | — | 10 | 1 | no | — |
| 312 | #41 | — | 10 | 8 | no | — |
| 313 | #41 | — | 10 | 2 | no | — |
| 314 | #41 | — | 10 | 2 | no | — |
| 315 | #41 | — | 20 | 8 | no | — |
| 316 | #41 | — | 20 | 8 | no | — |
| 317 | #41 | — | 20 | 4 | no | — |
| 318 | #41 | — | 20 | 4 | no | — |
| 319 | #41 | — | 20 | 4 | no | — |
| 320 | #41 | — | 20 | 1 | no | — |
| 321 | #41 | — | 20 | 1 | no | — |
| 322 | C2×Q8 | — | 2 | 2 | no | — |
| 323 | C2×Q8 | — | 2 | 2 | no | — |
| 324 | C2×Q8 | — | 2 | 2 | no | — |
| 325 | C2×Q8 | — | 4 | 1 | no | — |
| 326 | C2×Q8 | — | 4 | 1 | no | — |
| 327 | C2×Q8 | — | 4 | 1 | no | — |
| 328 | C2×Q8 | — | 5 | 1 | no | — |
| 329 | C2×Q8 | — | 10 | 8 | no | — |
| 330 | C2×Q8 | — | 10 | 1 | no | — |
| 331 | C2×Q8 | — | 20 | 2 | no | — |
| 332 | C2×Q8 | — | 20 | 4 | no | — |
| 333 | C2×Q8 | — | 20 | 4 | no | — |
| 334 | C2×Q8 | — | 20 | 4 | no | — |
| 335 | C2×D4 | — | 5 | 1 | no | — |
| 336 | C2×D4 | — | 10 | 1 | no | — |
| 337 | C2×D4 | — | 10 | 1 | no | — |
| 338 | C2×D4 | — | 20 | 2 | no | — |
| 339 | C2×D4 | — | 20 | 1 | no | — |
| 340 | C22×C4 | — | 4 | 1 | no | — |
| 341 | C22×C4 | — | 10 | 1 | no | — |
| 342 | C22×C4 | — | 20 | 2 | no | — |
| 343 | C22×C4 | — | 20 | 2 | no | — |
| 344 | C22×C4 | — | 20 | 1 | no | — |
| 345 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 346 | Q16 | — | 2 | 2 | no | — |
| 347 | Q16 | — | 2 | 2 | no | — |
| 348 | Q16 | — | 2 | 2 | no | — |
| 349 | Q16 | — | 5 | 2 | no | — |
| 350 | Q16 | — | 10 | 8 | no | — |
| 351 | Q16 | — | 10 | 1 | no | — |
| 352 | Q16 | #685 | 1 | 4 | yes | — |
| 353 | SD16 | — | 10 | 8 | no | — |
| 354 | SD16 | — | 10 | 2 | no | — |
| 355 | SD16 | — | 10 | 2 | no | — |
| 356 | D8 | — | 5 | 2 | no | — |
| 357 | D8 | — | 10 | 1 | no | — |
| 358 | M16 | — | 5 | 2 | no | — |
| 359 | M16 | — | 10 | 1 | no | — |
| 360 | M16 | — | 10 | 2 | no | — |
| 361 | M16 | — | 10 | 2 | no | — |
| 362 | M16 | — | 20 | 1 | no | — |
| 363 | M16 | — | 20 | 1 | no | — |
| 364 | C2×C8 | — | 10 | 1 | no | — |
| 365 | C2×C8 | — | 10 | 2 | no | — |
| 366 | C2×C8 | — | 10 | 2 | no | — |
| 367 | C2×C8 | — | 20 | 1 | no | — |
| 368 | C2×C8 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 369 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 370 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 371 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 372 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 373 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 374 | C4⋊C4 | — | 4 | 1 | no | — |
| 375 | C22⋊C4 | — | 4 | 1 | no | — |
| 376 | C42 | — | 4 | 1 | no | — |
| 377 | C16 | — | 4 | 1 | no | — |
| 378 | C16 | — | 20 | 1 | no | — |
| 379 | C2×C5 | — | 2 | 1 | no | — |
| 380 | C2×C5 | — | 2 | 1 | no | — |
| 381 | C2×C5 | — | 2 | 1 | no | — |
| 382 | C2×C5 | #1786 | 1 | 1 | yes | characteristic |
| 383 | D5 | — | 4 | 2 | no | — |
| 384 | D5 | — | 8 | 2 | no | — |
| 385 | C23 | — | 10 | 1 | no | — |
| 386 | C23 | — | 20 | 1 | no | — |
| 387 | C23 | #4057 | 1 | 1 | yes | characteristic |
| 388 | Q8 | — | 2 | 4 | no | — |
| 389 | Q8 | — | 4 | 2 | no | — |
| 390 | Q8 | — | 4 | 2 | no | — |
| 391 | Q8 | — | 4 | 2 | no | — |
| 392 | Q8 | — | 5 | 2 | no | — |
| 393 | Q8 | — | 10 | 1 | no | — |
| 394 | Q8 | — | 10 | 2 | no | — |
| 395 | Q8 | — | 20 | 8 | no | — |
| 396 | Q8 | — | 20 | 1 | no | — |
| 397 | D4 | — | 5 | 2 | no | — |
| 398 | D4 | — | 10 | 2 | no | — |
| 399 | D4 | — | 10 | 2 | no | — |
| 400 | D4 | — | 10 | 1 | no | — |
| 401 | D4 | — | 10 | 2 | no | — |
| 402 | D4 | — | 20 | 8 | no | — |
| 403 | D4 | — | 20 | 2 | no | — |
| 404 | D4 | — | 20 | 2 | no | — |
| 405 | D4 | — | 20 | 1 | no | — |
| 406 | C2×C4 | — | 4 | 2 | no | — |
| 407 | C2×C4 | — | 4 | 2 | no | — |
| 408 | C2×C4 | — | 4 | 2 | no | — |
| 409 | C2×C4 | — | 8 | 1 | no | — |
| 410 | C2×C4 | — | 10 | 1 | no | — |
| 411 | C2×C4 | — | 10 | 2 | no | — |
| 412 | C2×C4 | — | 10 | 2 | no | — |
| 413 | C2×C4 | — | 20 | 8 | no | — |
| 414 | C2×C4 | — | 20 | 8 | no | — |
| 415 | C2×C4 | — | 20 | 1 | no | — |
| 416 | C2×C4 | — | 20 | 2 | no | — |
| 417 | C2×C4 | — | 20 | 2 | no | — |
| 418 | C2×C4 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 420 | C2×C4 | D5×D8 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | D5×SD16 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | #4060 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 424 | C8 | — | 10 | 2 | no | — |
| 425 | C8 | — | 40 | 1 | no | — |
| 426 | C8 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 427 | C8 | #4028 | 1 | 1 | yes | characteristic |
| 428 | C8 | C2×#685 | 1 | 1 | yes | characteristic |
| 429 | C8 | #4083 | 1 | 1 | yes | characteristic |
| 430 | C5 | #12751 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 431 | C22 | — | 4 | 1 | no | — |
| 432 | C22 | — | 10 | 2 | no | — |
| 433 | C22 | — | 20 | 2 | no | — |
| 434 | C22 | — | 20 | 2 | no | — |
| 435 | C22 | — | 40 | 2 | no | — |
| 436 | C22 | #65059 | 1 | 1 | yes | characteristic |
| 437 | C22 | #65065 | 1 | 1 | yes | characteristic |
| 438 | C22 | #65445 | 1 | 1 | yes | characteristic |
| 439 | C4 | — | 4 | 4 | no | — |
| 440 | C4 | — | 10 | 2 | no | — |
| 441 | C4 | — | 16 | 1 | no | — |
| 442 | C4 | — | 20 | 2 | no | — |
| 443 | C4 | D5×#102 | 1 | 1 | yes | characteristic |
| 444 | C4 | #65062 | 1 | 1 | yes | characteristic |
| 445 | C4 | #65244 | 1 | 1 | yes | characteristic |
| 446 | C4 | #65458 | 1 | 1 | yes | characteristic |
| 447 | C2 | — | 2 | 1 | no | — |
| 448 | C2 | — | 2 | 1 | no | — |
| 449 | C2 | — | 2 | 1 | no | — |
| 450 | C2 | — | 20 | 2 | no | — |
| 451 | C2 | — | 40 | 2 | no | — |
| 452 | C2 | #10600991 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2141 | C2 | semidirect |
| 3. C2×#64785 | C2 | semidirect |
| 4. #10602235 | C2 | semidirect |
| 5. #10602231 | C2 | semidirect |
| 6. #10601458 | C2 | semidirect |
| 7. #10601449 | C2 | semidirect |
| 14. #66100 | C4 | semidirect |
| 93. #2141 | D5 | semidirect |
| 430. C5 | #12751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66100 | 2 |
| C5×#2141 | 2 |
| C2×#64785 | 2 |
| #10602235 | 2 |
| #10602231 | 2 |
| #10601458 | 2 |
| #10601449 | 2 |
| #12751 | 5 |