Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1400 conjugacy classes of subgroups.
The subgroup lattice has 564 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#92098 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C22×C3×#689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11754278 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#91315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#5225 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11749310 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11749309 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11748393 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11748349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10610692 | — | 3 | 1 | no | maximal, Hall |
| 11 | C22×C3×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 12 | #92098 | — | 2 | 4 | no | — |
| 13 | #92098 | — | 2 | 4 | no | — |
| 14 | C2×#6821 | — | 2 | 1 | no | — |
| 15 | C2×#6821 | C22 | 1 | 2 | yes | — |
| 16 | C2×Q8×D15 | — | 2 | 1 | no | — |
| 17 | C2×Q8×D15 | C22 | 1 | 2 | yes | — |
| 18 | C2×#6817 | — | 2 | 2 | no | — |
| 19 | C2×#6817 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6817 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×C3×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×#926 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C5×#208 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C3×#689 | — | 2 | 4 | no | — |
| 25 | C2×C3×#689 | C22 | 1 | 4 | yes | — |
| 26 | C22×C3×#168 | C22 | 1 | 1 | yes | characteristic |
| 27 | #91546 | — | 2 | 2 | no | — |
| 28 | #91390 | C22 | 1 | 4 | yes | — |
| 29 | #91389 | — | 2 | 1 | no | — |
| 30 | #91374 | — | 2 | 1 | no | — |
| 31 | C2×#6662 | C22 | 1 | 2 | yes | — |
| 32 | #91315 | — | 2 | 4 | no | — |
| 33 | C2×#6658 | C22 | 1 | 2 | yes | — |
| 34 | C5×#835 | C22 | 1 | 4 | yes | — |
| 35 | #90975 | C22 | 1 | 2 | yes | — |
| 36 | #90969 | C22 | 1 | 2 | yes | — |
| 37 | #90957 | C22 | 1 | 4 | yes | — |
| 38 | #83884 | — | 5 | 1 | no | maximal, Hall |
| 39 | C2×#4147 | — | 3 | 1 | no | — |
| 40 | C22×#689 | D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#4055 | — | 3 | 1 | no | — |
| 42 | #65860 | — | 3 | 1 | no | — |
| 43 | C5×#419 | — | 3 | 1 | no | — |
| 44 | #65418 | — | 3 | 1 | no | — |
| 45 | #65291 | — | 3 | 1 | no | — |
| 46 | #65099 | — | 3 | 4 | no | — |
| 47 | #65097 | — | 3 | 4 | no | — |
| 48 | C2×C3×C5×Q8 | — | 2 | 1 | no | — |
| 49 | C2×C3×C5×Q8 | — | 2 | 2 | no | — |
| 50 | C2×C3×C5×Q8 | D4 | 1 | 4 | yes | — |
| 51 | C2×C3×C5×Q8 | C23 | 1 | 2 | yes | — |
| 52 | C22×C3×C4×C5 | — | 2 | 1 | no | — |
| 53 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×#1220 | — | 2 | 1 | no | — |
| 55 | C2×#1220 | D4 | 1 | 2 | yes | — |
| 56 | #6821 | — | 2 | 8 | no | — |
| 57 | #6821 | — | 2 | 4 | no | — |
| 58 | #6821 | — | 2 | 4 | no | — |
| 59 | Q8×D15 | — | 2 | 8 | no | — |
| 60 | Q8×D15 | — | 2 | 4 | no | — |
| 61 | Q8×D15 | — | 2 | 4 | no | — |
| 62 | #6817 | — | 2 | 16 | no | — |
| 63 | #6817 | — | 2 | 2 | no | — |
| 64 | #6817 | — | 2 | 2 | no | — |
| 65 | #6817 | — | 2 | 2 | no | — |
| 66 | #6817 | D4 | 1 | 4 | yes | — |
| 67 | C2×D60 | — | 2 | 2 | no | — |
| 68 | C2×D60 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×D60 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C4×D15 | — | 2 | 2 | no | — |
| 71 | C2×C4×D15 | — | 2 | 1 | no | — |
| 72 | C2×C4×D15 | — | 2 | 2 | no | — |
| 73 | C2×C4×D15 | C23 | 1 | 2 | yes | — |
| 74 | C2×Dic30 | — | 2 | 2 | no | — |
| 75 | C2×Dic30 | D4 | 1 | 1 | yes | characteristic |
| 76 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×C3×Dic5 | — | 2 | 1 | no | — |
| 78 | C2×C3×Dic10 | — | 2 | 2 | no | — |
| 79 | C2×C3×Dic10 | — | 2 | 2 | no | — |
| 80 | C2×C3×Dic10 | — | 2 | 1 | no | — |
| 81 | C2×C3×Dic10 | C23 | 1 | 2 | yes | — |
| 82 | C5×#217 | — | 2 | 1 | no | — |
| 83 | C5×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 84 | C4×C5×Dic3 | — | 2 | 1 | no | — |
| 85 | C5×#208 | — | 2 | 2 | no | — |
| 86 | C2×C5×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 87 | C3×#689 | — | 2 | 8 | no | — |
| 88 | C2×C3×#168 | — | 2 | 2 | no | — |
| 89 | C2×C3×#168 | C23 | 1 | 2 | yes | — |
| 90 | Dic3⋊Dic5 | — | 2 | 4 | no | — |
| 91 | #6667 | — | 2 | 4 | no | — |
| 92 | #6662 | — | 2 | 4 | no | — |
| 93 | #6658 | — | 2 | 4 | no | — |
| 94 | C2×#1007 | — | 5 | 1 | no | — |
| 95 | C22×C3×Q16 | — | 5 | 1 | no | — |
| 96 | #5816 | — | 5 | 1 | no | — |
| 97 | C2×#942 | — | 5 | 1 | no | — |
| 98 | #5225 | D5 | 1 | 1 | yes | characteristic, complemented |
| 99 | #5187 | — | 5 | 4 | no | — |
| 100 | #5186 | — | 5 | 4 | no | — |
| 101 | #5113 | — | 5 | 1 | no | — |
| 102 | #5110 | — | 5 | 1 | no | — |
| 103 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | #4147 | — | 6 | 4 | no | — |
| 105 | #4147 | — | 6 | 4 | no | — |
| 106 | C2×#713 | — | 3 | 2 | no | — |
| 107 | C2×#713 | — | 6 | 1 | no | — |
| 108 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 109 | C2×Q8×D5 | — | 6 | 1 | no | — |
| 110 | C2×#709 | — | 3 | 1 | no | — |
| 111 | C2×#709 | — | 3 | 1 | no | — |
| 112 | C2×#709 | — | 6 | 2 | no | — |
| 113 | C22×Dic10 | C2×D3 | 1 | 1 | yes | characteristic |
| 114 | C2×C5×M16 | — | 3 | 1 | no | — |
| 115 | C5×#117 | — | 3 | 1 | no | — |
| 116 | C2×#689 | — | 2 | 4 | no | — |
| 117 | C2×#689 | C2×D3 | 1 | 4 | yes | — |
| 118 | C22×#168 | C2×D3 | 1 | 1 | yes | characteristic |
| 119 | #4055 | — | 6 | 4 | no | — |
| 120 | C2×Dic20 | — | 3 | 2 | no | — |
| 121 | C2×#677 | — | 3 | 2 | no | — |
| 122 | #4043 | — | 3 | 4 | no | — |
| 123 | #4032 | — | 6 | 2 | no | — |
| 124 | #4021 | — | 6 | 1 | no | — |
| 125 | #4015 | — | 6 | 1 | no | — |
| 126 | C5×#103 | — | 3 | 4 | no | — |
| 127 | #3952 | — | 3 | 4 | no | — |
| 128 | #3942 | — | 3 | 2 | no | — |
| 129 | #3941 | — | 3 | 2 | no | — |
| 130 | #3011 | — | 15 | 1 | no | Sylow |
| 131 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C22×D15 | — | 2 | 1 | no | — |
| 133 | C22×D15 | C2×D4 | 1 | 2 | yes | — |
| 134 | C3×C5×Q8 | — | 2 | 4 | no | — |
| 135 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 136 | C3×C5×Q8 | C2×D4 | 1 | 4 | yes | — |
| 137 | C2×C3×C4×C5 | — | 2 | 4 | no | — |
| 138 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 139 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 141 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 142 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 143 | #1220 | — | 2 | 4 | no | — |
| 144 | #1220 | — | 2 | 4 | no | — |
| 145 | C2×Dic15 | — | 2 | 1 | no | — |
| 146 | C2×Dic15 | C2×D4 | 1 | 2 | yes | — |
| 147 | D60 | — | 2 | 8 | no | — |
| 148 | D60 | — | 2 | 2 | no | — |
| 149 | D60 | — | 2 | 1 | no | — |
| 150 | D60 | C2×D4 | 1 | 2 | yes | — |
| 151 | C4×D15 | — | 2 | 8 | no | — |
| 152 | C4×D15 | — | 2 | 8 | no | — |
| 153 | C4×D15 | — | 2 | 4 | no | — |
| 154 | C4×D15 | — | 2 | 2 | no | — |
| 155 | C4×D15 | — | 2 | 2 | no | — |
| 156 | Dic30 | — | 2 | 8 | no | — |
| 157 | Dic30 | — | 2 | 2 | no | — |
| 158 | Dic30 | — | 2 | 1 | no | — |
| 159 | Dic30 | C2×D4 | 1 | 2 | yes | — |
| 160 | C2×C5×Dic3 | — | 2 | 2 | no | — |
| 161 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 162 | C2×C3×Dic5 | — | 4 | 2 | no | — |
| 163 | C3×Dic10 | — | 2 | 2 | no | — |
| 164 | C3×Dic10 | — | 2 | 2 | no | — |
| 165 | C3×Dic10 | — | 4 | 2 | no | — |
| 166 | C3×#168 | — | 2 | 2 | no | — |
| 167 | C5×C3⋊C8 | — | 2 | 2 | no | — |
| 168 | C22×C3×Q8 | — | 5 | 1 | no | — |
| 169 | C22×C3×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 170 | #1007 | — | 10 | 4 | no | — |
| 171 | #1007 | — | 10 | 4 | no | — |
| 172 | C2×#239 | — | 5 | 2 | no | — |
| 173 | C2×#239 | — | 10 | 1 | no | — |
| 174 | C2×D3×Q8 | — | 5 | 2 | no | — |
| 175 | C2×D3×Q8 | — | 10 | 1 | no | — |
| 176 | C2×#235 | — | 5 | 1 | no | — |
| 177 | C2×#235 | — | 5 | 1 | no | — |
| 178 | C2×#235 | — | 10 | 2 | no | — |
| 179 | C2×C3×Q16 | — | 5 | 4 | no | — |
| 180 | C2×C3×Q16 | — | 10 | 4 | no | — |
| 181 | C22×C3×C8 | — | 5 | 1 | no | — |
| 182 | #947 | — | 10 | 1 | no | — |
| 183 | #946 | — | 5 | 4 | no | — |
| 184 | #944 | — | 10 | 1 | no | — |
| 185 | C2×#216 | — | 5 | 2 | no | — |
| 186 | #942 | — | 10 | 4 | no | — |
| 187 | C2×#215 | — | 5 | 2 | no | — |
| 188 | #929 | — | 10 | 2 | no | — |
| 189 | #926 | C2×D5 | 1 | 1 | yes | characteristic |
| 190 | C2×#208 | C2×D5 | 1 | 1 | yes | characteristic |
| 191 | #835 | C2×D5 | 1 | 4 | yes | — |
| 192 | #821 | — | 5 | 2 | no | — |
| 193 | (C2×D3)⋊C8 | — | 5 | 4 | no | — |
| 194 | #816 | — | 5 | 2 | no | — |
| 195 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 196 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 197 | C2×C5×Q8 | #67 | 1 | 4 | yes | — |
| 198 | C2×C5×Q8 | C22×D3 | 1 | 2 | yes | — |
| 199 | C22×C4×C5 | — | 2 | 1 | no | — |
| 200 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 202 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 203 | C22×Dic5 | — | 2 | 1 | no | — |
| 204 | #713 | — | 6 | 4 | no | — |
| 205 | #713 | — | 6 | 8 | no | — |
| 206 | #713 | — | 6 | 4 | no | — |
| 207 | Q8×D5 | — | 6 | 4 | no | — |
| 208 | Q8×D5 | — | 6 | 8 | no | — |
| 209 | Q8×D5 | — | 6 | 4 | no | — |
| 210 | #709 | — | 3 | 4 | no | — |
| 211 | #709 | — | 6 | 16 | no | — |
| 212 | #709 | — | 6 | 2 | no | — |
| 213 | #709 | — | 6 | 2 | no | — |
| 214 | #709 | — | 6 | 2 | no | — |
| 215 | C2×D20 | — | 3 | 1 | no | — |
| 216 | C2×D20 | — | 3 | 1 | no | — |
| 217 | C2×D20 | — | 6 | 2 | no | — |
| 218 | C2×C4×D5 | — | 3 | 2 | no | — |
| 219 | C2×C4×D5 | — | 6 | 2 | no | — |
| 220 | C2×C4×D5 | — | 6 | 2 | no | — |
| 221 | C2×C4×D5 | — | 6 | 1 | no | — |
| 222 | C2×Dic10 | — | 2 | 2 | no | — |
| 223 | C2×Dic10 | — | 2 | 2 | no | — |
| 224 | C2×Dic10 | — | 2 | 1 | no | — |
| 225 | C2×Dic10 | — | 3 | 1 | no | — |
| 226 | C2×Dic10 | — | 3 | 1 | no | — |
| 227 | C2×Dic10 | — | 6 | 2 | no | — |
| 228 | C2×Dic10 | C22×D3 | 1 | 2 | yes | — |
| 229 | C5×M16 | — | 6 | 2 | no | — |
| 230 | C2×C5×C8 | — | 3 | 2 | no | — |
| 231 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 232 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 233 | C42×C5 | — | 6 | 1 | no | — |
| 234 | #689 | — | 2 | 8 | no | — |
| 235 | #685 | — | 6 | 4 | no | — |
| 236 | C4⋊Dic5 | — | 6 | 4 | no | — |
| 237 | C2×#168 | — | 2 | 2 | no | — |
| 238 | C2×#168 | C22×D3 | 1 | 2 | yes | — |
| 239 | Dic20 | — | 6 | 4 | no | — |
| 240 | #677 | — | 6 | 4 | no | — |
| 241 | C2×2−1+4 | — | 15 | 1 | no | — |
| 242 | C2×#137 | — | 15 | 1 | no | — |
| 243 | C22×Q16 | — | 5 | 1 | no | — |
| 244 | #536 | — | 15 | 1 | no | — |
| 245 | #452 | — | 15 | 4 | no | — |
| 246 | #451 | — | 15 | 4 | no | — |
| 247 | #419 | — | 3 | 1 | no | — |
| 248 | #416 | — | 15 | 1 | no | — |
| 249 | #408 | — | 15 | 1 | no | — |
| 250 | C22×C3×C5 | — | 2 | 2 | no | — |
| 251 | C22×C3×C5 | #120 | 1 | 2 | yes | — |
| 252 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×D15 | — | 2 | 2 | no | — |
| 254 | C2×D15 | — | 2 | 2 | no | — |
| 255 | C2×D15 | — | 2 | 4 | no | — |
| 256 | C2×D15 | — | 4 | 2 | no | — |
| 257 | C3×C4×C5 | — | 2 | 4 | no | — |
| 258 | C3×C4×C5 | #120 | 1 | 2 | yes | — |
| 259 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | Dic15 | — | 2 | 2 | no | — |
| 262 | Dic15 | — | 2 | 2 | no | — |
| 263 | C3×Dic5 | — | 4 | 2 | no | — |
| 264 | C5×Dic3 | — | 4 | 2 | no | — |
| 265 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 266 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 267 | C2×C3×Q8 | — | 5 | 2 | no | — |
| 268 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 269 | C2×C3×Q8 | — | 10 | 2 | no | — |
| 270 | C2×C3×Q8 | — | 10 | 2 | no | — |
| 271 | C2×C3×Q8 | D20 | 1 | 4 | yes | — |
| 272 | C2×C3×Q8 | C22×D5 | 1 | 2 | yes | — |
| 273 | C22×C3×C4 | — | 2 | 1 | no | — |
| 274 | C22×C3×C4 | — | 10 | 1 | no | — |
| 275 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 276 | C2×#67 | — | 5 | 2 | no | — |
| 277 | C2×#67 | — | 10 | 1 | no | — |
| 278 | #239 | — | 10 | 4 | no | — |
| 279 | #239 | — | 10 | 8 | no | — |
| 280 | #239 | — | 10 | 4 | no | — |
| 281 | D3×Q8 | — | 10 | 4 | no | — |
| 282 | D3×Q8 | — | 10 | 8 | no | — |
| 283 | D3×Q8 | — | 10 | 4 | no | — |
| 284 | #235 | — | 5 | 4 | no | — |
| 285 | #235 | — | 10 | 16 | no | — |
| 286 | #235 | — | 10 | 2 | no | — |
| 287 | #235 | — | 10 | 2 | no | — |
| 288 | #235 | — | 10 | 2 | no | — |
| 289 | C2×D12 | — | 5 | 1 | no | — |
| 290 | C2×D12 | — | 5 | 1 | no | — |
| 291 | C2×D12 | — | 10 | 2 | no | — |
| 292 | C2×C4×D3 | — | 5 | 2 | no | — |
| 293 | C2×C4×D3 | — | 10 | 2 | no | — |
| 294 | C2×C4×D3 | — | 10 | 2 | no | — |
| 295 | C2×C4×D3 | — | 10 | 1 | no | — |
| 296 | C2×Dic6 | — | 5 | 1 | no | — |
| 297 | C2×Dic6 | — | 5 | 1 | no | — |
| 298 | C2×Dic6 | — | 10 | 2 | no | — |
| 299 | C3×Q16 | — | 10 | 8 | no | — |
| 300 | C2×C3×C8 | — | 5 | 2 | no | — |
| 301 | C2×C3×C8 | — | 10 | 2 | no | — |
| 302 | #217 | — | 2 | 1 | no | — |
| 303 | #216 | — | 10 | 4 | no | — |
| 304 | #215 | — | 10 | 4 | no | — |
| 305 | (C2×D3)⋊C4 | — | 10 | 4 | no | — |
| 306 | C4⋊Dic3 | C22×D5 | 1 | 2 | yes | — |
| 307 | Dic3⋊C4 | — | 10 | 4 | no | — |
| 308 | C4×Dic3 | — | 2 | 1 | no | — |
| 309 | #208 | — | 2 | 2 | no | — |
| 310 | C2×C3⋊C8 | C22×D5 | 1 | 2 | yes | — |
| 311 | C23×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 312 | C22×D5 | — | 3 | 2 | no | — |
| 313 | C22×D5 | — | 6 | 1 | no | — |
| 314 | C5×Q8 | — | 2 | 4 | no | — |
| 315 | C5×Q8 | — | 2 | 2 | no | — |
| 316 | C5×Q8 | C2×#67 | 1 | 4 | yes | — |
| 317 | C2×C4×C5 | — | 2 | 4 | no | — |
| 318 | C2×C4×C5 | — | 2 | 2 | no | — |
| 319 | C2×C4×C5 | — | 6 | 2 | no | — |
| 320 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 321 | C2×C4×C5 | D3×D4 | 1 | 2 | yes | — |
| 322 | C2×C4×C5 | C2×#67 | 1 | 2 | yes | — |
| 323 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 324 | C22⋊D5 | — | 6 | 4 | no | — |
| 325 | C22⋊D5 | — | 6 | 4 | no | — |
| 326 | C2×Dic5 | — | 2 | 2 | no | — |
| 327 | C2×Dic5 | — | 3 | 2 | no | — |
| 328 | C2×Dic5 | — | 4 | 2 | no | — |
| 329 | C2×Dic5 | — | 6 | 1 | no | — |
| 330 | D20 | — | 3 | 2 | no | — |
| 331 | D20 | — | 6 | 8 | no | — |
| 332 | D20 | — | 6 | 2 | no | — |
| 333 | D20 | — | 6 | 1 | no | — |
| 334 | C4×D5 | — | 6 | 8 | no | — |
| 335 | C4×D5 | — | 6 | 8 | no | — |
| 336 | C4×D5 | — | 6 | 4 | no | — |
| 337 | C4×D5 | — | 6 | 2 | no | — |
| 338 | C4×D5 | — | 6 | 2 | no | — |
| 339 | Dic10 | — | 2 | 2 | no | — |
| 340 | Dic10 | — | 2 | 2 | no | — |
| 341 | Dic10 | — | 3 | 2 | no | — |
| 342 | Dic10 | — | 4 | 2 | no | — |
| 343 | Dic10 | — | 6 | 8 | no | — |
| 344 | Dic10 | — | 6 | 2 | no | — |
| 345 | Dic10 | — | 6 | 1 | no | — |
| 346 | C5×C8 | — | 6 | 2 | no | — |
| 347 | #168 | — | 2 | 2 | no | — |
| 348 | 2−1+4 | — | 30 | 4 | no | — |
| 349 | 2−1+4 | — | 30 | 4 | no | — |
| 350 | C2×#41 | — | 15 | 1 | no | — |
| 351 | C2×#41 | — | 15 | 2 | no | — |
| 352 | C2×#41 | — | 15 | 1 | no | — |
| 353 | C2×#41 | — | 30 | 2 | no | — |
| 354 | C2×#41 | — | 30 | 1 | no | — |
| 355 | C22×Q8 | — | 5 | 1 | no | — |
| 356 | C22×Q8 | — | 15 | 2 | no | — |
| 357 | C22×Q8 | — | 30 | 1 | no | — |
| 358 | C22×Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 359 | #137 | — | 30 | 4 | no | — |
| 360 | C2×Q16 | — | 5 | 4 | no | — |
| 361 | C2×Q16 | — | 10 | 4 | no | — |
| 362 | C2×Q16 | — | 15 | 2 | no | — |
| 363 | C2×SD16 | — | 15 | 2 | no | — |
| 364 | C2×M16 | — | 3 | 1 | no | — |
| 365 | C22×C8 | — | 5 | 1 | no | — |
| 366 | C4⋊Q8 | — | 30 | 1 | no | — |
| 367 | #124 | — | 30 | 1 | no | — |
| 368 | #123 | — | 30 | 2 | no | — |
| 369 | C22⋊Q8 | — | 15 | 4 | no | — |
| 370 | #117 | — | 3 | 1 | no | — |
| 371 | #103 | — | 3 | 4 | no | — |
| 372 | #103 | — | 15 | 2 | no | — |
| 373 | #102 | — | 15 | 2 | no | — |
| 374 | C22⋊C8 | — | 15 | 4 | no | — |
| 375 | C2×C3×C5 | — | 2 | 2 | no | — |
| 376 | C2×C3×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 377 | C2×C3×C5 | #578 | 1 | 2 | yes | — |
| 378 | D15 | — | 4 | 2 | no | — |
| 379 | D15 | — | 4 | 2 | no | — |
| 380 | C23×C3 | D4×D5 | 1 | 1 | yes | characteristic |
| 381 | C22×D3 | — | 5 | 2 | no | — |
| 382 | C22×D3 | — | 10 | 1 | no | — |
| 383 | C3×Q8 | — | 2 | 2 | no | — |
| 384 | C3×Q8 | — | 2 | 4 | no | — |
| 385 | C3×Q8 | — | 10 | 2 | no | — |
| 386 | C3×Q8 | — | 10 | 2 | no | — |
| 387 | C3×Q8 | — | 20 | 2 | no | — |
| 388 | C3×Q8 | C2×D20 | 1 | 4 | yes | — |
| 389 | C2×C3×C4 | — | 2 | 2 | no | — |
| 390 | C2×C3×C4 | — | 2 | 4 | no | — |
| 391 | C2×C3×C4 | — | 10 | 2 | no | — |
| 392 | C2×C3×C4 | — | 20 | 2 | no | — |
| 393 | C2×C3×C4 | C2×D20 | 1 | 2 | yes | — |
| 394 | C2×C3×C4 | D4×D5 | 1 | 2 | yes | — |
| 395 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 396 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 397 | #67 | — | 10 | 4 | no | — |
| 398 | #67 | — | 10 | 4 | no | — |
| 399 | C2×Dic3 | — | 2 | 2 | no | — |
| 400 | C2×Dic3 | — | 5 | 2 | no | — |
| 401 | C2×Dic3 | — | 10 | 1 | no | — |
| 402 | D12 | — | 5 | 2 | no | — |
| 403 | D12 | — | 10 | 8 | no | — |
| 404 | D12 | — | 10 | 1 | no | — |
| 405 | D12 | — | 10 | 2 | no | — |
| 406 | C4×D3 | — | 10 | 8 | no | — |
| 407 | C4×D3 | — | 10 | 8 | no | — |
| 408 | C4×D3 | — | 10 | 2 | no | — |
| 409 | C4×D3 | — | 10 | 2 | no | — |
| 410 | C4×D3 | — | 10 | 4 | no | — |
| 411 | Dic6 | — | 5 | 2 | no | — |
| 412 | Dic6 | — | 10 | 8 | no | — |
| 413 | Dic6 | — | 10 | 1 | no | — |
| 414 | Dic6 | — | 10 | 2 | no | — |
| 415 | C3×C8 | — | 10 | 2 | no | — |
| 416 | C3⋊C8 | — | 2 | 2 | no | — |
| 417 | C22×C5 | — | 2 | 2 | no | — |
| 418 | C22×C5 | #937 | 1 | 2 | yes | — |
| 419 | C22×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 420 | C2×D5 | — | 6 | 4 | no | — |
| 421 | C2×D5 | — | 6 | 2 | no | — |
| 422 | C2×D5 | — | 6 | 2 | no | — |
| 423 | C2×D5 | — | 12 | 2 | no | — |
| 424 | C4×C5 | — | 2 | 4 | no | — |
| 425 | C4×C5 | — | 12 | 2 | no | — |
| 426 | C4×C5 | #937 | 1 | 2 | yes | — |
| 427 | C4×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 428 | C4×C5 | C22×#67 | 1 | 1 | yes | characteristic |
| 429 | Dic5 | — | 4 | 2 | no | — |
| 430 | Dic5 | — | 6 | 2 | no | — |
| 431 | Dic5 | — | 6 | 2 | no | — |
| 432 | #41 | — | 15 | 4 | no | — |
| 433 | #41 | — | 30 | 16 | no | — |
| 434 | #41 | — | 30 | 4 | no | — |
| 435 | #41 | — | 30 | 8 | no | — |
| 436 | #41 | — | 30 | 4 | no | — |
| 437 | #41 | — | 30 | 2 | no | — |
| 438 | #41 | — | 30 | 2 | no | — |
| 439 | #41 | — | 30 | 2 | no | — |
| 440 | C2×Q8 | — | 2 | 1 | no | — |
| 441 | C2×Q8 | — | 2 | 2 | no | — |
| 442 | C2×Q8 | — | 5 | 2 | no | — |
| 443 | C2×Q8 | — | 10 | 1 | no | — |
| 444 | C2×Q8 | — | 10 | 2 | no | — |
| 445 | C2×Q8 | — | 10 | 2 | no | — |
| 446 | C2×Q8 | — | 15 | 1 | no | — |
| 447 | C2×Q8 | — | 15 | 1 | no | — |
| 448 | C2×Q8 | — | 30 | 2 | no | — |
| 449 | C2×Q8 | — | 30 | 4 | no | — |
| 450 | C2×Q8 | — | 30 | 8 | no | — |
| 451 | C2×Q8 | — | 30 | 4 | no | — |
| 452 | C2×Q8 | #1202 | 1 | 4 | yes | — |
| 453 | C2×Q8 | C2×D3×D5 | 1 | 2 | yes | — |
| 454 | C2×D4 | — | 15 | 2 | no | — |
| 455 | C2×D4 | — | 15 | 1 | no | — |
| 456 | C2×D4 | — | 15 | 1 | no | — |
| 457 | C2×D4 | — | 30 | 2 | no | — |
| 458 | C2×D4 | — | 30 | 1 | no | — |
| 459 | C22×C4 | — | 2 | 1 | no | — |
| 460 | C22×C4 | — | 10 | 1 | no | — |
| 461 | C22×C4 | — | 15 | 2 | no | — |
| 462 | C22×C4 | — | 30 | 2 | no | — |
| 463 | C22×C4 | — | 30 | 2 | no | — |
| 464 | C22×C4 | — | 30 | 1 | no | — |
| 465 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 466 | Q16 | — | 10 | 8 | no | — |
| 467 | Q16 | — | 30 | 4 | no | — |
| 468 | SD16 | — | 30 | 4 | no | — |
| 469 | M16 | — | 6 | 2 | no | — |
| 470 | C2×C8 | — | 3 | 2 | no | — |
| 471 | C2×C8 | — | 5 | 2 | no | — |
| 472 | C2×C8 | — | 10 | 2 | no | — |
| 473 | C4⋊C4 | — | 3 | 2 | no | — |
| 474 | C4⋊C4 | — | 30 | 4 | no | — |
| 475 | C22⋊C4 | — | 6 | 1 | no | — |
| 476 | C22⋊C4 | — | 30 | 4 | no | — |
| 477 | C42 | — | 6 | 1 | no | — |
| 478 | C3×C5 | #3011 | 1 | 1 | yes | characteristic, complemented, Hall |
| 479 | C22×C3 | — | 2 | 2 | no | — |
| 480 | C22×C3 | #4028 | 1 | 2 | yes | — |
| 481 | C22×C3 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 482 | C2×D3 | — | 10 | 2 | no | — |
| 483 | C2×D3 | — | 10 | 2 | no | — |
| 484 | C2×D3 | — | 10 | 4 | no | — |
| 485 | C2×D3 | — | 20 | 2 | no | — |
| 486 | C3×C4 | — | 2 | 4 | no | — |
| 487 | C3×C4 | — | 20 | 2 | no | — |
| 488 | C3×C4 | #4028 | 1 | 2 | yes | — |
| 489 | C3×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 490 | C3×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 491 | Dic3 | — | 4 | 2 | no | — |
| 492 | Dic3 | — | 10 | 2 | no | — |
| 493 | Dic3 | — | 10 | 2 | no | — |
| 494 | C2×C5 | — | 2 | 2 | no | — |
| 495 | C2×C5 | #5766 | 1 | 2 | yes | — |
| 496 | C2×C5 | C2×#937 | 1 | 1 | yes | characteristic |
| 497 | D5 | — | 12 | 2 | no | — |
| 498 | D5 | — | 12 | 2 | no | — |
| 499 | C23 | — | 15 | 2 | no | — |
| 500 | C23 | — | 30 | 1 | no | — |
| 501 | C23 | #6790 | 1 | 1 | yes | characteristic |
| 502 | Q8 | — | 2 | 2 | no | — |
| 503 | Q8 | — | 2 | 4 | no | — |
| 504 | Q8 | — | 10 | 2 | no | — |
| 505 | Q8 | — | 10 | 2 | no | — |
| 506 | Q8 | — | 15 | 2 | no | — |
| 507 | Q8 | — | 20 | 2 | no | — |
| 508 | Q8 | — | 30 | 8 | no | — |
| 509 | Q8 | — | 30 | 1 | no | — |
| 510 | Q8 | — | 30 | 2 | no | — |
| 511 | Q8 | C2×#1202 | 1 | 4 | yes | — |
| 512 | D4 | — | 15 | 2 | no | — |
| 513 | D4 | — | 30 | 8 | no | — |
| 514 | D4 | — | 30 | 4 | no | — |
| 515 | D4 | — | 30 | 4 | no | — |
| 516 | D4 | — | 30 | 1 | no | — |
| 517 | D4 | — | 30 | 2 | no | — |
| 518 | C2×C4 | — | 2 | 2 | no | — |
| 519 | C2×C4 | — | 2 | 4 | no | — |
| 520 | C2×C4 | — | 6 | 2 | no | — |
| 521 | C2×C4 | — | 10 | 2 | no | — |
| 522 | C2×C4 | — | 15 | 2 | no | — |
| 523 | C2×C4 | — | 20 | 2 | no | — |
| 524 | C2×C4 | — | 30 | 8 | no | — |
| 525 | C2×C4 | — | 30 | 8 | no | — |
| 526 | C2×C4 | — | 30 | 1 | no | — |
| 527 | C2×C4 | — | 30 | 2 | no | — |
| 528 | C2×C4 | — | 30 | 2 | no | — |
| 529 | C2×C4 | — | 30 | 4 | no | — |
| 530 | C2×C4 | C2×#1202 | 1 | 2 | yes | — |
| 531 | C2×C4 | #6790 | 1 | 2 | yes | — |
| 532 | C2×C4 | #6790 | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 534 | C8 | — | 6 | 2 | no | — |
| 535 | C8 | — | 10 | 2 | no | — |
| 536 | C2×C3 | — | 2 | 2 | no | — |
| 537 | C2×C3 | C2×#4028 | 1 | 1 | yes | characteristic |
| 538 | C2×C3 | #66113 | 1 | 2 | yes | — |
| 539 | D3 | — | 20 | 2 | no | — |
| 540 | D3 | — | 20 | 2 | no | — |
| 541 | C5 | #83884 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 542 | C22 | — | 2 | 2 | no | — |
| 543 | C22 | — | 30 | 4 | no | — |
| 544 | C22 | — | 30 | 2 | no | — |
| 545 | C22 | — | 30 | 2 | no | — |
| 546 | C22 | — | 60 | 2 | no | — |
| 547 | C22 | #91572 | 1 | 2 | yes | — |
| 548 | C22 | C2×#6790 | 1 | 1 | yes | characteristic |
| 549 | C4 | — | 2 | 4 | no | — |
| 550 | C4 | — | 12 | 2 | no | — |
| 551 | C4 | — | 20 | 2 | no | — |
| 552 | C4 | — | 30 | 2 | no | — |
| 553 | C4 | — | 30 | 2 | no | — |
| 554 | C4 | #91572 | 1 | 2 | yes | — |
| 555 | C4 | C22×#1202 | 1 | 1 | yes | characteristic |
| 556 | C4 | C2×#6790 | 1 | 1 | yes | characteristic |
| 557 | C3 | #10610692 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 558 | C2 | — | 2 | 2 | no | — |
| 559 | C2 | — | 60 | 2 | no | — |
| 560 | C2 | — | 60 | 2 | no | — |
| 561 | C2 | #11755122 | 1 | 2 | yes | — |
| 562 | C2 | C2×#91572 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3×#689 | C2 | semidirect |
| 3. #11754278 | C2 | semidirect |
| 4. C2×#91315 | C2 | semidirect |
| 5. C5×#5225 | C2 | semidirect |
| 6. #11749310 | C2 | semidirect |
| 7. #11749309 | C2 | semidirect |
| 8. #11748393 | C2 | semidirect |
| 9. #11748349 | C2 | semidirect |
| 40. C22×#689 | D3 | semidirect |
| 98. #5225 | D5 | semidirect |
| 478. C3×C5 | #3011 | semidirect |
| 541. C5 | #83884 | semidirect |
| 557. C3 | #10610692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92098 | 2 |
| C22×C3×#689 | 2 |
| #11754278 | 2 |
| C2×#91315 | 2 |
| C5×#5225 | 2 |
| #11749310 | 2 |
| #11749309 | 2 |
| #11748393 | 2 |
| #11748349 | 2 |
| #10610692 | 3 |
| #83884 | 5 |