Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
708 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 87 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 | C5×A4×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | A4×#709 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | A4×#686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×A4×#168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#4096 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 9 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C5×D4×A4 | — | 2 | 1 | no | — |
| 11 | C5×D4×A4 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C4×C5×A4 | — | 2 | 1 | no | — |
| 13 | C2×C4×C5×A4 | C22 | 1 | 1 | yes | characteristic |
| 14 | A4×C22⋊D5 | — | 2 | 1 | no | — |
| 15 | A4×D20 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×D5×A4 | — | 2 | 1 | no | — |
| 17 | A4×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#4096 | — | 4 | 1 | no | maximal |
| 19 | A4×#168 | C22 | 1 | 1 | yes | characteristic |
| 20 | A4×#168 | C22 | 1 | 1 | yes | characteristic |
| 21 | A4×#135 | — | 5 | 1 | no | maximal, Hall |
| 22 | C22×C5×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×#709 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#4096 | — | 3 | 1 | no | — |
| 25 | C2×#4096 | — | 3 | 1 | no | — |
| 26 | C2×#4096 | — | 3 | 1 | no | — |
| 27 | C2×#4096 | — | 3 | 1 | no | — |
| 28 | C2×#4096 | — | 3 | 1 | no | — |
| 29 | C2×#4096 | — | 3 | 1 | no | — |
| 30 | C2×#4096 | — | 3 | 1 | no | — |
| 31 | C2×#4096 | — | 3 | 1 | no | — |
| 32 | C22×#689 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | C22×#688 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C22×#687 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C22×#686 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C23×#168 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C22×C5×A4 | — | 2 | 1 | no | — |
| 38 | C22×C5×A4 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×D5×A4 | — | 2 | 1 | no | — |
| 40 | C3×C5×#41 | — | 4 | 1 | no | — |
| 41 | C3×#709 | — | 4 | 1 | no | — |
| 42 | C4×C5×A4 | — | 2 | 1 | no | — |
| 43 | C4×C5×A4 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 45 | A4×Dic5 | — | 2 | 1 | no | — |
| 46 | C3×#689 | — | 4 | 1 | no | — |
| 47 | C3×#688 | — | 4 | 1 | no | — |
| 48 | C3×#687 | — | 4 | 1 | no | — |
| 49 | C3×#686 | — | 4 | 1 | no | — |
| 50 | C2×C3×#168 | — | 4 | 1 | no | — |
| 51 | A4×#41 | — | 5 | 1 | no | — |
| 52 | A4×#41 | D5 | 1 | 1 | yes | characteristic, complemented |
| 53 | A4×Q16 | — | 5 | 1 | no | — |
| 54 | A4×SD16 | — | 5 | 1 | no | — |
| 55 | A4×SD16 | — | 5 | 1 | no | — |
| 56 | A4×D8 | — | 5 | 1 | no | — |
| 57 | C2×C8×A4 | — | 5 | 1 | no | — |
| 58 | C2×C5×#41 | — | 3 | 1 | no | — |
| 59 | C2×C5×#41 | — | 3 | 1 | no | — |
| 60 | C2×C5×#41 | — | 3 | 1 | no | — |
| 61 | C2×C5×#41 | — | 3 | 1 | no | — |
| 62 | C2×C5×#41 | — | 6 | 1 | no | — |
| 63 | C2×C5×#41 | — | 6 | 1 | no | — |
| 64 | C22×C5×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 65 | C22×C5×D4 | — | 2 | 1 | no | — |
| 66 | C22×C5×D4 | C22×C3 | 1 | 1 | yes | characteristic |
| 67 | C23×C4×C5 | — | 2 | 1 | no | — |
| 68 | C23×C4×C5 | C22×C3 | 1 | 1 | yes | characteristic |
| 69 | C22×C22⋊D5 | — | 2 | 1 | no | — |
| 70 | C2×#709 | — | 3 | 1 | no | — |
| 71 | C2×#709 | — | 3 | 1 | no | — |
| 72 | C2×#709 | — | 3 | 1 | no | — |
| 73 | C2×#709 | — | 3 | 1 | no | — |
| 74 | C2×#709 | — | 6 | 1 | no | — |
| 75 | C2×#709 | — | 6 | 1 | no | — |
| 76 | C22×D20 | C22×C3 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×D5 | — | 2 | 1 | no | — |
| 78 | C22×Dic10 | C22×C3 | 1 | 1 | yes | characteristic |
| 79 | #4096 | — | 3 | 2 | no | — |
| 80 | #4096 | — | 3 | 2 | no | — |
| 81 | #4096 | — | 3 | 2 | no | — |
| 82 | #4096 | — | 3 | 2 | no | — |
| 83 | #4096 | — | 3 | 2 | no | — |
| 84 | #4096 | — | 3 | 2 | no | — |
| 85 | #4096 | — | 3 | 2 | no | — |
| 86 | #4096 | — | 3 | 1 | no | — |
| 87 | #4096 | — | 3 | 1 | no | — |
| 88 | #4096 | — | 3 | 1 | no | — |
| 89 | #4096 | — | 3 | 1 | no | — |
| 90 | #4096 | — | 3 | 1 | no | — |
| 91 | #4096 | — | 3 | 1 | no | — |
| 92 | #4096 | — | 3 | 1 | no | — |
| 93 | #4096 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 94 | C2×#689 | — | 3 | 1 | no | — |
| 95 | C2×#689 | — | 3 | 1 | no | — |
| 96 | C2×#689 | — | 3 | 1 | no | — |
| 97 | C2×#689 | — | 3 | 1 | no | — |
| 98 | C2×#688 | — | 3 | 1 | no | — |
| 99 | C2×#688 | — | 3 | 1 | no | — |
| 100 | C2×#688 | — | 3 | 1 | no | — |
| 101 | C2×#688 | — | 3 | 1 | no | — |
| 102 | C2×#687 | — | 3 | 1 | no | — |
| 103 | C2×#687 | — | 3 | 1 | no | — |
| 104 | C2×#687 | — | 3 | 1 | no | — |
| 105 | C2×#687 | — | 3 | 1 | no | — |
| 106 | C2×#686 | — | 3 | 1 | no | — |
| 107 | C2×#686 | — | 3 | 1 | no | — |
| 108 | C2×#686 | — | 3 | 1 | no | — |
| 109 | C2×#686 | — | 3 | 1 | no | — |
| 110 | C22×#168 | — | 3 | 1 | no | — |
| 111 | C22×#168 | — | 3 | 1 | no | — |
| 112 | C22×#168 | — | 3 | 1 | no | — |
| 113 | C22×#168 | — | 3 | 1 | no | — |
| 114 | C22×#168 | C22×C3 | 1 | 1 | yes | characteristic |
| 115 | C22×#168 | C22×C3 | 1 | 1 | yes | characteristic |
| 116 | C22×#135 | — | 5 | 1 | no | Sylow |
| 117 | C2×C5×A4 | — | 2 | 1 | no | — |
| 118 | C2×C5×A4 | — | 4 | 1 | no | — |
| 119 | C2×C5×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | D5×A4 | — | 4 | 1 | no | — |
| 121 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 122 | C3×C5×D4 | — | 4 | 1 | no | — |
| 123 | C3×C5×D4 | — | 8 | 1 | no | — |
| 124 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 125 | C2×C3×C4×C5 | — | 8 | 1 | no | — |
| 126 | C3×C22⋊D5 | — | 8 | 1 | no | — |
| 127 | C3×D20 | — | 4 | 1 | no | — |
| 128 | C3×C4×D5 | — | 8 | 1 | no | — |
| 129 | C3×Dic10 | — | 4 | 1 | no | — |
| 130 | C3×#168 | — | 4 | 1 | no | — |
| 131 | C3×#168 | — | 4 | 1 | no | — |
| 132 | Q8×A4 | — | 5 | 1 | no | — |
| 133 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 134 | D4×A4 | — | 2 | 1 | no | — |
| 135 | D4×A4 | — | 5 | 1 | no | — |
| 136 | D4×A4 | — | 10 | 1 | no | — |
| 137 | D4×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×A4 | — | 2 | 1 | no | — |
| 139 | C2×C4×A4 | — | 10 | 1 | no | — |
| 140 | C2×C4×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 141 | C3×#135 | — | 20 | 1 | no | — |
| 142 | C8×A4 | — | 5 | 1 | no | — |
| 143 | C8×A4 | — | 5 | 1 | no | — |
| 144 | C24×C5 | — | 2 | 1 | no | — |
| 145 | C24×C5 | C3×D4 | 1 | 1 | yes | characteristic |
| 146 | C23×D5 | — | 2 | 1 | no | — |
| 147 | C5×#41 | — | 3 | 2 | no | — |
| 148 | C5×#41 | — | 3 | 1 | no | — |
| 149 | C5×#41 | — | 3 | 1 | no | — |
| 150 | C5×#41 | — | 3 | 1 | no | — |
| 151 | C5×#41 | — | 6 | 1 | no | — |
| 152 | C5×#41 | — | 6 | 1 | no | — |
| 153 | C5×#41 | — | 6 | 2 | no | — |
| 154 | C5×#41 | — | 6 | 2 | no | — |
| 155 | C5×#41 | — | 6 | 1 | no | — |
| 156 | C5×#41 | — | 6 | 1 | no | — |
| 157 | C5×#41 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 159 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 160 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 161 | C2×C5×D4 | — | 3 | 1 | no | — |
| 162 | C2×C5×D4 | — | 3 | 1 | no | — |
| 163 | C2×C5×D4 | — | 6 | 1 | no | — |
| 164 | C2×C5×D4 | — | 6 | 1 | no | — |
| 165 | C2×C5×D4 | — | 6 | 1 | no | — |
| 166 | C2×C5×D4 | — | 6 | 1 | no | — |
| 167 | C2×C5×D4 | — | 6 | 1 | no | — |
| 168 | C22×C4×C5 | — | 2 | 1 | no | — |
| 169 | C22×C4×C5 | — | 3 | 1 | no | — |
| 170 | C22×C4×C5 | — | 3 | 1 | no | — |
| 171 | C22×C4×C5 | — | 3 | 1 | no | — |
| 172 | C22×C4×C5 | — | 3 | 1 | no | — |
| 173 | C22×C4×C5 | — | 6 | 1 | no | — |
| 174 | C22×C4×C5 | — | 6 | 1 | no | — |
| 175 | C22×C4×C5 | — | 6 | 1 | no | — |
| 176 | C22×C4×C5 | — | 6 | 1 | no | — |
| 177 | C22×C4×C5 | C3×D4 | 1 | 1 | yes | characteristic |
| 178 | C22×C4×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 179 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 180 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 181 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 182 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 183 | C22×Dic5 | — | 2 | 1 | no | — |
| 184 | #709 | — | 3 | 2 | no | — |
| 185 | #709 | — | 3 | 1 | no | — |
| 186 | #709 | — | 3 | 1 | no | — |
| 187 | #709 | — | 3 | 1 | no | — |
| 188 | #709 | — | 6 | 1 | no | — |
| 189 | #709 | — | 6 | 1 | no | — |
| 190 | #709 | — | 6 | 2 | no | — |
| 191 | #709 | — | 6 | 2 | no | — |
| 192 | #709 | — | 6 | 1 | no | — |
| 193 | #709 | — | 6 | 1 | no | — |
| 194 | #709 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 195 | C2×D20 | — | 3 | 1 | no | — |
| 196 | C2×D20 | — | 3 | 1 | no | — |
| 197 | C2×D20 | — | 6 | 1 | no | — |
| 198 | C2×C4×D5 | — | 6 | 1 | no | — |
| 199 | C2×C4×D5 | — | 6 | 1 | no | — |
| 200 | C2×C4×D5 | — | 6 | 1 | no | — |
| 201 | C2×C4×D5 | — | 6 | 1 | no | — |
| 202 | C2×Dic10 | — | 3 | 1 | no | — |
| 203 | C2×Dic10 | — | 3 | 1 | no | — |
| 204 | C2×Dic10 | — | 6 | 1 | no | — |
| 205 | #689 | — | 3 | 2 | no | — |
| 206 | #689 | — | 3 | 1 | no | — |
| 207 | #689 | — | 3 | 1 | no | — |
| 208 | #689 | — | 3 | 1 | no | — |
| 209 | #689 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 210 | #688 | — | 3 | 2 | no | — |
| 211 | #688 | — | 3 | 1 | no | — |
| 212 | #688 | — | 3 | 1 | no | — |
| 213 | #688 | — | 3 | 1 | no | — |
| 214 | #688 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 215 | #687 | — | 3 | 2 | no | — |
| 216 | #687 | — | 3 | 1 | no | — |
| 217 | #687 | — | 3 | 1 | no | — |
| 218 | #687 | — | 3 | 1 | no | — |
| 219 | #687 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 220 | #686 | — | 3 | 2 | no | — |
| 221 | #686 | — | 3 | 1 | no | — |
| 222 | #686 | — | 3 | 1 | no | — |
| 223 | #686 | — | 3 | 1 | no | — |
| 224 | #686 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 225 | C2×#168 | — | 3 | 2 | no | — |
| 226 | C2×#168 | — | 3 | 1 | no | — |
| 227 | C2×#168 | — | 3 | 1 | no | — |
| 228 | C2×#168 | — | 3 | 1 | no | — |
| 229 | C2×#168 | — | 3 | 1 | no | — |
| 230 | C2×#168 | — | 3 | 1 | no | — |
| 231 | C2×#168 | — | 3 | 1 | no | — |
| 232 | C2×#168 | — | 3 | 1 | no | — |
| 233 | C2×#168 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 234 | C22×#41 | — | 5 | 1 | no | — |
| 235 | C22×#41 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 236 | C2×#135 | — | 15 | 1 | no | — |
| 237 | C2×#135 | — | 15 | 1 | no | — |
| 238 | C2×#135 | — | 15 | 1 | no | — |
| 239 | C2×#135 | — | 15 | 1 | no | — |
| 240 | C2×#135 | — | 15 | 1 | no | — |
| 241 | C2×#135 | — | 15 | 1 | no | — |
| 242 | C2×#135 | — | 15 | 1 | no | — |
| 243 | C2×#135 | — | 15 | 1 | no | — |
| 244 | C22×Q16 | — | 5 | 1 | no | — |
| 245 | C22×SD16 | — | 5 | 1 | no | — |
| 246 | C22×SD16 | — | 5 | 1 | no | — |
| 247 | C22×D8 | — | 5 | 1 | no | — |
| 248 | C23×C8 | — | 5 | 1 | no | — |
| 249 | C22×C3×C5 | — | 4 | 1 | no | — |
| 250 | C22×C3×C5 | — | 8 | 1 | no | — |
| 251 | C2×C3×D5 | — | 8 | 1 | no | — |
| 252 | C5×A4 | #135 | 1 | 1 | yes | characteristic, complemented |
| 253 | C3×C4×C5 | — | 4 | 1 | no | — |
| 254 | C3×C4×C5 | — | 4 | 1 | no | — |
| 255 | C3×C4×C5 | — | 8 | 1 | no | — |
| 256 | C3×Dic5 | — | 8 | 1 | no | — |
| 257 | C22×A4 | — | 2 | 1 | no | — |
| 258 | C22×A4 | — | 10 | 1 | no | — |
| 259 | C22×A4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 260 | C3×#41 | — | 4 | 1 | no | — |
| 261 | C3×#41 | — | 20 | 1 | no | — |
| 262 | C4×A4 | — | 2 | 1 | no | — |
| 263 | C4×A4 | — | 10 | 1 | no | — |
| 264 | C4×A4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 265 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 266 | C3×Q16 | — | 20 | 1 | no | — |
| 267 | C3×SD16 | — | 20 | 1 | no | — |
| 268 | C3×SD16 | — | 20 | 1 | no | — |
| 269 | C3×D8 | — | 20 | 1 | no | — |
| 270 | C2×C3×C8 | — | 20 | 1 | no | — |
| 271 | C23×C5 | — | 2 | 1 | no | — |
| 272 | C23×C5 | — | 3 | 1 | no | — |
| 273 | C23×C5 | — | 3 | 1 | no | — |
| 274 | C23×C5 | — | 4 | 1 | no | — |
| 275 | C23×C5 | — | 6 | 1 | no | — |
| 276 | C23×C5 | — | 6 | 1 | no | — |
| 277 | C23×C5 | — | 6 | 1 | no | — |
| 278 | C23×C5 | — | 12 | 1 | no | — |
| 279 | C23×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 280 | C22×D5 | — | 4 | 1 | no | — |
| 281 | C22×D5 | — | 6 | 1 | no | — |
| 282 | C22×D5 | — | 6 | 1 | no | — |
| 283 | C22×D5 | — | 12 | 1 | no | — |
| 284 | C5×Q8 | — | 3 | 1 | no | — |
| 285 | C5×Q8 | — | 6 | 1 | no | — |
| 286 | C5×Q8 | — | 6 | 1 | no | — |
| 287 | C5×Q8 | C22×A4 | 1 | 1 | yes | characteristic |
| 288 | C5×D4 | — | 2 | 1 | no | — |
| 289 | C5×D4 | — | 3 | 1 | no | — |
| 290 | C5×D4 | — | 6 | 1 | no | — |
| 291 | C5×D4 | — | 6 | 1 | no | — |
| 292 | C5×D4 | — | 6 | 1 | no | — |
| 293 | C5×D4 | — | 6 | 1 | no | — |
| 294 | C5×D4 | — | 6 | 2 | no | — |
| 295 | C5×D4 | — | 6 | 1 | no | — |
| 296 | C5×D4 | C22×A4 | 1 | 1 | yes | characteristic |
| 297 | C2×C4×C5 | — | 2 | 1 | no | — |
| 298 | C2×C4×C5 | — | 3 | 2 | no | — |
| 299 | C2×C4×C5 | — | 3 | 1 | no | — |
| 300 | C2×C4×C5 | — | 3 | 1 | no | — |
| 301 | C2×C4×C5 | — | 3 | 1 | no | — |
| 302 | C2×C4×C5 | — | 3 | 1 | no | — |
| 303 | C2×C4×C5 | — | 3 | 1 | no | — |
| 304 | C2×C4×C5 | — | 3 | 1 | no | — |
| 305 | C2×C4×C5 | — | 3 | 1 | no | — |
| 306 | C2×C4×C5 | — | 6 | 1 | no | — |
| 307 | C2×C4×C5 | — | 6 | 1 | no | — |
| 308 | C2×C4×C5 | — | 6 | 1 | no | — |
| 309 | C2×C4×C5 | — | 6 | 2 | no | — |
| 310 | C2×C4×C5 | — | 6 | 1 | no | — |
| 311 | C2×C4×C5 | — | 6 | 1 | no | — |
| 312 | C2×C4×C5 | C22×A4 | 1 | 1 | yes | characteristic |
| 313 | C22⋊D5 | — | 2 | 1 | no | — |
| 314 | C22⋊D5 | — | 6 | 1 | no | — |
| 315 | C22⋊D5 | — | 6 | 1 | no | — |
| 316 | C22⋊D5 | — | 6 | 2 | no | — |
| 317 | C22⋊D5 | — | 6 | 1 | no | — |
| 318 | C2×Dic5 | — | 6 | 1 | no | — |
| 319 | C2×Dic5 | — | 6 | 1 | no | — |
| 320 | D20 | — | 3 | 1 | no | — |
| 321 | D20 | — | 6 | 1 | no | — |
| 322 | D20 | — | 6 | 1 | no | — |
| 323 | D20 | C22×A4 | 1 | 1 | yes | characteristic |
| 324 | C4×D5 | — | 2 | 1 | no | — |
| 325 | C4×D5 | — | 6 | 1 | no | — |
| 326 | C4×D5 | — | 6 | 1 | no | — |
| 327 | C4×D5 | — | 6 | 2 | no | — |
| 328 | C4×D5 | — | 6 | 1 | no | — |
| 329 | Dic10 | — | 3 | 1 | no | — |
| 330 | Dic10 | — | 6 | 1 | no | — |
| 331 | Dic10 | — | 6 | 1 | no | — |
| 332 | Dic10 | C22×A4 | 1 | 1 | yes | characteristic |
| 333 | #168 | — | 3 | 1 | no | — |
| 334 | #168 | — | 3 | 1 | no | — |
| 335 | #168 | C22×A4 | 1 | 1 | yes | characteristic |
| 336 | #168 | C22×A4 | 1 | 1 | yes | characteristic |
| 337 | C2×#41 | — | 3 | 1 | no | — |
| 338 | C2×#41 | — | 3 | 1 | no | — |
| 339 | C2×#41 | — | 3 | 1 | no | — |
| 340 | C2×#41 | — | 3 | 1 | no | — |
| 341 | C2×#41 | — | 6 | 1 | no | — |
| 342 | C2×#41 | — | 6 | 1 | no | — |
| 343 | C2×#41 | — | 15 | 1 | no | — |
| 344 | C2×#41 | — | 15 | 1 | no | — |
| 345 | C2×#41 | — | 15 | 1 | no | — |
| 346 | C2×#41 | — | 15 | 1 | no | — |
| 347 | C2×#41 | — | 30 | 1 | no | — |
| 348 | C2×#41 | — | 30 | 1 | no | — |
| 349 | C22×Q8 | — | 5 | 1 | no | — |
| 350 | C22×Q8 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 351 | C22×D4 | — | 2 | 1 | no | — |
| 352 | C22×D4 | — | 5 | 1 | no | — |
| 353 | C22×D4 | — | 10 | 1 | no | — |
| 354 | C22×D4 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 355 | C23×C4 | — | 2 | 1 | no | — |
| 356 | C23×C4 | — | 10 | 1 | no | — |
| 357 | C23×C4 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 358 | #135 | — | 5 | 1 | no | — |
| 359 | #135 | — | 15 | 1 | no | — |
| 360 | #135 | — | 15 | 1 | no | — |
| 361 | #135 | — | 15 | 1 | no | — |
| 362 | #135 | — | 15 | 1 | no | — |
| 363 | #135 | — | 15 | 1 | no | — |
| 364 | #135 | — | 15 | 1 | no | — |
| 365 | #135 | — | 15 | 2 | no | — |
| 366 | #135 | — | 15 | 2 | no | — |
| 367 | #135 | — | 15 | 2 | no | — |
| 368 | #135 | — | 15 | 2 | no | — |
| 369 | #135 | — | 15 | 2 | no | — |
| 370 | #135 | — | 15 | 2 | no | — |
| 371 | #135 | — | 15 | 2 | no | — |
| 372 | #135 | — | 15 | 1 | no | — |
| 373 | C2×Q16 | — | 15 | 1 | no | — |
| 374 | C2×Q16 | — | 15 | 1 | no | — |
| 375 | C2×Q16 | — | 15 | 1 | no | — |
| 376 | C2×Q16 | — | 15 | 1 | no | — |
| 377 | C2×SD16 | — | 15 | 1 | no | — |
| 378 | C2×SD16 | — | 15 | 1 | no | — |
| 379 | C2×SD16 | — | 15 | 1 | no | — |
| 380 | C2×SD16 | — | 15 | 1 | no | — |
| 381 | C2×SD16 | — | 15 | 1 | no | — |
| 382 | C2×SD16 | — | 15 | 1 | no | — |
| 383 | C2×SD16 | — | 15 | 1 | no | — |
| 384 | C2×SD16 | — | 15 | 1 | no | — |
| 385 | C2×D8 | — | 15 | 1 | no | — |
| 386 | C2×D8 | — | 15 | 1 | no | — |
| 387 | C2×D8 | — | 15 | 1 | no | — |
| 388 | C2×D8 | — | 15 | 1 | no | — |
| 389 | C22×C8 | — | 5 | 1 | no | — |
| 390 | C22×C8 | — | 5 | 1 | no | — |
| 391 | C22×C8 | — | 15 | 1 | no | — |
| 392 | C22×C8 | — | 15 | 1 | no | — |
| 393 | C22×C8 | — | 15 | 1 | no | — |
| 394 | C22×C8 | — | 15 | 1 | no | — |
| 395 | C2×C3×C5 | — | 4 | 1 | no | — |
| 396 | C2×C3×C5 | — | 8 | 1 | no | — |
| 397 | C2×C3×C5 | — | 16 | 1 | no | — |
| 398 | C3×D5 | — | 16 | 1 | no | — |
| 399 | C2×A4 | — | 2 | 1 | no | — |
| 400 | C2×A4 | — | 4 | 1 | no | — |
| 401 | C2×A4 | — | 20 | 1 | no | — |
| 402 | C2×A4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 403 | C3×Q8 | — | 4 | 1 | no | — |
| 404 | C3×Q8 | — | 20 | 1 | no | — |
| 405 | C3×D4 | — | 4 | 1 | no | — |
| 406 | C3×D4 | — | 8 | 1 | no | — |
| 407 | C3×D4 | — | 20 | 1 | no | — |
| 408 | C3×D4 | — | 40 | 1 | no | — |
| 409 | C2×C3×C4 | — | 4 | 1 | no | — |
| 410 | C2×C3×C4 | — | 8 | 1 | no | — |
| 411 | C2×C3×C4 | — | 40 | 1 | no | — |
| 412 | C3×C8 | — | 20 | 1 | no | — |
| 413 | C3×C8 | — | 20 | 1 | no | — |
| 414 | C22×C5 | — | 2 | 1 | no | — |
| 415 | C22×C5 | — | 3 | 1 | no | — |
| 416 | C22×C5 | — | 3 | 1 | no | — |
| 417 | C22×C5 | — | 3 | 1 | no | — |
| 418 | C22×C5 | — | 6 | 1 | no | — |
| 419 | C22×C5 | — | 6 | 1 | no | — |
| 420 | C22×C5 | — | 6 | 1 | no | — |
| 421 | C22×C5 | — | 6 | 1 | no | — |
| 422 | C22×C5 | — | 6 | 1 | no | — |
| 423 | C22×C5 | — | 12 | 1 | no | — |
| 424 | C22×C5 | — | 12 | 1 | no | — |
| 425 | C22×C5 | — | 12 | 1 | no | — |
| 426 | C22×C5 | — | 12 | 1 | no | — |
| 427 | C22×C5 | C3×#135 | 1 | 1 | yes | characteristic, complemented |
| 428 | C22×C5 | D4×A4 | 1 | 1 | yes | characteristic |
| 429 | C2×D5 | — | 2 | 1 | no | — |
| 430 | C2×D5 | — | 6 | 1 | no | — |
| 431 | C2×D5 | — | 12 | 1 | no | — |
| 432 | C2×D5 | — | 12 | 1 | no | — |
| 433 | C2×D5 | — | 12 | 1 | no | — |
| 434 | C2×D5 | — | 12 | 1 | no | — |
| 435 | C4×C5 | — | 2 | 1 | no | — |
| 436 | C4×C5 | — | 3 | 1 | no | — |
| 437 | C4×C5 | — | 3 | 1 | no | — |
| 438 | C4×C5 | — | 6 | 1 | no | — |
| 439 | C4×C5 | D4×A4 | 1 | 1 | yes | characteristic |
| 440 | C4×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 441 | Dic5 | — | 2 | 1 | no | — |
| 442 | Dic5 | — | 6 | 1 | no | — |
| 443 | C24 | — | 2 | 1 | no | — |
| 444 | C24 | — | 10 | 1 | no | — |
| 445 | C24 | C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 446 | #41 | — | 3 | 2 | no | — |
| 447 | #41 | — | 3 | 1 | no | — |
| 448 | #41 | — | 3 | 1 | no | — |
| 449 | #41 | — | 3 | 1 | no | — |
| 450 | #41 | — | 5 | 1 | no | — |
| 451 | #41 | — | 6 | 1 | no | — |
| 452 | #41 | — | 6 | 1 | no | — |
| 453 | #41 | — | 6 | 2 | no | — |
| 454 | #41 | — | 6 | 2 | no | — |
| 455 | #41 | — | 6 | 1 | no | — |
| 456 | #41 | — | 6 | 1 | no | — |
| 457 | #41 | — | 15 | 1 | no | — |
| 458 | #41 | — | 15 | 1 | no | — |
| 459 | #41 | — | 15 | 2 | no | — |
| 460 | #41 | — | 15 | 1 | no | — |
| 461 | #41 | — | 30 | 1 | no | — |
| 462 | #41 | — | 30 | 1 | no | — |
| 463 | #41 | — | 30 | 2 | no | — |
| 464 | #41 | — | 30 | 2 | no | — |
| 465 | #41 | — | 30 | 1 | no | — |
| 466 | #41 | — | 30 | 1 | no | — |
| 467 | #41 | D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 468 | C2×Q8 | — | 3 | 1 | no | — |
| 469 | C2×Q8 | — | 3 | 1 | no | — |
| 470 | C2×Q8 | — | 6 | 1 | no | — |
| 471 | C2×Q8 | — | 15 | 1 | no | — |
| 472 | C2×Q8 | — | 15 | 1 | no | — |
| 473 | C2×Q8 | — | 30 | 1 | no | — |
| 474 | C2×D4 | — | 3 | 1 | no | — |
| 475 | C2×D4 | — | 3 | 1 | no | — |
| 476 | C2×D4 | — | 6 | 1 | no | — |
| 477 | C2×D4 | — | 6 | 1 | no | — |
| 478 | C2×D4 | — | 6 | 1 | no | — |
| 479 | C2×D4 | — | 6 | 1 | no | — |
| 480 | C2×D4 | — | 6 | 1 | no | — |
| 481 | C2×D4 | — | 15 | 1 | no | — |
| 482 | C2×D4 | — | 15 | 1 | no | — |
| 483 | C2×D4 | — | 30 | 1 | no | — |
| 484 | C2×D4 | — | 30 | 1 | no | — |
| 485 | C2×D4 | — | 30 | 1 | no | — |
| 486 | C2×D4 | — | 30 | 1 | no | — |
| 487 | C2×D4 | — | 30 | 1 | no | — |
| 488 | C22×C4 | — | 2 | 1 | no | — |
| 489 | C22×C4 | — | 3 | 1 | no | — |
| 490 | C22×C4 | — | 3 | 1 | no | — |
| 491 | C22×C4 | — | 3 | 1 | no | — |
| 492 | C22×C4 | — | 3 | 1 | no | — |
| 493 | C22×C4 | — | 6 | 1 | no | — |
| 494 | C22×C4 | — | 6 | 1 | no | — |
| 495 | C22×C4 | — | 6 | 1 | no | — |
| 496 | C22×C4 | — | 6 | 1 | no | — |
| 497 | C22×C4 | — | 10 | 1 | no | — |
| 498 | C22×C4 | — | 30 | 1 | no | — |
| 499 | C22×C4 | — | 30 | 1 | no | — |
| 500 | C22×C4 | — | 30 | 1 | no | — |
| 501 | C22×C4 | — | 30 | 1 | no | — |
| 502 | C22×C4 | C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 503 | C22×C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 504 | Q16 | — | 5 | 1 | no | — |
| 505 | Q16 | — | 15 | 1 | no | — |
| 506 | Q16 | — | 15 | 1 | no | — |
| 507 | Q16 | — | 15 | 2 | no | — |
| 508 | Q16 | — | 15 | 1 | no | — |
| 509 | SD16 | — | 5 | 1 | no | — |
| 510 | SD16 | — | 5 | 1 | no | — |
| 511 | SD16 | — | 15 | 1 | no | — |
| 512 | SD16 | — | 15 | 1 | no | — |
| 513 | SD16 | — | 15 | 1 | no | — |
| 514 | SD16 | — | 15 | 2 | no | — |
| 515 | SD16 | — | 15 | 1 | no | — |
| 516 | SD16 | — | 15 | 2 | no | — |
| 517 | SD16 | — | 15 | 1 | no | — |
| 518 | SD16 | — | 15 | 1 | no | — |
| 519 | D8 | — | 5 | 1 | no | — |
| 520 | D8 | — | 15 | 1 | no | — |
| 521 | D8 | — | 15 | 1 | no | — |
| 522 | D8 | — | 15 | 2 | no | — |
| 523 | D8 | — | 15 | 1 | no | — |
| 524 | C2×C8 | — | 5 | 1 | no | — |
| 525 | C2×C8 | — | 15 | 1 | no | — |
| 526 | C2×C8 | — | 15 | 1 | no | — |
| 527 | C2×C8 | — | 15 | 1 | no | — |
| 528 | C2×C8 | — | 15 | 1 | no | — |
| 529 | C2×C8 | — | 15 | 2 | no | — |
| 530 | C2×C8 | — | 15 | 1 | no | — |
| 531 | C2×C8 | — | 15 | 1 | no | — |
| 532 | C2×C8 | — | 15 | 1 | no | — |
| 533 | C3×C5 | — | 4 | 1 | no | Hall |
| 534 | C22×C3 | — | 4 | 1 | no | — |
| 535 | C22×C3 | — | 8 | 1 | no | — |
| 536 | C22×C3 | — | 40 | 1 | no | — |
| 537 | A4 | #4096 | 1 | 1 | yes | characteristic, direct product factor |
| 538 | C3×C4 | — | 4 | 1 | no | — |
| 539 | C3×C4 | — | 4 | 1 | no | — |
| 540 | C3×C4 | — | 8 | 1 | no | — |
| 541 | C3×C4 | — | 40 | 1 | no | — |
| 542 | C2×C5 | — | 2 | 1 | no | — |
| 543 | C2×C5 | — | 3 | 1 | no | — |
| 544 | C2×C5 | — | 3 | 1 | no | — |
| 545 | C2×C5 | — | 4 | 1 | no | — |
| 546 | C2×C5 | — | 6 | 1 | no | — |
| 547 | C2×C5 | — | 12 | 1 | no | — |
| 548 | C2×C5 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 549 | D5 | — | 4 | 1 | no | — |
| 550 | D5 | — | 12 | 1 | no | — |
| 551 | C23 | — | 2 | 1 | no | — |
| 552 | C23 | — | 3 | 1 | no | — |
| 553 | C23 | — | 3 | 1 | no | — |
| 554 | C23 | — | 4 | 1 | no | — |
| 555 | C23 | — | 6 | 1 | no | — |
| 556 | C23 | — | 6 | 1 | no | — |
| 557 | C23 | — | 6 | 1 | no | — |
| 558 | C23 | — | 12 | 1 | no | — |
| 559 | C23 | — | 20 | 1 | no | — |
| 560 | C23 | — | 30 | 1 | no | — |
| 561 | C23 | — | 30 | 1 | no | — |
| 562 | C23 | — | 60 | 1 | no | — |
| 563 | C23 | C2×C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 564 | Q8 | — | 3 | 1 | no | — |
| 565 | Q8 | — | 5 | 1 | no | — |
| 566 | Q8 | — | 6 | 1 | no | — |
| 567 | Q8 | — | 6 | 1 | no | — |
| 568 | Q8 | — | 15 | 1 | no | — |
| 569 | Q8 | — | 30 | 1 | no | — |
| 570 | Q8 | — | 30 | 1 | no | — |
| 571 | Q8 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 572 | D4 | — | 2 | 1 | no | — |
| 573 | D4 | — | 3 | 1 | no | — |
| 574 | D4 | — | 5 | 1 | no | — |
| 575 | D4 | — | 6 | 1 | no | — |
| 576 | D4 | — | 6 | 1 | no | — |
| 577 | D4 | — | 6 | 1 | no | — |
| 578 | D4 | — | 6 | 1 | no | — |
| 579 | D4 | — | 6 | 2 | no | — |
| 580 | D4 | — | 6 | 1 | no | — |
| 581 | D4 | — | 10 | 1 | no | — |
| 582 | D4 | — | 15 | 1 | no | — |
| 583 | D4 | — | 30 | 1 | no | — |
| 584 | D4 | — | 30 | 1 | no | — |
| 585 | D4 | — | 30 | 1 | no | — |
| 586 | D4 | — | 30 | 1 | no | — |
| 587 | D4 | — | 30 | 2 | no | — |
| 588 | D4 | — | 30 | 1 | no | — |
| 589 | D4 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 590 | C2×C4 | — | 2 | 1 | no | — |
| 591 | C2×C4 | — | 3 | 2 | no | — |
| 592 | C2×C4 | — | 3 | 1 | no | — |
| 593 | C2×C4 | — | 3 | 1 | no | — |
| 594 | C2×C4 | — | 3 | 1 | no | — |
| 595 | C2×C4 | — | 3 | 1 | no | — |
| 596 | C2×C4 | — | 3 | 1 | no | — |
| 597 | C2×C4 | — | 3 | 1 | no | — |
| 598 | C2×C4 | — | 3 | 1 | no | — |
| 599 | C2×C4 | — | 6 | 1 | no | — |
| 600 | C2×C4 | — | 6 | 1 | no | — |
| 601 | C2×C4 | — | 6 | 1 | no | — |
| 602 | C2×C4 | — | 6 | 2 | no | — |
| 603 | C2×C4 | — | 6 | 1 | no | — |
| 604 | C2×C4 | — | 6 | 1 | no | — |
| 605 | C2×C4 | — | 10 | 1 | no | — |
| 606 | C2×C4 | — | 30 | 1 | no | — |
| 607 | C2×C4 | — | 30 | 1 | no | — |
| 608 | C2×C4 | — | 30 | 2 | no | — |
| 609 | C2×C4 | — | 30 | 1 | no | — |
| 610 | C2×C4 | — | 30 | 1 | no | — |
| 611 | C2×C4 | — | 30 | 1 | no | — |
| 612 | C2×C4 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 613 | C8 | — | 5 | 1 | no | — |
| 614 | C8 | — | 5 | 1 | no | — |
| 615 | C8 | — | 15 | 1 | no | — |
| 616 | C8 | — | 15 | 1 | no | — |
| 617 | C2×C3 | — | 4 | 1 | no | — |
| 618 | C2×C3 | — | 8 | 1 | no | — |
| 619 | C2×C3 | — | 16 | 1 | no | — |
| 620 | C2×C3 | — | 80 | 1 | no | — |
| 621 | C5 | A4×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 622 | C22 | — | 2 | 1 | no | — |
| 623 | C22 | — | 3 | 1 | no | — |
| 624 | C22 | — | 3 | 1 | no | — |
| 625 | C22 | — | 3 | 1 | no | — |
| 626 | C22 | — | 6 | 1 | no | — |
| 627 | C22 | — | 6 | 1 | no | — |
| 628 | C22 | — | 6 | 1 | no | — |
| 629 | C22 | — | 6 | 1 | no | — |
| 630 | C22 | — | 6 | 1 | no | — |
| 631 | C22 | — | 10 | 1 | no | — |
| 632 | C22 | — | 12 | 1 | no | — |
| 633 | C22 | — | 12 | 1 | no | — |
| 634 | C22 | — | 12 | 1 | no | — |
| 635 | C22 | — | 12 | 1 | no | — |
| 636 | C22 | — | 30 | 1 | no | — |
| 637 | C22 | — | 60 | 1 | no | — |
| 638 | C22 | — | 60 | 1 | no | — |
| 639 | C22 | — | 60 | 1 | no | — |
| 640 | C22 | — | 60 | 1 | no | — |
| 641 | C22 | C3×#4096 | 1 | 1 | yes | characteristic, complemented |
| 642 | C22 | A4×C22⋊D5 | 1 | 1 | yes | characteristic |
| 643 | C4 | — | 2 | 1 | no | — |
| 644 | C4 | — | 3 | 1 | no | — |
| 645 | C4 | — | 3 | 1 | no | — |
| 646 | C4 | — | 6 | 1 | no | — |
| 647 | C4 | — | 10 | 1 | no | — |
| 648 | C4 | — | 30 | 1 | no | — |
| 649 | C4 | A4×C22⋊D5 | 1 | 1 | yes | characteristic |
| 650 | C4 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 651 | C3 | — | 4 | 1 | no | Sylow |
| 652 | C2 | — | 2 | 1 | no | — |
| 653 | C2 | — | 3 | 1 | no | — |
| 654 | C2 | — | 3 | 1 | no | — |
| 655 | C2 | — | 4 | 1 | no | — |
| 656 | C2 | — | 6 | 1 | no | — |
| 657 | C2 | — | 12 | 1 | no | — |
| 658 | C2 | — | 20 | 1 | no | — |
| 659 | C2 | — | 60 | 1 | no | — |
| 660 | C2 | C2×A4×C22⋊D5 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×A4×#41 | C2 | semidirect |
| 2. A4×#709 | C2 | semidirect |
| 3. A4×#689 | C2 | semidirect |
| 4. A4×#688 | C2 | semidirect |
| 5. A4×#687 | C2 | semidirect |
| 6. A4×#686 | C2 | semidirect |
| 7. C2×A4×#168 | C2 | semidirect |
| 8. C22×#4096 | C3 | semidirect |
| 22. C22×C5×#41 | C2×C3 | semidirect |
| 23. C22×#709 | C2×C3 | semidirect |
| 32. C22×#689 | C2×C3 | semidirect |
| 33. C22×#688 | C2×C3 | semidirect |
| 34. C22×#687 | C2×C3 | semidirect |
| 35. C22×#686 | C2×C3 | semidirect |
| 36. C23×#168 | C2×C3 | semidirect |
| 52. A4×#41 | D5 | semidirect |
| 93. #4096 | A4 | direct (N × H) |
| 157. C5×#41 | C2×A4 | semidirect |
| 194. #709 | C2×A4 | semidirect |
| 209. #689 | C2×A4 | semidirect |
| 214. #688 | C2×A4 | semidirect |
| 219. #687 | C2×A4 | semidirect |
| 224. #686 | C2×A4 | semidirect |
| 233. C2×#168 | C2×A4 | semidirect |
| 235. C22×#41 | C3×D5 | semidirect |
| 252. C5×A4 | #135 | semidirect |
| 427. C22×C5 | C3×#135 | semidirect |
| 467. #41 | D5×A4 | semidirect |
| 537. A4 | #4096 | direct (N × H) |
| 621. C5 | A4×#135 | semidirect |
| 641. C22 | C3×#4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| A4×#709 | 2 |
| A4×#689 | 2 |
| A4×#688 | 2 |
| A4×#687 | 2 |
| A4×#686 | 2 |
| C2×A4×#168 | 2 |
| C22×#4096 | 3 |
| C3×#4096 | 4 |
| A4×#135 | 5 |