Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #11754644 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11750839 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11748793 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11748553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#4470 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11745959 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10599079 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×Dic30 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×D5×#67 | — | 2 | 1 | no | — |
| 11 | #91819 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#6706 | — | 2 | 1 | no | — |
| 13 | C5×#930 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×#685 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91566 | — | 2 | 1 | no | — |
| 16 | C2×#6665 | — | 2 | 1 | no | — |
| 17 | #91476 | — | 2 | 1 | no | — |
| 18 | #91475 | — | 2 | 1 | no | — |
| 19 | #91414 | — | 2 | 1 | no | — |
| 20 | #91413 | — | 2 | 1 | no | — |
| 21 | C2×#6659 | — | 2 | 1 | no | — |
| 22 | C3×C5×C22⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #91100 | — | 2 | 1 | no | — |
| 24 | C5×C3⋊#95 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×C22⋊#168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #90994 | — | 2 | 1 | no | — |
| 27 | #90975 | — | 2 | 1 | no | — |
| 28 | #68108 | — | 5 | 1 | no | maximal, Hall |
| 29 | #65939 | — | 3 | 1 | no | — |
| 30 | #65329 | — | 3 | 1 | no | — |
| 31 | #65027 | — | 3 | 1 | no | — |
| 32 | #64962 | — | 3 | 1 | no | — |
| 33 | C5×#327 | — | 3 | 1 | no | — |
| 34 | #64688 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | #64671 | — | 3 | 1 | no | — |
| 36 | C23×C3×D5 | D4 | 1 | 1 | yes | characteristic |
| 37 | C22×D3×D5 | — | 2 | 1 | no | — |
| 38 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×#1220 | — | 2 | 1 | no | — |
| 40 | C22×Dic15 | — | 2 | 1 | no | — |
| 41 | C2×D60 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×Dic30 | — | 2 | 1 | no | — |
| 43 | C2×Dic30 | — | 2 | 1 | no | — |
| 44 | C2×Dic30 | — | 4 | 2 | no | — |
| 45 | C2×C5×#67 | — | 2 | 1 | no | — |
| 46 | C22×C5×Dic3 | — | 2 | 1 | no | — |
| 47 | C2×C5×D12 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×C3×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 49 | D5×#67 | — | 4 | 2 | no | — |
| 50 | D5×#67 | — | 4 | 2 | no | — |
| 51 | C2×#1203 | — | 2 | 1 | no | — |
| 52 | C2×#1202 | — | 2 | 1 | no | — |
| 53 | C2×#1201 | — | 2 | 1 | no | — |
| 54 | C2×D5×Dic3 | — | 2 | 1 | no | — |
| 55 | C2×C3×C5×C8 | — | 2 | 1 | no | — |
| 56 | #6714 | — | 2 | 1 | no | — |
| 57 | C4⋊Dic15 | D4 | 1 | 1 | yes | characteristic |
| 58 | #6706 | — | 4 | 2 | no | — |
| 59 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 60 | C5×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 61 | C3×#685 | — | 2 | 1 | no | — |
| 62 | C3×#685 | — | 2 | 1 | no | — |
| 63 | C2×C3×#168 | — | 2 | 1 | no | — |
| 64 | #6668 | — | 2 | 1 | no | — |
| 65 | #6667 | — | 2 | 1 | no | — |
| 66 | (C2×D3)⋊Dic5 | — | 2 | 1 | no | — |
| 67 | #6665 | — | 4 | 2 | no | — |
| 68 | #6659 | — | 4 | 2 | no | — |
| 69 | #5493 | — | 5 | 1 | no | — |
| 70 | #4947 | — | 5 | 1 | no | — |
| 71 | #4738 | — | 5 | 1 | no | — |
| 72 | #4738 | — | 5 | 1 | no | — |
| 73 | C3×#323 | — | 5 | 1 | no | — |
| 74 | #4470 | — | 5 | 1 | no | — |
| 75 | #4470 | D5 | 1 | 1 | yes | characteristic, complemented |
| 76 | C2×D4×D5 | — | 6 | 1 | no | — |
| 77 | C22×Dic10 | — | 3 | 1 | no | — |
| 78 | C5×#121 | — | 3 | 1 | no | — |
| 79 | #4085 | — | 6 | 1 | no | — |
| 80 | #4083 | — | 6 | 1 | no | — |
| 81 | C2×#687 | — | 6 | 1 | no | — |
| 82 | #4076 | — | 3 | 1 | no | — |
| 83 | C2×#685 | — | 6 | 1 | no | — |
| 84 | C2×#685 | C2×D3 | 1 | 1 | yes | characteristic |
| 85 | C2×#677 | — | 6 | 1 | no | — |
| 86 | #4040 | — | 6 | 1 | no | — |
| 87 | #4029 | — | 6 | 1 | no | — |
| 88 | #4028 | — | 6 | 1 | no | — |
| 89 | C5×C22⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 90 | C5×#95 | — | 3 | 1 | no | — |
| 91 | #3963 | — | 6 | 1 | no | — |
| 92 | C22⋊#168 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | #3948 | — | 6 | 1 | no | — |
| 94 | #3942 | — | 6 | 1 | no | — |
| 95 | #1601 | — | 15 | 1 | no | Sylow |
| 96 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×D15 | — | 2 | 1 | no | — |
| 98 | C22×C5×D3 | — | 2 | 1 | no | — |
| 99 | C22×C3×D5 | — | 2 | 1 | no | — |
| 100 | C22×C3×D5 | — | 2 | 1 | no | — |
| 101 | C22×C3×D5 | — | 4 | 1 | no | — |
| 102 | C22×C3×D5 | — | 4 | 1 | no | — |
| 103 | C22×C3×D5 | SD16 | 1 | 2 | yes | complemented |
| 104 | C2×D3×D5 | — | 4 | 2 | no | — |
| 105 | C2×D3×D5 | — | 8 | 1 | no | — |
| 106 | C2×D3×D5 | — | 8 | 1 | no | — |
| 107 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 108 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | #1220 | — | 4 | 1 | no | — |
| 111 | #1220 | — | 4 | 1 | no | — |
| 112 | C2×Dic15 | — | 2 | 2 | no | — |
| 113 | C2×Dic15 | — | 2 | 1 | no | — |
| 114 | C2×Dic15 | — | 4 | 1 | no | — |
| 115 | C2×Dic15 | — | 4 | 1 | no | — |
| 116 | D60 | — | 4 | 1 | no | — |
| 117 | Dic30 | — | 2 | 2 | no | — |
| 118 | Dic30 | — | 2 | 2 | no | — |
| 119 | Dic30 | — | 4 | 1 | no | — |
| 120 | Dic30 | — | 4 | 1 | no | — |
| 121 | C5×#67 | — | 4 | 1 | no | — |
| 122 | C5×#67 | — | 4 | 1 | no | — |
| 123 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 124 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 125 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 126 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 127 | C5×D12 | — | 4 | 1 | no | — |
| 128 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 129 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 130 | #1203 | — | 8 | 1 | no | — |
| 131 | #1202 | — | 4 | 2 | no | — |
| 132 | #1201 | — | 4 | 2 | no | — |
| 133 | D5×Dic3 | — | 4 | 2 | no | — |
| 134 | C3×C5×C8 | — | 4 | 1 | no | — |
| 135 | C3×#168 | — | 4 | 1 | no | — |
| 136 | C22×#67 | — | 10 | 1 | no | — |
| 137 | C22×Dic6 | — | 5 | 1 | no | — |
| 138 | C2×C3×C22⋊C4 | — | 5 | 1 | no | — |
| 139 | C2×#217 | — | 10 | 1 | no | — |
| 140 | #930 | — | 5 | 1 | no | — |
| 141 | #930 | — | 10 | 1 | no | — |
| 142 | #930 | C2×D5 | 1 | 1 | yes | characteristic |
| 143 | C2×#204 | — | 10 | 1 | no | — |
| 144 | C2×#204 | — | 10 | 1 | no | — |
| 145 | #886 | — | 10 | 1 | no | — |
| 146 | #886 | — | 10 | 1 | no | — |
| 147 | #882 | — | 10 | 1 | no | — |
| 148 | #882 | — | 10 | 1 | no | — |
| 149 | C3×C22⋊C8 | — | 5 | 1 | no | — |
| 150 | C3×C22⋊C8 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 151 | C3⋊#95 | — | 10 | 1 | no | — |
| 152 | C3⋊#95 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 153 | #816 | — | 10 | 1 | no | — |
| 154 | #816 | — | 10 | 1 | no | — |
| 155 | C23×D5 | — | 6 | 1 | no | — |
| 156 | C23×D5 | D12 | 1 | 1 | yes | characteristic |
| 157 | C2×C5×D4 | — | 3 | 1 | no | — |
| 158 | C2×C5×D4 | — | 6 | 1 | no | — |
| 159 | C22×C4×C5 | — | 6 | 1 | no | — |
| 160 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 161 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 162 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 163 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 164 | C22×Dic5 | — | 6 | 1 | no | — |
| 165 | C22×Dic5 | D12 | 1 | 1 | yes | characteristic |
| 166 | D4×D5 | — | 12 | 2 | no | — |
| 167 | D4×D5 | — | 12 | 2 | no | — |
| 168 | C2×D20 | — | 3 | 1 | no | — |
| 169 | C2×D20 | — | 6 | 1 | no | — |
| 170 | C2×C4×D5 | — | 6 | 1 | no | — |
| 171 | C2×Dic10 | — | 6 | 1 | no | — |
| 172 | C2×Dic10 | — | 6 | 1 | no | — |
| 173 | C2×Dic10 | — | 12 | 2 | no | — |
| 174 | C2×C5×C8 | — | 2 | 1 | no | — |
| 175 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 176 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 177 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 178 | #687 | — | 12 | 2 | no | — |
| 179 | #685 | — | 2 | 1 | no | — |
| 180 | #685 | — | 2 | 1 | no | — |
| 181 | #685 | — | 6 | 1 | no | — |
| 182 | #685 | — | 6 | 1 | no | — |
| 183 | #685 | — | 12 | 2 | no | — |
| 184 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 185 | #683 | — | 6 | 1 | no | — |
| 186 | C2×#168 | — | 2 | 1 | no | — |
| 187 | #677 | — | 12 | 2 | no | — |
| 188 | #534 | — | 15 | 1 | no | — |
| 189 | #448 | — | 15 | 1 | no | — |
| 190 | #448 | — | 15 | 1 | no | — |
| 191 | #393 | — | 15 | 1 | no | — |
| 192 | #327 | — | 3 | 1 | no | — |
| 193 | #327 | — | 15 | 1 | no | — |
| 194 | #323 | — | 5 | 1 | no | — |
| 195 | C22×C3×C5 | — | 2 | 1 | no | — |
| 196 | C22×C3×C5 | — | 2 | 1 | no | — |
| 197 | C22×C3×C5 | #120 | 1 | 1 | yes | characteristic |
| 198 | C22×C3×C5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 199 | C22×C3×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 200 | C2×D15 | — | 4 | 1 | no | — |
| 201 | C2×D15 | — | 4 | 1 | no | — |
| 202 | C2×D15 | — | 4 | 1 | no | — |
| 203 | C2×C5×D3 | — | 4 | 1 | no | — |
| 204 | C2×C5×D3 | — | 4 | 1 | no | — |
| 205 | C2×C5×D3 | — | 4 | 1 | no | — |
| 206 | C2×C3×D5 | — | 2 | 2 | no | — |
| 207 | C2×C3×D5 | — | 4 | 1 | no | — |
| 208 | C2×C3×D5 | — | 4 | 1 | no | — |
| 209 | C2×C3×D5 | — | 4 | 2 | no | — |
| 210 | C2×C3×D5 | — | 8 | 1 | no | — |
| 211 | D3×D5 | — | 8 | 4 | no | — |
| 212 | C3×C4×C5 | — | 2 | 1 | no | — |
| 213 | C3×C4×C5 | — | 2 | 1 | no | — |
| 214 | Dic15 | — | 4 | 1 | no | — |
| 215 | Dic15 | — | 4 | 2 | no | — |
| 216 | C3×Dic5 | — | 4 | 1 | no | — |
| 217 | C5×Dic3 | — | 4 | 1 | no | — |
| 218 | C5×Dic3 | — | 8 | 1 | no | — |
| 219 | C24×C3 | — | 5 | 1 | no | — |
| 220 | C23×D3 | — | 10 | 1 | no | — |
| 221 | C22×C3×C4 | — | 5 | 1 | no | — |
| 222 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 223 | C2×#67 | — | 2 | 1 | no | — |
| 224 | C2×#67 | — | 10 | 1 | no | — |
| 225 | C2×#67 | — | 10 | 1 | no | — |
| 226 | C2×#67 | — | 10 | 1 | no | — |
| 227 | C2×#67 | — | 20 | 2 | no | — |
| 228 | C2×#67 | — | 20 | 2 | no | — |
| 229 | C22×Dic3 | — | 2 | 1 | no | — |
| 230 | C22×Dic3 | — | 10 | 1 | no | — |
| 231 | C22×Dic3 | — | 10 | 1 | no | — |
| 232 | C2×D12 | — | 5 | 1 | no | — |
| 233 | C2×D12 | — | 10 | 1 | no | — |
| 234 | C2×D12 | D20 | 1 | 1 | yes | characteristic |
| 235 | C2×Dic6 | — | 10 | 1 | no | — |
| 236 | C2×Dic6 | — | 10 | 1 | no | — |
| 237 | C2×Dic6 | — | 20 | 2 | no | — |
| 238 | C2×C3×C8 | — | 2 | 1 | no | — |
| 239 | C2×C3×C8 | — | 10 | 1 | no | — |
| 240 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 241 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 242 | #217 | — | 20 | 2 | no | — |
| 243 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 244 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 245 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 246 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 247 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 248 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 249 | C4⋊Dic3 | D20 | 1 | 1 | yes | characteristic |
| 250 | #204 | — | 20 | 2 | no | — |
| 251 | #204 | — | 20 | 2 | no | — |
| 252 | C23×C5 | — | 6 | 1 | no | — |
| 253 | C23×C5 | C2×D12 | 1 | 1 | yes | characteristic |
| 254 | C22×D5 | — | 2 | 1 | no | — |
| 255 | C22×D5 | — | 2 | 1 | no | — |
| 256 | C22×D5 | — | 4 | 1 | no | — |
| 257 | C22×D5 | — | 4 | 1 | no | — |
| 258 | C22×D5 | — | 6 | 1 | no | — |
| 259 | C22×D5 | — | 12 | 2 | no | — |
| 260 | C22×D5 | — | 24 | 1 | no | — |
| 261 | C22×D5 | — | 24 | 1 | no | — |
| 262 | C22×D5 | #204 | 1 | 2 | yes | complemented |
| 263 | C5×D4 | — | 12 | 1 | no | — |
| 264 | C5×D4 | — | 12 | 1 | no | — |
| 265 | C5×D4 | — | 12 | 1 | no | — |
| 266 | C2×C4×C5 | — | 4 | 1 | no | — |
| 267 | C2×C4×C5 | — | 6 | 1 | no | — |
| 268 | C2×C4×C5 | — | 12 | 1 | no | — |
| 269 | C2×C4×C5 | — | 12 | 1 | no | — |
| 270 | C2×C4×C5 | — | 12 | 1 | no | — |
| 271 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 273 | C22⋊D5 | — | 12 | 2 | no | — |
| 274 | C22⋊D5 | — | 12 | 1 | no | — |
| 275 | C22⋊D5 | — | 12 | 1 | no | — |
| 276 | C22⋊D5 | — | 24 | 1 | no | — |
| 277 | C2×Dic5 | — | 2 | 1 | no | — |
| 278 | C2×Dic5 | — | 4 | 1 | no | — |
| 279 | C2×Dic5 | — | 6 | 2 | no | — |
| 280 | C2×Dic5 | — | 6 | 1 | no | — |
| 281 | C2×Dic5 | — | 12 | 1 | no | — |
| 282 | C2×Dic5 | — | 12 | 1 | no | — |
| 283 | D20 | — | 12 | 1 | no | — |
| 284 | D20 | — | 12 | 2 | no | — |
| 285 | C4×D5 | — | 12 | 2 | no | — |
| 286 | Dic10 | — | 6 | 2 | no | — |
| 287 | Dic10 | — | 6 | 2 | no | — |
| 288 | Dic10 | — | 12 | 1 | no | — |
| 289 | Dic10 | — | 12 | 1 | no | — |
| 290 | C5×C8 | — | 4 | 1 | no | — |
| 291 | #168 | — | 4 | 1 | no | — |
| 292 | C22×Q8 | — | 15 | 1 | no | — |
| 293 | C22×D4 | — | 30 | 1 | no | — |
| 294 | C2×SD16 | — | 30 | 1 | no | — |
| 295 | C2×SD16 | — | 30 | 1 | no | — |
| 296 | #123 | — | 30 | 1 | no | — |
| 297 | #123 | — | 30 | 1 | no | — |
| 298 | #121 | — | 3 | 1 | no | — |
| 299 | #121 | — | 15 | 1 | no | — |
| 300 | #121 | — | 30 | 1 | no | — |
| 301 | #120 | — | 30 | 1 | no | — |
| 302 | #120 | — | 30 | 1 | no | — |
| 303 | C2×C22⋊C4 | — | 5 | 1 | no | — |
| 304 | C2×C22⋊C4 | — | 30 | 1 | no | — |
| 305 | #103 | — | 30 | 1 | no | — |
| 306 | #103 | — | 30 | 1 | no | — |
| 307 | C22⋊C8 | — | 5 | 1 | no | — |
| 308 | C22⋊C8 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 309 | #95 | — | 3 | 1 | no | — |
| 310 | #95 | — | 30 | 1 | no | — |
| 311 | C2×C3×C5 | — | 2 | 1 | no | — |
| 312 | C2×C3×C5 | — | 2 | 1 | no | — |
| 313 | C2×C3×C5 | #450 | 1 | 1 | yes | characteristic |
| 314 | C2×C3×C5 | #455 | 1 | 1 | yes | characteristic |
| 315 | C2×C3×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 316 | D15 | — | 8 | 1 | no | — |
| 317 | C3×D5 | — | 4 | 2 | no | — |
| 318 | C5×D3 | — | 8 | 1 | no | — |
| 319 | C23×C3 | — | 5 | 2 | no | — |
| 320 | C23×C3 | — | 10 | 1 | no | — |
| 321 | C23×C3 | — | 10 | 1 | no | — |
| 322 | C23×C3 | — | 20 | 1 | no | — |
| 323 | C23×C3 | — | 20 | 1 | no | — |
| 324 | C23×C3 | D4×D5 | 1 | 1 | yes | characteristic |
| 325 | C22×D3 | — | 2 | 1 | no | — |
| 326 | C22×D3 | — | 10 | 1 | no | — |
| 327 | C22×D3 | — | 20 | 2 | no | — |
| 328 | C22×D3 | — | 40 | 1 | no | — |
| 329 | C22×D3 | — | 40 | 1 | no | — |
| 330 | C2×C3×C4 | — | 4 | 1 | no | — |
| 331 | C2×C3×C4 | — | 10 | 1 | no | — |
| 332 | C2×C3×C4 | — | 20 | 1 | no | — |
| 333 | C2×C3×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 334 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 335 | #67 | — | 4 | 1 | no | — |
| 336 | #67 | — | 4 | 1 | no | — |
| 337 | #67 | — | 20 | 2 | no | — |
| 338 | #67 | — | 20 | 2 | no | — |
| 339 | #67 | — | 20 | 1 | no | — |
| 340 | #67 | — | 20 | 1 | no | — |
| 341 | C2×Dic3 | — | 2 | 1 | no | — |
| 342 | C2×Dic3 | — | 4 | 1 | no | — |
| 343 | C2×Dic3 | — | 4 | 1 | no | — |
| 344 | C2×Dic3 | — | 4 | 1 | no | — |
| 345 | C2×Dic3 | — | 10 | 2 | no | — |
| 346 | C2×Dic3 | — | 10 | 1 | no | — |
| 347 | C2×Dic3 | — | 20 | 2 | no | — |
| 348 | C2×Dic3 | — | 20 | 1 | no | — |
| 349 | C2×Dic3 | — | 20 | 1 | no | — |
| 350 | D12 | — | 4 | 1 | no | — |
| 351 | D12 | — | 20 | 1 | no | — |
| 352 | D12 | — | 40 | 1 | no | — |
| 353 | Dic6 | — | 10 | 2 | no | — |
| 354 | Dic6 | — | 10 | 2 | no | — |
| 355 | Dic6 | — | 20 | 1 | no | — |
| 356 | Dic6 | — | 20 | 1 | no | — |
| 357 | C3×C8 | — | 4 | 1 | no | — |
| 358 | C3×C8 | — | 20 | 1 | no | — |
| 359 | C22×C5 | — | 2 | 1 | no | — |
| 360 | C22×C5 | — | 2 | 1 | no | — |
| 361 | C22×C5 | — | 12 | 1 | no | — |
| 362 | C22×C5 | — | 12 | 1 | no | — |
| 363 | C22×C5 | — | 12 | 1 | no | — |
| 364 | C22×C5 | #882 | 1 | 1 | yes | characteristic |
| 365 | C22×C5 | C2×#204 | 1 | 1 | yes | characteristic |
| 366 | C22×C5 | #908 | 1 | 1 | yes | characteristic |
| 367 | C2×D5 | — | 2 | 2 | no | — |
| 368 | C2×D5 | — | 4 | 1 | no | — |
| 369 | C2×D5 | — | 4 | 1 | no | — |
| 370 | C2×D5 | — | 4 | 2 | no | — |
| 371 | C2×D5 | — | 8 | 1 | no | — |
| 372 | C2×D5 | — | 12 | 1 | no | — |
| 373 | C2×D5 | — | 12 | 1 | no | — |
| 374 | C2×D5 | — | 12 | 1 | no | — |
| 375 | C2×D5 | — | 24 | 4 | no | — |
| 376 | C4×C5 | — | 2 | 1 | no | — |
| 377 | C4×C5 | — | 2 | 1 | no | — |
| 378 | C4×C5 | — | 12 | 1 | no | — |
| 379 | C4×C5 | — | 24 | 1 | no | — |
| 380 | Dic5 | — | 4 | 1 | no | — |
| 381 | Dic5 | — | 12 | 1 | no | — |
| 382 | Dic5 | — | 12 | 2 | no | — |
| 383 | C24 | — | 5 | 1 | no | — |
| 384 | C24 | — | 30 | 1 | no | — |
| 385 | C2×Q8 | — | 30 | 1 | no | — |
| 386 | C2×Q8 | — | 30 | 1 | no | — |
| 387 | C2×Q8 | — | 60 | 2 | no | — |
| 388 | C2×D4 | — | 3 | 1 | no | — |
| 389 | C2×D4 | — | 6 | 1 | no | — |
| 390 | C2×D4 | — | 15 | 1 | no | — |
| 391 | C2×D4 | — | 30 | 1 | no | — |
| 392 | C2×D4 | — | 30 | 1 | no | — |
| 393 | C2×D4 | — | 30 | 1 | no | — |
| 394 | C2×D4 | — | 30 | 1 | no | — |
| 395 | C2×D4 | — | 60 | 2 | no | — |
| 396 | C2×D4 | — | 60 | 2 | no | — |
| 397 | C22×C4 | — | 5 | 1 | no | — |
| 398 | C22×C4 | — | 6 | 1 | no | — |
| 399 | C22×C4 | — | 30 | 1 | no | — |
| 400 | C22×C4 | — | 30 | 1 | no | — |
| 401 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 402 | SD16 | — | 60 | 2 | no | — |
| 403 | SD16 | — | 60 | 2 | no | — |
| 404 | C2×C8 | — | 2 | 1 | no | — |
| 405 | C2×C8 | — | 10 | 1 | no | — |
| 406 | C4⋊C4 | — | 3 | 1 | no | — |
| 407 | C4⋊C4 | — | 15 | 1 | no | — |
| 408 | C4⋊C4 | — | 30 | 1 | no | — |
| 409 | C22⋊C4 | — | 6 | 1 | no | — |
| 410 | C22⋊C4 | — | 10 | 1 | no | — |
| 411 | C22⋊C4 | — | 10 | 1 | no | — |
| 412 | C22⋊C4 | — | 30 | 1 | no | — |
| 413 | C22⋊C4 | — | 30 | 1 | no | — |
| 414 | C22⋊C4 | — | 30 | 1 | no | — |
| 415 | C22⋊C4 | — | 60 | 2 | no | — |
| 416 | C3×C5 | #1601 | 1 | 1 | yes | characteristic, complemented, Hall |
| 417 | C22×C3 | — | 2 | 1 | no | — |
| 418 | C22×C3 | — | 2 | 1 | no | — |
| 419 | C22×C3 | — | 10 | 2 | no | — |
| 420 | C22×C3 | — | 20 | 2 | no | — |
| 421 | C22×C3 | — | 20 | 1 | no | — |
| 422 | C22×C3 | — | 20 | 1 | no | — |
| 423 | C22×C3 | — | 40 | 1 | no | — |
| 424 | C22×C3 | #4028 | 1 | 1 | yes | characteristic |
| 425 | C22×C3 | #4057 | 1 | 1 | yes | characteristic |
| 426 | C22×C3 | D5×SD16 | 1 | 1 | yes | characteristic |
| 427 | C2×D3 | — | 4 | 1 | no | — |
| 428 | C2×D3 | — | 4 | 1 | no | — |
| 429 | C2×D3 | — | 4 | 1 | no | — |
| 430 | C2×D3 | — | 20 | 1 | no | — |
| 431 | C2×D3 | — | 20 | 1 | no | — |
| 432 | C2×D3 | — | 20 | 1 | no | — |
| 433 | C2×D3 | — | 40 | 4 | no | — |
| 434 | C3×C4 | — | 2 | 1 | no | — |
| 435 | C3×C4 | — | 2 | 1 | no | — |
| 436 | C3×C4 | — | 20 | 1 | no | — |
| 437 | Dic3 | — | 4 | 1 | no | — |
| 438 | Dic3 | — | 8 | 1 | no | — |
| 439 | Dic3 | — | 20 | 2 | no | — |
| 440 | Dic3 | — | 20 | 1 | no | — |
| 441 | C2×C5 | — | 2 | 1 | no | — |
| 442 | C2×C5 | — | 2 | 1 | no | — |
| 443 | C2×C5 | — | 24 | 1 | no | — |
| 444 | C2×C5 | #4731 | 1 | 1 | yes | characteristic |
| 445 | C2×C5 | #4741 | 1 | 1 | yes | characteristic |
| 446 | C2×C5 | #4746 | 1 | 1 | yes | characteristic |
| 447 | D5 | — | 4 | 2 | no | — |
| 448 | D5 | — | 24 | 1 | no | — |
| 449 | C23 | — | 5 | 2 | no | — |
| 450 | C23 | — | 6 | 1 | no | — |
| 451 | C23 | — | 10 | 1 | no | — |
| 452 | C23 | — | 10 | 1 | no | — |
| 453 | C23 | — | 20 | 1 | no | — |
| 454 | C23 | — | 20 | 1 | no | — |
| 455 | C23 | — | 30 | 1 | no | — |
| 456 | C23 | — | 60 | 2 | no | — |
| 457 | C23 | — | 120 | 1 | no | — |
| 458 | C23 | — | 120 | 1 | no | — |
| 459 | C23 | D5×D12 | 1 | 1 | yes | characteristic |
| 460 | Q8 | — | 30 | 2 | no | — |
| 461 | Q8 | — | 30 | 2 | no | — |
| 462 | Q8 | — | 60 | 1 | no | — |
| 463 | Q8 | — | 60 | 1 | no | — |
| 464 | D4 | — | 12 | 1 | no | — |
| 465 | D4 | — | 12 | 1 | no | — |
| 466 | D4 | — | 12 | 1 | no | — |
| 467 | D4 | — | 60 | 1 | no | — |
| 468 | D4 | — | 60 | 2 | no | — |
| 469 | D4 | — | 60 | 2 | no | — |
| 470 | D4 | — | 60 | 1 | no | — |
| 471 | D4 | — | 60 | 1 | no | — |
| 472 | D4 | — | 120 | 1 | no | — |
| 473 | C2×C4 | — | 4 | 1 | no | — |
| 474 | C2×C4 | — | 6 | 1 | no | — |
| 475 | C2×C4 | — | 10 | 1 | no | — |
| 476 | C2×C4 | — | 12 | 1 | no | — |
| 477 | C2×C4 | — | 12 | 1 | no | — |
| 478 | C2×C4 | — | 12 | 1 | no | — |
| 479 | C2×C4 | — | 20 | 1 | no | — |
| 480 | C2×C4 | — | 30 | 2 | no | — |
| 481 | C2×C4 | — | 30 | 1 | no | — |
| 482 | C2×C4 | — | 60 | 2 | no | — |
| 483 | C2×C4 | — | 60 | 1 | no | — |
| 484 | C2×C4 | — | 60 | 1 | no | — |
| 485 | C2×C4 | D3×D20 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | #6790 | 1 | 1 | yes | characteristic |
| 487 | C8 | — | 4 | 1 | no | — |
| 488 | C8 | — | 20 | 1 | no | — |
| 489 | C2×C3 | — | 2 | 1 | no | — |
| 490 | C2×C3 | — | 2 | 1 | no | — |
| 491 | C2×C3 | — | 20 | 2 | no | — |
| 492 | C2×C3 | #65030 | 1 | 1 | yes | characteristic |
| 493 | C2×C3 | #65065 | 1 | 1 | yes | characteristic |
| 494 | C2×C3 | #65114 | 1 | 1 | yes | characteristic |
| 495 | D3 | — | 8 | 1 | no | — |
| 496 | D3 | — | 40 | 1 | no | — |
| 497 | C5 | #68108 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 498 | C22 | — | 2 | 1 | no | — |
| 499 | C22 | — | 2 | 1 | no | — |
| 500 | C22 | — | 10 | 2 | no | — |
| 501 | C22 | — | 12 | 1 | no | — |
| 502 | C22 | — | 12 | 1 | no | — |
| 503 | C22 | — | 12 | 1 | no | — |
| 504 | C22 | — | 20 | 2 | no | — |
| 505 | C22 | — | 20 | 1 | no | — |
| 506 | C22 | — | 20 | 1 | no | — |
| 507 | C22 | — | 40 | 1 | no | — |
| 508 | C22 | — | 60 | 1 | no | — |
| 509 | C22 | — | 60 | 1 | no | — |
| 510 | C22 | — | 60 | 1 | no | — |
| 511 | C22 | — | 120 | 4 | no | — |
| 512 | C22 | D5×#204 | 1 | 1 | yes | characteristic |
| 513 | C22 | #91250 | 1 | 1 | yes | characteristic |
| 514 | C22 | #91476 | 1 | 1 | yes | characteristic |
| 515 | C4 | — | 2 | 1 | no | — |
| 516 | C4 | — | 2 | 1 | no | — |
| 517 | C4 | — | 12 | 1 | no | — |
| 518 | C4 | — | 20 | 1 | no | — |
| 519 | C4 | — | 24 | 1 | no | — |
| 520 | C4 | — | 60 | 1 | no | — |
| 521 | C4 | — | 60 | 2 | no | — |
| 522 | C3 | #10599079 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | — | 2 | 1 | no | — |
| 525 | C2 | — | 20 | 2 | no | — |
| 526 | C2 | — | 24 | 1 | no | — |
| 527 | C2 | — | 120 | 1 | no | — |
| 528 | C2 | #11747137 | 1 | 1 | yes | characteristic |
| 529 | C2 | #11748115 | 1 | 1 | yes | characteristic |
| 530 | C2 | #11748250 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11750839 | C2 | semidirect |
| 3. #11748793 | C2 | semidirect |
| 4. #11748553 | C2 | semidirect |
| 5. C5×#4470 | C2 | semidirect |
| 6. C3×#64688 | C2 | semidirect |
| 7. #11745959 | C2 | semidirect |
| 9. C22×Dic30 | C22 | semidirect |
| 22. C3×C5×C22⋊C8 | C22 | semidirect |
| 24. C5×C3⋊#95 | C22 | semidirect |
| 25. C3×C22⋊#168 | C22 | semidirect |
| 34. #64688 | D3 | semidirect |
| 75. #4470 | D5 | semidirect |
| 89. C5×C22⋊C8 | C2×D3 | semidirect |
| 92. C22⋊#168 | C2×D3 | semidirect |
| 103. C22×C3×D5 | SD16 | semidirect |
| 150. C3×C22⋊C8 | C2×D5 | semidirect |
| 152. C3⋊#95 | C2×D5 | semidirect |
| 262. C22×D5 | #204 | semidirect |
| 308. C22⋊C8 | D3×D5 | semidirect |
| 416. C3×C5 | #1601 | semidirect |
| 497. C5 | #68108 | semidirect |
| 522. C3 | #10599079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754644 | 2 |
| #11750839 | 2 |
| #11748793 | 2 |
| #11748553 | 2 |
| C5×#4470 | 2 |
| C3×#64688 | 2 |
| #11745959 | 2 |
| #10599079 | 3 |
| #68108 | 5 |