Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
944 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 88 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 | D53⋊#353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D53⋊#352 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D53⋊AΣL(1,𝔽16) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20290725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20290724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20290722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #560×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811690 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16811615 | — | 2 | 1 | no | — |
| 10 | D53⋊#100 | C22 | 1 | 1 | yes | characteristic |
| 11 | D53⋊#99 | C22 | 1 | 1 | yes | characteristic |
| 12 | D53⋊#99 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16811566 | — | 2 | 1 | no | — |
| 14 | #16811564 | — | 2 | 1 | no | — |
| 15 | #16811528 | — | 2 | 1 | no | — |
| 16 | #16811527 | — | 2 | 1 | no | — |
| 17 | #16811526 | — | 2 | 1 | no | — |
| 18 | #16811525 | — | 2 | 1 | no | — |
| 19 | #16811524 | — | 2 | 1 | no | — |
| 20 | #16811523 | — | 2 | 1 | no | — |
| 21 | #16811500 | — | 2 | 1 | no | — |
| 22 | #16811500 | — | 2 | 1 | no | — |
| 23 | #16811494 | — | 2 | 1 | no | — |
| 24 | #16811364 | — | 2 | 1 | no | — |
| 25 | #16811363 | — | 2 | 1 | no | — |
| 26 | #16811363 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #16811362 | — | 2 | 1 | no | — |
| 28 | #16811362 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16811361 | — | 2 | 1 | no | — |
| 30 | #16811361 | — | 2 | 1 | no | — |
| 31 | #16811361 | — | 2 | 1 | no | — |
| 32 | #16811360 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #127×D53 | C22 | 1 | 1 | yes | characteristic |
| 34 | #126×D53 | — | 2 | 1 | no | — |
| 35 | #123×D53 | — | 2 | 1 | no | — |
| 36 | #123×D53 | C22 | 1 | 1 | yes | characteristic |
| 37 | #121×D53 | — | 2 | 1 | no | — |
| 38 | #121×D53 | — | 2 | 1 | no | — |
| 39 | #121×D53 | — | 2 | 1 | no | — |
| 40 | #120×D53 | — | 2 | 1 | no | — |
| 41 | #120×D53 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#560 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | D53⋊M16 | — | 2 | 1 | no | — |
| 44 | D4×#6157 | — | 4 | 2 | no | — |
| 45 | #13133296 | — | 2 | 1 | no | — |
| 46 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 47 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 48 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 49 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 50 | C2×C22⋊#6157 | — | 4 | 2 | no | — |
| 51 | #13133279 | — | 4 | 2 | no | — |
| 52 | #13133277 | — | 2 | 1 | no | — |
| 53 | #13133277 | — | 2 | 1 | no | — |
| 54 | #13133276 | — | 2 | 1 | no | — |
| 55 | #13133276 | — | 2 | 1 | no | — |
| 56 | #13133275 | — | 2 | 1 | no | — |
| 57 | #13133275 | — | 2 | 1 | no | — |
| 58 | (C2×#6157)⋊C4 | — | 4 | 2 | no | — |
| 59 | C24×D53 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×D4×D53 | — | 2 | 1 | no | — |
| 61 | C2×D4×D53 | — | 2 | 1 | no | — |
| 62 | C2×D4×D53 | — | 2 | 1 | no | — |
| 63 | C2×D4×D53 | — | 2 | 1 | no | — |
| 64 | C2×D4×D53 | — | 2 | 1 | no | — |
| 65 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×D4×D53 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C4×D53 | — | 2 | 1 | no | — |
| 68 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 69 | #13133214 | D4 | 1 | 1 | yes | characteristic |
| 70 | #13133213 | — | 2 | 1 | no | — |
| 71 | #13133213 | — | 2 | 1 | no | — |
| 72 | #13133213 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | #13133213 | D4 | 1 | 1 | yes | characteristic |
| 74 | #13133212 | — | 2 | 1 | no | — |
| 75 | #13133212 | — | 2 | 1 | no | — |
| 76 | #13133212 | — | 2 | 1 | no | — |
| 77 | #13133211 | — | 2 | 1 | no | — |
| 78 | #13133210 | — | 2 | 1 | no | — |
| 79 | #13133210 | — | 2 | 1 | no | — |
| 80 | #13133210 | — | 2 | 1 | no | — |
| 81 | #13133202 | — | 2 | 1 | no | — |
| 82 | #13133202 | — | 2 | 1 | no | — |
| 83 | #13133202 | — | 2 | 1 | no | — |
| 84 | #13133201 | — | 2 | 1 | no | — |
| 85 | #13133201 | D4 | 1 | 1 | yes | characteristic |
| 86 | #13133200 | — | 2 | 1 | no | — |
| 87 | #13133200 | D4 | 1 | 1 | yes | characteristic |
| 88 | #13133199 | — | 2 | 1 | no | — |
| 89 | #13133199 | — | 2 | 1 | no | — |
| 90 | #13133199 | — | 2 | 1 | no | — |
| 91 | #13133198 | — | 2 | 1 | no | — |
| 92 | #13133198 | C2×C4 | 1 | 1 | yes | characteristic |
| 93 | #13133192 | — | 2 | 1 | no | — |
| 94 | #13133192 | — | 2 | 1 | no | — |
| 95 | #13133192 | — | 2 | 1 | no | — |
| 96 | #13133191 | — | 2 | 1 | no | — |
| 97 | #13133191 | — | 2 | 1 | no | — |
| 98 | #13133191 | — | 2 | 1 | no | — |
| 99 | #13133190 | — | 2 | 1 | no | — |
| 100 | #13133190 | — | 2 | 1 | no | — |
| 101 | #13133190 | — | 2 | 1 | no | — |
| 102 | #13133190 | — | 2 | 1 | no | — |
| 103 | #13133190 | — | 2 | 1 | no | — |
| 104 | #13133190 | — | 2 | 1 | no | — |
| 105 | #13133189 | — | 2 | 1 | no | — |
| 106 | #13133189 | — | 2 | 1 | no | — |
| 107 | #13133189 | — | 2 | 1 | no | — |
| 108 | #13133189 | — | 2 | 1 | no | — |
| 109 | #13133189 | — | 2 | 1 | no | — |
| 110 | #13133189 | — | 2 | 1 | no | — |
| 111 | #13133188 | — | 2 | 1 | no | — |
| 112 | #13133188 | — | 2 | 1 | no | — |
| 113 | #13133188 | — | 2 | 1 | no | — |
| 114 | #13133187 | — | 2 | 1 | no | — |
| 115 | #13133187 | — | 2 | 1 | no | — |
| 116 | #13133187 | — | 2 | 1 | no | — |
| 117 | #13133187 | — | 2 | 1 | no | — |
| 118 | #13133187 | D4 | 1 | 1 | yes | characteristic |
| 119 | #13133186 | — | 2 | 1 | no | — |
| 120 | #13133186 | D4 | 1 | 1 | yes | characteristic |
| 121 | #13133185 | — | 2 | 1 | no | — |
| 122 | #13133185 | — | 2 | 1 | no | — |
| 123 | #13133185 | — | 2 | 1 | no | — |
| 124 | #13133185 | — | 2 | 1 | no | — |
| 125 | #13133185 | C2×C4 | 1 | 1 | yes | characteristic |
| 126 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 127 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 129 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 130 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 131 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 132 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 133 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 134 | C22⋊C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 135 | C22⋊C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 136 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 137 | #127×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 138 | #126×C53 | — | 2 | 1 | no | — |
| 139 | #123×C53 | — | 2 | 1 | no | — |
| 140 | #123×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 141 | #121×C53 | — | 2 | 1 | no | — |
| 142 | #121×C53 | — | 2 | 1 | no | — |
| 143 | #121×C53 | — | 2 | 1 | no | — |
| 144 | #120×C53 | — | 2 | 1 | no | — |
| 145 | #120×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 146 | C24×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 147 | C23×D53 | — | 2 | 1 | no | — |
| 148 | C23×D53 | — | 2 | 1 | no | — |
| 149 | C23×D53 | — | 2 | 1 | no | — |
| 150 | C23×D53 | — | 4 | 1 | no | — |
| 151 | C23×D53 | — | 4 | 1 | no | — |
| 152 | C23×D53 | — | 8 | 2 | no | — |
| 153 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 154 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×#6157 | — | 2 | 2 | no | — |
| 157 | C22×#6157 | — | 2 | 2 | no | — |
| 158 | C22×#6157 | — | 4 | 1 | no | — |
| 159 | C22×#6157 | — | 4 | 1 | no | — |
| 160 | C2×D4×C53 | — | 2 | 1 | no | — |
| 161 | C2×D4×C53 | — | 2 | 1 | no | — |
| 162 | C2×D4×C53 | — | 2 | 1 | no | — |
| 163 | C2×D4×C53 | — | 2 | 1 | no | — |
| 164 | C2×D4×C53 | — | 2 | 1 | no | — |
| 165 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 166 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 167 | C22×C4×C53 | — | 2 | 1 | no | — |
| 168 | C22×C4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 169 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 170 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 171 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 172 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 173 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 174 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 175 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 176 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 177 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 178 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 179 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 180 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C22×Dic53 | — | 2 | 1 | no | — |
| 183 | C22×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 184 | D4×D53 | — | 4 | 1 | no | — |
| 185 | D4×D53 | — | 4 | 1 | no | — |
| 186 | D4×D53 | — | 4 | 1 | no | — |
| 187 | D4×D53 | — | 4 | 1 | no | — |
| 188 | D4×D53 | — | 8 | 2 | no | — |
| 189 | D4×D53 | — | 8 | 2 | no | — |
| 190 | D4×D53 | — | 8 | 2 | no | — |
| 191 | D4×D53 | — | 8 | 2 | no | — |
| 192 | D4×D53 | — | 8 | 1 | no | — |
| 193 | D4×D53 | — | 8 | 1 | no | — |
| 194 | C2×D212 | — | 2 | 1 | no | — |
| 195 | C2×D212 | — | 2 | 1 | no | — |
| 196 | C2×D212 | — | 2 | 1 | no | — |
| 197 | C2×D212 | — | 2 | 1 | no | — |
| 198 | C2×D212 | — | 2 | 1 | no | — |
| 199 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 200 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×D53 | — | 2 | 1 | no | — |
| 202 | C2×C4×D53 | — | 2 | 1 | no | — |
| 203 | C2×C4×D53 | — | 2 | 1 | no | — |
| 204 | C2×C4×D53 | — | 2 | 1 | no | — |
| 205 | C2×C4×D53 | — | 2 | 1 | no | — |
| 206 | C2×C4×D53 | — | 2 | 1 | no | — |
| 207 | C2×C4×D53 | — | 2 | 1 | no | — |
| 208 | C2×C4×D53 | — | 4 | 1 | no | — |
| 209 | C2×C4×D53 | — | 4 | 1 | no | — |
| 210 | C2×C4×D53 | — | 8 | 2 | no | — |
| 211 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C22⋊#6157 | — | 4 | 1 | no | — |
| 213 | C22⋊#6157 | — | 4 | 1 | no | — |
| 214 | C22⋊#6157 | — | 4 | 1 | no | — |
| 215 | C22⋊#6157 | — | 4 | 1 | no | — |
| 216 | C22⋊#6157 | — | 4 | 1 | no | — |
| 217 | C22⋊#6157 | — | 4 | 1 | no | — |
| 218 | C22⋊#6157 | — | 4 | 1 | no | — |
| 219 | C22⋊#6157 | — | 8 | 4 | no | — |
| 220 | #11719940 | — | 4 | 1 | no | — |
| 221 | C4⋊#6157 | — | 2 | 2 | no | — |
| 222 | C4×#6157 | — | 4 | 1 | no | — |
| 223 | #11719936 | — | 4 | 1 | no | — |
| 224 | D53⋊C8 | — | 4 | 1 | no | — |
| 225 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 226 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 227 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 228 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 229 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 230 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 231 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 232 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 233 | C22⋊C4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C22⋊C4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 235 | C42×C53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 236 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 237 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 238 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 239 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 240 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 241 | C22⋊Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 242 | C22⋊Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 243 | #11719921 | — | 2 | 1 | no | — |
| 244 | #11719921 | — | 2 | 1 | no | — |
| 245 | #11719921 | — | 2 | 1 | no | — |
| 246 | #11719921 | — | 2 | 1 | no | — |
| 247 | #11719921 | — | 2 | 1 | no | — |
| 248 | #11719921 | — | 2 | 1 | no | — |
| 249 | #11719921 | — | 2 | 1 | no | — |
| 250 | #11719921 | — | 2 | 1 | no | — |
| 251 | #11719921 | — | 2 | 1 | no | — |
| 252 | #11719921 | — | 2 | 1 | no | — |
| 253 | #11719921 | — | 2 | 1 | no | — |
| 254 | #11719921 | — | 2 | 1 | no | — |
| 255 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 256 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 257 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 258 | #11719919 | — | 2 | 1 | no | — |
| 259 | #11719919 | — | 2 | 1 | no | — |
| 260 | #11719919 | — | 2 | 1 | no | — |
| 261 | #11719919 | — | 2 | 1 | no | — |
| 262 | #11719919 | — | 2 | 1 | no | — |
| 263 | #11719919 | — | 2 | 1 | no | — |
| 264 | C4×Dic53 | — | 2 | 1 | no | — |
| 265 | C4×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 266 | C23×C53 | — | 2 | 1 | no | — |
| 267 | C23×C53 | — | 2 | 1 | no | — |
| 268 | C23×C53 | — | 4 | 1 | no | — |
| 269 | C23×C53 | — | 8 | 1 | no | — |
| 270 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 271 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 272 | C22×D53 | — | 2 | 1 | no | — |
| 273 | C22×D53 | — | 2 | 1 | no | — |
| 274 | C22×D53 | — | 2 | 1 | no | — |
| 275 | C22×D53 | — | 2 | 1 | no | — |
| 276 | C22×D53 | — | 2 | 1 | no | — |
| 277 | C22×D53 | — | 2 | 1 | no | — |
| 278 | C22×D53 | — | 4 | 2 | no | — |
| 279 | C22×D53 | — | 4 | 2 | no | — |
| 280 | C22×D53 | — | 4 | 2 | no | — |
| 281 | C22×D53 | — | 4 | 2 | no | — |
| 282 | C22×D53 | — | 4 | 2 | no | — |
| 283 | C22×D53 | — | 4 | 2 | no | — |
| 284 | C22×D53 | — | 4 | 1 | no | — |
| 285 | C22×D53 | — | 4 | 4 | no | — |
| 286 | C22×D53 | — | 4 | 1 | no | — |
| 287 | C22×D53 | — | 4 | 1 | no | — |
| 288 | C22×D53 | — | 4 | 1 | no | — |
| 289 | C22×D53 | — | 4 | 1 | no | — |
| 290 | C22×D53 | — | 8 | 1 | no | — |
| 291 | C22×D53 | — | 8 | 1 | no | — |
| 292 | C22×D53 | — | 8 | 1 | no | — |
| 293 | C22×D53 | — | 8 | 1 | no | — |
| 294 | C22×D53 | — | 8 | 2 | no | — |
| 295 | C22×D53 | — | 8 | 2 | no | — |
| 296 | C22×D53 | — | 8 | 2 | no | — |
| 297 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 298 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 299 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 300 | C2×#6157 | — | 4 | 2 | no | — |
| 301 | C2×#6157 | — | 8 | 2 | no | — |
| 302 | C2×#6157 | — | 8 | 2 | no | — |
| 303 | C2×#6157 | — | 8 | 1 | no | — |
| 304 | C2×#6157 | — | 8 | 1 | no | — |
| 305 | C2×#6157 | — | 8 | 2 | no | — |
| 306 | C2×#6157 | — | 8 | 2 | no | — |
| 307 | D4×C53 | — | 4 | 1 | no | — |
| 308 | D4×C53 | — | 4 | 1 | no | — |
| 309 | D4×C53 | — | 8 | 1 | no | — |
| 310 | D4×C53 | — | 8 | 1 | no | — |
| 311 | D4×C53 | — | 8 | 1 | no | — |
| 312 | D4×C53 | — | 8 | 1 | no | — |
| 313 | D4×C53 | — | 8 | 1 | no | — |
| 314 | C2×C4×C53 | — | 2 | 1 | no | — |
| 315 | C2×C4×C53 | — | 2 | 1 | no | — |
| 316 | C2×C4×C53 | — | 2 | 1 | no | — |
| 317 | C2×C4×C53 | — | 2 | 1 | no | — |
| 318 | C2×C4×C53 | — | 4 | 1 | no | — |
| 319 | C2×C4×C53 | — | 8 | 1 | no | — |
| 320 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 321 | C22⋊D53 | — | 4 | 1 | no | — |
| 322 | C22⋊D53 | — | 4 | 1 | no | — |
| 323 | C22⋊D53 | — | 8 | 1 | no | — |
| 324 | C22⋊D53 | — | 8 | 1 | no | — |
| 325 | C22⋊D53 | — | 8 | 1 | no | — |
| 326 | C22⋊D53 | — | 8 | 1 | no | — |
| 327 | C22⋊D53 | — | 8 | 1 | no | — |
| 328 | C22⋊D53 | — | 8 | 1 | no | — |
| 329 | C22⋊D53 | — | 8 | 1 | no | — |
| 330 | C22⋊D53 | — | 8 | 1 | no | — |
| 331 | C22⋊D53 | — | 8 | 1 | no | — |
| 332 | C22⋊D53 | — | 8 | 1 | no | — |
| 333 | C22⋊D53 | — | 8 | 1 | no | — |
| 334 | C2×Dic53 | — | 2 | 1 | no | — |
| 335 | C2×Dic53 | — | 2 | 1 | no | — |
| 336 | C2×Dic53 | — | 2 | 1 | no | — |
| 337 | C2×Dic53 | — | 2 | 1 | no | — |
| 338 | C2×Dic53 | — | 4 | 1 | no | — |
| 339 | C2×Dic53 | — | 8 | 1 | no | — |
| 340 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 341 | D212 | — | 4 | 1 | no | — |
| 342 | D212 | — | 4 | 1 | no | — |
| 343 | D212 | — | 8 | 1 | no | — |
| 344 | D212 | — | 8 | 1 | no | — |
| 345 | D212 | — | 8 | 1 | no | — |
| 346 | D212 | — | 8 | 1 | no | — |
| 347 | D212 | — | 8 | 1 | no | — |
| 348 | C4×D53 | — | 2 | 1 | no | — |
| 349 | C4×D53 | — | 2 | 1 | no | — |
| 350 | C4×D53 | — | 4 | 2 | no | — |
| 351 | C4×D53 | — | 4 | 2 | no | — |
| 352 | C4×D53 | — | 4 | 2 | no | — |
| 353 | C4×D53 | — | 4 | 1 | no | — |
| 354 | C4×D53 | — | 4 | 1 | no | — |
| 355 | C4×D53 | — | 8 | 1 | no | — |
| 356 | C4×D53 | — | 8 | 1 | no | — |
| 357 | C4×D53 | — | 8 | 1 | no | — |
| 358 | #88324 | — | 8 | 1 | no | — |
| 359 | #12762 | — | 53 | 1 | no | maximal, Sylow |
| 360 | C22×C53 | — | 2 | 1 | no | — |
| 361 | C22×C53 | — | 2 | 1 | no | — |
| 362 | C22×C53 | — | 4 | 1 | no | — |
| 363 | C22×C53 | — | 4 | 1 | no | — |
| 364 | C22×C53 | — | 4 | 1 | no | — |
| 365 | C22×C53 | — | 4 | 1 | no | — |
| 366 | C22×C53 | — | 4 | 1 | no | — |
| 367 | C22×C53 | — | 4 | 1 | no | — |
| 368 | C22×C53 | — | 4 | 2 | no | — |
| 369 | C22×C53 | — | 4 | 1 | no | — |
| 370 | C22×C53 | — | 4 | 1 | no | — |
| 371 | C22×C53 | — | 8 | 1 | no | — |
| 372 | C22×C53 | #379 | 1 | 1 | yes | characteristic |
| 373 | C2×D53 | — | 2 | 2 | no | — |
| 374 | C2×D53 | — | 2 | 1 | no | — |
| 375 | C2×D53 | — | 2 | 1 | no | — |
| 376 | C2×D53 | — | 4 | 2 | no | — |
| 377 | C2×D53 | — | 4 | 2 | no | — |
| 378 | C2×D53 | — | 4 | 1 | no | — |
| 379 | C2×D53 | — | 4 | 1 | no | — |
| 380 | C2×D53 | — | 4 | 1 | no | — |
| 381 | C2×D53 | — | 4 | 1 | no | — |
| 382 | C2×D53 | — | 4 | 1 | no | — |
| 383 | C2×D53 | — | 4 | 1 | no | — |
| 384 | C2×D53 | — | 4 | 2 | no | — |
| 385 | C2×D53 | — | 4 | 1 | no | — |
| 386 | C2×D53 | — | 4 | 1 | no | — |
| 387 | C2×D53 | — | 8 | 1 | no | — |
| 388 | C2×D53 | — | 8 | 1 | no | — |
| 389 | C2×D53 | — | 8 | 2 | no | — |
| 390 | C2×D53 | — | 8 | 2 | no | — |
| 391 | C2×D53 | — | 8 | 4 | no | — |
| 392 | C2×D53 | — | 8 | 2 | no | — |
| 393 | C2×D53 | — | 8 | 2 | no | — |
| 394 | C2×D53 | — | 8 | 1 | no | — |
| 395 | C2×D53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 396 | C2×D53 | #458 | 1 | 1 | yes | characteristic |
| 397 | #6157 | — | 8 | 2 | no | — |
| 398 | #6157 | — | 16 | 1 | no | — |
| 399 | #6157 | — | 16 | 1 | no | — |
| 400 | C4×C53 | — | 2 | 1 | no | — |
| 401 | C4×C53 | — | 4 | 1 | no | — |
| 402 | C4×C53 | — | 4 | 1 | no | — |
| 403 | C4×C53 | — | 4 | 1 | no | — |
| 404 | C4×C53 | — | 4 | 1 | no | — |
| 405 | Dic53 | — | 2 | 1 | no | — |
| 406 | Dic53 | — | 4 | 1 | no | — |
| 407 | Dic53 | — | 4 | 1 | no | — |
| 408 | Dic53 | — | 4 | 1 | no | — |
| 409 | Dic53 | — | 4 | 1 | no | — |
| 410 | C2×#560 | — | 53 | 1 | no | — |
| 411 | C2×#353 | — | 53 | 1 | no | — |
| 412 | C2×#352 | — | 53 | 1 | no | — |
| 413 | C2×AΣL(1,𝔽16) | — | 53 | 1 | no | — |
| 414 | #1890 | — | 53 | 1 | no | — |
| 415 | #1889 | — | 53 | 1 | no | — |
| 416 | #1887 | — | 53 | 1 | no | — |
| 417 | C2×C53 | — | 2 | 1 | no | — |
| 418 | C2×C53 | — | 4 | 1 | no | — |
| 419 | C2×C53 | — | 4 | 1 | no | — |
| 420 | C2×C53 | — | 8 | 1 | no | — |
| 421 | C2×C53 | — | 8 | 1 | no | — |
| 422 | C2×C53 | #1790 | 1 | 1 | yes | characteristic |
| 423 | D53 | — | 2 | 1 | no | — |
| 424 | D53 | — | 4 | 1 | no | — |
| 425 | D53 | — | 4 | 1 | no | — |
| 426 | D53 | — | 8 | 1 | no | — |
| 427 | D53 | — | 8 | 1 | no | — |
| 428 | D53 | #2200 | 1 | 2 | yes | — |
| 429 | #560 | — | 53 | 1 | no | — |
| 430 | #560 | — | 53 | 1 | no | — |
| 431 | #560 | — | 53 | 1 | no | — |
| 432 | #560 | — | 106 | 1 | no | — |
| 433 | #560 | — | 106 | 1 | no | — |
| 434 | #560 | — | 106 | 1 | no | — |
| 435 | #560 | — | 106 | 1 | no | — |
| 436 | #560 | — | 106 | 1 | no | — |
| 437 | #560 | — | 106 | 1 | no | — |
| 438 | #560 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 439 | C2×#127 | — | 53 | 1 | no | — |
| 440 | C2×#126 | — | 106 | 1 | no | — |
| 441 | C2×#123 | — | 53 | 1 | no | — |
| 442 | C2×#123 | — | 106 | 1 | no | — |
| 443 | C2×#121 | — | 106 | 1 | no | — |
| 444 | C2×#121 | — | 106 | 1 | no | — |
| 445 | C2×#121 | — | 106 | 1 | no | — |
| 446 | C2×#120 | — | 53 | 1 | no | — |
| 447 | C2×#120 | — | 106 | 1 | no | — |
| 448 | #518 | — | 53 | 1 | no | — |
| 449 | #418 | — | 106 | 1 | no | — |
| 450 | C2×#100 | — | 53 | 1 | no | — |
| 451 | C2×#99 | — | 53 | 1 | no | — |
| 452 | C2×#99 | — | 53 | 1 | no | — |
| 453 | #381 | — | 106 | 1 | no | — |
| 454 | #379 | — | 106 | 1 | no | — |
| 455 | #353 | — | 106 | 1 | no | — |
| 456 | #353 | — | 106 | 1 | no | — |
| 457 | #352 | — | 106 | 1 | no | — |
| 458 | #352 | — | 106 | 1 | no | — |
| 459 | AΣL(1,𝔽16) | — | 106 | 1 | no | — |
| 460 | AΣL(1,𝔽16) | — | 106 | 1 | no | — |
| 461 | #342 | — | 106 | 1 | no | — |
| 462 | #342 | — | 106 | 1 | no | — |
| 463 | #339 | — | 106 | 1 | no | — |
| 464 | C53 | #12762 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 465 | C25 | — | 53 | 1 | no | — |
| 466 | C22×D4 | — | 53 | 1 | no | — |
| 467 | C22×D4 | — | 53 | 1 | no | — |
| 468 | C22×D4 | — | 106 | 1 | no | — |
| 469 | C22×D4 | — | 106 | 1 | no | — |
| 470 | C22×D4 | — | 106 | 1 | no | — |
| 471 | C22×D4 | — | 106 | 1 | no | — |
| 472 | C22×D4 | — | 106 | 1 | no | — |
| 473 | C23×C4 | — | 53 | 1 | no | — |
| 474 | C23×C4 | — | 106 | 1 | no | — |
| 475 | C2×M16 | — | 106 | 1 | no | — |
| 476 | #127 | — | 53 | 1 | no | — |
| 477 | #127 | — | 53 | 1 | no | — |
| 478 | #127 | — | 53 | 1 | no | — |
| 479 | #127 | — | 106 | 1 | no | — |
| 480 | #127 | — | 106 | 1 | no | — |
| 481 | #127 | C2×#6157 | 1 | 1 | yes | characteristic |
| 482 | #126 | — | 2 | 1 | no | — |
| 483 | #126 | — | 106 | 1 | no | — |
| 484 | #126 | — | 106 | 1 | no | — |
| 485 | #126 | — | 106 | 1 | no | — |
| 486 | #126 | — | 106 | 1 | no | — |
| 487 | #126 | — | 106 | 1 | no | — |
| 488 | #126 | — | 106 | 1 | no | — |
| 489 | #126 | — | 106 | 1 | no | — |
| 490 | #123 | — | 2 | 1 | no | — |
| 491 | #123 | — | 53 | 1 | no | — |
| 492 | #123 | — | 53 | 1 | no | — |
| 493 | #123 | — | 53 | 1 | no | — |
| 494 | #123 | — | 106 | 1 | no | — |
| 495 | #123 | — | 106 | 1 | no | — |
| 496 | #123 | — | 106 | 1 | no | — |
| 497 | #123 | — | 106 | 1 | no | — |
| 498 | #123 | — | 106 | 1 | no | — |
| 499 | #123 | — | 106 | 1 | no | — |
| 500 | #123 | — | 106 | 1 | no | — |
| 501 | #123 | — | 106 | 1 | no | — |
| 502 | #123 | — | 106 | 1 | no | — |
| 503 | #123 | C2×#6157 | 1 | 1 | yes | characteristic |
| 504 | #121 | — | 2 | 1 | no | — |
| 505 | #121 | — | 2 | 1 | no | — |
| 506 | #121 | — | 2 | 1 | no | — |
| 507 | #121 | — | 106 | 1 | no | — |
| 508 | #121 | — | 106 | 1 | no | — |
| 509 | #121 | — | 106 | 1 | no | — |
| 510 | #121 | — | 106 | 1 | no | — |
| 511 | #121 | — | 106 | 1 | no | — |
| 512 | #121 | — | 106 | 1 | no | — |
| 513 | #121 | — | 106 | 1 | no | — |
| 514 | #121 | — | 106 | 1 | no | — |
| 515 | #121 | — | 106 | 1 | no | — |
| 516 | #121 | — | 106 | 1 | no | — |
| 517 | #121 | — | 106 | 1 | no | — |
| 518 | #121 | — | 106 | 1 | no | — |
| 519 | #121 | — | 106 | 1 | no | — |
| 520 | #121 | — | 106 | 1 | no | — |
| 521 | #121 | — | 106 | 1 | no | — |
| 522 | #121 | — | 106 | 1 | no | — |
| 523 | #121 | — | 106 | 1 | no | — |
| 524 | #121 | — | 106 | 1 | no | — |
| 525 | #121 | — | 106 | 1 | no | — |
| 526 | #121 | — | 106 | 1 | no | — |
| 527 | #121 | — | 106 | 1 | no | — |
| 528 | #120 | — | 2 | 1 | no | — |
| 529 | #120 | — | 53 | 1 | no | — |
| 530 | #120 | — | 53 | 1 | no | — |
| 531 | #120 | — | 53 | 1 | no | — |
| 532 | #120 | — | 106 | 1 | no | — |
| 533 | #120 | — | 106 | 1 | no | — |
| 534 | #120 | — | 106 | 1 | no | — |
| 535 | #120 | — | 106 | 1 | no | — |
| 536 | #120 | — | 106 | 1 | no | — |
| 537 | #120 | — | 106 | 1 | no | — |
| 538 | #120 | — | 106 | 1 | no | — |
| 539 | #120 | — | 106 | 1 | no | — |
| 540 | #120 | — | 106 | 1 | no | — |
| 541 | #120 | C2×#6157 | 1 | 1 | yes | characteristic |
| 542 | C4×D4 | — | 212 | 2 | no | — |
| 543 | #117 | — | 106 | 1 | no | — |
| 544 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 545 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 546 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 547 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 548 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 549 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 550 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 551 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 552 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 553 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 554 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 555 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 556 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 557 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 558 | C2×C22⋊C4 | — | 212 | 2 | no | — |
| 559 | C2×C42 | — | 53 | 1 | no | — |
| 560 | #102 | — | 212 | 2 | no | — |
| 561 | #100 | — | 106 | 1 | no | — |
| 562 | #100 | — | 106 | 1 | no | — |
| 563 | #99 | — | 106 | 1 | no | — |
| 564 | #99 | — | 106 | 1 | no | — |
| 565 | #99 | — | 106 | 1 | no | — |
| 566 | #99 | — | 106 | 1 | no | — |
| 567 | #95 | — | 212 | 2 | no | — |
| 568 | C24 | — | 53 | 1 | no | — |
| 569 | C24 | — | 53 | 1 | no | — |
| 570 | C24 | — | 53 | 1 | no | — |
| 571 | C24 | — | 106 | 1 | no | — |
| 572 | C24 | — | 106 | 1 | no | — |
| 573 | C24 | — | 106 | 1 | no | — |
| 574 | C24 | — | 424 | 2 | no | — |
| 575 | C24 | — | 212 | 1 | no | — |
| 576 | C24 | — | 212 | 1 | no | — |
| 577 | C24 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 578 | C2×D4 | — | 2 | 1 | no | — |
| 579 | C2×D4 | — | 2 | 1 | no | — |
| 580 | C2×D4 | — | 2 | 1 | no | — |
| 581 | C2×D4 | — | 2 | 1 | no | — |
| 582 | C2×D4 | — | 2 | 1 | no | — |
| 583 | C2×D4 | — | 53 | 1 | no | — |
| 584 | C2×D4 | — | 53 | 1 | no | — |
| 585 | C2×D4 | — | 53 | 1 | no | — |
| 586 | C2×D4 | — | 53 | 1 | no | — |
| 587 | C2×D4 | — | 106 | 1 | no | — |
| 588 | C2×D4 | — | 106 | 1 | no | — |
| 589 | C2×D4 | — | 106 | 1 | no | — |
| 590 | C2×D4 | — | 106 | 1 | no | — |
| 591 | C2×D4 | — | 106 | 1 | no | — |
| 592 | C2×D4 | — | 106 | 1 | no | — |
| 593 | C2×D4 | — | 106 | 1 | no | — |
| 594 | C2×D4 | — | 106 | 1 | no | — |
| 595 | C2×D4 | — | 106 | 1 | no | — |
| 596 | C2×D4 | — | 106 | 1 | no | — |
| 597 | C2×D4 | — | 106 | 1 | no | — |
| 598 | C2×D4 | — | 106 | 1 | no | — |
| 599 | C2×D4 | — | 106 | 1 | no | — |
| 600 | C2×D4 | — | 106 | 1 | no | — |
| 601 | C2×D4 | — | 106 | 1 | no | — |
| 602 | C2×D4 | — | 106 | 1 | no | — |
| 603 | C2×D4 | — | 424 | 1 | no | — |
| 604 | C2×D4 | — | 424 | 1 | no | — |
| 605 | C2×D4 | — | 424 | 2 | no | — |
| 606 | C2×D4 | — | 424 | 2 | no | — |
| 607 | C2×D4 | — | 424 | 2 | no | — |
| 608 | C2×D4 | — | 424 | 2 | no | — |
| 609 | C2×D4 | — | 212 | 1 | no | — |
| 610 | C2×D4 | — | 212 | 1 | no | — |
| 611 | C2×D4 | — | 212 | 1 | no | — |
| 612 | C2×D4 | — | 212 | 1 | no | — |
| 613 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic, complemented |
| 614 | C2×D4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 615 | C22×C4 | — | 2 | 1 | no | — |
| 616 | C22×C4 | — | 53 | 1 | no | — |
| 617 | C22×C4 | — | 53 | 1 | no | — |
| 618 | C22×C4 | — | 106 | 1 | no | — |
| 619 | C22×C4 | — | 106 | 1 | no | — |
| 620 | C22×C4 | — | 106 | 1 | no | — |
| 621 | C22×C4 | — | 106 | 1 | no | — |
| 622 | C22×C4 | — | 106 | 1 | no | — |
| 623 | C22×C4 | — | 106 | 1 | no | — |
| 624 | C22×C4 | — | 106 | 1 | no | — |
| 625 | C22×C4 | — | 106 | 1 | no | — |
| 626 | C22×C4 | — | 106 | 2 | no | — |
| 627 | C22×C4 | — | 106 | 2 | no | — |
| 628 | C22×C4 | — | 424 | 2 | no | — |
| 629 | C22×C4 | — | 212 | 1 | no | — |
| 630 | C22×C4 | — | 212 | 1 | no | — |
| 631 | C22×C4 | — | 212 | 1 | no | — |
| 632 | C22×C4 | — | 212 | 1 | no | — |
| 633 | C22×C4 | C22⋊#6157 | 1 | 1 | yes | characteristic, complemented |
| 634 | M16 | — | 212 | 1 | no | — |
| 635 | M16 | — | 212 | 1 | no | — |
| 636 | C2×C8 | — | 212 | 1 | no | — |
| 637 | C4⋊C4 | — | 2 | 1 | no | — |
| 638 | C4⋊C4 | — | 2 | 1 | no | — |
| 639 | C4⋊C4 | — | 2 | 1 | no | — |
| 640 | C4⋊C4 | — | 106 | 1 | no | — |
| 641 | C4⋊C4 | — | 106 | 1 | no | — |
| 642 | C4⋊C4 | — | 106 | 1 | no | — |
| 643 | C4⋊C4 | — | 106 | 1 | no | — |
| 644 | C4⋊C4 | — | 106 | 1 | no | — |
| 645 | C4⋊C4 | — | 106 | 1 | no | — |
| 646 | C4⋊C4 | — | 106 | 1 | no | — |
| 647 | C4⋊C4 | — | 106 | 1 | no | — |
| 648 | C4⋊C4 | — | 106 | 1 | no | — |
| 649 | C4⋊C4 | — | 106 | 2 | no | — |
| 650 | C22⋊C4 | — | 2 | 1 | no | — |
| 651 | C22⋊C4 | — | 2 | 1 | no | — |
| 652 | C22⋊C4 | — | 2 | 1 | no | — |
| 653 | C22⋊C4 | — | 2 | 1 | no | — |
| 654 | C22⋊C4 | — | 2 | 1 | no | — |
| 655 | C22⋊C4 | — | 53 | 1 | no | — |
| 656 | C22⋊C4 | — | 53 | 1 | no | — |
| 657 | C22⋊C4 | — | 106 | 1 | no | — |
| 658 | C22⋊C4 | — | 106 | 1 | no | — |
| 659 | C22⋊C4 | — | 106 | 1 | no | — |
| 660 | C22⋊C4 | — | 106 | 1 | no | — |
| 661 | C22⋊C4 | — | 106 | 1 | no | — |
| 662 | C22⋊C4 | — | 106 | 1 | no | — |
| 663 | C22⋊C4 | — | 106 | 1 | no | — |
| 664 | C22⋊C4 | — | 106 | 1 | no | — |
| 665 | C22⋊C4 | — | 106 | 1 | no | — |
| 666 | C22⋊C4 | — | 106 | 1 | no | — |
| 667 | C22⋊C4 | — | 106 | 1 | no | — |
| 668 | C22⋊C4 | — | 106 | 1 | no | — |
| 669 | C22⋊C4 | — | 106 | 1 | no | — |
| 670 | C22⋊C4 | — | 106 | 1 | no | — |
| 671 | C22⋊C4 | — | 106 | 1 | no | — |
| 672 | C22⋊C4 | — | 106 | 1 | no | — |
| 673 | C22⋊C4 | — | 106 | 1 | no | — |
| 674 | C22⋊C4 | — | 424 | 4 | no | — |
| 675 | C22⋊C4 | — | 212 | 1 | no | — |
| 676 | C22⋊C4 | — | 212 | 1 | no | — |
| 677 | C22⋊C4 | — | 212 | 1 | no | — |
| 678 | C22⋊C4 | — | 212 | 1 | no | — |
| 679 | C22⋊C4 | — | 212 | 1 | no | — |
| 680 | C22⋊C4 | — | 212 | 1 | no | — |
| 681 | C22⋊C4 | — | 212 | 1 | no | — |
| 682 | C22⋊C4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 683 | C22⋊C4 | C22⋊#6157 | 1 | 1 | yes | characteristic, complemented |
| 684 | C42 | — | 53 | 1 | no | — |
| 685 | C42 | — | 106 | 1 | no | — |
| 686 | C42 | — | 212 | 1 | no | — |
| 687 | C42 | C22⋊#6157 | 1 | 1 | yes | characteristic, complemented |
| 688 | C23 | — | 2 | 1 | no | — |
| 689 | C23 | — | 2 | 1 | no | — |
| 690 | C23 | — | 4 | 1 | no | — |
| 691 | C23 | — | 8 | 1 | no | — |
| 692 | C23 | — | 53 | 1 | no | — |
| 693 | C23 | — | 53 | 1 | no | — |
| 694 | C23 | — | 53 | 1 | no | — |
| 695 | C23 | — | 106 | 1 | no | — |
| 696 | C23 | — | 106 | 1 | no | — |
| 697 | C23 | — | 106 | 1 | no | — |
| 698 | C23 | — | 106 | 1 | no | — |
| 699 | C23 | — | 106 | 1 | no | — |
| 700 | C23 | — | 106 | 1 | no | — |
| 701 | C23 | — | 424 | 1 | no | — |
| 702 | C23 | — | 424 | 2 | no | — |
| 703 | C23 | — | 424 | 1 | no | — |
| 704 | C23 | — | 424 | 1 | no | — |
| 705 | C23 | — | 424 | 1 | no | — |
| 706 | C23 | — | 424 | 2 | no | — |
| 707 | C23 | — | 424 | 2 | no | — |
| 708 | C23 | — | 212 | 1 | no | — |
| 709 | C23 | — | 212 | 1 | no | — |
| 710 | C23 | — | 212 | 1 | no | — |
| 711 | C23 | — | 212 | 1 | no | — |
| 712 | C23 | — | 212 | 1 | no | — |
| 713 | C23 | — | 212 | 2 | no | — |
| 714 | C23 | — | 212 | 2 | no | — |
| 715 | C23 | — | 212 | 2 | no | — |
| 716 | C23 | — | 212 | 2 | no | — |
| 717 | C23 | — | 212 | 2 | no | — |
| 718 | C23 | — | 212 | 2 | no | — |
| 719 | C23 | — | 212 | 4 | no | — |
| 720 | C23 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 721 | C23 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 722 | D4 | — | 4 | 1 | no | — |
| 723 | D4 | — | 4 | 1 | no | — |
| 724 | D4 | — | 8 | 1 | no | — |
| 725 | D4 | — | 8 | 1 | no | — |
| 726 | D4 | — | 8 | 1 | no | — |
| 727 | D4 | — | 8 | 1 | no | — |
| 728 | D4 | — | 8 | 1 | no | — |
| 729 | D4 | — | 424 | 1 | no | — |
| 730 | D4 | — | 424 | 1 | no | — |
| 731 | D4 | — | 424 | 1 | no | — |
| 732 | D4 | — | 424 | 1 | no | — |
| 733 | D4 | — | 424 | 1 | no | — |
| 734 | D4 | — | 424 | 1 | no | — |
| 735 | D4 | — | 424 | 1 | no | — |
| 736 | D4 | — | 424 | 1 | no | — |
| 737 | D4 | — | 424 | 1 | no | — |
| 738 | D4 | — | 424 | 1 | no | — |
| 739 | D4 | — | 424 | 1 | no | — |
| 740 | D4 | — | 424 | 1 | no | — |
| 741 | D4 | — | 424 | 1 | no | — |
| 742 | D4 | — | 424 | 1 | no | — |
| 743 | D4 | — | 424 | 1 | no | — |
| 744 | D4 | — | 424 | 1 | no | — |
| 745 | D4 | — | 212 | 1 | no | — |
| 746 | D4 | — | 212 | 1 | no | — |
| 747 | D4 | — | 212 | 1 | no | — |
| 748 | D4 | — | 212 | 1 | no | — |
| 749 | C2×C4 | — | 2 | 1 | no | — |
| 750 | C2×C4 | — | 2 | 1 | no | — |
| 751 | C2×C4 | — | 2 | 1 | no | — |
| 752 | C2×C4 | — | 2 | 1 | no | — |
| 753 | C2×C4 | — | 4 | 1 | no | — |
| 754 | C2×C4 | — | 8 | 1 | no | — |
| 755 | C2×C4 | — | 53 | 1 | no | — |
| 756 | C2×C4 | — | 106 | 1 | no | — |
| 757 | C2×C4 | — | 106 | 1 | no | — |
| 758 | C2×C4 | — | 106 | 1 | no | — |
| 759 | C2×C4 | — | 106 | 1 | no | — |
| 760 | C2×C4 | — | 106 | 1 | no | — |
| 761 | C2×C4 | — | 106 | 1 | no | — |
| 762 | C2×C4 | — | 424 | 1 | no | — |
| 763 | C2×C4 | — | 424 | 1 | no | — |
| 764 | C2×C4 | — | 424 | 1 | no | — |
| 765 | C2×C4 | — | 424 | 1 | no | — |
| 766 | C2×C4 | — | 424 | 1 | no | — |
| 767 | C2×C4 | — | 424 | 2 | no | — |
| 768 | C2×C4 | — | 424 | 2 | no | — |
| 769 | C2×C4 | — | 424 | 2 | no | — |
| 770 | C2×C4 | — | 424 | 2 | no | — |
| 771 | C2×C4 | — | 424 | 1 | no | — |
| 772 | C2×C4 | — | 212 | 1 | no | — |
| 773 | C2×C4 | — | 212 | 1 | no | — |
| 774 | C2×C4 | — | 212 | 2 | no | — |
| 775 | C2×C4 | — | 212 | 2 | no | — |
| 776 | C2×C4 | — | 212 | 2 | no | — |
| 777 | C2×C4 | — | 212 | 2 | no | — |
| 778 | C2×C4 | — | 212 | 1 | no | — |
| 779 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 780 | C8 | — | 424 | 1 | no | — |
| 781 | C22 | — | 2 | 1 | no | — |
| 782 | C22 | — | 2 | 1 | no | — |
| 783 | C22 | — | 4 | 1 | no | — |
| 784 | C22 | — | 4 | 1 | no | — |
| 785 | C22 | — | 4 | 1 | no | — |
| 786 | C22 | — | 4 | 1 | no | — |
| 787 | C22 | — | 4 | 1 | no | — |
| 788 | C22 | — | 4 | 1 | no | — |
| 789 | C22 | — | 4 | 2 | no | — |
| 790 | C22 | — | 4 | 1 | no | — |
| 791 | C22 | — | 4 | 1 | no | — |
| 792 | C22 | — | 8 | 1 | no | — |
| 793 | C22 | — | 53 | 1 | no | — |
| 794 | C22 | — | 53 | 1 | no | — |
| 795 | C22 | — | 106 | 2 | no | — |
| 796 | C22 | — | 106 | 1 | no | — |
| 797 | C22 | — | 106 | 1 | no | — |
| 798 | C22 | — | 424 | 1 | no | — |
| 799 | C22 | — | 424 | 1 | no | — |
| 800 | C22 | — | 424 | 1 | no | — |
| 801 | C22 | — | 424 | 2 | no | — |
| 802 | C22 | — | 424 | 2 | no | — |
| 803 | C22 | — | 424 | 2 | no | — |
| 804 | C22 | — | 424 | 2 | no | — |
| 805 | C22 | — | 424 | 4 | no | — |
| 806 | C22 | — | 212 | 1 | no | — |
| 807 | C22 | — | 212 | 1 | no | — |
| 808 | C22 | — | 212 | 1 | no | — |
| 809 | C22 | — | 212 | 1 | no | — |
| 810 | C22 | — | 212 | 1 | no | — |
| 811 | C22 | — | 212 | 1 | no | — |
| 812 | C22 | — | 212 | 2 | no | — |
| 813 | C22 | — | 212 | 2 | no | — |
| 814 | C22 | — | 212 | 2 | no | — |
| 815 | C22 | — | 212 | 1 | no | — |
| 816 | C22 | — | 212 | 1 | no | — |
| 817 | C22 | #16811564 | 1 | 1 | yes | characteristic |
| 818 | C4 | — | 2 | 1 | no | — |
| 819 | C4 | — | 4 | 1 | no | — |
| 820 | C4 | — | 4 | 1 | no | — |
| 821 | C4 | — | 4 | 1 | no | — |
| 822 | C4 | — | 4 | 1 | no | — |
| 823 | C4 | — | 848 | 1 | no | — |
| 824 | C4 | — | 848 | 1 | no | — |
| 825 | C4 | — | 106 | 1 | no | — |
| 826 | C4 | — | 424 | 2 | no | — |
| 827 | C4 | — | 212 | 1 | no | — |
| 828 | C4 | — | 212 | 1 | no | — |
| 829 | C4 | — | 212 | 1 | no | — |
| 830 | C4 | — | 212 | 1 | no | — |
| 831 | C2 | — | 2 | 1 | no | — |
| 832 | C2 | — | 4 | 1 | no | — |
| 833 | C2 | — | 4 | 1 | no | — |
| 834 | C2 | — | 8 | 1 | no | — |
| 835 | C2 | — | 8 | 1 | no | — |
| 836 | C2 | — | 53 | 2 | no | — |
| 837 | C2 | — | 106 | 1 | no | — |
| 838 | C2 | — | 424 | 1 | no | — |
| 839 | C2 | — | 424 | 1 | no | — |
| 840 | C2 | — | 212 | 1 | no | — |
| 841 | C2 | — | 212 | 1 | no | — |
| 842 | C2 | #20290559 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊#353 | C2 | semidirect |
| 2. D53⋊#352 | C2 | semidirect |
| 3. D53⋊AΣL(1,𝔽16) | C2 | semidirect |
| 4. #20290725 | C2 | semidirect |
| 5. #20290724 | C2 | semidirect |
| 6. #20290722 | C2 | semidirect |
| 26. #16811363 | C4 | semidirect |
| 28. #16811362 | C4 | semidirect |
| 32. #16811360 | C4 | semidirect |
| 42. C53×#560 | C4 | semidirect |
| 165. C2×D4×C53 | C22⋊C4 | semidirect |
| 168. C22×C4×C53 | C22⋊C4 | semidirect |
| 183. C22×Dic53 | C22⋊C4 | semidirect |
| 199. C2×D212 | C22⋊C4 | semidirect |
| 234. C22⋊C4×C53 | C22⋊C4 | semidirect |
| 235. C42×C53 | C22⋊C4 | semidirect |
| 242. C22⋊Dic53 | C22⋊C4 | semidirect |
| 265. C4×Dic53 | C22⋊C4 | semidirect |
| 438. #560 | #6157 | semidirect |
| 464. C53 | #12762 | semidirect |
| 613. C2×D4 | C22⋊#6157 | semidirect |
| 633. C22×C4 | C22⋊#6157 | semidirect |
| 683. C22⋊C4 | C22⋊#6157 | semidirect |
| 687. C42 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#353 | 2 |
| D53⋊#352 | 2 |
| D53⋊AΣL(1,𝔽16) | 2 |
| #20290725 | 2 |
| #20290724 | 2 |
| #20290722 | 2 |
| #560×D53 | 2 |
| #12762 | 53 |