Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1406 conjugacy classes of subgroups.
The subgroup lattice has 914 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D53⋊#413 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D53⋊#410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290976 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20290975 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20290974 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D53⋊AΣL(1,𝔽16) | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #535×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×D53⋊M16 | — | 2 | 1 | no | — |
| 9 | C2×#13133296 | — | 2 | 1 | no | — |
| 10 | #16811610 | — | 2 | 1 | no | — |
| 11 | #16811610 | C22 | 1 | 2 | yes | complemented |
| 12 | #16811609 | — | 2 | 1 | no | — |
| 13 | #16811609 | C22 | 1 | 2 | yes | complemented |
| 14 | D53⋊#101 | — | 2 | 1 | no | — |
| 15 | D53⋊#100 | C22 | 1 | 2 | yes | — |
| 16 | #16811604 | — | 2 | 1 | no | — |
| 17 | #16811603 | C22 | 1 | 2 | yes | complemented |
| 18 | #16811602 | — | 2 | 1 | no | — |
| 19 | #16811602 | C22 | 1 | 2 | yes | complemented |
| 20 | D53⋊#99 | — | 2 | 1 | no | — |
| 21 | D53⋊#99 | C22 | 1 | 2 | yes | — |
| 22 | #16811524 | C22 | 1 | 8 | yes | complemented |
| 23 | #16811523 | C22 | 1 | 8 | yes | complemented |
| 24 | C2×#41×D53 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×D4×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #16811192 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16811191 | — | 2 | 1 | no | — |
| 28 | #16811190 | C22 | 1 | 1 | yes | characteristic |
| 29 | #16811189 | — | 2 | 1 | no | — |
| 30 | #16811189 | — | 2 | 1 | no | — |
| 31 | #16811188 | C4 | 1 | 2 | yes | complemented |
| 32 | #16811188 | C22 | 1 | 2 | yes | — |
| 33 | #16811187 | C4 | 1 | 1 | yes | characteristic, complemented |
| 34 | #16811186 | — | 2 | 1 | no | — |
| 35 | #127×D53 | — | 2 | 1 | no | — |
| 36 | #124×D53 | — | 2 | 1 | no | — |
| 37 | #121×D53 | — | 2 | 1 | no | — |
| 38 | #121×D53 | — | 2 | 1 | no | — |
| 39 | #120×D53 | C4 | 1 | 2 | yes | complemented |
| 40 | #120×D53 | C22 | 1 | 2 | yes | — |
| 41 | #117×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 42 | C53×#535 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#11719936 | — | 4 | 1 | no | — |
| 44 | D53⋊M16 | — | 2 | 2 | no | — |
| 45 | D53⋊M16 | — | 2 | 2 | no | — |
| 46 | D53⋊M16 | — | 4 | 1 | no | — |
| 47 | D53⋊M16 | — | 4 | 1 | no | — |
| 48 | C2×#11719940 | — | 2 | 2 | no | — |
| 49 | C2×D53⋊C8 | — | 4 | 1 | no | — |
| 50 | #13133296 | — | 2 | 2 | no | — |
| 51 | #13133296 | — | 2 | 2 | no | — |
| 52 | #13133296 | — | 4 | 1 | no | — |
| 53 | #13133296 | — | 4 | 1 | no | — |
| 54 | C2×C4⋊#6157 | — | 4 | 1 | no | — |
| 55 | C2×C22⋊#6157 | — | 2 | 2 | no | — |
| 56 | C2×C4×#6157 | — | 4 | 1 | no | — |
| 57 | #13133278 | — | 2 | 2 | no | — |
| 58 | #13133278 | — | 2 | 2 | no | — |
| 59 | #13133277 | — | 2 | 2 | no | — |
| 60 | #13133277 | C23 | 1 | 4 | yes | — |
| 61 | #13133276 | — | 2 | 2 | no | — |
| 62 | #13133276 | — | 2 | 2 | no | — |
| 63 | #13133275 | — | 2 | 2 | no | — |
| 64 | #13133275 | C23 | 1 | 4 | yes | — |
| 65 | C24×D53 | C2×C4 | 1 | 2 | yes | — |
| 66 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 67 | C2×#11719945 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×#11719945 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×#11719945 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×#11719947 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×#11719947 | C23 | 1 | 1 | yes | characteristic |
| 73 | #41×D53 | — | 4 | 1 | no | — |
| 74 | #41×D53 | — | 4 | 1 | no | — |
| 75 | #41×D53 | — | 4 | 1 | no | — |
| 76 | #41×D53 | — | 4 | 1 | no | — |
| 77 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 78 | C22×D212 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 79 | C22×C22⋊D53 | C2×C4 | 1 | 2 | yes | complemented |
| 80 | C2×D4×D53 | — | 2 | 2 | no | — |
| 81 | C2×D4×D53 | — | 2 | 2 | no | — |
| 82 | C2×D4×D53 | — | 2 | 1 | no | — |
| 83 | C2×D4×D53 | — | 2 | 1 | no | — |
| 84 | C2×D4×D53 | — | 2 | 1 | no | — |
| 85 | C2×D4×D53 | — | 2 | 1 | no | — |
| 86 | C2×D4×D53 | — | 4 | 1 | no | — |
| 87 | C2×D4×D53 | — | 4 | 1 | no | — |
| 88 | C2×D4×D53 | — | 4 | 1 | no | — |
| 89 | C2×D4×D53 | — | 4 | 1 | no | — |
| 90 | C2×D4×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 91 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 92 | C2×D4×D53 | C23 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 94 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 95 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 96 | #13133214 | — | 2 | 1 | no | — |
| 97 | #13133213 | — | 2 | 1 | no | — |
| 98 | #13133213 | — | 2 | 2 | no | — |
| 99 | #13133213 | — | 2 | 2 | no | — |
| 100 | #13133213 | — | 2 | 1 | no | — |
| 101 | #13133206 | — | 2 | 1 | no | — |
| 102 | #13133205 | — | 2 | 1 | no | — |
| 103 | #13133204 | — | 2 | 1 | no | — |
| 104 | #13133203 | — | 2 | 2 | no | — |
| 105 | #13133203 | — | 2 | 2 | no | — |
| 106 | #13133192 | — | 2 | 1 | no | — |
| 107 | #13133192 | — | 2 | 1 | no | — |
| 108 | #13133191 | — | 2 | 1 | no | — |
| 109 | #13133191 | — | 2 | 1 | no | — |
| 110 | #13133190 | — | 2 | 2 | no | — |
| 111 | #13133190 | — | 2 | 2 | no | — |
| 112 | #13133189 | — | 2 | 2 | no | — |
| 113 | #13133189 | — | 2 | 2 | no | — |
| 114 | #13133188 | — | 2 | 1 | no | — |
| 115 | #13133188 | — | 2 | 1 | no | — |
| 116 | #13133187 | — | 2 | 2 | no | — |
| 117 | #13133187 | — | 2 | 2 | no | — |
| 118 | #13133187 | C2×C4 | 1 | 2 | yes | complemented |
| 119 | #13133187 | C23 | 1 | 2 | yes | — |
| 120 | #13133186 | C2×C4 | 1 | 2 | yes | complemented |
| 121 | #13133186 | C23 | 1 | 2 | yes | — |
| 122 | #13133185 | — | 2 | 2 | no | — |
| 123 | #13133185 | — | 2 | 2 | no | — |
| 124 | #13133185 | C2×C4 | 1 | 2 | yes | — |
| 125 | #13133185 | C2×C4 | 1 | 2 | yes | complemented |
| 126 | #13133176 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 127 | #13133175 | — | 2 | 1 | no | — |
| 128 | #13133174 | — | 2 | 1 | no | — |
| 129 | #13133173 | C2×C4 | 1 | 2 | yes | complemented |
| 130 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 131 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 132 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 133 | C22⋊C4×D53 | C2×C4 | 1 | 2 | yes | — |
| 134 | C42×D53 | — | 2 | 1 | no | — |
| 135 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 136 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 137 | #127×C53 | — | 2 | 1 | no | — |
| 138 | #124×C53 | — | 2 | 1 | no | — |
| 139 | #121×C53 | — | 2 | 1 | no | — |
| 140 | #121×C53 | — | 2 | 1 | no | — |
| 141 | #120×C53 | C2×C4 | 1 | 2 | yes | — |
| 142 | #120×C53 | C2×C4 | 1 | 2 | yes | complemented |
| 143 | #117×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 144 | C24×C53 | C22×C4 | 1 | 2 | yes | — |
| 145 | C23×D53 | — | 2 | 2 | no | — |
| 146 | C23×D53 | — | 2 | 2 | no | — |
| 147 | C23×D53 | — | 4 | 2 | no | — |
| 148 | C23×D53 | — | 4 | 2 | no | — |
| 149 | C23×D53 | — | 8 | 4 | no | — |
| 150 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C23×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 152 | C23×D53 | C22×C4 | 1 | 2 | yes | — |
| 153 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×#6157 | — | 4 | 2 | no | — |
| 155 | #41×C53 | — | 4 | 1 | no | — |
| 156 | #41×C53 | — | 4 | 1 | no | — |
| 157 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C2×D4×C53 | — | 2 | 2 | no | — |
| 159 | C2×D4×C53 | — | 2 | 2 | no | — |
| 160 | C2×D4×C53 | — | 2 | 1 | no | — |
| 161 | C2×D4×C53 | — | 2 | 1 | no | — |
| 162 | C2×D4×C53 | — | 4 | 1 | no | — |
| 163 | C2×D4×C53 | — | 4 | 1 | no | — |
| 164 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 167 | C22×C4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C22×C4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 169 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 170 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 171 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 172 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 173 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 174 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 175 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 176 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 177 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 178 | C2×C22⋊D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 179 | C2×C22⋊D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 180 | C2×C22⋊D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 181 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C22⋊D53 | C24 | 1 | 1 | yes | characteristic |
| 184 | C22×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 185 | C22×Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 186 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | #11719949 | — | 4 | 1 | no | — |
| 188 | #11719949 | — | 4 | 1 | no | — |
| 189 | Q8×D53 | — | 4 | 1 | no | — |
| 190 | Q8×D53 | — | 4 | 1 | no | — |
| 191 | #11719947 | — | 4 | 1 | no | — |
| 192 | #11719947 | — | 4 | 1 | no | — |
| 193 | #11719947 | — | 4 | 1 | no | — |
| 194 | #11719947 | — | 4 | 1 | no | — |
| 195 | #11719947 | — | 4 | 1 | no | — |
| 196 | #11719947 | — | 4 | 1 | no | — |
| 197 | D4×D53 | — | 4 | 1 | no | — |
| 198 | D4×D53 | — | 4 | 1 | no | — |
| 199 | D4×D53 | — | 4 | 1 | no | — |
| 200 | D4×D53 | — | 4 | 1 | no | — |
| 201 | D4×D53 | — | 4 | 1 | no | — |
| 202 | D4×D53 | — | 4 | 1 | no | — |
| 203 | D4×D53 | — | 4 | 2 | no | — |
| 204 | D4×D53 | — | 4 | 2 | no | — |
| 205 | D4×D53 | — | 4 | 2 | no | — |
| 206 | D4×D53 | — | 4 | 2 | no | — |
| 207 | D4×D53 | — | 4 | 2 | no | — |
| 208 | D4×D53 | — | 4 | 2 | no | — |
| 209 | D4×D53 | — | 4 | 1 | no | — |
| 210 | D4×D53 | — | 4 | 1 | no | — |
| 211 | D4×D53 | — | 4 | 1 | no | — |
| 212 | D4×D53 | — | 4 | 1 | no | — |
| 213 | D4×D53 | — | 8 | 4 | no | — |
| 214 | D4×D53 | — | 8 | 4 | no | — |
| 215 | #11719945 | — | 4 | 1 | no | — |
| 216 | #11719945 | — | 4 | 1 | no | — |
| 217 | #11719945 | — | 4 | 1 | no | — |
| 218 | #11719945 | — | 4 | 1 | no | — |
| 219 | #11719945 | — | 4 | 1 | no | — |
| 220 | #11719945 | — | 4 | 1 | no | — |
| 221 | C2×D212 | — | 2 | 1 | no | — |
| 222 | C2×D212 | — | 2 | 1 | no | — |
| 223 | C2×D212 | — | 2 | 2 | no | — |
| 224 | C2×D212 | — | 2 | 2 | no | — |
| 225 | C2×D212 | — | 4 | 1 | no | — |
| 226 | C2×D212 | — | 4 | 1 | no | — |
| 227 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 228 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×D53 | — | 2 | 1 | no | — |
| 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 | — | 2 | 1 | no | — |
| 235 | C2×C4×D53 | — | 2 | 1 | no | — |
| 236 | C2×C4×D53 | — | 2 | 1 | no | — |
| 237 | C2×C4×D53 | — | 2 | 1 | no | — |
| 238 | C2×C4×D53 | — | 2 | 1 | no | — |
| 239 | C2×C4×D53 | — | 2 | 1 | no | — |
| 240 | C2×C4×D53 | — | 2 | 1 | no | — |
| 241 | C2×C4×D53 | — | 2 | 1 | no | — |
| 242 | C2×C4×D53 | — | 2 | 2 | no | — |
| 243 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 246 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 254 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | C22⋊#6157 | — | 2 | 4 | no | — |
| 257 | C22⋊#6157 | — | 4 | 2 | no | — |
| 258 | #11719940 | — | 2 | 4 | no | — |
| 259 | #11719940 | — | 4 | 2 | no | — |
| 260 | C2×#88324 | — | 4 | 2 | no | — |
| 261 | C4⋊#6157 | — | 4 | 2 | no | — |
| 262 | C4⋊#6157 | — | 4 | 2 | no | — |
| 263 | C4×#6157 | — | 4 | 2 | no | — |
| 264 | C4×#6157 | — | 4 | 2 | no | — |
| 265 | #11719936 | — | 4 | 2 | no | — |
| 266 | #11719936 | — | 4 | 2 | no | — |
| 267 | D53⋊C8 | — | 4 | 2 | no | — |
| 268 | D53⋊C8 | — | 4 | 2 | no | — |
| 269 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 270 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 271 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 272 | C22⋊C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 273 | C42×C53 | — | 2 | 1 | no | — |
| 274 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 275 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 276 | C22⋊Dic53 | C22×C4 | 1 | 2 | yes | — |
| 277 | #11719921 | — | 2 | 2 | no | — |
| 278 | #11719921 | — | 2 | 2 | no | — |
| 279 | #11719921 | — | 2 | 2 | no | — |
| 280 | #11719921 | — | 2 | 2 | no | — |
| 281 | #11719921 | — | 2 | 2 | no | — |
| 282 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 283 | #11719919 | — | 2 | 2 | no | — |
| 284 | C4×Dic53 | — | 2 | 1 | no | — |
| 285 | C4×Dic53 | — | 2 | 2 | no | — |
| 286 | C23×C53 | — | 2 | 2 | no | — |
| 287 | C23×C53 | — | 4 | 2 | no | — |
| 288 | C23×C53 | — | 8 | 2 | no | — |
| 289 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 290 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 291 | C23×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 292 | C22×D53 | — | 2 | 1 | no | — |
| 293 | C22×D53 | — | 2 | 1 | no | — |
| 294 | C22×D53 | — | 2 | 1 | no | — |
| 295 | C22×D53 | — | 2 | 1 | no | — |
| 296 | C22×D53 | — | 2 | 1 | no | — |
| 297 | C22×D53 | — | 2 | 1 | no | — |
| 298 | C22×D53 | — | 2 | 2 | no | — |
| 299 | C22×D53 | — | 4 | 2 | no | — |
| 300 | C22×D53 | — | 4 | 2 | no | — |
| 301 | C22×D53 | — | 4 | 2 | no | — |
| 302 | C22×D53 | — | 4 | 4 | no | — |
| 303 | C22×D53 | — | 4 | 4 | no | — |
| 304 | C22×D53 | — | 4 | 4 | no | — |
| 305 | C22×D53 | — | 4 | 2 | no | — |
| 306 | C22×D53 | — | 4 | 2 | no | — |
| 307 | C22×D53 | — | 4 | 2 | no | — |
| 308 | C22×D53 | — | 8 | 2 | no | — |
| 309 | C22×D53 | — | 8 | 2 | no | — |
| 310 | C22×D53 | — | 8 | 2 | no | — |
| 311 | C22×D53 | — | 8 | 8 | no | — |
| 312 | C22×D53 | — | 8 | 8 | no | — |
| 313 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 314 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 315 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 316 | C22×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 317 | C2×#6157 | — | 4 | 4 | no | — |
| 318 | C2×#6157 | — | 8 | 4 | no | — |
| 319 | Q8×C53 | — | 4 | 1 | no | — |
| 320 | D4×C53 | — | 4 | 1 | no | — |
| 321 | D4×C53 | — | 4 | 1 | no | — |
| 322 | D4×C53 | — | 4 | 1 | no | — |
| 323 | D4×C53 | — | 4 | 2 | no | — |
| 324 | D4×C53 | — | 4 | 1 | no | — |
| 325 | D4×C53 | — | 4 | 1 | no | — |
| 326 | D4×C53 | — | 8 | 2 | no | — |
| 327 | D4×C53 | — | 8 | 2 | no | — |
| 328 | C2×C4×C53 | — | 2 | 1 | no | — |
| 329 | C2×C4×C53 | — | 2 | 1 | no | — |
| 330 | C2×C4×C53 | — | 2 | 1 | no | — |
| 331 | C2×C4×C53 | — | 2 | 1 | no | — |
| 332 | C2×C4×C53 | — | 2 | 1 | no | — |
| 333 | C2×C4×C53 | — | 2 | 1 | no | — |
| 334 | C2×C4×C53 | — | 2 | 2 | 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 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 339 | C22⋊D53 | — | 4 | 1 | no | — |
| 340 | C22⋊D53 | — | 4 | 1 | no | — |
| 341 | C22⋊D53 | — | 4 | 1 | no | — |
| 342 | C22⋊D53 | — | 4 | 1 | no | — |
| 343 | C22⋊D53 | — | 4 | 1 | no | — |
| 344 | C22⋊D53 | — | 4 | 1 | no | — |
| 345 | C22⋊D53 | — | 4 | 4 | no | — |
| 346 | C22⋊D53 | — | 4 | 2 | no | — |
| 347 | C22⋊D53 | — | 4 | 2 | no | — |
| 348 | C22⋊D53 | — | 8 | 2 | no | — |
| 349 | C22⋊D53 | — | 8 | 2 | no | — |
| 350 | C22⋊D53 | — | 8 | 2 | no | — |
| 351 | C22⋊D53 | — | 8 | 2 | no | — |
| 352 | C2×Dic53 | — | 2 | 1 | no | — |
| 353 | C2×Dic53 | — | 2 | 1 | no | — |
| 354 | C2×Dic53 | — | 2 | 1 | no | — |
| 355 | C2×Dic53 | — | 2 | 1 | no | — |
| 356 | C2×Dic53 | — | 2 | 1 | no | — |
| 357 | C2×Dic53 | — | 2 | 1 | no | — |
| 358 | C2×Dic53 | — | 2 | 2 | no | — |
| 359 | C2×Dic53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 360 | C2×Dic53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 361 | C2×Dic53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 362 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 363 | D212 | — | 4 | 1 | no | — |
| 364 | D212 | — | 4 | 1 | no | — |
| 365 | D212 | — | 4 | 1 | no | — |
| 366 | D212 | — | 4 | 2 | no | — |
| 367 | D212 | — | 4 | 1 | no | — |
| 368 | D212 | — | 4 | 1 | no | — |
| 369 | D212 | — | 8 | 2 | no | — |
| 370 | D212 | — | 8 | 2 | no | — |
| 371 | C4×D53 | — | 2 | 1 | no | — |
| 372 | C4×D53 | — | 2 | 1 | no | — |
| 373 | C4×D53 | — | 2 | 1 | no | — |
| 374 | C4×D53 | — | 2 | 1 | no | — |
| 375 | C4×D53 | — | 2 | 1 | no | — |
| 376 | C4×D53 | — | 2 | 1 | no | — |
| 377 | C4×D53 | — | 2 | 1 | no | — |
| 378 | C4×D53 | — | 2 | 1 | no | — |
| 379 | C4×D53 | — | 2 | 1 | no | — |
| 380 | C4×D53 | — | 2 | 1 | no | — |
| 381 | C4×D53 | — | 2 | 1 | no | — |
| 382 | C4×D53 | — | 2 | 1 | no | — |
| 383 | C4×D53 | — | 2 | 1 | no | — |
| 384 | C4×D53 | — | 2 | 1 | no | — |
| 385 | C4×D53 | — | 2 | 1 | no | — |
| 386 | C4×D53 | — | 2 | 1 | no | — |
| 387 | C4×D53 | — | 2 | 1 | no | — |
| 388 | C4×D53 | — | 2 | 1 | no | — |
| 389 | C4×D53 | — | 4 | 4 | no | — |
| 390 | C4×D53 | #99 | 1 | 1 | yes | characteristic |
| 391 | C4×D53 | #99 | 1 | 1 | yes | characteristic |
| 392 | C4×D53 | #99 | 1 | 1 | yes | characteristic |
| 393 | C4×D53 | #99 | 1 | 1 | yes | characteristic |
| 394 | Dic106 | — | 4 | 1 | no | — |
| 395 | Dic106 | — | 4 | 1 | no | — |
| 396 | Dic106 | — | 4 | 1 | no | — |
| 397 | #88324 | — | 4 | 4 | no | — |
| 398 | C2×#2122 | — | 53 | 1 | no | maximal, Sylow |
| 399 | C22×C53 | — | 2 | 1 | no | — |
| 400 | C22×C53 | — | 2 | 1 | no | — |
| 401 | C22×C53 | — | 2 | 1 | no | — |
| 402 | C22×C53 | — | 4 | 1 | no | — |
| 403 | C22×C53 | — | 4 | 1 | no | — |
| 404 | C22×C53 | — | 4 | 1 | no | — |
| 405 | C22×C53 | — | 4 | 2 | no | — |
| 406 | C22×C53 | — | 4 | 2 | no | — |
| 407 | C22×C53 | — | 4 | 2 | no | — |
| 408 | C22×C53 | — | 8 | 4 | no | — |
| 409 | C22×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 410 | C2×D53 | — | 2 | 2 | no | — |
| 411 | C2×D53 | — | 2 | 1 | no | — |
| 412 | C2×D53 | — | 2 | 1 | no | — |
| 413 | C2×D53 | — | 2 | 1 | no | — |
| 414 | C2×D53 | — | 4 | 2 | no | — |
| 415 | C2×D53 | — | 4 | 2 | no | — |
| 416 | C2×D53 | — | 4 | 2 | no | — |
| 417 | C2×D53 | — | 4 | 2 | no | — |
| 418 | C2×D53 | — | 4 | 1 | no | — |
| 419 | C2×D53 | — | 4 | 1 | no | — |
| 420 | C2×D53 | — | 4 | 1 | no | — |
| 421 | C2×D53 | — | 4 | 2 | no | — |
| 422 | C2×D53 | — | 4 | 2 | no | — |
| 423 | C2×D53 | — | 4 | 2 | no | — |
| 424 | C2×D53 | — | 8 | 1 | no | — |
| 425 | C2×D53 | — | 8 | 1 | no | — |
| 426 | C2×D53 | — | 8 | 4 | no | — |
| 427 | C2×D53 | — | 8 | 8 | no | — |
| 428 | C2×D53 | — | 8 | 4 | no | — |
| 429 | C2×D53 | — | 8 | 4 | no | — |
| 430 | C2×D53 | C2×#99 | 1 | 1 | yes | characteristic |
| 431 | C2×D53 | C2×#99 | 1 | 1 | yes | characteristic |
| 432 | #6157 | — | 8 | 4 | no | — |
| 433 | C4×C53 | — | 2 | 1 | no | — |
| 434 | C4×C53 | — | 2 | 1 | no | — |
| 435 | C4×C53 | — | 2 | 1 | no | — |
| 436 | C4×C53 | — | 4 | 2 | no | — |
| 437 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 438 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 439 | Dic53 | — | 2 | 1 | no | — |
| 440 | Dic53 | — | 2 | 1 | no | — |
| 441 | Dic53 | — | 2 | 1 | no | — |
| 442 | Dic53 | — | 4 | 2 | no | — |
| 443 | Dic53 | C2×#99 | 1 | 1 | yes | characteristic |
| 444 | Dic53 | C2×#99 | 1 | 1 | yes | characteristic |
| 445 | C2×#535 | — | 53 | 1 | no | — |
| 446 | C2×#413 | — | 53 | 1 | no | — |
| 447 | C2×#410 | — | 53 | 1 | no | — |
| 448 | #2122 | — | 53 | 2 | no | — |
| 449 | #2122 | — | 53 | 4 | no | — |
| 450 | #2122 | — | 53 | 2 | no | — |
| 451 | C2×AΣL(1,𝔽16) | — | 53 | 4 | no | — |
| 452 | C2×C53 | — | 2 | 1 | no | — |
| 453 | C2×C53 | — | 4 | 1 | no | — |
| 454 | C2×C53 | — | 4 | 1 | no | — |
| 455 | C2×C53 | — | 4 | 1 | no | — |
| 456 | C2×C53 | — | 8 | 2 | no | — |
| 457 | C2×C53 | C22×#99 | 1 | 1 | yes | characteristic |
| 458 | D53 | — | 2 | 1 | no | — |
| 459 | D53 | — | 4 | 1 | no | — |
| 460 | D53 | — | 4 | 1 | no | — |
| 461 | D53 | — | 4 | 1 | no | — |
| 462 | D53 | — | 8 | 2 | no | — |
| 463 | D53 | #2122 | 1 | 2 | yes | complemented |
| 464 | C22×#41 | — | 53 | 1 | no | — |
| 465 | C23×D4 | — | 53 | 1 | no | — |
| 466 | C22×M16 | — | 106 | 1 | no | — |
| 467 | #535 | — | 53 | 1 | no | — |
| 468 | #535 | — | 53 | 1 | no | — |
| 469 | #535 | — | 53 | 2 | no | — |
| 470 | #535 | — | 53 | 2 | no | — |
| 471 | #535 | — | 53 | 1 | no | — |
| 472 | #535 | — | 106 | 1 | no | — |
| 473 | #535 | — | 106 | 1 | no | — |
| 474 | #535 | — | 106 | 1 | no | — |
| 475 | #535 | — | 106 | 1 | no | — |
| 476 | #535 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 477 | C2×#127 | — | 106 | 1 | no | — |
| 478 | C2×#124 | — | 106 | 1 | no | — |
| 479 | C2×#121 | — | 106 | 1 | no | — |
| 480 | C2×#121 | — | 106 | 1 | no | — |
| 481 | C2×#120 | — | 53 | 2 | no | — |
| 482 | C2×#120 | — | 53 | 2 | no | — |
| 483 | C2×#117 | — | 53 | 1 | no | — |
| 484 | C2×#117 | — | 106 | 1 | no | — |
| 485 | #413 | — | 53 | 2 | no | — |
| 486 | #413 | — | 53 | 2 | no | — |
| 487 | #413 | — | 106 | 1 | no | — |
| 488 | #413 | — | 106 | 1 | no | — |
| 489 | C2×#101 | — | 106 | 1 | no | — |
| 490 | C2×#100 | — | 53 | 2 | no | — |
| 491 | #410 | — | 53 | 2 | no | — |
| 492 | #410 | — | 53 | 2 | no | — |
| 493 | #410 | — | 106 | 1 | no | — |
| 494 | #410 | — | 106 | 1 | no | — |
| 495 | C2×#99 | — | 53 | 2 | no | — |
| 496 | C2×#99 | — | 106 | 1 | no | — |
| 497 | AΣL(1,𝔽16) | — | 53 | 8 | no | — |
| 498 | AΣL(1,𝔽16) | — | 53 | 8 | no | — |
| 499 | C53 | C2×#2122 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 500 | C25 | — | 53 | 2 | no | — |
| 501 | C2×#41 | — | 53 | 1 | no | — |
| 502 | C2×#41 | — | 53 | 1 | no | — |
| 503 | C2×#41 | — | 53 | 1 | no | — |
| 504 | C2×#41 | — | 53 | 1 | no | — |
| 505 | C2×#41 | — | 53 | 1 | no | — |
| 506 | C2×#41 | — | 53 | 1 | no | — |
| 507 | C2×#41 | — | 53 | 1 | no | — |
| 508 | C2×#41 | — | 212 | 1 | no | — |
| 509 | C2×#41 | — | 212 | 1 | no | — |
| 510 | C2×#41 | — | 212 | 1 | no | — |
| 511 | C2×#41 | — | 212 | 1 | no | — |
| 512 | C2×#41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 513 | C22×Q8 | — | 53 | 1 | no | — |
| 514 | C22×D4 | — | 53 | 1 | no | — |
| 515 | C22×D4 | — | 53 | 1 | no | — |
| 516 | C22×D4 | — | 53 | 1 | no | — |
| 517 | C22×D4 | — | 53 | 2 | no | — |
| 518 | C22×D4 | — | 53 | 1 | no | — |
| 519 | C22×D4 | — | 106 | 1 | no | — |
| 520 | C22×D4 | — | 106 | 1 | no | — |
| 521 | C22×D4 | — | 106 | 1 | no | — |
| 522 | C22×D4 | — | 106 | 1 | no | — |
| 523 | C22×D4 | — | 106 | 2 | no | — |
| 524 | C22×D4 | — | 106 | 2 | no | — |
| 525 | C22×D4 | — | 212 | 1 | no | — |
| 526 | C22×D4 | — | 212 | 1 | no | — |
| 527 | C22×D4 | — | 212 | 1 | no | — |
| 528 | C22×D4 | — | 212 | 1 | no | — |
| 529 | C22×D4 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 530 | C23×C4 | — | 53 | 1 | no | — |
| 531 | C23×C4 | — | 53 | 1 | no | — |
| 532 | C23×C4 | — | 53 | 1 | no | — |
| 533 | C2×M16 | — | 106 | 2 | no | — |
| 534 | C2×M16 | — | 106 | 2 | no | — |
| 535 | C2×M16 | — | 106 | 2 | no | — |
| 536 | C2×M16 | — | 212 | 1 | no | — |
| 537 | C2×M16 | — | 212 | 1 | no | — |
| 538 | C2×M16 | — | 212 | 1 | no | — |
| 539 | C22×C8 | — | 212 | 1 | no | — |
| 540 | #127 | — | 2 | 1 | no | — |
| 541 | #127 | — | 106 | 1 | no | — |
| 542 | #127 | — | 106 | 2 | no | — |
| 543 | #127 | — | 106 | 2 | no | — |
| 544 | #127 | — | 106 | 1 | no | — |
| 545 | #127 | — | 106 | 1 | no | — |
| 546 | #124 | — | 2 | 1 | no | — |
| 547 | #124 | — | 106 | 1 | no | — |
| 548 | #124 | — | 106 | 2 | no | — |
| 549 | #124 | — | 106 | 2 | no | — |
| 550 | #124 | — | 106 | 1 | no | — |
| 551 | #124 | — | 106 | 1 | no | — |
| 552 | #121 | — | 2 | 1 | no | — |
| 553 | #121 | — | 2 | 1 | no | — |
| 554 | #121 | — | 106 | 2 | no | — |
| 555 | #121 | — | 106 | 2 | no | — |
| 556 | #121 | — | 106 | 1 | no | — |
| 557 | #121 | — | 106 | 1 | no | — |
| 558 | #121 | — | 106 | 1 | no | — |
| 559 | #121 | — | 106 | 1 | no | — |
| 560 | #121 | — | 106 | 2 | no | — |
| 561 | #121 | — | 106 | 2 | no | — |
| 562 | #121 | — | 106 | 1 | no | — |
| 563 | #121 | — | 106 | 1 | no | — |
| 564 | #120 | — | 53 | 2 | no | — |
| 565 | #120 | — | 53 | 2 | no | — |
| 566 | #120 | — | 53 | 2 | no | — |
| 567 | #120 | — | 53 | 2 | no | — |
| 568 | #120 | — | 53 | 2 | no | — |
| 569 | #120 | — | 53 | 2 | no | — |
| 570 | #120 | — | 106 | 2 | no | — |
| 571 | #120 | — | 106 | 2 | no | — |
| 572 | #120 | — | 106 | 2 | no | — |
| 573 | #120 | — | 106 | 2 | no | — |
| 574 | #120 | C2×#6157 | 1 | 2 | yes | — |
| 575 | #120 | C2×#6157 | 1 | 2 | yes | complemented |
| 576 | #117 | — | 53 | 1 | no | — |
| 577 | #117 | — | 53 | 2 | no | — |
| 578 | #117 | — | 106 | 1 | no | — |
| 579 | #117 | — | 106 | 1 | no | — |
| 580 | #117 | — | 106 | 2 | no | — |
| 581 | #117 | — | 106 | 2 | no | — |
| 582 | #117 | — | 212 | 1 | no | — |
| 583 | #117 | — | 212 | 1 | no | — |
| 584 | #117 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 585 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 586 | C2×C4⋊C4 | — | 212 | 1 | no | — |
| 587 | C2×C22⋊C4 | — | 53 | 2 | no | — |
| 588 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 589 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 590 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 591 | C2×C42 | — | 106 | 1 | no | — |
| 592 | C2×C42 | — | 212 | 1 | no | — |
| 593 | #101 | — | 106 | 2 | no | — |
| 594 | #101 | — | 106 | 2 | no | — |
| 595 | #100 | — | 53 | 4 | no | — |
| 596 | #100 | — | 106 | 2 | no | — |
| 597 | #99 | — | 53 | 4 | no | — |
| 598 | #99 | — | 106 | 2 | no | — |
| 599 | #99 | — | 106 | 2 | no | — |
| 600 | #99 | — | 106 | 2 | no | — |
| 601 | C24 | — | 53 | 1 | no | — |
| 602 | C24 | — | 53 | 1 | no | — |
| 603 | C24 | — | 53 | 1 | no | — |
| 604 | C24 | — | 53 | 2 | no | — |
| 605 | C24 | — | 106 | 2 | no | — |
| 606 | C24 | — | 106 | 2 | no | — |
| 607 | C24 | — | 424 | 4 | no | — |
| 608 | C24 | — | 212 | 2 | no | — |
| 609 | C24 | — | 212 | 2 | no | — |
| 610 | C24 | C22×#6157 | 1 | 2 | yes | — |
| 611 | #41 | — | 4 | 1 | no | — |
| 612 | #41 | — | 4 | 1 | no | — |
| 613 | #41 | — | 212 | 1 | no | — |
| 614 | #41 | — | 212 | 1 | no | — |
| 615 | #41 | — | 212 | 1 | no | — |
| 616 | #41 | — | 212 | 1 | no | — |
| 617 | #41 | — | 212 | 1 | no | — |
| 618 | #41 | — | 212 | 1 | no | — |
| 619 | #41 | — | 212 | 1 | no | — |
| 620 | #41 | — | 212 | 1 | no | — |
| 621 | #41 | — | 212 | 1 | no | — |
| 622 | #41 | — | 212 | 1 | no | — |
| 623 | #41 | — | 212 | 1 | no | — |
| 624 | #41 | — | 212 | 1 | no | — |
| 625 | #41 | — | 212 | 1 | no | — |
| 626 | #41 | — | 212 | 1 | no | — |
| 627 | C2×Q8 | — | 53 | 1 | no | — |
| 628 | C2×Q8 | — | 53 | 1 | no | — |
| 629 | C2×Q8 | — | 53 | 1 | no | — |
| 630 | C2×Q8 | — | 212 | 1 | no | — |
| 631 | C2×Q8 | — | 212 | 1 | no | — |
| 632 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 633 | C2×D4 | — | 2 | 2 | no | — |
| 634 | C2×D4 | — | 2 | 2 | no | — |
| 635 | C2×D4 | — | 2 | 1 | no | — |
| 636 | C2×D4 | — | 2 | 1 | no | — |
| 637 | C2×D4 | — | 4 | 1 | no | — |
| 638 | C2×D4 | — | 4 | 1 | no | — |
| 639 | C2×D4 | — | 53 | 1 | no | — |
| 640 | C2×D4 | — | 53 | 1 | no | — |
| 641 | C2×D4 | — | 53 | 1 | no | — |
| 642 | C2×D4 | — | 53 | 1 | no | — |
| 643 | C2×D4 | — | 53 | 1 | no | — |
| 644 | C2×D4 | — | 53 | 1 | no | — |
| 645 | C2×D4 | — | 53 | 1 | no | — |
| 646 | C2×D4 | — | 53 | 1 | no | — |
| 647 | C2×D4 | — | 53 | 1 | no | — |
| 648 | C2×D4 | — | 106 | 2 | no | — |
| 649 | C2×D4 | — | 106 | 2 | no | — |
| 650 | C2×D4 | — | 106 | 2 | no | — |
| 651 | C2×D4 | — | 106 | 2 | no | — |
| 652 | C2×D4 | — | 106 | 2 | no | — |
| 653 | C2×D4 | — | 106 | 2 | no | — |
| 654 | C2×D4 | — | 106 | 2 | no | — |
| 655 | C2×D4 | — | 106 | 2 | no | — |
| 656 | C2×D4 | — | 106 | 1 | no | — |
| 657 | C2×D4 | — | 106 | 1 | no | — |
| 658 | C2×D4 | — | 424 | 4 | no | — |
| 659 | C2×D4 | — | 424 | 4 | no | — |
| 660 | C2×D4 | — | 212 | 1 | no | — |
| 661 | C2×D4 | — | 212 | 1 | no | — |
| 662 | C2×D4 | — | 212 | 1 | no | — |
| 663 | C2×D4 | — | 212 | 1 | no | — |
| 664 | C2×D4 | — | 212 | 1 | no | — |
| 665 | C2×D4 | — | 212 | 1 | no | — |
| 666 | C2×D4 | — | 212 | 1 | no | — |
| 667 | C2×D4 | — | 212 | 1 | no | — |
| 668 | C2×D4 | — | 212 | 1 | no | — |
| 669 | C2×D4 | — | 212 | 1 | no | — |
| 670 | C2×D4 | — | 212 | 1 | no | — |
| 671 | C2×D4 | — | 212 | 1 | no | — |
| 672 | C2×D4 | — | 212 | 2 | no | — |
| 673 | C2×D4 | — | 212 | 2 | no | — |
| 674 | C2×D4 | — | 212 | 2 | no | — |
| 675 | C2×D4 | — | 212 | 2 | no | — |
| 676 | C2×D4 | — | 212 | 2 | no | — |
| 677 | C2×D4 | — | 212 | 2 | no | — |
| 678 | C2×D4 | — | 212 | 2 | no | — |
| 679 | C2×D4 | — | 212 | 2 | no | — |
| 680 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 681 | C2×D4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 682 | C2×D4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 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 | — | 53 | 1 | no | — |
| 696 | C22×C4 | — | 106 | 1 | no | — |
| 697 | C22×C4 | — | 106 | 1 | no | — |
| 698 | C22×C4 | — | 106 | 1 | no | — |
| 699 | C22×C4 | — | 106 | 1 | no | — |
| 700 | C22×C4 | — | 106 | 1 | no | — |
| 701 | C22×C4 | — | 106 | 1 | no | — |
| 702 | C22×C4 | — | 106 | 1 | no | — |
| 703 | C22×C4 | — | 106 | 1 | no | — |
| 704 | C22×C4 | — | 106 | 1 | no | — |
| 705 | C22×C4 | — | 106 | 1 | no | — |
| 706 | C22×C4 | — | 106 | 1 | no | — |
| 707 | C22×C4 | — | 106 | 1 | no | — |
| 708 | C22×C4 | — | 106 | 2 | no | — |
| 709 | C22×C4 | — | 212 | 2 | no | — |
| 710 | C22×C4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 711 | C22×C4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 712 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 713 | M16 | — | 106 | 4 | no | — |
| 714 | M16 | — | 212 | 2 | no | — |
| 715 | M16 | — | 212 | 2 | no | — |
| 716 | M16 | — | 212 | 2 | no | — |
| 717 | C2×C8 | — | 212 | 2 | no | — |
| 718 | C2×C8 | — | 212 | 2 | no | — |
| 719 | C2×C8 | — | 212 | 2 | no | — |
| 720 | C4⋊C4 | — | 2 | 1 | no | — |
| 721 | C4⋊C4 | — | 106 | 2 | no | — |
| 722 | C4⋊C4 | — | 106 | 1 | no | — |
| 723 | C4⋊C4 | — | 212 | 2 | no | — |
| 724 | C4⋊C4 | — | 212 | 2 | no | — |
| 725 | C22⋊C4 | — | 2 | 2 | no | — |
| 726 | C22⋊C4 | — | 2 | 2 | no | — |
| 727 | C22⋊C4 | — | 53 | 2 | no | — |
| 728 | C22⋊C4 | — | 106 | 2 | no | — |
| 729 | C22⋊C4 | — | 106 | 2 | no | — |
| 730 | C22⋊C4 | — | 106 | 2 | no | — |
| 731 | C22⋊C4 | — | 106 | 2 | no | — |
| 732 | C22⋊C4 | — | 106 | 2 | no | — |
| 733 | C22⋊C4 | — | 106 | 2 | no | — |
| 734 | C22⋊C4 | — | 106 | 2 | no | — |
| 735 | C22⋊C4 | — | 106 | 4 | no | — |
| 736 | C22⋊C4 | — | 212 | 2 | no | — |
| 737 | C22⋊C4 | C22×#6157 | 1 | 2 | yes | — |
| 738 | C42 | — | 2 | 1 | no | — |
| 739 | C42 | — | 106 | 2 | no | — |
| 740 | C42 | — | 106 | 1 | no | — |
| 741 | C42 | — | 212 | 2 | no | — |
| 742 | C42 | — | 212 | 2 | no | — |
| 743 | C23 | — | 2 | 2 | no | — |
| 744 | C23 | — | 4 | 2 | no | — |
| 745 | C23 | — | 8 | 2 | no | — |
| 746 | C23 | — | 53 | 1 | no | — |
| 747 | C23 | — | 53 | 1 | no | — |
| 748 | C23 | — | 53 | 1 | no | — |
| 749 | C23 | — | 53 | 1 | no | — |
| 750 | C23 | — | 106 | 1 | no | — |
| 751 | C23 | — | 106 | 1 | no | — |
| 752 | C23 | — | 106 | 1 | no | — |
| 753 | C23 | — | 106 | 1 | no | — |
| 754 | C23 | — | 106 | 1 | no | — |
| 755 | C23 | — | 106 | 1 | no | — |
| 756 | C23 | — | 106 | 2 | no | — |
| 757 | C23 | — | 424 | 2 | no | — |
| 758 | C23 | — | 424 | 2 | no | — |
| 759 | C23 | — | 424 | 2 | no | — |
| 760 | C23 | — | 424 | 8 | no | — |
| 761 | C23 | — | 424 | 8 | no | — |
| 762 | C23 | — | 212 | 2 | no | — |
| 763 | C23 | — | 212 | 2 | no | — |
| 764 | C23 | — | 212 | 2 | no | — |
| 765 | C23 | — | 212 | 4 | no | — |
| 766 | C23 | — | 212 | 4 | no | — |
| 767 | C23 | — | 212 | 4 | no | — |
| 768 | C23 | — | 212 | 2 | no | — |
| 769 | C23 | — | 212 | 2 | no | — |
| 770 | C23 | — | 212 | 2 | no | — |
| 771 | C23 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 772 | C23 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 773 | C23 | C23×#6157 | 1 | 1 | yes | characteristic |
| 774 | Q8 | — | 4 | 1 | no | — |
| 775 | Q8 | — | 212 | 1 | no | — |
| 776 | Q8 | — | 212 | 1 | no | — |
| 777 | Q8 | — | 212 | 1 | no | — |
| 778 | D4 | — | 4 | 1 | no | — |
| 779 | D4 | — | 4 | 1 | no | — |
| 780 | D4 | — | 4 | 1 | no | — |
| 781 | D4 | — | 4 | 2 | no | — |
| 782 | D4 | — | 4 | 1 | no | — |
| 783 | D4 | — | 4 | 1 | no | — |
| 784 | D4 | — | 8 | 2 | no | — |
| 785 | D4 | — | 8 | 2 | no | — |
| 786 | D4 | — | 424 | 2 | no | — |
| 787 | D4 | — | 424 | 2 | no | — |
| 788 | D4 | — | 424 | 2 | no | — |
| 789 | D4 | — | 424 | 2 | no | — |
| 790 | D4 | — | 424 | 2 | no | — |
| 791 | D4 | — | 424 | 2 | no | — |
| 792 | D4 | — | 212 | 1 | no | — |
| 793 | D4 | — | 212 | 1 | no | — |
| 794 | D4 | — | 212 | 1 | no | — |
| 795 | D4 | — | 212 | 2 | no | — |
| 796 | D4 | — | 212 | 2 | no | — |
| 797 | D4 | — | 212 | 2 | no | — |
| 798 | D4 | — | 212 | 1 | no | — |
| 799 | D4 | — | 212 | 1 | no | — |
| 800 | D4 | — | 212 | 1 | no | — |
| 801 | D4 | — | 212 | 1 | no | — |
| 802 | D4 | — | 212 | 1 | no | — |
| 803 | D4 | — | 212 | 1 | no | — |
| 804 | D4 | — | 212 | 4 | no | — |
| 805 | D4 | — | 212 | 1 | no | — |
| 806 | D4 | — | 212 | 1 | no | — |
| 807 | C2×C4 | — | 2 | 1 | no | — |
| 808 | C2×C4 | — | 2 | 1 | no | — |
| 809 | C2×C4 | — | 2 | 1 | no | — |
| 810 | C2×C4 | — | 2 | 1 | no | — |
| 811 | C2×C4 | — | 2 | 1 | no | — |
| 812 | C2×C4 | — | 2 | 1 | no | — |
| 813 | C2×C4 | — | 2 | 2 | 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 | — | 106 | 1 | no | — |
| 823 | C2×C4 | — | 106 | 1 | no | — |
| 824 | C2×C4 | — | 106 | 1 | no | — |
| 825 | C2×C4 | — | 106 | 1 | no | — |
| 826 | C2×C4 | — | 106 | 1 | no | — |
| 827 | C2×C4 | — | 106 | 1 | no | — |
| 828 | C2×C4 | — | 106 | 1 | no | — |
| 829 | C2×C4 | — | 106 | 1 | no | — |
| 830 | C2×C4 | — | 106 | 1 | no | — |
| 831 | C2×C4 | — | 106 | 1 | no | — |
| 832 | C2×C4 | — | 106 | 1 | no | — |
| 833 | C2×C4 | — | 106 | 1 | no | — |
| 834 | C2×C4 | — | 106 | 1 | no | — |
| 835 | C2×C4 | — | 106 | 1 | no | — |
| 836 | C2×C4 | — | 106 | 1 | no | — |
| 837 | C2×C4 | — | 106 | 1 | no | — |
| 838 | C2×C4 | — | 106 | 1 | no | — |
| 839 | C2×C4 | — | 106 | 1 | no | — |
| 840 | C2×C4 | — | 106 | 1 | no | — |
| 841 | C2×C4 | — | 106 | 1 | no | — |
| 842 | C2×C4 | — | 106 | 1 | no | — |
| 843 | C2×C4 | — | 106 | 1 | no | — |
| 844 | C2×C4 | — | 106 | 1 | no | — |
| 845 | C2×C4 | — | 106 | 1 | no | — |
| 846 | C2×C4 | — | 106 | 2 | no | — |
| 847 | C2×C4 | — | 424 | 4 | no | — |
| 848 | C2×C4 | — | 212 | 4 | no | — |
| 849 | C2×C4 | — | 212 | 4 | no | — |
| 850 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 851 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 852 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 853 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 854 | C8 | — | 212 | 4 | no | — |
| 855 | C22 | — | 2 | 1 | no | — |
| 856 | C22 | — | 2 | 1 | no | — |
| 857 | C22 | — | 2 | 1 | no | — |
| 858 | C22 | — | 4 | 1 | no | — |
| 859 | C22 | — | 4 | 1 | no | — |
| 860 | C22 | — | 4 | 1 | no | — |
| 861 | C22 | — | 4 | 2 | no | — |
| 862 | C22 | — | 4 | 2 | no | — |
| 863 | C22 | — | 4 | 2 | no | — |
| 864 | C22 | — | 8 | 4 | no | — |
| 865 | C22 | — | 53 | 1 | no | — |
| 866 | C22 | — | 53 | 1 | no | — |
| 867 | C22 | — | 106 | 2 | no | — |
| 868 | C22 | — | 106 | 1 | no | — |
| 869 | C22 | — | 106 | 1 | no | — |
| 870 | C22 | — | 106 | 1 | no | — |
| 871 | C22 | — | 424 | 1 | no | — |
| 872 | C22 | — | 424 | 1 | no | — |
| 873 | C22 | — | 424 | 4 | no | — |
| 874 | C22 | — | 424 | 4 | no | — |
| 875 | C22 | — | 424 | 4 | no | — |
| 876 | C22 | — | 424 | 8 | no | — |
| 877 | C22 | — | 212 | 2 | no | — |
| 878 | C22 | — | 212 | 2 | no | — |
| 879 | C22 | — | 212 | 1 | no | — |
| 880 | C22 | — | 212 | 1 | no | — |
| 881 | C22 | — | 212 | 1 | no | — |
| 882 | C22 | — | 212 | 2 | no | — |
| 883 | C22 | — | 212 | 2 | no | — |
| 884 | C22 | — | 212 | 2 | no | — |
| 885 | C22 | — | 212 | 2 | no | — |
| 886 | C22 | — | 212 | 2 | no | — |
| 887 | C22 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 888 | C4 | — | 2 | 1 | no | — |
| 889 | C4 | — | 2 | 1 | no | — |
| 890 | C4 | — | 2 | 1 | no | — |
| 891 | C4 | — | 4 | 2 | no | — |
| 892 | C4 | — | 53 | 1 | no | — |
| 893 | C4 | — | 53 | 1 | no | — |
| 894 | C4 | — | 106 | 1 | no | — |
| 895 | C4 | — | 106 | 1 | no | — |
| 896 | C4 | — | 106 | 1 | no | — |
| 897 | C4 | — | 424 | 4 | no | — |
| 898 | C4 | — | 212 | 2 | no | — |
| 899 | C4 | D53⋊#99 | 1 | 1 | yes | characteristic |
| 900 | C4 | D53⋊#99 | 1 | 1 | yes | characteristic |
| 901 | C2 | — | 2 | 1 | no | — |
| 902 | C2 | — | 4 | 1 | no | — |
| 903 | C2 | — | 4 | 1 | no | — |
| 904 | C2 | — | 4 | 1 | no | — |
| 905 | C2 | — | 8 | 2 | no | — |
| 906 | C2 | — | 53 | 2 | no | — |
| 907 | C2 | — | 106 | 1 | no | — |
| 908 | C2 | — | 424 | 2 | no | — |
| 909 | C2 | — | 212 | 1 | no | — |
| 910 | C2 | — | 212 | 1 | no | — |
| 911 | C2 | — | 212 | 1 | no | — |
| 912 | C2 | C2×D53⋊#99 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊#413 | C2 | semidirect |
| 2. D53⋊#410 | C2 | semidirect |
| 3. #20290976 | C2 | semidirect |
| 4. #20290975 | C2 | semidirect |
| 5. #20290974 | C2 | semidirect |
| 6. D53⋊AΣL(1,𝔽16) | C2 | semidirect |
| 11. #16811610 | C22 | semidirect |
| 13. #16811609 | C22 | semidirect |
| 17. #16811603 | C22 | semidirect |
| 19. #16811602 | C22 | semidirect |
| 22. #16811524 | C22 | semidirect |
| 23. #16811523 | C22 | semidirect |
| 25. C22×D4×D53 | C4 | semidirect |
| 31. #16811188 | C4 | semidirect |
| 33. #16811187 | C4 | semidirect |
| 39. #120×D53 | C4 | semidirect |
| 41. #117×D53 | C4 | semidirect |
| 42. C53×#535 | C4 | semidirect |
| 78. C22×D212 | C2×C4 | semidirect |
| 79. C22×C22⋊D53 | C2×C4 | semidirect |
| 118. #13133187 | C2×C4 | semidirect |
| 120. #13133186 | C2×C4 | semidirect |
| 125. #13133185 | C2×C4 | semidirect |
| 126. #13133176 | C2×C4 | semidirect |
| 129. #13133173 | C2×C4 | semidirect |
| 136. C22×D4×C53 | C2×C4 | semidirect |
| 142. #120×C53 | C2×C4 | semidirect |
| 143. #117×C53 | C2×C4 | semidirect |
| 463. D53 | #2122 | semidirect |
| 476. #535 | #6157 | semidirect |
| 499. C53 | C2×#2122 | semidirect |
| 529. C22×D4 | C2×#6157 | semidirect |
| 575. #120 | C2×#6157 | semidirect |
| 584. #117 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#413 | 2 |
| D53⋊#410 | 2 |
| #20290976 | 2 |
| #20290975 | 2 |
| #20290974 | 2 |
| D53⋊AΣL(1,𝔽16) | 2 |
| #535×D53 | 2 |
| C2×#2122 | 53 |