Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 81 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 | A4×#713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×D5×A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×A4×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | A4×D40 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | A4×#676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#4060 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 9 | C22×D5×A4 | — | 2 | 1 | no | — |
| 10 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×D4×A4 | C22 | 1 | 1 | yes | characteristic |
| 12 | A4×C22⋊D5 | — | 2 | 1 | no | — |
| 13 | A4×D20 | — | 2 | 1 | no | — |
| 14 | A4×D20 | C22 | 1 | 1 | yes | characteristic |
| 15 | A4×D20 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C4×D5×A4 | — | 2 | 1 | no | — |
| 17 | C4×D5×A4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#4060 | — | 4 | 1 | no | maximal |
| 19 | C5×C8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | A4×#168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | A4×AGL(1,ℤ/8) | — | 5 | 1 | no | maximal, Hall |
| 22 | C22×#713 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×D4×D5 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C22×C5×SD16 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C22×#688 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C22×#686 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#4060 | — | 3 | 1 | no | — |
| 28 | C2×#4060 | — | 3 | 1 | no | — |
| 29 | C2×#4060 | — | 3 | 1 | no | — |
| 30 | C2×#4060 | — | 3 | 1 | no | — |
| 31 | C2×#4060 | — | 3 | 1 | no | — |
| 32 | C2×#4060 | — | 3 | 1 | no | — |
| 33 | C2×#4060 | — | 3 | 1 | no | — |
| 34 | C2×#4060 | — | 3 | 1 | no | — |
| 35 | C22×D40 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C22×#676 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C22×C5×A4 | — | 2 | 1 | no | — |
| 38 | C2×D5×A4 | — | 2 | 1 | no | — |
| 39 | C2×D5×A4 | — | 2 | 1 | no | — |
| 40 | C2×D5×A4 | — | 4 | 2 | no | — |
| 41 | C2×D5×A4 | D4 | 1 | 1 | yes | characteristic |
| 42 | C3×#713 | — | 4 | 1 | no | — |
| 43 | C3×D4×D5 | — | 4 | 1 | no | — |
| 44 | C4×C5×A4 | — | 2 | 1 | no | — |
| 45 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 46 | A4×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 47 | C3×C5×SD16 | — | 4 | 1 | no | — |
| 48 | C3×#688 | — | 4 | 1 | no | — |
| 49 | C3×#686 | — | 4 | 1 | no | — |
| 50 | C3×D40 | — | 4 | 1 | no | — |
| 51 | C3×#676 | — | 4 | 1 | no | — |
| 52 | A4×#41 | — | 5 | 1 | no | — |
| 53 | C2×D4×A4 | — | 5 | 1 | no | — |
| 54 | A4×SD16 | — | 5 | 1 | no | — |
| 55 | A4×SD16 | D5 | 1 | 1 | yes | characteristic, complemented |
| 56 | A4×D8 | — | 5 | 1 | no | — |
| 57 | A4×D8 | — | 5 | 1 | no | — |
| 58 | A4×M16 | — | 5 | 1 | no | — |
| 59 | C24×D5 | — | 2 | 1 | no | — |
| 60 | C22×C5×Q8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 61 | C22×C5×D4 | C22×C3 | 1 | 1 | yes | characteristic |
| 62 | C22×C22⋊D5 | — | 2 | 1 | no | — |
| 63 | C2×#713 | — | 3 | 1 | no | — |
| 64 | C2×#713 | — | 3 | 1 | no | — |
| 65 | C2×#713 | — | 3 | 1 | no | — |
| 66 | C2×#713 | — | 3 | 1 | no | — |
| 67 | C2×#713 | — | 6 | 1 | no | — |
| 68 | C2×#713 | — | 6 | 1 | no | — |
| 69 | C2×D4×D5 | — | 3 | 1 | no | — |
| 70 | C2×D4×D5 | — | 3 | 1 | no | — |
| 71 | C2×D4×D5 | — | 3 | 1 | no | — |
| 72 | C2×D4×D5 | — | 3 | 1 | no | — |
| 73 | C2×D4×D5 | — | 6 | 1 | no | — |
| 74 | C2×D4×D5 | — | 6 | 1 | no | — |
| 75 | C22×D20 | — | 2 | 1 | no | — |
| 76 | C22×D20 | C22×C3 | 1 | 1 | yes | characteristic |
| 77 | C22×D20 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 78 | C22×C4×D5 | — | 2 | 1 | no | — |
| 79 | C22×C4×D5 | C22×C3 | 1 | 1 | yes | characteristic |
| 80 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 81 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 82 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 83 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 84 | C22×C5×C8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 85 | C2×#688 | — | 3 | 1 | no | — |
| 86 | C2×#688 | — | 3 | 1 | no | — |
| 87 | C2×#688 | — | 3 | 1 | no | — |
| 88 | C2×#688 | — | 3 | 1 | no | — |
| 89 | C2×#686 | — | 3 | 1 | no | — |
| 90 | C2×#686 | — | 3 | 1 | no | — |
| 91 | C2×#686 | — | 3 | 1 | no | — |
| 92 | C2×#686 | — | 3 | 1 | no | — |
| 93 | C22×#168 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 94 | #4060 | — | 3 | 2 | no | — |
| 95 | #4060 | — | 3 | 2 | no | — |
| 96 | #4060 | — | 3 | 2 | no | — |
| 97 | #4060 | — | 3 | 2 | no | — |
| 98 | #4060 | — | 3 | 2 | no | — |
| 99 | #4060 | — | 3 | 2 | no | — |
| 100 | #4060 | — | 3 | 2 | no | — |
| 101 | #4060 | — | 3 | 1 | no | — |
| 102 | #4060 | — | 3 | 1 | no | — |
| 103 | #4060 | — | 3 | 1 | no | — |
| 104 | #4060 | — | 3 | 1 | no | — |
| 105 | #4060 | — | 3 | 1 | no | — |
| 106 | #4060 | — | 3 | 1 | no | — |
| 107 | #4060 | — | 3 | 1 | no | — |
| 108 | #4060 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 109 | C2×D40 | — | 3 | 1 | no | — |
| 110 | C2×D40 | — | 3 | 1 | no | — |
| 111 | C2×D40 | — | 3 | 1 | no | — |
| 112 | C2×D40 | — | 3 | 1 | no | — |
| 113 | C2×#676 | — | 3 | 1 | no | — |
| 114 | C2×#676 | — | 3 | 1 | no | — |
| 115 | C2×#676 | — | 3 | 1 | no | — |
| 116 | C2×#676 | — | 3 | 1 | no | — |
| 117 | C22×AGL(1,ℤ/8) | — | 5 | 1 | no | Sylow |
| 118 | C22×C3×D5 | — | 8 | 1 | no | — |
| 119 | C2×C5×A4 | — | 4 | 1 | no | — |
| 120 | C2×C5×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | D5×A4 | — | 2 | 1 | no | — |
| 122 | D5×A4 | — | 4 | 1 | no | — |
| 123 | D5×A4 | — | 4 | 1 | no | — |
| 124 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 125 | C3×C5×D4 | — | 4 | 1 | no | — |
| 126 | C3×C22⋊D5 | — | 8 | 1 | no | — |
| 127 | C3×D20 | — | 4 | 1 | no | — |
| 128 | C3×D20 | — | 4 | 1 | no | — |
| 129 | C3×D20 | — | 8 | 1 | no | — |
| 130 | C3×C4×D5 | — | 4 | 1 | no | — |
| 131 | C3×C4×D5 | — | 8 | 1 | no | — |
| 132 | C3×C5×C8 | — | 4 | 1 | no | — |
| 133 | C3×#168 | — | 4 | 1 | no | — |
| 134 | C23×A4 | — | 10 | 1 | no | — |
| 135 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 136 | D4×A4 | — | 5 | 1 | no | — |
| 137 | D4×A4 | — | 5 | 1 | no | — |
| 138 | D4×A4 | — | 10 | 1 | no | — |
| 139 | D4×A4 | — | 10 | 1 | no | — |
| 140 | D4×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 141 | C2×C4×A4 | — | 5 | 1 | no | — |
| 142 | C2×C4×A4 | — | 10 | 1 | no | — |
| 143 | C3×AGL(1,ℤ/8) | — | 20 | 1 | no | — |
| 144 | C8×A4 | — | 5 | 1 | no | — |
| 145 | C8×A4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 146 | C24×C5 | — | 2 | 1 | no | — |
| 147 | C23×D5 | — | 2 | 1 | no | — |
| 148 | C23×D5 | — | 2 | 1 | no | — |
| 149 | C23×D5 | — | 4 | 2 | no | — |
| 150 | C23×D5 | — | 6 | 1 | no | — |
| 151 | C23×D5 | — | 6 | 1 | no | — |
| 152 | C23×D5 | — | 6 | 1 | no | — |
| 153 | C23×D5 | — | 6 | 1 | no | — |
| 154 | C23×D5 | — | 12 | 2 | no | — |
| 155 | C23×D5 | C3×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 157 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 158 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 159 | C2×C5×D4 | — | 3 | 1 | no | — |
| 160 | C2×C5×D4 | — | 3 | 1 | no | — |
| 161 | C2×C5×D4 | — | 6 | 1 | no | — |
| 162 | C22×C4×C5 | — | 2 | 1 | no | — |
| 163 | C22×C4×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 164 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 165 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 166 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 167 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 168 | C22×Dic5 | C3×D4 | 1 | 1 | yes | characteristic |
| 169 | #713 | — | 3 | 2 | no | — |
| 170 | #713 | — | 3 | 1 | no | — |
| 171 | #713 | — | 3 | 1 | no | — |
| 172 | #713 | — | 3 | 1 | no | — |
| 173 | #713 | — | 6 | 1 | no | — |
| 174 | #713 | — | 6 | 1 | no | — |
| 175 | #713 | — | 6 | 2 | no | — |
| 176 | #713 | — | 6 | 2 | no | — |
| 177 | #713 | — | 6 | 1 | no | — |
| 178 | #713 | — | 6 | 1 | no | — |
| 179 | #713 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 180 | D4×D5 | — | 3 | 2 | no | — |
| 181 | D4×D5 | — | 3 | 1 | no | — |
| 182 | D4×D5 | — | 3 | 1 | no | — |
| 183 | D4×D5 | — | 3 | 1 | no | — |
| 184 | D4×D5 | — | 6 | 1 | no | — |
| 185 | D4×D5 | — | 6 | 1 | no | — |
| 186 | D4×D5 | — | 6 | 1 | no | — |
| 187 | D4×D5 | — | 6 | 2 | no | — |
| 188 | D4×D5 | — | 6 | 2 | no | — |
| 189 | D4×D5 | — | 6 | 1 | no | — |
| 190 | D4×D5 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 191 | C2×D20 | — | 3 | 1 | no | — |
| 192 | C2×D20 | — | 3 | 1 | no | — |
| 193 | C2×D20 | — | 3 | 1 | no | — |
| 194 | C2×D20 | — | 3 | 1 | no | — |
| 195 | C2×D20 | — | 6 | 1 | no | — |
| 196 | C2×D20 | — | 6 | 1 | no | — |
| 197 | C2×D20 | — | 6 | 1 | no | — |
| 198 | C2×D20 | — | 6 | 1 | no | — |
| 199 | C2×D20 | — | 6 | 1 | no | — |
| 200 | C2×D20 | — | 6 | 1 | no | — |
| 201 | C2×C4×D5 | — | 3 | 1 | no | — |
| 202 | C2×C4×D5 | — | 3 | 1 | no | — |
| 203 | C2×C4×D5 | — | 3 | 1 | no | — |
| 204 | C2×C4×D5 | — | 3 | 1 | no | — |
| 205 | C2×C4×D5 | — | 6 | 1 | no | — |
| 206 | C2×C4×D5 | — | 6 | 1 | no | — |
| 207 | C2×C4×D5 | — | 6 | 1 | no | — |
| 208 | C2×C4×D5 | — | 6 | 1 | no | — |
| 209 | C5×SD16 | — | 3 | 2 | no | — |
| 210 | C5×SD16 | — | 3 | 1 | no | — |
| 211 | C5×SD16 | — | 3 | 1 | no | — |
| 212 | C5×SD16 | — | 3 | 1 | no | — |
| 213 | C5×SD16 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 214 | C2×C5×C8 | — | 3 | 1 | no | — |
| 215 | C2×C5×C8 | — | 3 | 1 | no | — |
| 216 | #688 | — | 3 | 2 | no | — |
| 217 | #688 | — | 3 | 1 | no | — |
| 218 | #688 | — | 3 | 1 | no | — |
| 219 | #688 | — | 3 | 1 | no | — |
| 220 | #688 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 221 | #686 | — | 3 | 2 | no | — |
| 222 | #686 | — | 3 | 1 | no | — |
| 223 | #686 | — | 3 | 1 | no | — |
| 224 | #686 | — | 3 | 1 | no | — |
| 225 | #686 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 226 | C2×#168 | — | 3 | 1 | no | — |
| 227 | C2×#168 | — | 3 | 1 | no | — |
| 228 | D40 | — | 3 | 2 | no | — |
| 229 | D40 | — | 3 | 1 | no | — |
| 230 | D40 | — | 3 | 1 | no | — |
| 231 | D40 | — | 3 | 1 | no | — |
| 232 | D40 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 233 | #676 | — | 3 | 2 | no | — |
| 234 | #676 | — | 3 | 1 | no | — |
| 235 | #676 | — | 3 | 1 | no | — |
| 236 | #676 | — | 3 | 1 | no | — |
| 237 | #676 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 238 | C22×#41 | — | 5 | 1 | no | — |
| 239 | C23×D4 | — | 5 | 1 | no | — |
| 240 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 241 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 242 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 243 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 244 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 245 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 246 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 247 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 248 | C22×SD16 | — | 5 | 1 | no | — |
| 249 | C22×SD16 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 250 | C22×D8 | — | 5 | 1 | no | — |
| 251 | C22×D8 | — | 5 | 1 | no | — |
| 252 | C22×M16 | — | 5 | 1 | no | — |
| 253 | C22×C3×C5 | — | 8 | 1 | no | — |
| 254 | C2×C3×D5 | — | 4 | 1 | no | — |
| 255 | C2×C3×D5 | — | 8 | 1 | no | — |
| 256 | C2×C3×D5 | — | 8 | 1 | no | — |
| 257 | C2×C3×D5 | — | 16 | 2 | no | — |
| 258 | C5×A4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented |
| 259 | C3×C4×C5 | — | 4 | 1 | no | — |
| 260 | C3×C4×C5 | — | 8 | 1 | no | — |
| 261 | C3×Dic5 | — | 4 | 1 | no | — |
| 262 | C22×A4 | — | 2 | 1 | no | — |
| 263 | C22×A4 | — | 5 | 1 | no | — |
| 264 | C22×A4 | — | 10 | 1 | no | — |
| 265 | C22×A4 | — | 10 | 1 | no | — |
| 266 | C22×A4 | — | 20 | 2 | no | — |
| 267 | C3×#41 | — | 20 | 1 | no | — |
| 268 | C2×C3×D4 | — | 20 | 1 | no | — |
| 269 | C4×A4 | — | 2 | 1 | no | — |
| 270 | C4×A4 | — | 5 | 1 | no | — |
| 271 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 272 | C3×SD16 | — | 4 | 1 | no | — |
| 273 | C3×SD16 | — | 20 | 1 | no | — |
| 274 | C3×D8 | — | 20 | 1 | no | — |
| 275 | C3×D8 | — | 20 | 1 | no | — |
| 276 | C3×M16 | — | 20 | 1 | no | — |
| 277 | C23×C5 | — | 4 | 1 | no | — |
| 278 | C23×C5 | — | 6 | 1 | no | — |
| 279 | C23×C5 | — | 6 | 1 | no | — |
| 280 | C23×C5 | — | 12 | 1 | no | — |
| 281 | C23×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 282 | C22×D5 | — | 2 | 1 | no | — |
| 283 | C22×D5 | — | 2 | 1 | no | — |
| 284 | C22×D5 | — | 3 | 1 | no | — |
| 285 | C22×D5 | — | 3 | 1 | no | — |
| 286 | C22×D5 | — | 4 | 1 | no | — |
| 287 | C22×D5 | — | 4 | 1 | no | — |
| 288 | C22×D5 | — | 6 | 1 | no | — |
| 289 | C22×D5 | — | 6 | 1 | no | — |
| 290 | C22×D5 | — | 6 | 1 | no | — |
| 291 | C22×D5 | — | 6 | 1 | no | — |
| 292 | C22×D5 | — | 6 | 2 | no | — |
| 293 | C22×D5 | — | 6 | 1 | no | — |
| 294 | C22×D5 | — | 6 | 1 | no | — |
| 295 | C22×D5 | — | 6 | 1 | no | — |
| 296 | C22×D5 | — | 6 | 1 | no | — |
| 297 | C22×D5 | — | 12 | 2 | no | — |
| 298 | C22×D5 | — | 12 | 2 | no | — |
| 299 | C22×D5 | — | 12 | 2 | no | — |
| 300 | C22×D5 | — | 12 | 2 | no | — |
| 301 | C22×D5 | — | 12 | 2 | no | — |
| 302 | C22×D5 | — | 12 | 2 | no | — |
| 303 | C22×D5 | — | 12 | 2 | no | — |
| 304 | C22×D5 | — | 12 | 2 | no | — |
| 305 | C22×D5 | — | 12 | 1 | no | — |
| 306 | C22×D5 | — | 12 | 1 | no | — |
| 307 | C5×Q8 | — | 3 | 1 | no | — |
| 308 | C5×Q8 | — | 6 | 1 | no | — |
| 309 | C5×Q8 | — | 6 | 1 | no | — |
| 310 | C5×Q8 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 311 | C5×D4 | — | 3 | 1 | no | — |
| 312 | C5×D4 | — | 6 | 1 | no | — |
| 313 | C5×D4 | — | 6 | 1 | no | — |
| 314 | C5×D4 | C22×A4 | 1 | 1 | yes | characteristic |
| 315 | C2×C4×C5 | — | 3 | 1 | no | — |
| 316 | C2×C4×C5 | — | 3 | 1 | no | — |
| 317 | C2×C4×C5 | — | 6 | 1 | no | — |
| 318 | C2×C4×C5 | — | 6 | 1 | no | — |
| 319 | C22⋊D5 | — | 2 | 1 | no | — |
| 320 | C22⋊D5 | — | 6 | 1 | no | — |
| 321 | C22⋊D5 | — | 6 | 1 | no | — |
| 322 | C22⋊D5 | — | 6 | 2 | no | — |
| 323 | C22⋊D5 | — | 6 | 1 | no | — |
| 324 | C2×Dic5 | — | 3 | 1 | no | — |
| 325 | C2×Dic5 | — | 3 | 1 | no | — |
| 326 | D20 | — | 2 | 1 | no | — |
| 327 | D20 | — | 3 | 1 | no | — |
| 328 | D20 | — | 3 | 1 | no | — |
| 329 | D20 | — | 6 | 1 | no | — |
| 330 | D20 | — | 6 | 1 | no | — |
| 331 | D20 | — | 6 | 1 | no | — |
| 332 | D20 | — | 6 | 1 | no | — |
| 333 | D20 | — | 6 | 1 | no | — |
| 334 | D20 | — | 6 | 1 | no | — |
| 335 | D20 | — | 6 | 2 | no | — |
| 336 | D20 | — | 6 | 1 | no | — |
| 337 | D20 | C22×A4 | 1 | 1 | yes | characteristic |
| 338 | D20 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 339 | C4×D5 | — | 2 | 1 | no | — |
| 340 | C4×D5 | — | 3 | 2 | no | — |
| 341 | C4×D5 | — | 3 | 1 | no | — |
| 342 | C4×D5 | — | 3 | 1 | no | — |
| 343 | C4×D5 | — | 3 | 1 | no | — |
| 344 | C4×D5 | — | 6 | 1 | no | — |
| 345 | C4×D5 | — | 6 | 1 | no | — |
| 346 | C4×D5 | — | 6 | 2 | no | — |
| 347 | C4×D5 | — | 6 | 1 | no | — |
| 348 | C4×D5 | C22×A4 | 1 | 1 | yes | characteristic |
| 349 | C5×C8 | — | 3 | 1 | no | — |
| 350 | C5×C8 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 351 | #168 | — | 3 | 1 | no | — |
| 352 | #168 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 353 | C25 | — | 10 | 1 | no | — |
| 354 | C2×#41 | — | 15 | 1 | no | — |
| 355 | C2×#41 | — | 15 | 1 | no | — |
| 356 | C2×#41 | — | 15 | 1 | no | — |
| 357 | C2×#41 | — | 15 | 1 | no | — |
| 358 | C2×#41 | — | 30 | 1 | no | — |
| 359 | C2×#41 | — | 30 | 1 | no | — |
| 360 | C22×Q8 | C2×C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 361 | C22×D4 | — | 5 | 1 | no | — |
| 362 | C22×D4 | — | 5 | 1 | no | — |
| 363 | C22×D4 | — | 10 | 1 | no | — |
| 364 | C22×D4 | — | 10 | 1 | no | — |
| 365 | C22×D4 | — | 15 | 1 | no | — |
| 366 | C22×D4 | — | 15 | 1 | no | — |
| 367 | C22×D4 | — | 15 | 1 | no | — |
| 368 | C22×D4 | — | 15 | 1 | no | — |
| 369 | C22×D4 | — | 30 | 1 | no | — |
| 370 | C22×D4 | — | 30 | 1 | no | — |
| 371 | C22×D4 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 372 | C23×C4 | — | 5 | 1 | no | — |
| 373 | C23×C4 | — | 10 | 1 | no | — |
| 374 | AGL(1,ℤ/8) | — | 5 | 1 | no | — |
| 375 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 376 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 377 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 378 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 379 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 380 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 381 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 383 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 384 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 385 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 386 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 387 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 388 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 389 | C2×SD16 | — | 3 | 1 | no | — |
| 390 | C2×SD16 | — | 3 | 1 | no | — |
| 391 | C2×SD16 | — | 3 | 1 | no | — |
| 392 | C2×SD16 | — | 3 | 1 | no | — |
| 393 | C2×SD16 | — | 15 | 1 | no | — |
| 394 | C2×SD16 | — | 15 | 1 | no | — |
| 395 | C2×SD16 | — | 15 | 1 | no | — |
| 396 | C2×SD16 | — | 15 | 1 | no | — |
| 397 | C2×D8 | — | 15 | 1 | no | — |
| 398 | C2×D8 | — | 15 | 1 | no | — |
| 399 | C2×D8 | — | 15 | 1 | no | — |
| 400 | C2×D8 | — | 15 | 1 | no | — |
| 401 | C2×D8 | — | 15 | 1 | no | — |
| 402 | C2×D8 | — | 15 | 1 | no | — |
| 403 | C2×D8 | — | 15 | 1 | no | — |
| 404 | C2×D8 | — | 15 | 1 | no | — |
| 405 | C2×M16 | — | 15 | 1 | no | — |
| 406 | C2×M16 | — | 15 | 1 | no | — |
| 407 | C2×M16 | — | 15 | 1 | no | — |
| 408 | C2×M16 | — | 15 | 1 | no | — |
| 409 | C22×C8 | — | 5 | 1 | no | — |
| 410 | C22×C8 | C2×C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 411 | C2×C3×C5 | — | 4 | 1 | no | — |
| 412 | C2×C3×C5 | — | 16 | 1 | no | — |
| 413 | C3×D5 | — | 8 | 1 | no | — |
| 414 | C3×D5 | — | 16 | 1 | no | — |
| 415 | C3×D5 | — | 16 | 1 | no | — |
| 416 | C23×C3 | — | 40 | 1 | no | — |
| 417 | C2×A4 | — | 4 | 1 | no | — |
| 418 | C2×A4 | — | 10 | 1 | no | — |
| 419 | C2×A4 | — | 20 | 1 | no | — |
| 420 | C2×A4 | — | 20 | 1 | no | — |
| 421 | C2×A4 | D4×D5 | 1 | 1 | yes | characteristic |
| 422 | C3×Q8 | — | 4 | 1 | no | — |
| 423 | C3×D4 | — | 4 | 1 | no | — |
| 424 | C3×D4 | — | 20 | 1 | no | — |
| 425 | C3×D4 | — | 20 | 1 | no | — |
| 426 | C3×D4 | — | 40 | 1 | no | — |
| 427 | C3×D4 | — | 40 | 1 | no | — |
| 428 | C2×C3×C4 | — | 20 | 1 | no | — |
| 429 | C2×C3×C4 | — | 40 | 1 | no | — |
| 430 | C3×C8 | — | 4 | 1 | no | — |
| 431 | C3×C8 | — | 20 | 1 | no | — |
| 432 | C22×C5 | — | 2 | 1 | no | — |
| 433 | C22×C5 | — | 3 | 1 | no | — |
| 434 | C22×C5 | — | 3 | 1 | no | — |
| 435 | C22×C5 | — | 6 | 1 | no | — |
| 436 | C22×C5 | — | 12 | 1 | no | — |
| 437 | C22×C5 | — | 12 | 1 | no | — |
| 438 | C22×C5 | — | 12 | 1 | no | — |
| 439 | C22×C5 | — | 12 | 1 | no | — |
| 440 | C22×C5 | C3×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented |
| 441 | C2×D5 | — | 2 | 1 | no | — |
| 442 | C2×D5 | — | 2 | 1 | no | — |
| 443 | C2×D5 | — | 3 | 1 | no | — |
| 444 | C2×D5 | — | 4 | 2 | no | — |
| 445 | C2×D5 | — | 6 | 1 | no | — |
| 446 | C2×D5 | — | 6 | 1 | no | — |
| 447 | C2×D5 | — | 6 | 1 | no | — |
| 448 | C2×D5 | — | 6 | 1 | no | — |
| 449 | C2×D5 | — | 6 | 1 | no | — |
| 450 | C2×D5 | — | 6 | 1 | no | — |
| 451 | C2×D5 | — | 12 | 2 | no | — |
| 452 | C2×D5 | — | 12 | 2 | no | — |
| 453 | C2×D5 | — | 12 | 1 | no | — |
| 454 | C2×D5 | — | 12 | 1 | no | — |
| 455 | C2×D5 | — | 12 | 1 | no | — |
| 456 | C2×D5 | — | 12 | 1 | no | — |
| 457 | C2×D5 | — | 12 | 2 | no | — |
| 458 | C2×D5 | — | 12 | 4 | no | — |
| 459 | C2×D5 | — | 12 | 1 | no | — |
| 460 | C2×D5 | — | 12 | 1 | no | — |
| 461 | C2×D5 | — | 12 | 1 | no | — |
| 462 | C2×D5 | — | 12 | 1 | no | — |
| 463 | C2×D5 | D4×A4 | 1 | 1 | yes | characteristic |
| 464 | C4×C5 | — | 2 | 1 | no | — |
| 465 | C4×C5 | — | 3 | 1 | no | — |
| 466 | C4×C5 | — | 6 | 1 | no | — |
| 467 | C4×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 468 | Dic5 | — | 3 | 1 | no | — |
| 469 | Dic5 | D4×A4 | 1 | 1 | yes | characteristic |
| 470 | C24 | — | 2 | 1 | no | — |
| 471 | C24 | — | 5 | 1 | no | — |
| 472 | C24 | — | 10 | 1 | no | — |
| 473 | C24 | — | 10 | 1 | no | — |
| 474 | C24 | — | 20 | 2 | no | — |
| 475 | C24 | — | 30 | 1 | no | — |
| 476 | C24 | — | 30 | 1 | no | — |
| 477 | C24 | — | 30 | 1 | no | — |
| 478 | C24 | — | 30 | 1 | no | — |
| 479 | C24 | — | 60 | 2 | no | — |
| 480 | #41 | — | 5 | 1 | no | — |
| 481 | #41 | — | 15 | 1 | no | — |
| 482 | #41 | — | 15 | 1 | no | — |
| 483 | #41 | — | 15 | 2 | no | — |
| 484 | #41 | — | 15 | 1 | no | — |
| 485 | #41 | — | 30 | 1 | no | — |
| 486 | #41 | — | 30 | 1 | no | — |
| 487 | #41 | — | 30 | 2 | no | — |
| 488 | #41 | — | 30 | 2 | no | — |
| 489 | #41 | — | 30 | 1 | no | — |
| 490 | #41 | — | 30 | 1 | no | — |
| 491 | C2×Q8 | — | 3 | 1 | no | — |
| 492 | C2×Q8 | — | 3 | 1 | no | — |
| 493 | C2×Q8 | — | 6 | 1 | no | — |
| 494 | C2×D4 | — | 3 | 1 | no | — |
| 495 | C2×D4 | — | 3 | 1 | no | — |
| 496 | C2×D4 | — | 5 | 1 | no | — |
| 497 | C2×D4 | — | 6 | 1 | no | — |
| 498 | C2×D4 | — | 15 | 1 | no | — |
| 499 | C2×D4 | — | 15 | 1 | no | — |
| 500 | C2×D4 | — | 15 | 1 | no | — |
| 501 | C2×D4 | — | 15 | 1 | no | — |
| 502 | C2×D4 | — | 15 | 1 | no | — |
| 503 | C2×D4 | — | 15 | 1 | no | — |
| 504 | C2×D4 | — | 15 | 2 | no | — |
| 505 | C2×D4 | — | 15 | 1 | no | — |
| 506 | C2×D4 | — | 30 | 1 | no | — |
| 507 | C2×D4 | — | 30 | 1 | no | — |
| 508 | C2×D4 | — | 30 | 1 | no | — |
| 509 | C2×D4 | — | 30 | 1 | no | — |
| 510 | C2×D4 | — | 30 | 1 | no | — |
| 511 | C2×D4 | — | 30 | 1 | no | — |
| 512 | C2×D4 | — | 30 | 1 | no | — |
| 513 | C2×D4 | — | 30 | 1 | no | — |
| 514 | C2×D4 | — | 30 | 1 | no | — |
| 515 | C2×D4 | — | 30 | 2 | no | — |
| 516 | C2×D4 | — | 30 | 2 | no | — |
| 517 | C2×D4 | — | 30 | 1 | no | — |
| 518 | C2×D4 | — | 30 | 1 | no | — |
| 519 | C2×D4 | — | 30 | 1 | no | — |
| 520 | C2×D4 | — | 30 | 1 | no | — |
| 521 | C2×D4 | — | 30 | 1 | no | — |
| 522 | C22×C4 | — | 2 | 1 | no | — |
| 523 | C22×C4 | — | 5 | 1 | no | — |
| 524 | C22×C4 | — | 15 | 1 | no | — |
| 525 | C22×C4 | — | 15 | 1 | no | — |
| 526 | C22×C4 | — | 15 | 1 | no | — |
| 527 | C22×C4 | — | 15 | 1 | no | — |
| 528 | C22×C4 | — | 30 | 1 | no | — |
| 529 | C22×C4 | — | 30 | 1 | no | — |
| 530 | C22×C4 | — | 30 | 1 | no | — |
| 531 | C22×C4 | — | 30 | 1 | no | — |
| 532 | C22×C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 533 | SD16 | — | 3 | 2 | no | — |
| 534 | SD16 | — | 3 | 1 | no | — |
| 535 | SD16 | — | 3 | 1 | no | — |
| 536 | SD16 | — | 3 | 1 | no | — |
| 537 | SD16 | — | 5 | 1 | no | — |
| 538 | SD16 | — | 15 | 1 | no | — |
| 539 | SD16 | — | 15 | 1 | no | — |
| 540 | SD16 | — | 15 | 2 | no | — |
| 541 | SD16 | — | 15 | 1 | no | — |
| 542 | SD16 | D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 543 | D8 | — | 5 | 1 | no | — |
| 544 | D8 | — | 5 | 1 | no | — |
| 545 | D8 | — | 15 | 1 | no | — |
| 546 | D8 | — | 15 | 1 | no | — |
| 547 | D8 | — | 15 | 2 | no | — |
| 548 | D8 | — | 15 | 1 | no | — |
| 549 | D8 | — | 15 | 1 | no | — |
| 550 | D8 | — | 15 | 2 | no | — |
| 551 | D8 | — | 15 | 1 | no | — |
| 552 | D8 | — | 15 | 1 | no | — |
| 553 | M16 | — | 5 | 1 | no | — |
| 554 | M16 | — | 15 | 1 | no | — |
| 555 | M16 | — | 15 | 1 | no | — |
| 556 | M16 | — | 15 | 2 | no | — |
| 557 | M16 | — | 15 | 1 | no | — |
| 558 | C2×C8 | — | 3 | 1 | no | — |
| 559 | C2×C8 | — | 3 | 1 | no | — |
| 560 | C2×C8 | — | 15 | 1 | no | — |
| 561 | C2×C8 | — | 15 | 1 | no | — |
| 562 | C3×C5 | — | 4 | 1 | no | Hall |
| 563 | C22×C3 | — | 8 | 1 | no | — |
| 564 | C22×C3 | — | 20 | 1 | no | — |
| 565 | C22×C3 | — | 40 | 1 | no | — |
| 566 | C22×C3 | — | 40 | 1 | no | — |
| 567 | C22×C3 | — | 80 | 2 | no | — |
| 568 | A4 | #4060 | 1 | 1 | yes | characteristic, direct product factor |
| 569 | C3×C4 | — | 4 | 1 | no | — |
| 570 | C3×C4 | — | 8 | 1 | no | — |
| 571 | C3×C4 | — | 20 | 1 | no | — |
| 572 | C2×C5 | — | 3 | 1 | no | — |
| 573 | C2×C5 | — | 3 | 1 | no | — |
| 574 | C2×C5 | — | 4 | 1 | no | — |
| 575 | C2×C5 | — | 12 | 1 | no | — |
| 576 | C2×C5 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 577 | D5 | — | 2 | 1 | no | — |
| 578 | D5 | — | 4 | 1 | no | — |
| 579 | D5 | — | 4 | 1 | no | — |
| 580 | D5 | — | 6 | 1 | no | — |
| 581 | D5 | — | 12 | 1 | no | — |
| 582 | D5 | — | 12 | 1 | no | — |
| 583 | C23 | — | 4 | 1 | no | — |
| 584 | C23 | — | 6 | 1 | no | — |
| 585 | C23 | — | 6 | 1 | no | — |
| 586 | C23 | — | 10 | 1 | no | — |
| 587 | C23 | — | 10 | 1 | no | — |
| 588 | C23 | — | 12 | 1 | no | — |
| 589 | C23 | — | 15 | 1 | no | — |
| 590 | C23 | — | 15 | 1 | no | — |
| 591 | C23 | — | 20 | 1 | no | — |
| 592 | C23 | — | 20 | 1 | no | — |
| 593 | C23 | — | 30 | 1 | no | — |
| 594 | C23 | — | 30 | 1 | no | — |
| 595 | C23 | — | 30 | 1 | no | — |
| 596 | C23 | — | 30 | 1 | no | — |
| 597 | C23 | — | 30 | 1 | no | — |
| 598 | C23 | — | 30 | 1 | no | — |
| 599 | C23 | — | 30 | 1 | no | — |
| 600 | C23 | — | 30 | 1 | no | — |
| 601 | C23 | — | 30 | 2 | no | — |
| 602 | C23 | — | 60 | 1 | no | — |
| 603 | C23 | — | 60 | 1 | no | — |
| 604 | C23 | — | 60 | 2 | no | — |
| 605 | C23 | — | 60 | 2 | no | — |
| 606 | C23 | — | 60 | 2 | no | — |
| 607 | C23 | — | 60 | 2 | no | — |
| 608 | C23 | — | 60 | 2 | no | — |
| 609 | C23 | — | 60 | 2 | no | — |
| 610 | C23 | — | 60 | 2 | no | — |
| 611 | C23 | — | 60 | 2 | no | — |
| 612 | C23 | C3×D4×D5 | 1 | 1 | yes | characteristic |
| 613 | Q8 | — | 3 | 1 | no | — |
| 614 | Q8 | — | 6 | 1 | no | — |
| 615 | Q8 | — | 6 | 1 | no | — |
| 616 | Q8 | C2×D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 617 | D4 | — | 3 | 1 | no | — |
| 618 | D4 | — | 5 | 1 | no | — |
| 619 | D4 | — | 5 | 1 | no | — |
| 620 | D4 | — | 6 | 1 | no | — |
| 621 | D4 | — | 6 | 1 | no | — |
| 622 | D4 | — | 10 | 1 | no | — |
| 623 | D4 | — | 10 | 1 | no | — |
| 624 | D4 | — | 15 | 1 | no | — |
| 625 | D4 | — | 15 | 1 | no | — |
| 626 | D4 | — | 30 | 1 | no | — |
| 627 | D4 | — | 30 | 1 | no | — |
| 628 | D4 | — | 30 | 1 | no | — |
| 629 | D4 | — | 30 | 1 | no | — |
| 630 | D4 | — | 30 | 1 | no | — |
| 631 | D4 | — | 30 | 1 | no | — |
| 632 | D4 | — | 30 | 1 | no | — |
| 633 | D4 | — | 30 | 1 | no | — |
| 634 | D4 | — | 30 | 2 | no | — |
| 635 | D4 | — | 30 | 1 | no | — |
| 636 | D4 | — | 30 | 1 | no | — |
| 637 | D4 | — | 30 | 2 | no | — |
| 638 | D4 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | — | 3 | 1 | no | — |
| 640 | C2×C4 | — | 3 | 1 | no | — |
| 641 | C2×C4 | — | 5 | 1 | no | — |
| 642 | C2×C4 | — | 6 | 1 | no | — |
| 643 | C2×C4 | — | 6 | 1 | no | — |
| 644 | C2×C4 | — | 10 | 1 | no | — |
| 645 | C2×C4 | — | 15 | 1 | no | — |
| 646 | C2×C4 | — | 15 | 1 | no | — |
| 647 | C2×C4 | — | 15 | 2 | no | — |
| 648 | C2×C4 | — | 15 | 1 | no | — |
| 649 | C2×C4 | — | 15 | 1 | no | — |
| 650 | C2×C4 | — | 15 | 1 | no | — |
| 651 | C2×C4 | — | 30 | 1 | no | — |
| 652 | C2×C4 | — | 30 | 1 | no | — |
| 653 | C2×C4 | — | 30 | 1 | no | — |
| 654 | C2×C4 | — | 30 | 2 | no | — |
| 655 | C8 | — | 3 | 1 | no | — |
| 656 | C8 | — | 5 | 1 | no | — |
| 657 | C8 | — | 15 | 1 | no | — |
| 658 | C8 | C2×D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 659 | C2×C3 | — | 4 | 1 | no | — |
| 660 | C2×C3 | — | 16 | 1 | no | — |
| 661 | C2×C3 | — | 40 | 1 | no | — |
| 662 | C2×C3 | — | 80 | 1 | no | — |
| 663 | C2×C3 | — | 80 | 1 | no | — |
| 664 | C5 | A4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 665 | C22 | — | 2 | 1 | no | — |
| 666 | C22 | — | 3 | 1 | no | — |
| 667 | C22 | — | 3 | 1 | no | — |
| 668 | C22 | — | 5 | 1 | no | — |
| 669 | C22 | — | 6 | 1 | no | — |
| 670 | C22 | — | 10 | 1 | no | — |
| 671 | C22 | — | 10 | 1 | no | — |
| 672 | C22 | — | 12 | 1 | no | — |
| 673 | C22 | — | 12 | 1 | no | — |
| 674 | C22 | — | 12 | 1 | no | — |
| 675 | C22 | — | 12 | 1 | no | — |
| 676 | C22 | — | 15 | 1 | no | — |
| 677 | C22 | — | 20 | 2 | no | — |
| 678 | C22 | — | 30 | 1 | no | — |
| 679 | C22 | — | 30 | 1 | no | — |
| 680 | C22 | — | 30 | 1 | no | — |
| 681 | C22 | — | 30 | 1 | no | — |
| 682 | C22 | — | 30 | 1 | no | — |
| 683 | C22 | — | 30 | 1 | no | — |
| 684 | C22 | — | 60 | 1 | no | — |
| 685 | C22 | — | 60 | 1 | no | — |
| 686 | C22 | — | 60 | 1 | no | — |
| 687 | C22 | — | 60 | 1 | no | — |
| 688 | C22 | — | 60 | 1 | no | — |
| 689 | C22 | — | 60 | 1 | no | — |
| 690 | C22 | — | 60 | 1 | no | — |
| 691 | C22 | — | 60 | 1 | no | — |
| 692 | C22 | — | 60 | 2 | no | — |
| 693 | C22 | — | 60 | 2 | no | — |
| 694 | C22 | — | 60 | 2 | no | — |
| 695 | C22 | — | 60 | 4 | no | — |
| 696 | C22 | C3×#4060 | 1 | 1 | yes | characteristic, complemented |
| 697 | C4 | — | 2 | 1 | no | — |
| 698 | C4 | — | 3 | 1 | no | — |
| 699 | C4 | — | 5 | 1 | no | — |
| 700 | C4 | — | 6 | 1 | no | — |
| 701 | C4 | — | 15 | 1 | no | — |
| 702 | C4 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 703 | C3 | — | 4 | 1 | no | Sylow |
| 704 | C2 | — | 3 | 1 | no | — |
| 705 | C2 | — | 3 | 1 | no | — |
| 706 | C2 | — | 4 | 1 | no | — |
| 707 | C2 | — | 10 | 1 | no | — |
| 708 | C2 | — | 12 | 1 | no | — |
| 709 | C2 | — | 20 | 1 | no | — |
| 710 | C2 | — | 20 | 1 | no | — |
| 711 | C2 | — | 30 | 1 | no | — |
| 712 | C2 | — | 60 | 1 | no | — |
| 713 | C2 | — | 60 | 1 | no | — |
| 714 | C2 | D4×D5×A4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#713 | C2 | semidirect |
| 2. D4×D5×A4 | C2 | semidirect |
| 3. C5×A4×SD16 | C2 | semidirect |
| 4. A4×#688 | C2 | semidirect |
| 5. A4×#686 | C2 | semidirect |
| 6. A4×D40 | C2 | semidirect |
| 7. A4×#676 | C2 | semidirect |
| 8. C22×#4060 | C3 | semidirect |
| 10. C5×Q8×A4 | C22 | semidirect |
| 15. A4×D20 | C22 | semidirect |
| 19. C5×C8×A4 | C22 | semidirect |
| 20. A4×#168 | C22 | semidirect |
| 22. C22×#713 | C2×C3 | semidirect |
| 23. C22×D4×D5 | C2×C3 | semidirect |
| 24. C22×C5×SD16 | C2×C3 | semidirect |
| 25. C22×#688 | C2×C3 | semidirect |
| 26. C22×#686 | C2×C3 | semidirect |
| 35. C22×D40 | C2×C3 | semidirect |
| 36. C22×#676 | C2×C3 | semidirect |
| 55. A4×SD16 | D5 | semidirect |
| 60. C22×C5×Q8 | C22×C3 | semidirect |
| 77. C22×D20 | C22×C3 | semidirect |
| 84. C22×C5×C8 | C22×C3 | semidirect |
| 93. C22×#168 | C22×C3 | semidirect |
| 108. #4060 | A4 | direct (N × H) |
| 135. Q8×A4 | C2×D5 | semidirect |
| 145. C8×A4 | C2×D5 | semidirect |
| 179. #713 | C2×A4 | semidirect |
| 190. D4×D5 | C2×A4 | semidirect |
| 213. C5×SD16 | C2×A4 | semidirect |
| 220. #688 | C2×A4 | semidirect |
| 225. #686 | C2×A4 | semidirect |
| 232. D40 | C2×A4 | semidirect |
| 237. #676 | C2×A4 | semidirect |
| 249. C22×SD16 | C3×D5 | semidirect |
| 258. C5×A4 | AGL(1,ℤ/8) | semidirect |
| 310. C5×Q8 | C22×A4 | semidirect |
| 338. D20 | C22×A4 | semidirect |
| 350. C5×C8 | C22×A4 | semidirect |
| 352. #168 | C22×A4 | semidirect |
| 360. C22×Q8 | C2×C3×D5 | semidirect |
| 410. C22×C8 | C2×C3×D5 | semidirect |
| 440. C22×C5 | C3×AGL(1,ℤ/8) | semidirect |
| 542. SD16 | D5×A4 | semidirect |
| 568. A4 | #4060 | direct (N × H) |
| 616. Q8 | C2×D5×A4 | semidirect |
| 658. C8 | C2×D5×A4 | semidirect |
| 664. C5 | A4×AGL(1,ℤ/8) | semidirect |
| 696. C22 | C3×#4060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#713 | 2 |
| D4×D5×A4 | 2 |
| C5×A4×SD16 | 2 |
| A4×#688 | 2 |
| A4×#686 | 2 |
| A4×D40 | 2 |
| A4×#676 | 2 |
| C22×#4060 | 3 |
| C3×#4060 | 4 |
| A4×AGL(1,ℤ/8) | 5 |