Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
888 conjugacy classes of subgroups.
The subgroup lattice has 508 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11755114 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11755102 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11751193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#65384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11749382 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11749378 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11747124 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11747106 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10612034 | — | 3 | 1 | no | maximal, Hall |
| 11 | C5×#1007 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#4147 | C22 | 1 | 1 | yes | characteristic |
| 13 | #92001 | C22 | 1 | 2 | yes | — |
| 14 | C3×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#6718 | C22 | 1 | 2 | yes | — |
| 16 | C2×#6718 | C22 | 1 | 2 | yes | — |
| 17 | #91758 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#942 | C22 | 1 | 2 | yes | — |
| 19 | C3×#4088 | C22 | 1 | 2 | yes | — |
| 20 | #91518 | — | 2 | 2 | no | — |
| 21 | #91517 | — | 2 | 2 | no | — |
| 22 | #91514 | — | 2 | 2 | no | — |
| 23 | #91513 | — | 2 | 2 | no | — |
| 24 | #91510 | — | 2 | 2 | no | — |
| 25 | D3×#689 | — | 2 | 2 | no | — |
| 26 | #91508 | — | 2 | 2 | no | — |
| 27 | D5×#216 | — | 2 | 2 | no | — |
| 28 | #91322 | C22 | 1 | 2 | yes | — |
| 29 | #91313 | C22 | 1 | 2 | yes | — |
| 30 | #91297 | C22 | 1 | 2 | yes | — |
| 31 | #91288 | C22 | 1 | 2 | yes | — |
| 32 | #91284 | C22 | 1 | 2 | yes | — |
| 33 | C4×C3⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 34 | C5×#836 | C22 | 1 | 1 | yes | characteristic |
| 35 | C5×#805 | C22 | 1 | 2 | yes | — |
| 36 | C3×#3968 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#3937 | C22 | 1 | 2 | yes | — |
| 38 | #90992 | C22 | 1 | 2 | yes | — |
| 39 | #90963 | C22 | 1 | 2 | yes | — |
| 40 | #80303 | — | 5 | 1 | no | maximal, Hall |
| 41 | #66172 | — | 3 | 2 | no | — |
| 42 | #66113 | — | 3 | 2 | no | — |
| 43 | C5×#456 | — | 3 | 1 | no | — |
| 44 | #65493 | — | 3 | 2 | no | — |
| 45 | #65384 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #65381 | — | 3 | 1 | no | — |
| 47 | #65115 | — | 3 | 2 | no | — |
| 48 | #65113 | — | 3 | 2 | no | — |
| 49 | #65044 | — | 3 | 2 | no | — |
| 50 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×Dic30 | C23 | 1 | 2 | yes | — |
| 53 | C5×#239 | — | 2 | 2 | no | — |
| 54 | C5×D3×Q8 | — | 2 | 2 | no | — |
| 55 | C5×#235 | — | 4 | 1 | no | — |
| 56 | C5×#235 | C23 | 1 | 2 | yes | — |
| 57 | C3×#713 | — | 2 | 2 | no | — |
| 58 | C3×Q8×D5 | — | 2 | 2 | no | — |
| 59 | C3×#709 | — | 4 | 1 | no | — |
| 60 | C3×#709 | C23 | 1 | 2 | yes | — |
| 61 | #6780 | — | 4 | 2 | no | — |
| 62 | #6772 | — | 2 | 2 | no | — |
| 63 | D3×Dic10 | — | 2 | 2 | no | — |
| 64 | #6765 | — | 2 | 2 | no | — |
| 65 | D5×Dic6 | — | 2 | 2 | no | — |
| 66 | C3×C5×C4⋊C4 | — | 4 | 1 | no | — |
| 67 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 68 | #6718 | — | 2 | 2 | no | — |
| 69 | #6718 | — | 2 | 2 | no | — |
| 70 | #6718 | — | 2 | 2 | no | — |
| 71 | #6718 | — | 2 | 2 | no | — |
| 72 | C4⋊Dic15 | — | 4 | 1 | no | — |
| 73 | C2×C3⋊#168 | C23 | 1 | 2 | yes | — |
| 74 | C5×#216 | — | 2 | 2 | no | — |
| 75 | C5×#215 | — | 2 | 2 | no | — |
| 76 | C5×#208 | C23 | 1 | 2 | yes | — |
| 77 | C3×#689 | — | 2 | 2 | no | — |
| 78 | C3×#688 | — | 2 | 2 | no | — |
| 79 | C3×#681 | C23 | 1 | 2 | yes | — |
| 80 | #6663 | — | 2 | 2 | no | — |
| 81 | #6662 | — | 2 | 2 | no | — |
| 82 | #6661 | D4 | 1 | 2 | yes | — |
| 83 | #6659 | — | 2 | 2 | no | — |
| 84 | #6657 | — | 2 | 2 | no | — |
| 85 | #6656 | D4 | 1 | 2 | yes | — |
| 86 | #6655 | D4 | 1 | 2 | yes | — |
| 87 | #6652 | D4 | 1 | 2 | yes | — |
| 88 | #6650 | — | 2 | 2 | no | — |
| 89 | #6649 | — | 2 | 2 | no | — |
| 90 | D3×#168 | — | 2 | 2 | no | — |
| 91 | D5×C3⋊C8 | — | 2 | 2 | no | — |
| 92 | #5838 | — | 5 | 2 | no | — |
| 93 | #5779 | — | 5 | 2 | no | — |
| 94 | C3×#456 | — | 5 | 1 | no | — |
| 95 | #5204 | — | 5 | 2 | no | — |
| 96 | #5095 | D5 | 1 | 1 | yes | characteristic, complemented |
| 97 | #5092 | — | 5 | 1 | no | — |
| 98 | #4826 | — | 5 | 2 | no | — |
| 99 | #4824 | — | 5 | 2 | no | — |
| 100 | #4755 | — | 5 | 2 | no | — |
| 101 | C5×2−1+4 | — | 3 | 1 | no | — |
| 102 | #4150 | — | 3 | 2 | no | — |
| 103 | #4147 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | C5×#137 | — | 3 | 2 | no | — |
| 105 | C5×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | #4097 | — | 3 | 2 | no | — |
| 107 | #4097 | — | 6 | 2 | no | — |
| 108 | #4096 | — | 3 | 2 | no | — |
| 109 | #4096 | — | 6 | 2 | no | — |
| 110 | #4094 | — | 3 | 2 | no | — |
| 111 | C2×#689 | — | 3 | 2 | no | — |
| 112 | C2×#689 | — | 3 | 2 | no | — |
| 113 | C2×#689 | — | 6 | 2 | no | — |
| 114 | #4088 | — | 6 | 2 | no | — |
| 115 | #4088 | C2×D3 | 1 | 2 | yes | — |
| 116 | #4064 | — | 6 | 2 | no | — |
| 117 | D5×Q16 | — | 6 | 2 | no | — |
| 118 | #4062 | — | 6 | 2 | no | — |
| 119 | #4061 | — | 6 | 2 | no | — |
| 120 | #4055 | — | 3 | 2 | no | — |
| 121 | #4053 | — | 3 | 2 | no | — |
| 122 | #4015 | — | 3 | 1 | no | — |
| 123 | C5×#104 | — | 3 | 2 | no | — |
| 124 | C5×#101 | — | 3 | 1 | no | — |
| 125 | #3968 | C2×D3 | 1 | 1 | yes | characteristic |
| 126 | #3956 | — | 3 | 2 | no | — |
| 127 | #3954 | — | 3 | 2 | no | — |
| 128 | #3937 | C2×D3 | 1 | 2 | yes | — |
| 129 | C4×#168 | — | 3 | 1 | no | — |
| 130 | #3293 | — | 15 | 1 | no | Sylow |
| 131 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 132 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 133 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 134 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 135 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 136 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 137 | C2×Dic15 | — | 2 | 2 | no | — |
| 138 | Dic30 | — | 2 | 2 | no | — |
| 139 | Dic30 | — | 2 | 2 | no | — |
| 140 | C5×#67 | — | 2 | 2 | no | — |
| 141 | C5×D12 | — | 4 | 1 | no | — |
| 142 | C5×D12 | C2×D4 | 1 | 2 | yes | — |
| 143 | C4×C5×D3 | — | 2 | 2 | no | — |
| 144 | C4×C5×D3 | — | 4 | 2 | no | — |
| 145 | C5×Dic6 | — | 4 | 1 | no | — |
| 146 | C5×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 147 | C3×C22⋊D5 | — | 2 | 2 | no | — |
| 148 | C3×D20 | — | 4 | 1 | no | — |
| 149 | C3×D20 | C2×D4 | 1 | 2 | yes | — |
| 150 | C3×C4×D5 | — | 2 | 2 | no | — |
| 151 | C3×C4×D5 | — | 4 | 2 | no | — |
| 152 | C3×Dic10 | — | 4 | 1 | no | — |
| 153 | C3×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 154 | #1204 | — | 4 | 2 | no | — |
| 155 | #1201 | — | 4 | 2 | no | — |
| 156 | D3×Dic5 | — | 4 | 2 | no | — |
| 157 | D5×Dic3 | — | 4 | 2 | no | — |
| 158 | C3⋊#168 | C2×D4 | 1 | 2 | yes | — |
| 159 | C3⋊#168 | C2×D4 | 1 | 2 | yes | — |
| 160 | C3×#168 | — | 2 | 2 | no | — |
| 161 | C5×C3⋊C8 | — | 2 | 2 | no | — |
| 162 | C3×2−1+4 | — | 5 | 1 | no | — |
| 163 | #1010 | — | 5 | 2 | no | — |
| 164 | #1007 | C2×D5 | 1 | 1 | yes | characteristic |
| 165 | C3×#137 | — | 5 | 2 | no | — |
| 166 | C3×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 167 | #951 | — | 5 | 2 | no | — |
| 168 | #951 | — | 10 | 2 | no | — |
| 169 | #950 | — | 5 | 2 | no | — |
| 170 | #950 | — | 10 | 2 | no | — |
| 171 | #948 | — | 5 | 2 | no | — |
| 172 | C2×#216 | — | 5 | 2 | no | — |
| 173 | C2×#216 | — | 5 | 2 | no | — |
| 174 | C2×#216 | — | 10 | 2 | no | — |
| 175 | #942 | — | 10 | 2 | no | — |
| 176 | #942 | C2×D5 | 1 | 2 | yes | — |
| 177 | #918 | — | 10 | 2 | no | — |
| 178 | D3×Q16 | — | 10 | 2 | no | — |
| 179 | #916 | — | 10 | 2 | no | — |
| 180 | #915 | — | 10 | 2 | no | — |
| 181 | #909 | — | 5 | 2 | no | — |
| 182 | #907 | — | 5 | 2 | no | — |
| 183 | #869 | — | 5 | 1 | no | — |
| 184 | C3×#104 | — | 5 | 2 | no | — |
| 185 | C3×#101 | — | 5 | 1 | no | — |
| 186 | #836 | C2×D5 | 1 | 1 | yes | characteristic |
| 187 | #824 | — | 5 | 2 | no | — |
| 188 | #822 | — | 5 | 2 | no | — |
| 189 | #805 | C2×D5 | 1 | 2 | yes | — |
| 190 | C4×C3⋊C8 | — | 5 | 1 | no | — |
| 191 | C5×#41 | — | 3 | 2 | no | — |
| 192 | C5×#41 | — | 6 | 2 | no | — |
| 193 | C5×#41 | — | 12 | 1 | no | — |
| 194 | C2×C5×Q8 | — | 6 | 2 | no | — |
| 195 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 196 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | #713 | — | 2 | 2 | no | — |
| 198 | Q8×D5 | — | 2 | 2 | no | — |
| 199 | Q8×D5 | — | 6 | 2 | no | — |
| 200 | #711 | — | 6 | 2 | no | — |
| 201 | #711 | — | 12 | 2 | no | — |
| 202 | #709 | — | 4 | 1 | no | — |
| 203 | #709 | — | 6 | 2 | no | — |
| 204 | #709 | C22×D3 | 1 | 2 | yes | — |
| 205 | C2×Dic10 | — | 3 | 2 | no | — |
| 206 | C2×Dic10 | — | 6 | 2 | no | — |
| 207 | C5×Q16 | — | 6 | 2 | no | — |
| 208 | C5×SD16 | — | 6 | 2 | no | — |
| 209 | C5×M16 | — | 3 | 2 | no | — |
| 210 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 211 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 212 | #689 | — | 2 | 2 | no | — |
| 213 | #689 | — | 3 | 2 | no | — |
| 214 | #689 | — | 6 | 2 | no | — |
| 215 | #689 | — | 6 | 2 | no | — |
| 216 | #689 | — | 6 | 2 | no | — |
| 217 | #689 | — | 6 | 2 | no | — |
| 218 | #689 | — | 6 | 2 | no | — |
| 219 | #688 | — | 2 | 2 | no | — |
| 220 | #688 | — | 3 | 2 | no | — |
| 221 | #687 | — | 3 | 2 | no | — |
| 222 | #687 | — | 6 | 2 | no | — |
| 223 | #686 | — | 3 | 2 | no | — |
| 224 | C4⋊Dic5 | — | 12 | 1 | no | — |
| 225 | #681 | — | 6 | 2 | no | — |
| 226 | #681 | C22×D3 | 1 | 2 | yes | — |
| 227 | C2×#168 | — | 3 | 2 | no | — |
| 228 | C2×#168 | — | 6 | 2 | no | — |
| 229 | Dic20 | — | 6 | 2 | no | — |
| 230 | #677 | — | 6 | 2 | no | — |
| 231 | #676 | — | 6 | 2 | no | — |
| 232 | C8×D5 | — | 6 | 2 | no | — |
| 233 | #578 | — | 15 | 2 | no | — |
| 234 | #578 | — | 15 | 2 | no | — |
| 235 | #494 | — | 15 | 1 | no | — |
| 236 | #473 | — | 15 | 2 | no | — |
| 237 | #473 | — | 15 | 2 | no | — |
| 238 | #456 | — | 3 | 1 | no | — |
| 239 | #456 | — | 5 | 1 | no | — |
| 240 | #456 | — | 15 | 2 | no | — |
| 241 | #443 | — | 15 | 2 | no | — |
| 242 | C22×C3×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 243 | C2×C5×D3 | — | 2 | 2 | no | — |
| 244 | C2×C3×D5 | — | 2 | 2 | no | — |
| 245 | C3×C4×C5 | — | 2 | 2 | no | — |
| 246 | C3×C4×C5 | — | 4 | 1 | no | — |
| 247 | C3×C4×C5 | — | 4 | 1 | no | — |
| 248 | C3×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 249 | Dic15 | — | 4 | 2 | no | — |
| 250 | C3×Dic5 | — | 2 | 2 | no | — |
| 251 | C5×Dic3 | — | 2 | 2 | no | — |
| 252 | C3×#41 | — | 5 | 2 | no | — |
| 253 | C3×#41 | — | 10 | 2 | no | — |
| 254 | C3×#41 | — | 20 | 1 | no | — |
| 255 | C2×C3×Q8 | — | 10 | 2 | no | — |
| 256 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 257 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 258 | #239 | — | 2 | 2 | no | — |
| 259 | D3×Q8 | — | 2 | 2 | no | — |
| 260 | D3×Q8 | — | 10 | 2 | no | — |
| 261 | #237 | — | 10 | 2 | no | — |
| 262 | #237 | — | 20 | 2 | no | — |
| 263 | #235 | — | 4 | 1 | no | — |
| 264 | #235 | — | 10 | 2 | no | — |
| 265 | #235 | C22×D5 | 1 | 2 | yes | — |
| 266 | C2×Dic6 | — | 5 | 2 | no | — |
| 267 | C2×Dic6 | — | 10 | 2 | no | — |
| 268 | C3×Q16 | — | 10 | 2 | no | — |
| 269 | C3×SD16 | — | 10 | 2 | no | — |
| 270 | C3×M16 | — | 5 | 2 | no | — |
| 271 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 272 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 273 | #216 | — | 2 | 2 | no | — |
| 274 | #216 | — | 5 | 2 | no | — |
| 275 | #216 | — | 10 | 2 | no | — |
| 276 | #216 | — | 10 | 2 | no | — |
| 277 | #216 | — | 10 | 2 | no | — |
| 278 | #216 | — | 10 | 2 | no | — |
| 279 | #216 | — | 10 | 2 | no | — |
| 280 | #215 | — | 2 | 2 | no | — |
| 281 | #215 | — | 5 | 2 | no | — |
| 282 | #214 | — | 5 | 2 | no | — |
| 283 | #214 | — | 10 | 2 | no | — |
| 284 | #213 | — | 5 | 2 | no | — |
| 285 | C4⋊Dic3 | — | 20 | 1 | no | — |
| 286 | #208 | — | 10 | 2 | no | — |
| 287 | #208 | C22×D5 | 1 | 2 | yes | — |
| 288 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 289 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 290 | Dic12 | — | 10 | 2 | no | — |
| 291 | #204 | — | 10 | 2 | no | — |
| 292 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 293 | D3×C8 | — | 10 | 2 | no | — |
| 294 | C5×Q8 | — | 2 | 2 | no | — |
| 295 | C5×Q8 | — | 2 | 2 | no | — |
| 296 | C5×Q8 | — | 3 | 2 | no | — |
| 297 | C5×Q8 | — | 12 | 1 | no | — |
| 298 | C5×D4 | — | 3 | 2 | no | — |
| 299 | C5×D4 | — | 6 | 2 | no | — |
| 300 | C5×D4 | — | 12 | 1 | no | — |
| 301 | C2×C4×C5 | — | 2 | 1 | no | — |
| 302 | C2×C4×C5 | — | 2 | 1 | no | — |
| 303 | C2×C4×C5 | — | 2 | 1 | no | — |
| 304 | C2×C4×C5 | — | 6 | 2 | no | — |
| 305 | C2×C4×C5 | — | 12 | 2 | no | — |
| 306 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 307 | C22⋊D5 | — | 2 | 2 | no | — |
| 308 | C22⋊D5 | — | 12 | 2 | no | — |
| 309 | C2×Dic5 | — | 6 | 2 | no | — |
| 310 | C2×Dic5 | — | 12 | 2 | no | — |
| 311 | D20 | — | 4 | 1 | no | — |
| 312 | D20 | D3×D4 | 1 | 2 | yes | — |
| 313 | C4×D5 | — | 2 | 2 | no | — |
| 314 | C4×D5 | — | 4 | 2 | no | — |
| 315 | C4×D5 | — | 12 | 2 | no | — |
| 316 | Dic10 | — | 4 | 1 | no | — |
| 317 | Dic10 | — | 6 | 2 | no | — |
| 318 | Dic10 | — | 6 | 2 | no | — |
| 319 | Dic10 | — | 12 | 2 | no | — |
| 320 | Dic10 | D3×D4 | 1 | 2 | yes | — |
| 321 | C5×C8 | — | 6 | 2 | no | — |
| 322 | #168 | — | 2 | 2 | no | — |
| 323 | #168 | — | 3 | 2 | no | — |
| 324 | #168 | — | 3 | 2 | no | — |
| 325 | 2−1+4 | — | 3 | 1 | no | — |
| 326 | 2−1+4 | — | 5 | 1 | no | — |
| 327 | 2−1+4 | — | 15 | 2 | no | — |
| 328 | #137 | — | 3 | 2 | no | — |
| 329 | #137 | — | 5 | 2 | no | — |
| 330 | #137 | — | 15 | 2 | no | — |
| 331 | #137 | — | 15 | 2 | no | — |
| 332 | #137 | — | 30 | 2 | no | — |
| 333 | #137 | — | 30 | 2 | no | — |
| 334 | #137 | — | 30 | 2 | no | — |
| 335 | #137 | — | 30 | 2 | no | — |
| 336 | #135 | — | 15 | 2 | no | — |
| 337 | #135 | — | 30 | 2 | no | — |
| 338 | #135 | — | 30 | 2 | no | — |
| 339 | C2×Q16 | — | 15 | 2 | no | — |
| 340 | C2×Q16 | — | 15 | 2 | no | — |
| 341 | C2×Q16 | — | 30 | 2 | no | — |
| 342 | C2×Q16 | — | 30 | 2 | no | — |
| 343 | #131 | — | 15 | 2 | no | — |
| 344 | #131 | — | 15 | 2 | no | — |
| 345 | C4⋊Q8 | — | 15 | 1 | no | — |
| 346 | C4⋊Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 347 | #108 | — | 15 | 2 | no | — |
| 348 | #104 | — | 3 | 2 | no | — |
| 349 | #104 | — | 5 | 2 | no | — |
| 350 | #101 | — | 3 | 1 | no | — |
| 351 | #101 | — | 5 | 1 | no | — |
| 352 | #101 | — | 15 | 2 | no | — |
| 353 | C4×C8 | — | 15 | 1 | no | — |
| 354 | C2×C3×C5 | — | 2 | 1 | no | — |
| 355 | C2×C3×C5 | D42 | 1 | 1 | yes | characteristic |
| 356 | C3×D5 | — | 4 | 2 | no | — |
| 357 | C5×D3 | — | 4 | 2 | no | — |
| 358 | C3×Q8 | — | 2 | 2 | no | — |
| 359 | C3×Q8 | — | 2 | 2 | no | — |
| 360 | C3×Q8 | — | 5 | 2 | no | — |
| 361 | C3×Q8 | — | 20 | 1 | no | — |
| 362 | C3×D4 | — | 5 | 2 | no | — |
| 363 | C3×D4 | — | 10 | 2 | no | — |
| 364 | C3×D4 | — | 20 | 1 | no | — |
| 365 | C2×C3×C4 | — | 2 | 1 | no | — |
| 366 | C2×C3×C4 | — | 2 | 1 | no | — |
| 367 | C2×C3×C4 | — | 2 | 1 | no | — |
| 368 | C2×C3×C4 | — | 10 | 2 | no | — |
| 369 | C2×C3×C4 | — | 20 | 2 | no | — |
| 370 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 371 | #67 | — | 2 | 2 | no | — |
| 372 | #67 | — | 20 | 2 | no | — |
| 373 | C2×Dic3 | — | 10 | 2 | no | — |
| 374 | C2×Dic3 | — | 20 | 2 | no | — |
| 375 | D12 | — | 4 | 1 | no | — |
| 376 | D12 | D4×D5 | 1 | 2 | yes | — |
| 377 | C4×D3 | — | 2 | 2 | no | — |
| 378 | C4×D3 | — | 4 | 2 | no | — |
| 379 | C4×D3 | — | 20 | 2 | no | — |
| 380 | Dic6 | — | 4 | 1 | no | — |
| 381 | Dic6 | — | 10 | 2 | no | — |
| 382 | Dic6 | — | 10 | 2 | no | — |
| 383 | Dic6 | — | 20 | 2 | no | — |
| 384 | Dic6 | D4×D5 | 1 | 2 | yes | — |
| 385 | C3×C8 | — | 10 | 2 | no | — |
| 386 | C3⋊C8 | — | 2 | 2 | no | — |
| 387 | C3⋊C8 | — | 5 | 2 | no | — |
| 388 | C3⋊C8 | — | 5 | 2 | no | — |
| 389 | C22×C5 | — | 6 | 2 | no | — |
| 390 | C22×C5 | #1004 | 1 | 1 | yes | characteristic |
| 391 | C2×D5 | — | 2 | 2 | no | — |
| 392 | C4×C5 | — | 2 | 2 | no | — |
| 393 | C4×C5 | — | 4 | 1 | no | — |
| 394 | C4×C5 | — | 4 | 1 | no | — |
| 395 | C4×C5 | — | 6 | 2 | no | — |
| 396 | C4×C5 | C2×D3×D4 | 1 | 2 | yes | — |
| 397 | Dic5 | — | 2 | 2 | no | — |
| 398 | Dic5 | — | 12 | 2 | no | — |
| 399 | #41 | — | 3 | 2 | no | — |
| 400 | #41 | — | 5 | 2 | no | — |
| 401 | #41 | — | 6 | 2 | no | — |
| 402 | #41 | — | 10 | 2 | no | — |
| 403 | #41 | — | 12 | 1 | no | — |
| 404 | #41 | — | 20 | 1 | no | — |
| 405 | #41 | — | 30 | 2 | no | — |
| 406 | #41 | — | 30 | 2 | no | — |
| 407 | #41 | — | 60 | 2 | no | — |
| 408 | C2×Q8 | — | 6 | 2 | no | — |
| 409 | C2×Q8 | — | 10 | 2 | no | — |
| 410 | C2×Q8 | — | 15 | 2 | no | — |
| 411 | C2×Q8 | — | 30 | 2 | no | — |
| 412 | C2×Q8 | — | 30 | 2 | no | — |
| 413 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 414 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 415 | Q16 | — | 6 | 2 | no | — |
| 416 | Q16 | — | 10 | 2 | no | — |
| 417 | Q16 | — | 15 | 2 | no | — |
| 418 | Q16 | — | 30 | 2 | no | — |
| 419 | Q16 | — | 30 | 2 | no | — |
| 420 | Q16 | — | 30 | 2 | no | — |
| 421 | Q16 | — | 30 | 2 | no | — |
| 422 | Q16 | — | 30 | 2 | no | — |
| 423 | Q16 | — | 30 | 2 | no | — |
| 424 | SD16 | — | 6 | 2 | no | — |
| 425 | SD16 | — | 10 | 2 | no | — |
| 426 | SD16 | — | 15 | 2 | no | — |
| 427 | SD16 | — | 15 | 2 | no | — |
| 428 | SD16 | — | 30 | 2 | no | — |
| 429 | SD16 | — | 30 | 2 | no | — |
| 430 | D8 | — | 15 | 2 | no | — |
| 431 | M16 | — | 3 | 2 | no | — |
| 432 | M16 | — | 5 | 2 | no | — |
| 433 | M16 | — | 30 | 2 | no | — |
| 434 | M16 | — | 30 | 2 | no | — |
| 435 | C2×C8 | — | 15 | 2 | no | — |
| 436 | C2×C8 | — | 30 | 2 | no | — |
| 437 | C2×C8 | — | 30 | 2 | no | — |
| 438 | C4⋊C4 | — | 4 | 1 | no | — |
| 439 | C4⋊C4 | — | 60 | 1 | no | — |
| 440 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 441 | C3×C5 | #3293 | 1 | 1 | yes | characteristic, complemented, Hall |
| 442 | C22×C3 | — | 10 | 2 | no | — |
| 443 | C22×C3 | #4144 | 1 | 1 | yes | characteristic |
| 444 | C2×D3 | — | 2 | 2 | no | — |
| 445 | C3×C4 | — | 2 | 2 | no | — |
| 446 | C3×C4 | — | 4 | 1 | no | — |
| 447 | C3×C4 | — | 4 | 1 | no | — |
| 448 | C3×C4 | — | 10 | 2 | no | — |
| 449 | C3×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 450 | Dic3 | — | 2 | 2 | no | — |
| 451 | Dic3 | — | 20 | 2 | no | — |
| 452 | C2×C5 | — | 2 | 1 | no | — |
| 453 | C2×C5 | — | 12 | 2 | no | — |
| 454 | C2×C5 | #5590 | 1 | 1 | yes | characteristic |
| 455 | D5 | — | 4 | 2 | no | — |
| 456 | Q8 | — | 2 | 2 | no | — |
| 457 | Q8 | — | 2 | 2 | no | — |
| 458 | Q8 | — | 3 | 2 | no | — |
| 459 | Q8 | — | 5 | 2 | no | — |
| 460 | Q8 | — | 12 | 1 | no | — |
| 461 | Q8 | — | 20 | 1 | no | — |
| 462 | Q8 | — | 30 | 2 | no | — |
| 463 | Q8 | — | 30 | 2 | no | — |
| 464 | Q8 | — | 60 | 2 | no | — |
| 465 | D4 | — | 3 | 2 | no | — |
| 466 | D4 | — | 5 | 2 | no | — |
| 467 | D4 | — | 6 | 2 | no | — |
| 468 | D4 | — | 10 | 2 | no | — |
| 469 | D4 | — | 12 | 1 | no | — |
| 470 | D4 | — | 20 | 1 | no | — |
| 471 | D4 | — | 60 | 2 | no | — |
| 472 | C2×C4 | — | 2 | 1 | no | — |
| 473 | C2×C4 | — | 2 | 1 | no | — |
| 474 | C2×C4 | — | 2 | 1 | no | — |
| 475 | C2×C4 | — | 6 | 2 | no | — |
| 476 | C2×C4 | — | 10 | 2 | no | — |
| 477 | C2×C4 | — | 12 | 2 | no | — |
| 478 | C2×C4 | — | 20 | 2 | no | — |
| 479 | C2×C4 | — | 30 | 2 | no | — |
| 480 | C2×C4 | — | 60 | 2 | no | — |
| 481 | C2×C4 | — | 60 | 2 | no | — |
| 482 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 483 | C8 | — | 6 | 2 | no | — |
| 484 | C8 | — | 10 | 2 | no | — |
| 485 | C8 | — | 15 | 2 | no | — |
| 486 | C8 | — | 15 | 2 | no | — |
| 487 | C2×C3 | — | 2 | 1 | no | — |
| 488 | C2×C3 | — | 20 | 2 | no | — |
| 489 | C2×C3 | #65924 | 1 | 1 | yes | characteristic |
| 490 | D3 | — | 4 | 2 | no | — |
| 491 | C5 | #80303 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 492 | C22 | — | 6 | 2 | no | — |
| 493 | C22 | — | 10 | 2 | no | — |
| 494 | C22 | #92049 | 1 | 1 | yes | characteristic |
| 495 | C4 | — | 2 | 2 | no | — |
| 496 | C4 | — | 4 | 1 | no | — |
| 497 | C4 | — | 4 | 1 | no | — |
| 498 | C4 | — | 6 | 2 | no | — |
| 499 | C4 | — | 10 | 2 | no | — |
| 500 | C4 | — | 60 | 2 | no | — |
| 501 | C4 | D3×D4×D5 | 1 | 2 | yes | — |
| 502 | C3 | #10612034 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 503 | C2 | — | 2 | 1 | no | — |
| 504 | C2 | — | 12 | 2 | no | — |
| 505 | C2 | — | 20 | 2 | no | — |
| 506 | C2 | #11755034 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11755114 | C2 | semidirect |
| 2. #11755102 | C2 | semidirect |
| 3. #11751193 | C2 | semidirect |
| 4. C5×#5095 | C2 | semidirect |
| 5. C3×#65384 | C2 | semidirect |
| 6. #11749382 | C2 | semidirect |
| 7. #11749378 | C2 | semidirect |
| 8. #11747124 | C2 | semidirect |
| 9. #11747106 | C2 | semidirect |
| 45. #65384 | D3 | semidirect |
| 96. #5095 | D5 | semidirect |
| 441. C3×C5 | #3293 | semidirect |
| 491. C5 | #80303 | semidirect |
| 502. C3 | #10612034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11755114 | 2 |
| #11755102 | 2 |
| #11751193 | 2 |
| C5×#5095 | 2 |
| C3×#65384 | 2 |
| #11749382 | 2 |
| #11749378 | 2 |
| #11747124 | 2 |
| #11747106 | 2 |
| #10612034 | 3 |
| #80303 | 5 |