Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1252 conjugacy classes of subgroups.
The subgroup lattice has 908 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D53⋊#421 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16811621 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D53⋊#413 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20291301 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20290419 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20290408 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#16811419 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×D53⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×D53⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×D53⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#13133296 | C22 | 1 | 1 | yes | characteristic |
| 12 | #16811622 | — | 2 | 1 | no | — |
| 13 | #16811621 | — | 2 | 2 | no | — |
| 14 | #16811621 | — | 2 | 2 | no | — |
| 15 | #16811621 | — | 2 | 1 | no | — |
| 16 | #16811620 | — | 2 | 2 | no | — |
| 17 | D53⋊#104 | — | 2 | 2 | no | — |
| 18 | C2×#13133281 | — | 2 | 2 | no | — |
| 19 | #16811610 | — | 2 | 2 | no | — |
| 20 | #16811609 | — | 2 | 2 | no | — |
| 21 | D53⋊#101 | — | 2 | 1 | no | — |
| 22 | D53⋊#100 | — | 2 | 1 | no | — |
| 23 | #16811597 | — | 2 | 2 | no | — |
| 24 | #16811597 | — | 2 | 2 | no | — |
| 25 | #16811593 | — | 2 | 2 | no | — |
| 26 | #16811502 | — | 2 | 2 | no | — |
| 27 | #16811498 | — | 2 | 2 | no | — |
| 28 | C22×#11719947 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#41×D53 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16811419 | — | 2 | 2 | no | — |
| 31 | #16811419 | — | 2 | 2 | no | — |
| 32 | #16811419 | — | 2 | 2 | no | — |
| 33 | #16811419 | — | 2 | 2 | no | — |
| 34 | C2×#13133250 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×#13133247 | C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#13133246 | — | 2 | 1 | no | — |
| 37 | C2×#13133243 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#13133241 | — | 2 | 1 | no | — |
| 39 | C2×#13133238 | — | 2 | 1 | no | — |
| 40 | C2×#13133236 | — | 2 | 1 | no | — |
| 41 | C2×M16×D53 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×AGL(1,ℤ/8)×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#11719936 | — | 2 | 1 | no | — |
| 44 | C2×#11719936 | — | 2 | 1 | no | — |
| 45 | C2×#11719936 | D4 | 1 | 2 | yes | — |
| 46 | D53⋊M16 | — | 2 | 1 | no | — |
| 47 | D53⋊M16 | — | 2 | 1 | no | — |
| 48 | D53⋊M16 | — | 2 | 1 | no | — |
| 49 | D53⋊M16 | — | 2 | 1 | no | — |
| 50 | D53⋊M16 | — | 2 | 1 | no | — |
| 51 | D53⋊M16 | — | 2 | 1 | no | — |
| 52 | D53⋊M16 | — | 2 | 1 | no | — |
| 53 | D53⋊M16 | — | 2 | 1 | no | — |
| 54 | D53⋊M16 | — | 2 | 1 | no | — |
| 55 | D53⋊M16 | — | 2 | 1 | no | — |
| 56 | D53⋊M16 | — | 2 | 1 | no | — |
| 57 | D53⋊M16 | D4 | 1 | 2 | yes | — |
| 58 | C2×#11719940 | — | 2 | 1 | no | — |
| 59 | C2×#11719940 | — | 2 | 1 | no | — |
| 60 | C2×#11719940 | D4 | 1 | 2 | yes | — |
| 61 | C2×D53⋊C8 | — | 2 | 1 | no | — |
| 62 | C2×D53⋊C8 | — | 2 | 1 | no | — |
| 63 | C2×D53⋊C8 | — | 2 | 1 | no | — |
| 64 | #13133296 | — | 2 | 1 | no | — |
| 65 | #13133296 | — | 2 | 1 | no | — |
| 66 | #13133296 | — | 2 | 1 | no | — |
| 67 | #13133296 | — | 2 | 1 | no | — |
| 68 | C2×C4⋊#6157 | — | 2 | 1 | no | — |
| 69 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 70 | C2×C4×#6157 | D4 | 1 | 2 | yes | — |
| 71 | #13133282 | — | 2 | 4 | no | — |
| 72 | #13133281 | — | 2 | 8 | no | — |
| 73 | #13133281 | — | 2 | 4 | no | — |
| 74 | #13133278 | — | 2 | 4 | no | — |
| 75 | #13133277 | — | 2 | 4 | no | — |
| 76 | C22⋊#88324 | — | 2 | 8 | no | — |
| 77 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×#11719945 | — | 2 | 1 | no | — |
| 79 | C2×#11719945 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C2×#11719947 | — | 2 | 1 | no | — |
| 81 | C2×#11719947 | — | 2 | 1 | no | — |
| 82 | C2×#11719947 | — | 2 | 1 | no | — |
| 83 | C2×#11719947 | — | 2 | 1 | no | — |
| 84 | C2×#11719947 | — | 2 | 1 | no | — |
| 85 | C2×#11719947 | — | 2 | 1 | no | — |
| 86 | C2×#11719947 | — | 2 | 1 | no | — |
| 87 | C2×#11719947 | — | 2 | 1 | no | — |
| 88 | C2×#11719947 | — | 2 | 1 | no | — |
| 89 | C2×#11719947 | — | 2 | 1 | no | — |
| 90 | C2×#11719947 | — | 2 | 1 | no | — |
| 91 | C2×#11719947 | D4 | 1 | 2 | yes | — |
| 92 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×#11719947 | D4 | 1 | 2 | yes | — |
| 94 | #41×D53 | — | 2 | 1 | no | — |
| 95 | #41×D53 | — | 2 | 1 | no | — |
| 96 | #41×D53 | — | 2 | 1 | no | — |
| 97 | #41×D53 | — | 2 | 1 | no | — |
| 98 | #41×D53 | — | 2 | 1 | no | — |
| 99 | #41×D53 | — | 2 | 1 | no | — |
| 100 | #41×D53 | — | 2 | 1 | no | — |
| 101 | #41×D53 | — | 2 | 1 | no | — |
| 102 | C22×Dic106 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 104 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 105 | C2×D4×D53 | — | 2 | 1 | no | — |
| 106 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 107 | C23×Dic53 | — | 2 | 1 | no | — |
| 108 | C22×C4×D53 | — | 2 | 1 | no | — |
| 109 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 110 | #13133250 | — | 2 | 2 | no | — |
| 111 | #13133250 | — | 2 | 2 | no | — |
| 112 | #13133247 | — | 2 | 2 | no | — |
| 113 | #13133247 | — | 2 | 2 | no | — |
| 114 | #13133246 | — | 2 | 4 | no | — |
| 115 | #13133246 | — | 2 | 4 | no | — |
| 116 | #13133243 | — | 2 | 2 | no | — |
| 117 | #13133243 | — | 2 | 2 | no | — |
| 118 | #13133241 | — | 2 | 4 | no | — |
| 119 | #13133241 | — | 2 | 4 | no | — |
| 120 | #13133238 | — | 2 | 4 | no | — |
| 121 | #13133238 | — | 2 | 4 | no | — |
| 122 | #13133236 | — | 2 | 4 | no | — |
| 123 | #13133236 | — | 2 | 4 | no | — |
| 124 | C2×Dic212 | — | 2 | 1 | no | — |
| 125 | C2×#11719925 | — | 2 | 1 | no | — |
| 126 | C2×#11719913 | — | 2 | 1 | no | — |
| 127 | C2×#11719923 | — | 2 | 1 | no | — |
| 128 | C2×#11719923 | — | 2 | 1 | no | — |
| 129 | C2×#11719922 | — | 2 | 1 | no | — |
| 130 | C2×#11719917 | C2×C4 | 1 | 1 | yes | characteristic |
| 131 | C2×#11719912 | — | 2 | 1 | no | — |
| 132 | M16×D53 | — | 2 | 1 | no | — |
| 133 | M16×D53 | — | 2 | 1 | no | — |
| 134 | M16×D53 | D4 | 1 | 2 | yes | — |
| 135 | M16×D53 | D4 | 1 | 2 | yes | — |
| 136 | C2×C8×D53 | — | 2 | 1 | no | — |
| 137 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 138 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 139 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 140 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 141 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 142 | C2×D8×C53 | — | 2 | 1 | no | — |
| 143 | C2×M16×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 144 | C24×C53 | — | 2 | 1 | no | — |
| 145 | C23×D53 | — | 2 | 1 | no | — |
| 146 | C23×D53 | #41 | 1 | 1 | yes | characteristic |
| 147 | C22×#6157 | — | 2 | 2 | no | — |
| 148 | #41×C53 | — | 2 | 1 | no | — |
| 149 | #41×C53 | — | 2 | 1 | no | — |
| 150 | #41×C53 | — | 2 | 1 | no | — |
| 151 | #41×C53 | — | 2 | 1 | no | — |
| 152 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 153 | C2×D4×C53 | — | 2 | 1 | no | — |
| 154 | C2×D4×C53 | — | 2 | 1 | no | — |
| 155 | C2×D4×C53 | — | 2 | 1 | no | — |
| 156 | C2×D4×C53 | — | 2 | 1 | no | — |
| 157 | C2×D4×C53 | — | 2 | 1 | no | — |
| 158 | C2×D4×C53 | — | 2 | 1 | no | — |
| 159 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 160 | C2×D4×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 161 | C22×C4×C53 | — | 2 | 1 | no | — |
| 162 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 163 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 164 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 165 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 166 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 167 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 168 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 169 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 170 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 171 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 172 | C22×Dic53 | — | 2 | 1 | no | — |
| 173 | C22×Dic53 | — | 2 | 2 | no | — |
| 174 | C22×Dic53 | — | 2 | 1 | no | — |
| 175 | C22×Dic53 | — | 2 | 2 | no | — |
| 176 | C22×Dic53 | — | 4 | 1 | no | — |
| 177 | C22×Dic53 | — | 4 | 1 | no | — |
| 178 | C22×Dic53 | — | 4 | 1 | no | — |
| 179 | C22×Dic53 | — | 4 | 1 | no | — |
| 180 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | #11719949 | — | 2 | 1 | no | — |
| 182 | #11719949 | — | 2 | 1 | no | — |
| 183 | #11719949 | — | 2 | 1 | no | — |
| 184 | #11719949 | — | 2 | 1 | no | — |
| 185 | Q8×D53 | — | 2 | 1 | no | — |
| 186 | Q8×D53 | — | 2 | 1 | no | — |
| 187 | Q8×D53 | — | 2 | 1 | no | — |
| 188 | Q8×D53 | — | 2 | 1 | no | — |
| 189 | #11719947 | — | 2 | 1 | no | — |
| 190 | #11719947 | — | 2 | 1 | no | — |
| 191 | #11719947 | — | 2 | 2 | no | — |
| 192 | #11719947 | — | 2 | 2 | no | — |
| 193 | #11719947 | — | 2 | 2 | no | — |
| 194 | #11719947 | — | 2 | 2 | no | — |
| 195 | #11719947 | — | 2 | 1 | no | — |
| 196 | #11719947 | — | 2 | 2 | no | — |
| 197 | #11719947 | — | 2 | 2 | no | — |
| 198 | #11719947 | — | 2 | 2 | no | — |
| 199 | #11719947 | — | 2 | 1 | no | — |
| 200 | #11719947 | — | 2 | 2 | no | — |
| 201 | #11719947 | — | 4 | 1 | no | — |
| 202 | #11719947 | — | 4 | 1 | no | — |
| 203 | #11719947 | — | 4 | 1 | no | — |
| 204 | #11719947 | — | 4 | 1 | no | — |
| 205 | #11719947 | — | 4 | 1 | no | — |
| 206 | #11719947 | — | 4 | 1 | no | — |
| 207 | #11719947 | — | 4 | 1 | no | — |
| 208 | #11719947 | — | 4 | 1 | no | — |
| 209 | #11719947 | — | 4 | 1 | no | — |
| 210 | #11719947 | — | 4 | 1 | no | — |
| 211 | #11719947 | — | 4 | 1 | no | — |
| 212 | #11719947 | — | 4 | 1 | no | — |
| 213 | D4×D53 | — | 2 | 1 | no | — |
| 214 | D4×D53 | — | 2 | 1 | no | — |
| 215 | D4×D53 | — | 2 | 1 | no | — |
| 216 | D4×D53 | — | 2 | 1 | no | — |
| 217 | D4×D53 | — | 4 | 1 | no | — |
| 218 | D4×D53 | — | 4 | 1 | no | — |
| 219 | D4×D53 | — | 4 | 1 | no | — |
| 220 | D4×D53 | — | 4 | 1 | no | — |
| 221 | #11719945 | — | 2 | 1 | no | — |
| 222 | #11719945 | — | 2 | 1 | no | — |
| 223 | #11719945 | — | 2 | 1 | no | — |
| 224 | #11719945 | — | 2 | 1 | no | — |
| 225 | #11719945 | — | 4 | 1 | no | — |
| 226 | #11719945 | — | 4 | 1 | no | — |
| 227 | #11719945 | — | 4 | 1 | no | — |
| 228 | #11719945 | — | 4 | 1 | no | — |
| 229 | C2×D212 | — | 2 | 1 | no | — |
| 230 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×D53 | — | 2 | 1 | no | — |
| 232 | C2×C4×D53 | — | 2 | 1 | no | — |
| 233 | C2×C4×D53 | — | 2 | 1 | no | — |
| 234 | C2×C4×D53 | — | 4 | 1 | no | — |
| 235 | C2×C4×D53 | — | 4 | 1 | no | — |
| 236 | C2×C4×D53 | — | 4 | 1 | no | — |
| 237 | C2×C4×D53 | — | 4 | 1 | no | — |
| 238 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 250 | C2×Dic106 | — | 2 | 1 | no | — |
| 251 | C2×Dic106 | — | 2 | 1 | no | — |
| 252 | C2×Dic106 | — | 2 | 1 | no | — |
| 253 | C2×Dic106 | — | 2 | 1 | no | — |
| 254 | C2×Dic106 | — | 2 | 1 | no | — |
| 255 | C2×Dic106 | — | 2 | 1 | no | — |
| 256 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 257 | C2×Dic106 | C22⋊C4 | 1 | 2 | yes | — |
| 258 | C22⋊#6157 | — | 4 | 1 | no | — |
| 259 | C22⋊#6157 | — | 4 | 1 | no | — |
| 260 | #11719940 | — | 2 | 2 | no | — |
| 261 | #11719940 | — | 2 | 2 | no | — |
| 262 | #11719940 | — | 2 | 2 | no | — |
| 263 | #11719940 | — | 4 | 1 | no | — |
| 264 | #11719940 | — | 4 | 1 | no | — |
| 265 | #11719940 | — | 4 | 1 | no | — |
| 266 | C2×#88324 | — | 2 | 2 | no | — |
| 267 | C2×#88324 | — | 2 | 2 | no | — |
| 268 | C2×#88324 | — | 4 | 1 | no | — |
| 269 | C4⋊#6157 | — | 4 | 1 | no | — |
| 270 | C4⋊#6157 | — | 4 | 1 | no | — |
| 271 | C4×#6157 | — | 2 | 2 | no | — |
| 272 | C4×#6157 | — | 2 | 2 | no | — |
| 273 | #11719936 | — | 2 | 2 | no | — |
| 274 | #11719936 | — | 2 | 2 | no | — |
| 275 | #11719936 | — | 2 | 2 | no | — |
| 276 | #11719936 | — | 4 | 1 | no | — |
| 277 | #11719936 | — | 4 | 1 | no | — |
| 278 | #11719936 | — | 4 | 1 | no | — |
| 279 | D53⋊C8 | — | 2 | 2 | no | — |
| 280 | D53⋊C8 | — | 4 | 1 | no | — |
| 281 | D53⋊C8 | — | 4 | 1 | no | — |
| 282 | D53⋊C8 | — | 4 | 1 | no | — |
| 283 | D53⋊C8 | — | 4 | 1 | no | — |
| 284 | D53⋊C8 | — | 4 | 1 | no | — |
| 285 | SD16×C53 | — | 2 | 4 | no | — |
| 286 | D8×C53 | — | 2 | 4 | no | — |
| 287 | M16×C53 | — | 2 | 1 | no | — |
| 288 | M16×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 289 | C2×C8×C53 | — | 2 | 1 | no | — |
| 290 | #11719925 | — | 2 | 4 | no | — |
| 291 | #11719923 | — | 2 | 4 | no | — |
| 292 | #11719923 | — | 2 | 4 | no | — |
| 293 | #11719922 | — | 2 | 4 | no | — |
| 294 | #11719917 | — | 2 | 1 | no | — |
| 295 | #11719917 | C22⋊C4 | 1 | 2 | yes | — |
| 296 | C2×#88322 | — | 2 | 1 | no | — |
| 297 | Dic212 | — | 2 | 4 | no | — |
| 298 | #11719913 | — | 2 | 4 | no | — |
| 299 | #11719912 | — | 2 | 2 | no | — |
| 300 | #11719912 | — | 2 | 2 | no | — |
| 301 | C8×D53 | — | 2 | 2 | no | — |
| 302 | C8×D53 | — | 2 | 2 | no | — |
| 303 | C23×C53 | — | 2 | 2 | no | — |
| 304 | C23×C53 | — | 2 | 1 | no | — |
| 305 | C23×C53 | — | 4 | 1 | no | — |
| 306 | C23×C53 | — | 4 | 1 | no | — |
| 307 | C23×C53 | — | 8 | 2 | no | — |
| 308 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 309 | C22×D53 | — | 2 | 1 | no | — |
| 310 | C22×D53 | — | 4 | 1 | no | — |
| 311 | C22×D53 | — | 4 | 1 | no | — |
| 312 | C22×D53 | — | 8 | 1 | no | — |
| 313 | C22×D53 | — | 8 | 2 | no | — |
| 314 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 315 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 316 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 317 | C22×D53 | #123 | 1 | 1 | yes | characteristic |
| 318 | C22×D53 | #123 | 1 | 1 | yes | characteristic |
| 319 | C22×D53 | #124 | 1 | 1 | yes | characteristic |
| 320 | C2×#6157 | — | 4 | 2 | no | — |
| 321 | C2×#6157 | — | 8 | 2 | no | — |
| 322 | Q8×C53 | — | 2 | 1 | no | — |
| 323 | Q8×C53 | — | 2 | 1 | no | — |
| 324 | D4×C53 | — | 2 | 1 | no | — |
| 325 | D4×C53 | — | 2 | 2 | no | — |
| 326 | D4×C53 | — | 2 | 1 | no | — |
| 327 | D4×C53 | — | 2 | 2 | no | — |
| 328 | D4×C53 | — | 4 | 1 | no | — |
| 329 | D4×C53 | — | 4 | 1 | no | — |
| 330 | D4×C53 | — | 4 | 1 | no | — |
| 331 | D4×C53 | — | 4 | 1 | no | — |
| 332 | C2×C4×C53 | — | 2 | 1 | no | — |
| 333 | C2×C4×C53 | — | 4 | 1 | no | — |
| 334 | C2×C4×C53 | — | 4 | 1 | no | — |
| 335 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 336 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 337 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 338 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 340 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 341 | C22⋊D53 | — | 4 | 1 | no | — |
| 342 | C22⋊D53 | — | 4 | 1 | no | — |
| 343 | C22⋊D53 | — | 4 | 1 | no | — |
| 344 | C22⋊D53 | — | 4 | 2 | no | — |
| 345 | C22⋊D53 | — | 4 | 1 | no | — |
| 346 | C22⋊D53 | — | 4 | 2 | no | — |
| 347 | C22⋊D53 | — | 4 | 2 | no | — |
| 348 | C22⋊D53 | — | 4 | 2 | no | — |
| 349 | C22⋊D53 | — | 4 | 1 | no | — |
| 350 | C22⋊D53 | — | 4 | 1 | no | — |
| 351 | C2×Dic53 | — | 2 | 1 | no | — |
| 352 | C2×Dic53 | — | 2 | 2 | no | — |
| 353 | C2×Dic53 | — | 4 | 1 | no | — |
| 354 | C2×Dic53 | — | 4 | 1 | no | — |
| 355 | C2×Dic53 | — | 4 | 1 | no | — |
| 356 | C2×Dic53 | — | 4 | 2 | no | — |
| 357 | C2×Dic53 | — | 4 | 2 | no | — |
| 358 | C2×Dic53 | — | 4 | 2 | no | — |
| 359 | C2×Dic53 | — | 4 | 1 | no | — |
| 360 | C2×Dic53 | — | 4 | 2 | no | — |
| 361 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 362 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 363 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 364 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 365 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 366 | C2×Dic53 | #127 | 1 | 1 | yes | characteristic |
| 367 | D212 | — | 2 | 1 | no | — |
| 368 | D212 | — | 2 | 1 | no | — |
| 369 | D212 | — | 4 | 1 | no | — |
| 370 | D212 | — | 4 | 1 | no | — |
| 371 | C4×D53 | — | 4 | 1 | no | — |
| 372 | C4×D53 | — | 4 | 1 | no | — |
| 373 | C4×D53 | — | 4 | 1 | no | — |
| 374 | C4×D53 | — | 4 | 1 | no | — |
| 375 | C4×D53 | — | 4 | 1 | no | — |
| 376 | C4×D53 | — | 4 | 1 | no | — |
| 377 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 378 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 379 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 380 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 381 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 382 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 383 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 384 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 385 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 386 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 387 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 388 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 389 | C4×D53 | #123 | 1 | 1 | yes | characteristic |
| 390 | C4×D53 | #123 | 1 | 1 | yes | characteristic |
| 391 | C4×D53 | #124 | 1 | 1 | yes | characteristic |
| 392 | C4×D53 | #127 | 1 | 1 | yes | characteristic |
| 393 | Dic106 | — | 2 | 2 | no | — |
| 394 | Dic106 | — | 2 | 1 | no | — |
| 395 | Dic106 | — | 2 | 2 | no | — |
| 396 | Dic106 | — | 2 | 1 | no | — |
| 397 | Dic106 | — | 4 | 1 | no | — |
| 398 | Dic106 | — | 4 | 1 | no | — |
| 399 | Dic106 | — | 4 | 1 | no | — |
| 400 | Dic106 | — | 4 | 1 | no | — |
| 401 | #88324 | — | 4 | 2 | no | — |
| 402 | #88324 | — | 4 | 2 | no | — |
| 403 | #88324 | — | 4 | 2 | no | — |
| 404 | C8×C53 | — | 2 | 2 | no | — |
| 405 | #88322 | — | 2 | 2 | no | — |
| 406 | #11032 | — | 53 | 1 | no | maximal, Sylow |
| 407 | C22×C53 | — | 4 | 1 | no | — |
| 408 | C22×C53 | — | 4 | 4 | no | — |
| 409 | C22×C53 | — | 4 | 2 | no | — |
| 410 | C22×C53 | — | 4 | 1 | no | — |
| 411 | C22×C53 | — | 8 | 1 | no | — |
| 412 | C22×C53 | — | 8 | 2 | no | — |
| 413 | C22×C53 | — | 8 | 2 | no | — |
| 414 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 415 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 416 | C22×C53 | #390 | 1 | 1 | yes | characteristic |
| 417 | C2×D53 | — | 4 | 1 | no | — |
| 418 | C2×D53 | — | 4 | 1 | no | — |
| 419 | C2×D53 | — | 4 | 1 | no | — |
| 420 | C2×D53 | — | 4 | 1 | no | — |
| 421 | C2×D53 | — | 4 | 1 | no | — |
| 422 | C2×D53 | — | 4 | 1 | no | — |
| 423 | C2×D53 | — | 4 | 1 | no | — |
| 424 | C2×D53 | — | 8 | 2 | no | — |
| 425 | C2×D53 | — | 8 | 2 | no | — |
| 426 | C2×D53 | — | 8 | 1 | no | — |
| 427 | C2×D53 | #392 | 1 | 1 | yes | characteristic |
| 428 | C2×D53 | #394 | 1 | 1 | yes | characteristic |
| 429 | C2×D53 | #394 | 1 | 1 | yes | characteristic |
| 430 | C2×D53 | #394 | 1 | 1 | yes | characteristic |
| 431 | #6157 | — | 8 | 2 | no | — |
| 432 | C4×C53 | — | 4 | 1 | no | — |
| 433 | C4×C53 | #379 | 1 | 1 | yes | characteristic |
| 434 | C4×C53 | #386 | 1 | 1 | yes | characteristic |
| 435 | C4×C53 | #386 | 1 | 1 | yes | characteristic |
| 436 | C4×C53 | #390 | 1 | 1 | yes | characteristic |
| 437 | Dic53 | — | 4 | 1 | no | — |
| 438 | Dic53 | — | 4 | 2 | no | — |
| 439 | Dic53 | #392 | 1 | 1 | yes | characteristic |
| 440 | Dic53 | #392 | 1 | 1 | yes | characteristic |
| 441 | Dic53 | #392 | 1 | 1 | yes | characteristic |
| 442 | Dic53 | #394 | 1 | 1 | yes | characteristic |
| 443 | C2×#575 | — | 53 | 1 | no | — |
| 444 | C2×#421 | — | 53 | 1 | no | — |
| 445 | C2×#421 | — | 53 | 1 | no | — |
| 446 | C2×#413 | — | 53 | 1 | no | — |
| 447 | #2879 | — | 53 | 1 | no | — |
| 448 | #1742 | — | 53 | 1 | no | — |
| 449 | #1738 | — | 53 | 1 | no | — |
| 450 | C2×C53 | — | 2 | 1 | no | — |
| 451 | C2×C53 | — | 2 | 1 | no | — |
| 452 | C2×C53 | — | 2 | 1 | no | — |
| 453 | C2×C53 | — | 8 | 1 | no | — |
| 454 | C2×C53 | — | 8 | 2 | no | — |
| 455 | C2×C53 | #1438 | 1 | 1 | yes | characteristic |
| 456 | D53 | — | 2 | 1 | no | — |
| 457 | D53 | — | 2 | 1 | no | — |
| 458 | D53 | — | 2 | 1 | no | — |
| 459 | D53 | — | 2 | 1 | no | — |
| 460 | D53 | — | 8 | 1 | no | — |
| 461 | C22×#41 | — | 53 | 1 | no | — |
| 462 | C22×#41 | — | 53 | 1 | no | — |
| 463 | #575 | — | 106 | 2 | no | — |
| 464 | #575 | — | 106 | 2 | no | — |
| 465 | #575 | — | 106 | 2 | no | — |
| 466 | #575 | — | 106 | 2 | no | — |
| 467 | C2×#137 | — | 53 | 1 | no | — |
| 468 | C2×#137 | — | 53 | 1 | no | — |
| 469 | C2×#137 | — | 106 | 1 | no | — |
| 470 | C2×AGL(1,ℤ/8) | — | 53 | 1 | no | — |
| 471 | C2×AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 472 | C2×AGL(1,ℤ/8) | #6157 | 1 | 1 | yes | characteristic, complemented |
| 473 | C2×#135 | — | 106 | 1 | no | — |
| 474 | C2×#135 | — | 106 | 1 | no | — |
| 475 | C22×M16 | — | 53 | 1 | no | — |
| 476 | C22×M16 | — | 53 | 1 | no | — |
| 477 | C22×M16 | — | 53 | 1 | no | — |
| 478 | C22×M16 | — | 53 | 1 | no | — |
| 479 | C2×#117 | — | 53 | 1 | no | — |
| 480 | #421 | — | 106 | 2 | no | — |
| 481 | #421 | — | 106 | 2 | no | — |
| 482 | #421 | — | 106 | 1 | no | — |
| 483 | #421 | — | 106 | 2 | no | — |
| 484 | #421 | — | 106 | 1 | no | — |
| 485 | C2×#104 | — | 106 | 2 | no | — |
| 486 | C2×#104 | — | 106 | 2 | no | — |
| 487 | #413 | — | 106 | 2 | no | — |
| 488 | #413 | — | 106 | 2 | no | — |
| 489 | C2×#101 | — | 106 | 1 | no | — |
| 490 | C2×#100 | — | 106 | 1 | no | — |
| 491 | #408 | — | 106 | 2 | no | — |
| 492 | #408 | — | 106 | 2 | no | — |
| 493 | #407 | — | 106 | 2 | no | — |
| 494 | #343 | — | 106 | 2 | no | — |
| 495 | #341 | — | 106 | 2 | no | — |
| 496 | C53 | #11032 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 497 | C2×#41 | — | 53 | 1 | no | — |
| 498 | C2×#41 | — | 53 | 1 | no | — |
| 499 | C2×#41 | — | 53 | 2 | no | — |
| 500 | C2×#41 | — | 53 | 2 | no | — |
| 501 | C2×#41 | — | 53 | 1 | no | — |
| 502 | C2×#41 | — | 106 | 1 | no | — |
| 503 | C2×#41 | — | 106 | 1 | no | — |
| 504 | C2×#41 | — | 106 | 1 | no | — |
| 505 | C2×#41 | — | 106 | 1 | no | — |
| 506 | C2×#41 | — | 106 | 1 | no | — |
| 507 | C2×#41 | — | 106 | 1 | no | — |
| 508 | C2×#41 | — | 106 | 1 | no | — |
| 509 | C2×#41 | — | 106 | 1 | no | — |
| 510 | C2×#41 | — | 106 | 1 | no | — |
| 511 | C2×#41 | — | 106 | 1 | no | — |
| 512 | C2×#41 | — | 106 | 1 | no | — |
| 513 | C2×#41 | — | 106 | 1 | no | — |
| 514 | C2×#41 | — | 106 | 1 | no | — |
| 515 | C2×#41 | — | 106 | 1 | no | — |
| 516 | C2×#41 | — | 106 | 1 | no | — |
| 517 | C2×#41 | — | 106 | 1 | no | — |
| 518 | C2×#41 | — | 106 | 1 | no | — |
| 519 | C2×#41 | — | 106 | 1 | no | — |
| 520 | C2×#41 | — | 106 | 1 | no | — |
| 521 | C2×#41 | — | 106 | 1 | no | — |
| 522 | C2×#41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 523 | C22×Q8 | — | 53 | 1 | no | — |
| 524 | C22×Q8 | — | 53 | 1 | no | — |
| 525 | C22×D4 | — | 53 | 1 | no | — |
| 526 | C22×D4 | — | 106 | 1 | no | — |
| 527 | C22×D4 | — | 106 | 1 | no | — |
| 528 | C22×D4 | C2×#6157 | 1 | 1 | yes | characteristic |
| 529 | C23×C4 | — | 53 | 1 | no | — |
| 530 | C23×C4 | — | 106 | 1 | no | — |
| 531 | C23×C4 | — | 106 | 1 | no | — |
| 532 | #137 | — | 106 | 2 | no | — |
| 533 | #137 | — | 106 | 2 | no | — |
| 534 | #137 | — | 106 | 4 | no | — |
| 535 | #137 | — | 106 | 4 | no | — |
| 536 | #137 | — | 106 | 2 | no | — |
| 537 | #137 | — | 106 | 2 | no | — |
| 538 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 539 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 540 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 541 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 542 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 543 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 544 | #135 | — | 106 | 4 | no | — |
| 545 | #135 | — | 106 | 4 | no | — |
| 546 | #135 | — | 106 | 4 | no | — |
| 547 | #135 | — | 106 | 4 | no | — |
| 548 | C2×Q16 | — | 106 | 1 | no | — |
| 549 | C2×Q16 | — | 106 | 1 | no | — |
| 550 | C2×SD16 | — | 2 | 1 | no | — |
| 551 | C2×SD16 | — | 106 | 1 | no | — |
| 552 | C2×SD16 | — | 106 | 1 | no | — |
| 553 | C2×SD16 | — | 106 | 1 | no | — |
| 554 | C2×D8 | — | 2 | 1 | no | — |
| 555 | C2×D8 | — | 106 | 1 | no | — |
| 556 | C2×M16 | — | 53 | 1 | no | — |
| 557 | C2×M16 | — | 53 | 2 | no | — |
| 558 | C2×M16 | — | 53 | 2 | no | — |
| 559 | C2×M16 | — | 53 | 2 | no | — |
| 560 | C2×M16 | — | 53 | 2 | no | — |
| 561 | C2×M16 | — | 53 | 2 | no | — |
| 562 | C2×M16 | — | 106 | 1 | no | — |
| 563 | C2×M16 | — | 106 | 1 | no | — |
| 564 | C2×M16 | — | 106 | 1 | no | — |
| 565 | C2×M16 | — | 106 | 1 | no | — |
| 566 | C2×M16 | — | 106 | 1 | no | — |
| 567 | C2×M16 | — | 106 | 1 | no | — |
| 568 | C2×M16 | — | 106 | 1 | no | — |
| 569 | C2×M16 | — | 106 | 1 | no | — |
| 570 | C2×M16 | — | 106 | 1 | no | — |
| 571 | C2×M16 | — | 106 | 1 | no | — |
| 572 | C2×M16 | — | 106 | 1 | no | — |
| 573 | C2×M16 | — | 106 | 1 | no | — |
| 574 | C2×M16 | — | 106 | 1 | no | — |
| 575 | C2×M16 | — | 106 | 1 | no | — |
| 576 | C2×M16 | — | 106 | 1 | no | — |
| 577 | C2×M16 | — | 106 | 1 | no | — |
| 578 | C2×M16 | — | 106 | 1 | no | — |
| 579 | C2×M16 | — | 106 | 1 | no | — |
| 580 | C2×M16 | C2×#6157 | 1 | 1 | yes | characteristic |
| 581 | C22×C8 | — | 106 | 1 | no | — |
| 582 | C22×C8 | — | 106 | 1 | no | — |
| 583 | C22×C8 | — | 106 | 1 | no | — |
| 584 | C22×C8 | — | 106 | 1 | no | — |
| 585 | #117 | — | 106 | 1 | no | — |
| 586 | #117 | — | 106 | 1 | no | — |
| 587 | #117 | — | 106 | 1 | no | — |
| 588 | #117 | — | 106 | 1 | no | — |
| 589 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 590 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 591 | C2×C42 | — | 53 | 2 | no | — |
| 592 | #104 | — | 106 | 8 | no | — |
| 593 | #104 | — | 106 | 4 | no | — |
| 594 | #104 | — | 106 | 4 | no | — |
| 595 | #101 | — | 106 | 4 | no | — |
| 596 | #100 | — | 106 | 4 | no | — |
| 597 | C22⋊C8 | — | 106 | 8 | no | — |
| 598 | C24 | — | 2 | 1 | no | — |
| 599 | C24 | — | 53 | 1 | no | — |
| 600 | C24 | — | 106 | 1 | no | — |
| 601 | #41 | — | 2 | 1 | no | — |
| 602 | #41 | — | 2 | 1 | no | — |
| 603 | #41 | — | 2 | 1 | no | — |
| 604 | #41 | — | 2 | 1 | no | — |
| 605 | #41 | — | 106 | 2 | no | — |
| 606 | #41 | — | 106 | 1 | no | — |
| 607 | #41 | — | 106 | 1 | no | — |
| 608 | #41 | — | 106 | 2 | no | — |
| 609 | #41 | — | 106 | 1 | no | — |
| 610 | #41 | — | 106 | 2 | no | — |
| 611 | #41 | — | 106 | 2 | no | — |
| 612 | #41 | — | 106 | 2 | no | — |
| 613 | #41 | — | 106 | 2 | no | — |
| 614 | #41 | — | 106 | 2 | no | — |
| 615 | #41 | — | 106 | 2 | no | — |
| 616 | #41 | — | 106 | 1 | no | — |
| 617 | #41 | — | 106 | 1 | no | — |
| 618 | #41 | — | 106 | 1 | no | — |
| 619 | #41 | — | 106 | 1 | no | — |
| 620 | #41 | — | 106 | 1 | no | — |
| 621 | #41 | — | 106 | 1 | no | — |
| 622 | #41 | — | 106 | 1 | no | — |
| 623 | #41 | — | 106 | 1 | no | — |
| 624 | #41 | — | 106 | 1 | no | — |
| 625 | #41 | — | 212 | 1 | no | — |
| 626 | #41 | — | 212 | 1 | no | — |
| 627 | #41 | — | 212 | 1 | no | — |
| 628 | #41 | — | 212 | 1 | no | — |
| 629 | #41 | — | 212 | 1 | no | — |
| 630 | #41 | — | 212 | 1 | no | — |
| 631 | #41 | — | 212 | 1 | no | — |
| 632 | #41 | — | 212 | 1 | no | — |
| 633 | #41 | — | 212 | 1 | no | — |
| 634 | #41 | — | 212 | 1 | no | — |
| 635 | #41 | — | 212 | 1 | no | — |
| 636 | #41 | — | 212 | 1 | no | — |
| 637 | #41 | — | 212 | 1 | no | — |
| 638 | #41 | — | 212 | 1 | no | — |
| 639 | #41 | — | 212 | 1 | no | — |
| 640 | #41 | — | 212 | 1 | no | — |
| 641 | C2×Q8 | — | 53 | 1 | no | — |
| 642 | C2×Q8 | — | 53 | 2 | no | — |
| 643 | C2×Q8 | — | 106 | 1 | no | — |
| 644 | C2×Q8 | — | 106 | 1 | no | — |
| 645 | C2×Q8 | — | 106 | 1 | no | — |
| 646 | C2×Q8 | — | 106 | 1 | no | — |
| 647 | C2×Q8 | — | 106 | 1 | no | — |
| 648 | C2×Q8 | — | 106 | 1 | no | — |
| 649 | C2×Q8 | — | 106 | 1 | no | — |
| 650 | C2×Q8 | — | 106 | 1 | no | — |
| 651 | C2×Q8 | — | 106 | 1 | no | — |
| 652 | C2×Q8 | — | 106 | 1 | no | — |
| 653 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 654 | C2×D4 | — | 2 | 1 | no | — |
| 655 | C2×D4 | — | 2 | 1 | no | — |
| 656 | C2×D4 | — | 2 | 1 | no | — |
| 657 | C2×D4 | — | 2 | 1 | no | — |
| 658 | C2×D4 | — | 2 | 1 | no | — |
| 659 | C2×D4 | — | 2 | 1 | no | — |
| 660 | C2×D4 | — | 53 | 1 | no | — |
| 661 | C2×D4 | — | 106 | 1 | no | — |
| 662 | C2×D4 | — | 106 | 1 | no | — |
| 663 | C2×D4 | — | 106 | 1 | no | — |
| 664 | C2×D4 | — | 106 | 1 | no | — |
| 665 | C2×D4 | — | 106 | 1 | no | — |
| 666 | C2×D4 | — | 106 | 1 | no | — |
| 667 | C2×D4 | — | 106 | 2 | no | — |
| 668 | C2×D4 | — | 106 | 2 | no | — |
| 669 | C2×D4 | — | 106 | 1 | no | — |
| 670 | C2×D4 | — | 106 | 1 | no | — |
| 671 | C2×D4 | — | 212 | 1 | no | — |
| 672 | C2×D4 | — | 212 | 1 | no | — |
| 673 | C2×D4 | — | 212 | 1 | no | — |
| 674 | C2×D4 | — | 212 | 1 | no | — |
| 675 | C2×D4 | — | 212 | 1 | no | — |
| 676 | C2×D4 | — | 212 | 1 | no | — |
| 677 | C2×D4 | — | 212 | 1 | no | — |
| 678 | C2×D4 | — | 212 | 1 | no | — |
| 679 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 680 | C2×D4 | C22⋊#6157 | 1 | 2 | yes | — |
| 681 | C22×C4 | — | 2 | 1 | no | — |
| 682 | C22×C4 | — | 53 | 1 | no | — |
| 683 | C22×C4 | — | 53 | 1 | no | — |
| 684 | C22×C4 | — | 53 | 1 | no | — |
| 685 | C22×C4 | — | 53 | 1 | no | — |
| 686 | C22×C4 | — | 53 | 1 | no | — |
| 687 | C22×C4 | — | 53 | 1 | no | — |
| 688 | C22×C4 | — | 53 | 1 | no | — |
| 689 | C22×C4 | — | 53 | 1 | no | — |
| 690 | C22×C4 | — | 53 | 1 | no | — |
| 691 | C22×C4 | — | 53 | 1 | no | — |
| 692 | C22×C4 | — | 53 | 1 | no | — |
| 693 | C22×C4 | — | 53 | 1 | no | — |
| 694 | C22×C4 | — | 53 | 1 | no | — |
| 695 | C22×C4 | — | 106 | 1 | no | — |
| 696 | C22×C4 | — | 106 | 1 | no | — |
| 697 | C22×C4 | — | 106 | 2 | no | — |
| 698 | C22×C4 | — | 106 | 1 | no | — |
| 699 | C22×C4 | — | 106 | 2 | no | — |
| 700 | C22×C4 | — | 106 | 1 | no | — |
| 701 | C22×C4 | — | 106 | 1 | no | — |
| 702 | C22×C4 | — | 106 | 2 | no | — |
| 703 | C22×C4 | — | 212 | 1 | no | — |
| 704 | C22×C4 | — | 212 | 1 | no | — |
| 705 | C22×C4 | — | 212 | 1 | no | — |
| 706 | C22×C4 | — | 212 | 1 | no | — |
| 707 | C22×C4 | — | 212 | 1 | no | — |
| 708 | C22×C4 | — | 212 | 1 | no | — |
| 709 | C22×C4 | — | 212 | 1 | no | — |
| 710 | C22×C4 | — | 212 | 1 | no | — |
| 711 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 712 | Q16 | — | 106 | 4 | no | — |
| 713 | Q16 | — | 106 | 4 | no | — |
| 714 | SD16 | — | 2 | 4 | no | — |
| 715 | SD16 | — | 106 | 4 | no | — |
| 716 | SD16 | — | 106 | 4 | no | — |
| 717 | SD16 | — | 106 | 4 | no | — |
| 718 | D8 | — | 2 | 4 | no | — |
| 719 | D8 | — | 106 | 4 | no | — |
| 720 | M16 | — | 2 | 1 | no | — |
| 721 | M16 | — | 53 | 2 | no | — |
| 722 | M16 | — | 106 | 2 | no | — |
| 723 | M16 | — | 106 | 2 | no | — |
| 724 | M16 | — | 106 | 1 | no | — |
| 725 | M16 | — | 106 | 2 | no | — |
| 726 | M16 | — | 106 | 2 | no | — |
| 727 | M16 | — | 106 | 2 | no | — |
| 728 | M16 | — | 106 | 2 | no | — |
| 729 | M16 | — | 106 | 2 | no | — |
| 730 | M16 | — | 106 | 2 | no | — |
| 731 | M16 | — | 212 | 1 | no | — |
| 732 | M16 | — | 212 | 1 | no | — |
| 733 | M16 | — | 212 | 1 | no | — |
| 734 | M16 | — | 212 | 1 | no | — |
| 735 | M16 | — | 212 | 1 | no | — |
| 736 | M16 | — | 212 | 1 | no | — |
| 737 | M16 | C22⋊#6157 | 1 | 2 | yes | — |
| 738 | C2×C8 | — | 2 | 1 | no | — |
| 739 | C2×C8 | — | 106 | 2 | no | — |
| 740 | C2×C8 | — | 106 | 2 | no | — |
| 741 | C2×C8 | — | 106 | 1 | no | — |
| 742 | C2×C8 | — | 106 | 2 | no | — |
| 743 | C2×C8 | — | 106 | 2 | no | — |
| 744 | C2×C8 | — | 106 | 2 | no | — |
| 745 | C2×C8 | — | 212 | 1 | no | — |
| 746 | C2×C8 | — | 212 | 1 | no | — |
| 747 | C2×C8 | — | 212 | 1 | no | — |
| 748 | C2×C8 | — | 212 | 1 | no | — |
| 749 | C2×C8 | — | 212 | 1 | no | — |
| 750 | C2×C8 | — | 212 | 1 | no | — |
| 751 | C4⋊C4 | — | 212 | 1 | no | — |
| 752 | C4⋊C4 | — | 212 | 1 | no | — |
| 753 | C22⋊C4 | — | 212 | 1 | no | — |
| 754 | C22⋊C4 | — | 212 | 1 | no | — |
| 755 | C42 | — | 106 | 2 | no | — |
| 756 | C42 | — | 106 | 2 | no | — |
| 757 | C23 | — | 2 | 2 | no | — |
| 758 | C23 | — | 2 | 1 | no | — |
| 759 | C23 | — | 4 | 1 | no | — |
| 760 | C23 | — | 4 | 1 | no | — |
| 761 | C23 | — | 8 | 2 | no | — |
| 762 | C23 | — | 53 | 1 | no | — |
| 763 | C23 | — | 53 | 1 | no | — |
| 764 | C23 | — | 53 | 1 | no | — |
| 765 | C23 | — | 53 | 1 | no | — |
| 766 | C23 | — | 53 | 1 | no | — |
| 767 | C23 | — | 53 | 1 | no | — |
| 768 | C23 | — | 106 | 1 | no | — |
| 769 | C23 | — | 424 | 1 | no | — |
| 770 | C23 | — | 424 | 2 | no | — |
| 771 | C23 | — | 212 | 1 | no | — |
| 772 | C23 | — | 212 | 1 | no | — |
| 773 | C23 | D4×#6157 | 1 | 1 | yes | characteristic |
| 774 | Q8 | — | 2 | 1 | no | — |
| 775 | Q8 | — | 2 | 1 | no | — |
| 776 | Q8 | — | 106 | 2 | no | — |
| 777 | Q8 | — | 106 | 1 | no | — |
| 778 | Q8 | — | 106 | 2 | no | — |
| 779 | Q8 | — | 106 | 1 | no | — |
| 780 | Q8 | — | 212 | 1 | no | — |
| 781 | Q8 | — | 212 | 1 | no | — |
| 782 | Q8 | — | 212 | 1 | no | — |
| 783 | Q8 | — | 212 | 1 | no | — |
| 784 | D4 | — | 2 | 1 | no | — |
| 785 | D4 | — | 2 | 2 | no | — |
| 786 | D4 | — | 2 | 2 | no | — |
| 787 | D4 | — | 2 | 1 | no | — |
| 788 | D4 | — | 4 | 1 | no | — |
| 789 | D4 | — | 4 | 1 | no | — |
| 790 | D4 | — | 4 | 1 | no | — |
| 791 | D4 | — | 4 | 1 | no | — |
| 792 | D4 | — | 106 | 1 | no | — |
| 793 | D4 | — | 106 | 1 | no | — |
| 794 | D4 | — | 212 | 1 | no | — |
| 795 | D4 | — | 212 | 1 | no | — |
| 796 | D4 | — | 212 | 1 | no | — |
| 797 | D4 | — | 212 | 1 | no | — |
| 798 | D4 | — | 212 | 1 | no | — |
| 799 | D4 | — | 212 | 1 | no | — |
| 800 | D4 | — | 212 | 2 | no | — |
| 801 | D4 | — | 212 | 2 | no | — |
| 802 | D4 | — | 212 | 2 | no | — |
| 803 | D4 | — | 212 | 2 | no | — |
| 804 | D4 | — | 212 | 1 | no | — |
| 805 | D4 | — | 212 | 1 | no | — |
| 806 | C2×C4 | — | 2 | 1 | no | — |
| 807 | C2×C4 | — | 4 | 1 | no | — |
| 808 | C2×C4 | — | 4 | 1 | no | — |
| 809 | C2×C4 | — | 53 | 1 | no | — |
| 810 | C2×C4 | — | 53 | 1 | no | — |
| 811 | C2×C4 | — | 53 | 1 | no | — |
| 812 | C2×C4 | — | 53 | 1 | no | — |
| 813 | C2×C4 | — | 53 | 1 | no | — |
| 814 | C2×C4 | — | 53 | 1 | no | — |
| 815 | C2×C4 | — | 53 | 1 | no | — |
| 816 | C2×C4 | — | 53 | 1 | no | — |
| 817 | C2×C4 | — | 53 | 1 | no | — |
| 818 | C2×C4 | — | 53 | 1 | no | — |
| 819 | C2×C4 | — | 53 | 1 | no | — |
| 820 | C2×C4 | — | 53 | 1 | no | — |
| 821 | C2×C4 | — | 53 | 1 | no | — |
| 822 | C2×C4 | — | 53 | 1 | no | — |
| 823 | C2×C4 | — | 53 | 1 | no | — |
| 824 | C2×C4 | — | 53 | 1 | no | — |
| 825 | C2×C4 | — | 53 | 1 | no | — |
| 826 | C2×C4 | — | 53 | 1 | no | — |
| 827 | C2×C4 | — | 53 | 1 | no | — |
| 828 | C2×C4 | — | 53 | 1 | no | — |
| 829 | C2×C4 | — | 53 | 1 | no | — |
| 830 | C2×C4 | — | 53 | 1 | no | — |
| 831 | C2×C4 | — | 106 | 1 | no | — |
| 832 | C2×C4 | — | 106 | 2 | no | — |
| 833 | C2×C4 | — | 424 | 2 | no | — |
| 834 | C2×C4 | — | 212 | 1 | no | — |
| 835 | C2×C4 | — | 212 | 1 | no | — |
| 836 | C2×C4 | — | 212 | 1 | no | — |
| 837 | C2×C4 | — | 212 | 1 | no | — |
| 838 | C2×C4 | — | 212 | 1 | no | — |
| 839 | C2×C4 | — | 212 | 2 | no | — |
| 840 | C2×C4 | — | 212 | 2 | no | — |
| 841 | C2×C4 | — | 212 | 2 | no | — |
| 842 | C2×C4 | — | 212 | 1 | no | — |
| 843 | C2×C4 | — | 212 | 2 | no | — |
| 844 | C2×C4 | — | 212 | 2 | no | — |
| 845 | C2×C4 | — | 212 | 1 | no | — |
| 846 | C2×C4 | — | 212 | 1 | no | — |
| 847 | C2×C4 | — | 212 | 1 | no | — |
| 848 | C2×C4 | — | 212 | 1 | no | — |
| 849 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 850 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 851 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 852 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 853 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 854 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 855 | C8 | — | 2 | 2 | no | — |
| 856 | C8 | — | 106 | 2 | no | — |
| 857 | C8 | — | 212 | 2 | no | — |
| 858 | C8 | — | 212 | 2 | no | — |
| 859 | C8 | — | 212 | 2 | no | — |
| 860 | C22 | — | 4 | 1 | no | — |
| 861 | C22 | — | 4 | 4 | no | — |
| 862 | C22 | — | 4 | 1 | no | — |
| 863 | C22 | — | 4 | 2 | no | — |
| 864 | C22 | — | 8 | 1 | no | — |
| 865 | C22 | — | 8 | 2 | no | — |
| 866 | C22 | — | 8 | 2 | no | — |
| 867 | C22 | — | 53 | 1 | no | — |
| 868 | C22 | — | 53 | 1 | no | — |
| 869 | C22 | — | 53 | 1 | no | — |
| 870 | C22 | — | 53 | 1 | no | — |
| 871 | C22 | — | 424 | 1 | no | — |
| 872 | C22 | — | 424 | 2 | no | — |
| 873 | C22 | — | 424 | 2 | no | — |
| 874 | C22 | — | 212 | 1 | no | — |
| 875 | C22 | — | 212 | 1 | no | — |
| 876 | C22 | — | 212 | 1 | no | — |
| 877 | C22 | — | 212 | 1 | no | — |
| 878 | C22 | — | 212 | 1 | no | — |
| 879 | C22 | — | 212 | 1 | no | — |
| 880 | C22 | — | 212 | 1 | no | — |
| 881 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 882 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 883 | C22 | #16811575 | 1 | 1 | yes | characteristic |
| 884 | C4 | — | 4 | 1 | no | — |
| 885 | C4 | — | 53 | 1 | no | — |
| 886 | C4 | — | 53 | 1 | no | — |
| 887 | C4 | — | 53 | 1 | no | — |
| 888 | C4 | — | 53 | 1 | no | — |
| 889 | C4 | — | 424 | 2 | no | — |
| 890 | C4 | — | 212 | 1 | no | — |
| 891 | C4 | — | 212 | 2 | no | — |
| 892 | C4 | #16811564 | 1 | 1 | yes | characteristic |
| 893 | C4 | #16811571 | 1 | 1 | yes | characteristic |
| 894 | C4 | #16811571 | 1 | 1 | yes | characteristic |
| 895 | C4 | #16811575 | 1 | 1 | yes | characteristic |
| 896 | C2 | — | 2 | 1 | no | — |
| 897 | C2 | — | 2 | 1 | no | — |
| 898 | C2 | — | 2 | 1 | no | — |
| 899 | C2 | — | 8 | 2 | no | — |
| 900 | C2 | — | 8 | 1 | no | — |
| 901 | C2 | — | 106 | 1 | no | — |
| 902 | C2 | — | 106 | 1 | no | — |
| 903 | C2 | — | 106 | 1 | no | — |
| 904 | C2 | — | 106 | 1 | no | — |
| 905 | C2 | — | 424 | 1 | no | — |
| 906 | C2 | #20289897 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊#421 | C2 | semidirect |
| 2. C2×#16811621 | C2 | semidirect |
| 3. D53⋊#413 | C2 | semidirect |
| 4. #20291301 | C2 | semidirect |
| 5. #20290419 | C2 | semidirect |
| 6. #20290408 | C2 | semidirect |
| 34. C2×#13133250 | C4 | semidirect |
| 35. C2×#13133247 | C4 | semidirect |
| 37. C2×#13133243 | C4 | semidirect |
| 42. C2×AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 472. C2×AGL(1,ℤ/8) | #6157 | semidirect |
| 496. C53 | #11032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#421 | 2 |
| C2×#16811621 | 2 |
| D53⋊#413 | 2 |
| #20291301 | 2 |
| #20290419 | 2 |
| #20290408 | 2 |
| C2×#16811419 | 2 |
| #11032 | 53 |