Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4782 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#4150 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10619176 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#66085 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5×#2880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10615537 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10610411 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10610409 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10610376 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10610370 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#65027 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #10610341 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C22×C5×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#4150 | — | 2 | 3 | no | — |
| 14 | C2×#4150 | — | 2 | 1 | no | — |
| 15 | C2×#4150 | — | 2 | 16 | no | — |
| 16 | C2×#4150 | C22 | 1 | 2 | yes | — |
| 17 | C2×#4150 | C22 | 1 | 6 | yes | complemented |
| 18 | C2×#4149 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C22×Q8×D5 | — | 2 | 1 | no | — |
| 20 | C22×#711 | — | 2 | 3 | no | — |
| 21 | C22×#709 | C22 | 1 | 3 | yes | complemented |
| 22 | C23×Dic10 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×C5×#131 | C22 | 1 | 2 | yes | complemented |
| 24 | #66168 | — | 2 | 1 | no | — |
| 25 | #66167 | C22 | 1 | 3 | yes | complemented |
| 26 | #66164 | C22 | 1 | 3 | yes | complemented |
| 27 | #66163 | — | 2 | 3 | no | — |
| 28 | #66161 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #66151 | — | 2 | 1 | no | — |
| 30 | D4×C22⋊D5 | — | 2 | 3 | no | — |
| 31 | #66125 | C22 | 1 | 3 | yes | — |
| 32 | C2×#4076 | C22 | 1 | 3 | yes | — |
| 33 | #66085 | — | 2 | 16 | no | — |
| 34 | C2×#4055 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#4054 | C22 | 1 | 6 | yes | complemented |
| 36 | C2×#4050 | C22 | 1 | 6 | yes | complemented |
| 37 | C22×#677 | C22 | 1 | 6 | yes | complemented |
| 38 | C5×#408 | C22 | 1 | 6 | yes | complemented |
| 39 | C5×#407 | C22 | 1 | 3 | yes | complemented |
| 40 | C2×C5×C22⋊C8 | C22 | 1 | 3 | yes | complemented |
| 41 | #65422 | C22 | 1 | 6 | yes | complemented |
| 42 | #65409 | C22 | 1 | 6 | yes | complemented |
| 43 | #65402 | C22 | 1 | 6 | yes | complemented |
| 44 | C2×#3948 | C22 | 1 | 6 | yes | complemented |
| 45 | #65028 | C22 | 1 | 3 | yes | complemented |
| 46 | #65028 | C22 | 1 | 6 | yes | complemented |
| 47 | #65027 | C22 | 1 | 3 | yes | complemented |
| 48 | #65027 | C22 | 1 | 6 | yes | complemented |
| 49 | #65027 | C22 | 1 | 12 | yes | complemented |
| 50 | #65027 | C22 | 1 | 6 | yes | complemented |
| 51 | #65023 | C22 | 1 | 6 | yes | complemented |
| 52 | #65023 | C22 | 1 | 12 | yes | complemented |
| 53 | #65022 | C22 | 1 | 6 | yes | complemented |
| 54 | #65021 | C22 | 1 | 3 | yes | complemented |
| 55 | #65020 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #60374 | — | 5 | 1 | no | maximal, Sylow |
| 57 | C2×C5×#41 | — | 2 | 8 | no | — |
| 58 | C2×C5×#41 | D4 | 1 | 3 | yes | — |
| 59 | C2×C5×#41 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C5×#41 | C23 | 1 | 3 | yes | — |
| 61 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 63 | C22×C5×D4 | D4 | 1 | 3 | yes | — |
| 64 | C23×C4×C5 | C23 | 1 | 3 | yes | — |
| 65 | C22×C22⋊D5 | — | 2 | 3 | no | — |
| 66 | C22×C22⋊D5 | — | 2 | 3 | no | — |
| 67 | C23×Dic5 | — | 2 | 3 | no | — |
| 68 | #4150 | — | 2 | 16 | no | — |
| 69 | #4150 | — | 2 | 48 | no | — |
| 70 | #4150 | — | 2 | 8 | no | — |
| 71 | #4150 | — | 2 | 24 | no | — |
| 72 | #4150 | — | 2 | 24 | no | — |
| 73 | #4150 | D4 | 1 | 16 | yes | complemented |
| 74 | #4149 | — | 2 | 8 | no | — |
| 75 | C2×#713 | — | 2 | 1 | no | — |
| 76 | C2×Q8×D5 | — | 2 | 16 | no | — |
| 77 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 78 | C2×Q8×D5 | — | 2 | 6 | no | — |
| 79 | C2×#711 | — | 2 | 48 | no | — |
| 80 | C2×#711 | — | 2 | 6 | no | — |
| 81 | C2×#711 | — | 2 | 12 | no | — |
| 82 | C2×#711 | — | 2 | 6 | no | — |
| 83 | C2×D4×D5 | — | 2 | 3 | no | — |
| 84 | C2×#709 | — | 2 | 3 | no | — |
| 85 | C2×#709 | — | 2 | 3 | no | — |
| 86 | C2×#709 | — | 2 | 24 | no | — |
| 87 | C2×#709 | C23 | 1 | 3 | yes | — |
| 88 | C2×#709 | C23 | 1 | 6 | yes | — |
| 89 | C2×#709 | C23 | 1 | 6 | yes | — |
| 90 | C22×D20 | C23 | 1 | 3 | yes | — |
| 91 | C22×D20 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×D5 | — | 2 | 3 | no | — |
| 93 | C22×Dic10 | — | 2 | 3 | no | — |
| 94 | C22×Dic10 | — | 2 | 3 | no | — |
| 95 | C22×Dic10 | — | 2 | 3 | no | — |
| 96 | C22×Dic10 | — | 2 | 24 | no | — |
| 97 | C22×Dic10 | C23 | 1 | 3 | yes | — |
| 98 | C22×Dic10 | C23 | 1 | 6 | yes | — |
| 99 | C22×Dic10 | C23 | 1 | 6 | yes | — |
| 100 | C5×#131 | — | 2 | 8 | no | — |
| 101 | C2×C5×M16 | C23 | 1 | 6 | yes | — |
| 102 | C22×C5×C8 | C23 | 1 | 6 | yes | — |
| 103 | #4099 | — | 2 | 3 | no | — |
| 104 | #4093 | — | 2 | 3 | no | — |
| 105 | #4092 | — | 2 | 3 | no | — |
| 106 | Q8×Dic5 | — | 2 | 1 | no | — |
| 107 | #4086 | — | 2 | 3 | no | — |
| 108 | #4085 | — | 2 | 6 | no | — |
| 109 | #4084 | — | 2 | 3 | no | — |
| 110 | #4083 | — | 2 | 6 | no | — |
| 111 | D4×Dic5 | — | 2 | 3 | no | — |
| 112 | #4076 | — | 2 | 3 | no | — |
| 113 | #4076 | — | 2 | 3 | no | — |
| 114 | #4076 | C23 | 1 | 3 | yes | — |
| 115 | #4076 | C23 | 1 | 6 | yes | — |
| 116 | #4076 | C23 | 1 | 3 | yes | — |
| 117 | #4075 | — | 2 | 3 | no | — |
| 118 | C4×C22⋊D5 | — | 2 | 3 | no | — |
| 119 | C4×C22⋊D5 | — | 2 | 3 | no | — |
| 120 | C2×#685 | — | 2 | 3 | no | — |
| 121 | #4072 | C23 | 1 | 3 | yes | — |
| 122 | C2×C4⋊Dic5 | C23 | 1 | 3 | yes | — |
| 123 | #4070 | C23 | 1 | 1 | yes | characteristic |
| 124 | #4070 | C23 | 1 | 3 | yes | — |
| 125 | #4055 | — | 2 | 24 | no | — |
| 126 | #4054 | — | 2 | 24 | no | — |
| 127 | C2×Dic20 | C23 | 1 | 6 | yes | — |
| 128 | #4050 | — | 2 | 24 | no | — |
| 129 | C2×D40 | C23 | 1 | 6 | yes | — |
| 130 | C2×#677 | — | 2 | 24 | no | — |
| 131 | C2×#677 | C23 | 1 | 6 | yes | — |
| 132 | C2×#677 | C23 | 1 | 12 | yes | — |
| 133 | C2×#677 | C23 | 1 | 2 | yes | — |
| 134 | C5×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 135 | C5×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 136 | C5×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 137 | C5×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 138 | #3953 | C23 | 1 | 2 | yes | — |
| 139 | #3953 | C23 | 1 | 6 | yes | — |
| 140 | #3948 | C23 | 1 | 6 | yes | — |
| 141 | #3948 | C23 | 1 | 12 | yes | — |
| 142 | #3948 | C23 | 1 | 6 | yes | — |
| 143 | C22×2−1+4 | — | 5 | 1 | no | — |
| 144 | C2×#577 | — | 5 | 2 | no | — |
| 145 | #3488 | — | 5 | 1 | no | — |
| 146 | #3013 | — | 5 | 6 | no | — |
| 147 | #3010 | — | 5 | 6 | no | — |
| 148 | #3006 | — | 5 | 3 | no | — |
| 149 | #3004 | — | 5 | 3 | no | — |
| 150 | #3002 | — | 5 | 3 | no | — |
| 151 | C2×#448 | — | 5 | 3 | no | — |
| 152 | #2898 | — | 5 | 2 | no | — |
| 153 | #2880 | D5 | 1 | 1 | yes | characteristic, complemented |
| 154 | C24×C5 | C2×D4 | 1 | 3 | yes | — |
| 155 | C23×D5 | — | 2 | 1 | no | — |
| 156 | C23×D5 | — | 2 | 3 | no | — |
| 157 | C5×#41 | — | 2 | 4 | no | — |
| 158 | C5×#41 | — | 2 | 12 | no | — |
| 159 | C5×#41 | — | 2 | 12 | no | — |
| 160 | C5×#41 | C2×D4 | 1 | 8 | yes | — |
| 161 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 162 | C2×C5×Q8 | C2×D4 | 1 | 3 | yes | — |
| 163 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C5×D4 | — | 2 | 12 | no | — |
| 165 | C2×C5×D4 | C2×D4 | 1 | 6 | yes | — |
| 166 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 167 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 168 | C22×C4×C5 | — | 2 | 12 | no | — |
| 169 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 170 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 171 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 172 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 173 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 174 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 175 | C2×C22⋊D5 | — | 2 | 24 | no | — |
| 176 | C2×C22⋊D5 | — | 2 | 6 | no | — |
| 177 | C2×C22⋊D5 | — | 2 | 6 | no | — |
| 178 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 179 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 180 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 181 | C2×C22⋊D5 | — | 2 | 6 | no | — |
| 182 | C2×C22⋊D5 | — | 8 | 6 | no | — |
| 183 | C22×Dic5 | — | 2 | 24 | no | — |
| 184 | C22×Dic5 | — | 2 | 3 | no | — |
| 185 | C22×Dic5 | — | 2 | 6 | no | — |
| 186 | C22×Dic5 | — | 2 | 6 | no | — |
| 187 | C22×Dic5 | — | 2 | 3 | no | — |
| 188 | #713 | — | 4 | 4 | no | — |
| 189 | Q8×D5 | — | 2 | 48 | no | — |
| 190 | Q8×D5 | — | 2 | 16 | no | — |
| 191 | #711 | — | 2 | 96 | no | — |
| 192 | #711 | — | 2 | 48 | no | — |
| 193 | #711 | — | 2 | 48 | no | — |
| 194 | D4×D5 | — | 4 | 12 | no | — |
| 195 | #709 | — | 2 | 24 | no | — |
| 196 | #709 | — | 2 | 24 | no | — |
| 197 | #709 | — | 2 | 12 | no | — |
| 198 | #709 | — | 2 | 12 | no | — |
| 199 | #709 | — | 2 | 12 | no | — |
| 200 | #709 | — | 2 | 12 | no | — |
| 201 | #709 | C2×D4 | 1 | 24 | yes | complemented |
| 202 | C2×D20 | — | 2 | 1 | no | — |
| 203 | C2×D20 | — | 2 | 4 | no | — |
| 204 | C2×D20 | — | 2 | 12 | no | — |
| 205 | C2×D20 | — | 2 | 3 | no | — |
| 206 | C2×D20 | C24 | 1 | 3 | yes | — |
| 207 | C2×D20 | C24 | 1 | 2 | yes | — |
| 208 | C2×C4×D5 | — | 2 | 24 | no | — |
| 209 | C2×C4×D5 | — | 2 | 6 | no | — |
| 210 | C2×C4×D5 | — | 2 | 6 | no | — |
| 211 | C2×C4×D5 | — | 2 | 3 | no | — |
| 212 | C2×Dic10 | — | 2 | 24 | no | — |
| 213 | C2×Dic10 | — | 2 | 24 | no | — |
| 214 | C2×Dic10 | — | 2 | 24 | no | — |
| 215 | C2×Dic10 | — | 2 | 3 | no | — |
| 216 | C2×Dic10 | — | 2 | 6 | no | — |
| 217 | C2×Dic10 | — | 2 | 6 | no | — |
| 218 | C2×Dic10 | — | 2 | 12 | no | — |
| 219 | C2×Dic10 | — | 2 | 12 | no | — |
| 220 | C2×Dic10 | — | 2 | 24 | no | — |
| 221 | C2×Dic10 | C2×D4 | 1 | 24 | yes | complemented |
| 222 | C2×Dic10 | C24 | 1 | 1 | yes | characteristic |
| 223 | C2×Dic10 | C24 | 1 | 6 | yes | — |
| 224 | C5×M16 | — | 2 | 12 | no | — |
| 225 | C2×C5×C8 | — | 2 | 12 | no | — |
| 226 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 227 | C2×C5×C8 | C24 | 1 | 6 | yes | — |
| 228 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 229 | C22⋊Dic5 | — | 2 | 3 | no | — |
| 230 | C22⋊Dic5 | — | 2 | 3 | no | — |
| 231 | #685 | — | 2 | 3 | no | — |
| 232 | #685 | — | 2 | 6 | no | — |
| 233 | #685 | — | 2 | 3 | no | — |
| 234 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 235 | C4⋊Dic5 | C24 | 1 | 3 | yes | — |
| 236 | C4⋊Dic5 | C24 | 1 | 1 | yes | characteristic |
| 237 | #683 | — | 2 | 1 | no | — |
| 238 | #683 | — | 2 | 3 | no | — |
| 239 | C4×Dic5 | — | 2 | 3 | no | — |
| 240 | Dic20 | — | 2 | 12 | no | — |
| 241 | D40 | — | 2 | 12 | no | — |
| 242 | #677 | — | 2 | 4 | no | — |
| 243 | #677 | — | 2 | 12 | no | — |
| 244 | #677 | — | 2 | 24 | no | — |
| 245 | C2×2−1+4 | — | 5 | 2 | no | — |
| 246 | C2×2−1+4 | — | 5 | 6 | no | — |
| 247 | C2×2−1+4 | — | 10 | 16 | no | — |
| 248 | C2×2−1+4 | — | 10 | 3 | no | — |
| 249 | C2×2−1+4 | — | 10 | 1 | no | — |
| 250 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 251 | C22×#41 | — | 5 | 3 | no | — |
| 252 | C22×#41 | — | 10 | 3 | no | — |
| 253 | C22×#41 | C2×D5 | 1 | 1 | yes | characteristic |
| 254 | C23×Q8 | — | 5 | 3 | no | — |
| 255 | C23×Q8 | — | 10 | 1 | no | — |
| 256 | #577 | — | 10 | 16 | no | — |
| 257 | C2×#137 | — | 5 | 6 | no | — |
| 258 | C2×AGL(1,ℤ/8) | — | 5 | 6 | no | — |
| 259 | C2×#135 | — | 5 | 6 | no | — |
| 260 | C22×SD16 | — | 5 | 6 | no | — |
| 261 | C2×#131 | C2×D5 | 1 | 2 | yes | complemented |
| 262 | #550 | — | 10 | 1 | no | — |
| 263 | #548 | — | 10 | 1 | no | — |
| 264 | #546 | — | 10 | 3 | no | — |
| 265 | D42 | — | 10 | 3 | no | — |
| 266 | #537 | — | 5 | 3 | no | — |
| 267 | #535 | — | 5 | 3 | no | — |
| 268 | #525 | — | 5 | 3 | no | — |
| 269 | C2×#121 | — | 5 | 3 | no | — |
| 270 | #520 | — | 5 | 1 | no | — |
| 271 | #452 | — | 5 | 6 | no | — |
| 272 | #451 | — | 5 | 3 | no | — |
| 273 | #451 | — | 5 | 6 | no | — |
| 274 | #450 | — | 5 | 1 | no | — |
| 275 | #449 | — | 5 | 6 | no | — |
| 276 | #449 | — | 5 | 12 | no | — |
| 277 | #448 | — | 5 | 3 | no | — |
| 278 | #448 | — | 5 | 6 | no | — |
| 279 | #448 | — | 5 | 12 | no | — |
| 280 | #448 | — | 5 | 6 | no | — |
| 281 | #447 | — | 5 | 3 | no | — |
| 282 | #419 | — | 5 | 6 | no | — |
| 283 | #417 | — | 5 | 6 | no | — |
| 284 | #416 | — | 5 | 6 | no | — |
| 285 | C2×#103 | — | 5 | 6 | no | — |
| 286 | #408 | C2×D5 | 1 | 6 | yes | complemented |
| 287 | #407 | C2×D5 | 1 | 3 | yes | complemented |
| 288 | C2×C22⋊C8 | C2×D5 | 1 | 3 | yes | complemented |
| 289 | C23×C5 | — | 2 | 6 | no | — |
| 290 | C23×C5 | — | 2 | 6 | no | — |
| 291 | C23×C5 | — | 4 | 3 | no | — |
| 292 | C23×C5 | C22×D4 | 1 | 3 | yes | — |
| 293 | C23×C5 | C22×D4 | 1 | 3 | yes | — |
| 294 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 295 | C22×D5 | — | 2 | 4 | no | — |
| 296 | C22×D5 | — | 2 | 2 | no | — |
| 297 | C22×D5 | — | 2 | 3 | no | — |
| 298 | C22×D5 | — | 4 | 2 | no | — |
| 299 | C22×D5 | — | 4 | 2 | no | — |
| 300 | C22×D5 | — | 4 | 6 | no | — |
| 301 | C22×D5 | — | 8 | 3 | no | — |
| 302 | C22×D5 | — | 8 | 3 | no | — |
| 303 | C5×Q8 | — | 2 | 6 | no | — |
| 304 | C5×Q8 | #120 | 1 | 4 | yes | — |
| 305 | C5×D4 | — | 2 | 12 | no | — |
| 306 | C5×D4 | — | 2 | 6 | no | — |
| 307 | C5×D4 | #120 | 1 | 12 | yes | — |
| 308 | C2×C4×C5 | — | 2 | 6 | no | — |
| 309 | C2×C4×C5 | — | 2 | 6 | no | — |
| 310 | C2×C4×C5 | — | 2 | 6 | no | — |
| 311 | C2×C4×C5 | — | 2 | 2 | no | — |
| 312 | C2×C4×C5 | — | 2 | 6 | no | — |
| 313 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 315 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 316 | C2×C4×C5 | C22×D4 | 1 | 12 | yes | — |
| 317 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 318 | C22⋊D5 | — | 2 | 24 | no | — |
| 319 | C22⋊D5 | — | 2 | 24 | no | — |
| 320 | C22⋊D5 | — | 4 | 6 | no | — |
| 321 | C22⋊D5 | — | 4 | 6 | no | — |
| 322 | C22⋊D5 | — | 8 | 3 | no | — |
| 323 | C22⋊D5 | — | 8 | 6 | no | — |
| 324 | C2×Dic5 | — | 2 | 12 | no | — |
| 325 | C2×Dic5 | — | 2 | 24 | no | — |
| 326 | C2×Dic5 | — | 2 | 24 | no | — |
| 327 | C2×Dic5 | — | 2 | 6 | no | — |
| 328 | C2×Dic5 | — | 2 | 1 | no | — |
| 329 | C2×Dic5 | — | 2 | 3 | no | — |
| 330 | C2×Dic5 | — | 2 | 1 | no | — |
| 331 | C2×Dic5 | — | 8 | 3 | no | — |
| 332 | D20 | — | 2 | 4 | no | — |
| 333 | D20 | — | 2 | 2 | no | — |
| 334 | D20 | — | 2 | 6 | no | — |
| 335 | D20 | — | 4 | 6 | no | — |
| 336 | D20 | C22×D4 | 1 | 4 | yes | — |
| 337 | C4×D5 | — | 2 | 24 | no | — |
| 338 | C4×D5 | — | 2 | 24 | no | — |
| 339 | C4×D5 | — | 4 | 6 | no | — |
| 340 | Dic10 | — | 2 | 12 | no | — |
| 341 | Dic10 | — | 2 | 24 | no | — |
| 342 | Dic10 | — | 2 | 24 | no | — |
| 343 | Dic10 | — | 2 | 6 | no | — |
| 344 | Dic10 | — | 2 | 2 | no | — |
| 345 | Dic10 | C22×D4 | 1 | 12 | yes | — |
| 346 | C5×C8 | — | 2 | 2 | no | — |
| 347 | C5×C8 | — | 2 | 6 | no | — |
| 348 | 2−1+4 | — | 5 | 16 | no | — |
| 349 | 2−1+4 | — | 10 | 24 | no | — |
| 350 | 2−1+4 | — | 10 | 24 | no | — |
| 351 | 2−1+4 | — | 10 | 48 | no | — |
| 352 | 2−1+4 | — | 10 | 16 | no | — |
| 353 | 2−1+4 | — | 10 | 8 | no | — |
| 354 | H(5,𝔽2) | — | 10 | 8 | no | — |
| 355 | C2×#41 | — | 2 | 8 | no | — |
| 356 | C2×#41 | — | 5 | 6 | no | — |
| 357 | C2×#41 | — | 5 | 3 | no | — |
| 358 | C2×#41 | — | 5 | 6 | no | — |
| 359 | C2×#41 | — | 10 | 24 | no | — |
| 360 | C2×#41 | — | 10 | 48 | no | — |
| 361 | C2×#41 | — | 10 | 1 | no | — |
| 362 | C2×#41 | — | 10 | 12 | no | — |
| 363 | C2×#41 | — | 10 | 6 | no | — |
| 364 | C2×#41 | — | 10 | 6 | no | — |
| 365 | C2×#41 | — | 10 | 3 | no | — |
| 366 | C2×#41 | — | 10 | 3 | no | — |
| 367 | C2×#41 | D20 | 1 | 3 | yes | — |
| 368 | C2×#41 | D20 | 1 | 1 | yes | characteristic |
| 369 | C2×#41 | C22×D5 | 1 | 3 | yes | — |
| 370 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 371 | C22×Q8 | — | 5 | 6 | no | — |
| 372 | C22×Q8 | — | 5 | 3 | no | — |
| 373 | C22×Q8 | — | 5 | 6 | no | — |
| 374 | C22×Q8 | — | 10 | 24 | no | — |
| 375 | C22×Q8 | — | 10 | 16 | no | — |
| 376 | C22×Q8 | — | 10 | 6 | no | — |
| 377 | C22×Q8 | — | 10 | 2 | no | — |
| 378 | C22×Q8 | — | 10 | 3 | no | — |
| 379 | C22×Q8 | — | 10 | 3 | no | — |
| 380 | C22×Q8 | — | 10 | 3 | no | — |
| 381 | C22×Q8 | D20 | 1 | 1 | yes | characteristic |
| 382 | C22×D4 | — | 5 | 3 | no | — |
| 383 | C22×D4 | — | 5 | 1 | no | — |
| 384 | C22×D4 | — | 10 | 3 | no | — |
| 385 | C22×D4 | — | 10 | 3 | no | — |
| 386 | C22×D4 | — | 10 | 3 | no | — |
| 387 | C22×D4 | D20 | 1 | 3 | yes | — |
| 388 | C23×C4 | — | 10 | 3 | no | — |
| 389 | C23×C4 | — | 10 | 3 | no | — |
| 390 | C23×C4 | C22×D5 | 1 | 3 | yes | — |
| 391 | #137 | — | 10 | 24 | no | — |
| 392 | AGL(1,ℤ/8) | — | 10 | 24 | no | — |
| 393 | #135 | — | 10 | 24 | no | — |
| 394 | C2×Q16 | — | 5 | 6 | no | — |
| 395 | C2×SD16 | — | 5 | 6 | no | — |
| 396 | C2×SD16 | — | 5 | 12 | no | — |
| 397 | C2×SD16 | — | 5 | 2 | no | — |
| 398 | C2×SD16 | — | 10 | 24 | no | — |
| 399 | C2×D8 | — | 5 | 6 | no | — |
| 400 | #131 | — | 2 | 8 | no | — |
| 401 | C2×M16 | C22×D5 | 1 | 6 | yes | — |
| 402 | C22×C8 | C22×D5 | 1 | 6 | yes | — |
| 403 | #127 | — | 10 | 3 | no | — |
| 404 | #124 | — | 10 | 3 | no | — |
| 405 | #123 | — | 10 | 3 | no | — |
| 406 | C22⋊Q8 | — | 5 | 1 | no | — |
| 407 | C22⋊Q8 | — | 5 | 3 | no | — |
| 408 | C22⋊Q8 | — | 10 | 3 | no | — |
| 409 | #121 | — | 5 | 3 | no | — |
| 410 | #121 | — | 5 | 6 | no | — |
| 411 | #121 | — | 5 | 3 | no | — |
| 412 | #121 | — | 10 | 6 | no | — |
| 413 | #121 | — | 10 | 3 | no | — |
| 414 | #121 | — | 10 | 3 | no | — |
| 415 | #121 | — | 10 | 3 | no | — |
| 416 | #120 | — | 10 | 3 | no | — |
| 417 | #120 | — | 10 | 6 | no | — |
| 418 | C4×Q8 | — | 10 | 1 | no | — |
| 419 | C4×D4 | — | 10 | 3 | no | — |
| 420 | C4×D4 | — | 10 | 3 | no | — |
| 421 | C4×D4 | — | 10 | 3 | no | — |
| 422 | #117 | — | 5 | 3 | no | — |
| 423 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 424 | C2×C22⋊C4 | — | 10 | 3 | no | — |
| 425 | #103 | — | 5 | 6 | no | — |
| 426 | #103 | — | 5 | 12 | no | — |
| 427 | #103 | — | 5 | 6 | no | — |
| 428 | #102 | — | 5 | 2 | no | — |
| 429 | #102 | — | 5 | 6 | no | — |
| 430 | C22⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 431 | C22⋊C8 | C22×D5 | 1 | 3 | yes | — |
| 432 | C22⋊C8 | C22×D5 | 1 | 6 | yes | — |
| 433 | C22⋊C8 | C22×D5 | 1 | 6 | yes | — |
| 434 | C22×C5 | — | 2 | 1 | no | — |
| 435 | C22×C5 | — | 2 | 3 | no | — |
| 436 | C22×C5 | — | 2 | 1 | no | — |
| 437 | C22×C5 | — | 2 | 3 | no | — |
| 438 | C22×C5 | — | 2 | 3 | no | — |
| 439 | C22×C5 | — | 2 | 3 | no | — |
| 440 | C22×C5 | — | 2 | 3 | no | — |
| 441 | C22×C5 | — | 4 | 12 | no | — |
| 442 | C22×C5 | C2×#120 | 1 | 6 | yes | — |
| 443 | C22×C5 | #577 | 1 | 2 | yes | complemented |
| 444 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 445 | C2×D5 | — | 2 | 4 | no | — |
| 446 | C2×D5 | — | 4 | 8 | no | — |
| 447 | C2×D5 | — | 4 | 2 | no | — |
| 448 | C2×D5 | — | 4 | 2 | no | — |
| 449 | C2×D5 | — | 4 | 3 | no | — |
| 450 | C2×D5 | — | 4 | 3 | no | — |
| 451 | C2×D5 | — | 4 | 3 | no | — |
| 452 | C2×D5 | — | 16 | 6 | no | — |
| 453 | C4×C5 | — | 2 | 1 | no | — |
| 454 | C4×C5 | — | 2 | 3 | no | — |
| 455 | C4×C5 | C2×#120 | 1 | 6 | yes | — |
| 456 | C4×C5 | C23×D4 | 1 | 2 | yes | — |
| 457 | Dic5 | — | 2 | 12 | no | — |
| 458 | Dic5 | — | 4 | 1 | no | — |
| 459 | Dic5 | — | 4 | 1 | no | — |
| 460 | Dic5 | — | 4 | 3 | no | — |
| 461 | C24 | — | 10 | 1 | no | — |
| 462 | C24 | — | 10 | 3 | no | — |
| 463 | C24 | C2×D20 | 1 | 3 | yes | — |
| 464 | #41 | — | 2 | 4 | no | — |
| 465 | #41 | — | 2 | 12 | no | — |
| 466 | #41 | — | 2 | 12 | no | — |
| 467 | #41 | — | 5 | 24 | no | — |
| 468 | #41 | — | 10 | 12 | no | — |
| 469 | #41 | — | 10 | 12 | no | — |
| 470 | #41 | — | 10 | 24 | no | — |
| 471 | #41 | — | 10 | 24 | no | — |
| 472 | #41 | — | 10 | 96 | no | — |
| 473 | #41 | — | 10 | 48 | no | — |
| 474 | #41 | — | 10 | 48 | no | — |
| 475 | #41 | — | 10 | 12 | no | — |
| 476 | #41 | — | 10 | 12 | no | — |
| 477 | #41 | — | 20 | 4 | no | — |
| 478 | #41 | D4×D5 | 1 | 8 | yes | — |
| 479 | C2×Q8 | — | 2 | 4 | no | — |
| 480 | C2×Q8 | — | 5 | 24 | no | — |
| 481 | C2×Q8 | — | 5 | 6 | no | — |
| 482 | C2×Q8 | — | 5 | 1 | no | — |
| 483 | C2×Q8 | — | 10 | 12 | no | — |
| 484 | C2×Q8 | — | 10 | 24 | no | — |
| 485 | C2×Q8 | — | 10 | 24 | no | — |
| 486 | C2×Q8 | — | 10 | 24 | no | — |
| 487 | C2×Q8 | — | 10 | 24 | no | — |
| 488 | C2×Q8 | — | 10 | 48 | no | — |
| 489 | C2×Q8 | — | 10 | 16 | no | — |
| 490 | C2×Q8 | — | 10 | 6 | no | — |
| 491 | C2×Q8 | — | 10 | 3 | no | — |
| 492 | C2×Q8 | — | 10 | 6 | no | — |
| 493 | C2×Q8 | — | 10 | 12 | no | — |
| 494 | C2×Q8 | C2×D20 | 1 | 3 | yes | — |
| 495 | C2×Q8 | C2×D20 | 1 | 1 | yes | characteristic |
| 496 | C2×D4 | — | 2 | 12 | no | — |
| 497 | C2×D4 | — | 5 | 2 | no | — |
| 498 | C2×D4 | — | 5 | 3 | no | — |
| 499 | C2×D4 | — | 10 | 4 | no | — |
| 500 | C2×D4 | — | 10 | 24 | no | — |
| 501 | C2×D4 | — | 10 | 6 | no | — |
| 502 | C2×D4 | — | 10 | 6 | no | — |
| 503 | C2×D4 | — | 10 | 3 | no | — |
| 504 | C2×D4 | — | 10 | 3 | no | — |
| 505 | C2×D4 | — | 10 | 3 | no | — |
| 506 | C2×D4 | — | 10 | 6 | no | — |
| 507 | C2×D4 | — | 10 | 1 | no | — |
| 508 | C2×D4 | — | 10 | 3 | no | — |
| 509 | C2×D4 | — | 10 | 12 | no | — |
| 510 | C2×D4 | — | 20 | 12 | no | — |
| 511 | C2×D4 | — | 40 | 6 | no | — |
| 512 | C2×D4 | C2×D20 | 1 | 6 | yes | — |
| 513 | C2×D4 | C2×D20 | 1 | 3 | yes | — |
| 514 | C2×D4 | C2×D20 | 1 | 3 | yes | — |
| 515 | C22×C4 | — | 2 | 12 | no | — |
| 516 | C22×C4 | — | 10 | 24 | no | — |
| 517 | C22×C4 | — | 10 | 24 | no | — |
| 518 | C22×C4 | — | 10 | 3 | no | — |
| 519 | C22×C4 | — | 10 | 6 | no | — |
| 520 | C22×C4 | — | 10 | 6 | no | — |
| 521 | C22×C4 | — | 10 | 6 | no | — |
| 522 | C22×C4 | — | 10 | 6 | no | — |
| 523 | C22×C4 | — | 10 | 3 | no | — |
| 524 | C22×C4 | — | 10 | 3 | no | — |
| 525 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 526 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 527 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 528 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 529 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 530 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 531 | Q16 | — | 10 | 12 | no | — |
| 532 | SD16 | — | 10 | 4 | no | — |
| 533 | SD16 | — | 10 | 12 | no | — |
| 534 | SD16 | — | 10 | 24 | no | — |
| 535 | D8 | — | 10 | 12 | no | — |
| 536 | M16 | — | 2 | 12 | no | — |
| 537 | C2×C8 | — | 2 | 12 | no | — |
| 538 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 539 | C2×C8 | C23×D5 | 1 | 6 | yes | — |
| 540 | C4⋊C4 | — | 5 | 3 | no | — |
| 541 | C4⋊C4 | — | 5 | 1 | no | — |
| 542 | C4⋊C4 | — | 10 | 3 | no | — |
| 543 | C4⋊C4 | — | 10 | 1 | no | — |
| 544 | C4⋊C4 | — | 10 | 3 | no | — |
| 545 | C22⋊C4 | — | 10 | 3 | no | — |
| 546 | C22⋊C4 | — | 10 | 1 | no | — |
| 547 | C22⋊C4 | — | 10 | 3 | no | — |
| 548 | C22⋊C4 | — | 10 | 3 | no | — |
| 549 | C22⋊C4 | — | 10 | 6 | no | — |
| 550 | C22⋊C4 | — | 10 | 3 | no | — |
| 551 | C42 | — | 10 | 3 | no | — |
| 552 | C2×C5 | — | 2 | 2 | no | — |
| 553 | C2×C5 | — | 2 | 6 | no | — |
| 554 | C2×C5 | — | 4 | 3 | no | — |
| 555 | C2×C5 | C22×#120 | 1 | 1 | yes | characteristic |
| 556 | C2×C5 | C2×#577 | 1 | 1 | yes | characteristic |
| 557 | C2×C5 | #3586 | 1 | 1 | yes | characteristic |
| 558 | D5 | — | 4 | 4 | no | — |
| 559 | D5 | — | 8 | 3 | no | — |
| 560 | C23 | — | 2 | 6 | no | — |
| 561 | C23 | — | 2 | 6 | no | — |
| 562 | C23 | — | 4 | 3 | no | — |
| 563 | C23 | — | 10 | 4 | no | — |
| 564 | C23 | — | 10 | 2 | no | — |
| 565 | C23 | — | 10 | 3 | no | — |
| 566 | C23 | — | 20 | 2 | no | — |
| 567 | C23 | — | 20 | 2 | no | — |
| 568 | C23 | — | 20 | 6 | no | — |
| 569 | C23 | — | 40 | 3 | no | — |
| 570 | C23 | — | 40 | 3 | no | — |
| 571 | C23 | C22×D20 | 1 | 3 | yes | — |
| 572 | C23 | C22×D20 | 1 | 3 | yes | — |
| 573 | C23 | C22×D20 | 1 | 1 | yes | characteristic |
| 574 | Q8 | — | 2 | 6 | no | — |
| 575 | Q8 | — | 5 | 12 | no | — |
| 576 | Q8 | — | 10 | 12 | no | — |
| 577 | Q8 | — | 10 | 24 | no | — |
| 578 | Q8 | — | 10 | 24 | no | — |
| 579 | Q8 | — | 10 | 6 | no | — |
| 580 | Q8 | — | 10 | 2 | no | — |
| 581 | Q8 | #4028 | 1 | 4 | yes | — |
| 582 | D4 | — | 2 | 12 | no | — |
| 583 | D4 | — | 2 | 6 | no | — |
| 584 | D4 | — | 5 | 4 | no | — |
| 585 | D4 | — | 10 | 4 | no | — |
| 586 | D4 | — | 10 | 24 | no | — |
| 587 | D4 | — | 10 | 24 | no | — |
| 588 | D4 | — | 10 | 2 | no | — |
| 589 | D4 | — | 10 | 6 | no | — |
| 590 | D4 | — | 20 | 6 | no | — |
| 591 | D4 | — | 20 | 6 | no | — |
| 592 | D4 | — | 20 | 6 | no | — |
| 593 | D4 | — | 40 | 6 | no | — |
| 594 | D4 | — | 40 | 3 | no | — |
| 595 | D4 | #4028 | 1 | 12 | yes | — |
| 596 | C2×C4 | — | 2 | 6 | no | — |
| 597 | C2×C4 | — | 2 | 6 | no | — |
| 598 | C2×C4 | — | 2 | 6 | no | — |
| 599 | C2×C4 | — | 2 | 2 | no | — |
| 600 | C2×C4 | — | 2 | 6 | no | — |
| 601 | C2×C4 | — | 10 | 24 | no | — |
| 602 | C2×C4 | — | 10 | 12 | no | — |
| 603 | C2×C4 | — | 10 | 24 | no | — |
| 604 | C2×C4 | — | 10 | 24 | no | — |
| 605 | C2×C4 | — | 10 | 6 | no | — |
| 606 | C2×C4 | — | 10 | 24 | no | — |
| 607 | C2×C4 | — | 10 | 1 | no | — |
| 608 | C2×C4 | — | 10 | 3 | no | — |
| 609 | C2×C4 | — | 10 | 1 | no | — |
| 610 | C2×C4 | — | 20 | 6 | no | — |
| 611 | C2×C4 | — | 40 | 3 | no | — |
| 612 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 613 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 614 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 615 | C2×C4 | C2×D4×D5 | 1 | 12 | yes | — |
| 616 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 617 | C8 | — | 2 | 2 | no | — |
| 618 | C8 | — | 2 | 6 | no | — |
| 619 | C5 | #60374 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 620 | C22 | — | 2 | 3 | no | — |
| 621 | C22 | — | 2 | 1 | no | — |
| 622 | C22 | — | 2 | 3 | no | — |
| 623 | C22 | — | 2 | 1 | no | — |
| 624 | C22 | — | 2 | 3 | no | — |
| 625 | C22 | — | 2 | 3 | no | — |
| 626 | C22 | — | 2 | 3 | no | — |
| 627 | C22 | — | 4 | 12 | no | — |
| 628 | C22 | — | 10 | 4 | no | — |
| 629 | C22 | — | 20 | 8 | no | — |
| 630 | C22 | — | 20 | 2 | no | — |
| 631 | C22 | — | 20 | 2 | no | — |
| 632 | C22 | — | 20 | 3 | no | — |
| 633 | C22 | — | 20 | 3 | no | — |
| 634 | C22 | — | 20 | 3 | no | — |
| 635 | C22 | — | 80 | 6 | no | — |
| 636 | C22 | C2×#4028 | 1 | 6 | yes | — |
| 637 | C22 | #66085 | 1 | 2 | yes | complemented |
| 638 | C22 | C23×D20 | 1 | 1 | yes | characteristic |
| 639 | C4 | — | 2 | 1 | no | — |
| 640 | C4 | — | 2 | 3 | no | — |
| 641 | C4 | — | 10 | 12 | no | — |
| 642 | C4 | — | 20 | 3 | no | — |
| 643 | C4 | — | 20 | 1 | no | — |
| 644 | C4 | — | 20 | 1 | no | — |
| 645 | C4 | C2×#4028 | 1 | 6 | yes | — |
| 646 | C4 | C22×D4×D5 | 1 | 2 | yes | — |
| 647 | C2 | — | 2 | 2 | no | — |
| 648 | C2 | — | 2 | 6 | no | — |
| 649 | C2 | — | 4 | 3 | no | — |
| 650 | C2 | — | 20 | 4 | no | — |
| 651 | C2 | — | 40 | 3 | no | — |
| 652 | C2 | C22×#4028 | 1 | 1 | yes | characteristic |
| 653 | C2 | C2×#66085 | 1 | 1 | yes | characteristic |
| 654 | C2 | #10619069 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#4150 | C2 | semidirect |
| 2. #10619176 | C2 | semidirect |
| 3. C2×#66085 | C2 | semidirect |
| 4. C5×#2880 | C2 | semidirect |
| 5. #10615537 | C2 | semidirect |
| 6. #10610411 | C2 | semidirect |
| 7. #10610409 | C2 | semidirect |
| 8. #10610376 | C2 | semidirect |
| 9. #10610370 | C2 | semidirect |
| 10. C2×#65027 | C2 | semidirect |
| 11. #10610341 | C2 | semidirect |
| 17. C2×#4150 | C22 | semidirect |
| 18. C2×#4149 | C22 | semidirect |
| 21. C22×#709 | C22 | semidirect |
| 22. C23×Dic10 | C22 | semidirect |
| 23. C2×C5×#131 | C22 | semidirect |
| 25. #66167 | C22 | semidirect |
| 26. #66164 | C22 | semidirect |
| 28. #66161 | C22 | semidirect |
| 34. C2×#4055 | C22 | semidirect |
| 35. C2×#4054 | C22 | semidirect |
| 36. C2×#4050 | C22 | semidirect |
| 37. C22×#677 | C22 | semidirect |
| 38. C5×#408 | C22 | semidirect |
| 39. C5×#407 | C22 | semidirect |
| 40. C2×C5×C22⋊C8 | C22 | semidirect |
| 41. #65422 | C22 | semidirect |
| 42. #65409 | C22 | semidirect |
| 43. #65402 | C22 | semidirect |
| 44. C2×#3948 | C22 | semidirect |
| 45. #65028 | C22 | semidirect |
| 46. #65028 | C22 | semidirect |
| 47. #65027 | C22 | semidirect |
| 48. #65027 | C22 | semidirect |
| 49. #65027 | C22 | semidirect |
| 50. #65027 | C22 | semidirect |
| 51. #65023 | C22 | semidirect |
| 52. #65023 | C22 | semidirect |
| 53. #65022 | C22 | semidirect |
| 54. #65021 | C22 | semidirect |
| 55. #65020 | C22 | semidirect |
| 73. #4150 | D4 | semidirect |
| 153. #2880 | D5 | semidirect |
| 201. #709 | C2×D4 | semidirect |
| 221. C2×Dic10 | C2×D4 | semidirect |
| 261. C2×#131 | C2×D5 | semidirect |
| 286. #408 | C2×D5 | semidirect |
| 287. #407 | C2×D5 | semidirect |
| 288. C2×C22⋊C8 | C2×D5 | semidirect |
| 443. C22×C5 | #577 | semidirect |
| 619. C5 | #60374 | semidirect |
| 637. C22 | #66085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4150 | 2 |
| #10619176 | 2 |
| C2×#66085 | 2 |
| C5×#2880 | 2 |
| #10615537 | 2 |
| #10610411 | 2 |
| #10610409 | 2 |
| #10610376 | 2 |
| #10610370 | 2 |
| C2×#65027 | 2 |
| #10610341 | 2 |
| #60374 | 5 |