Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2116 conjugacy classes of subgroups.
The subgroup lattice has 756 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11756427 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5683 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#66006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11755216 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11755170 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11754999 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11754824 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11753185 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11753059 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11752996 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #11752842 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #11752656 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #11752628 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #10618986 | — | 3 | 1 | no | maximal, Hall |
| 15 | C2×#6821 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#6819 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×D3×Dic5 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×#6768 | C22 | 1 | 2 | yes | — |
| 19 | C3×C5×#124 | C22 | 1 | 1 | yes | characteristic |
| 20 | #91833 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #91829 | C22 | 1 | 1 | yes | characteristic |
| 22 | #91773 | C22 | 1 | 4 | yes | complemented |
| 23 | #91770 | C22 | 1 | 4 | yes | complemented |
| 24 | #91764 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C42×D15 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C5×#947 | C22 | 1 | 2 | yes | — |
| 27 | C5×#937 | C22 | 1 | 2 | yes | — |
| 28 | C5×#885 | C22 | 1 | 4 | yes | — |
| 29 | C5×#882 | C22 | 1 | 4 | yes | — |
| 30 | C5×#875 | C22 | 1 | 2 | yes | — |
| 31 | C3×#4090 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×#4081 | C22 | 1 | 2 | yes | — |
| 33 | C3×#4025 | C22 | 1 | 4 | yes | complemented |
| 34 | C3×#4024 | C22 | 1 | 4 | yes | complemented |
| 35 | C3×#4016 | C22 | 1 | 2 | yes | complemented |
| 36 | #91570 | C22 | 1 | 2 | yes | complemented |
| 37 | #91570 | C22 | 1 | 4 | yes | complemented |
| 38 | #91566 | C22 | 1 | 4 | yes | — |
| 39 | #91562 | C22 | 1 | 4 | yes | complemented |
| 40 | #67⋊Dic5 | C22 | 1 | 4 | yes | — |
| 41 | #91558 | C22 | 1 | 4 | yes | — |
| 42 | #91557 | C22 | 1 | 4 | yes | — |
| 43 | #91546 | C22 | 1 | 2 | yes | complemented |
| 44 | #91532 | C22 | 1 | 2 | yes | complemented |
| 45 | #91466 | C22 | 1 | 2 | yes | — |
| 46 | #91451 | C22 | 1 | 2 | yes | — |
| 47 | #91438 | C22 | 1 | 4 | yes | complemented |
| 48 | #91435 | C22 | 1 | 2 | yes | — |
| 49 | #91432 | C22 | 1 | 4 | yes | complemented |
| 50 | #91427 | C22 | 1 | 4 | yes | complemented |
| 51 | #91424 | C22 | 1 | 4 | yes | complemented |
| 52 | #91423 | C22 | 1 | 4 | yes | — |
| 53 | #91420 | C22 | 1 | 4 | yes | complemented |
| 54 | #91420 | C22 | 1 | 4 | yes | complemented |
| 55 | #91416 | C22 | 1 | 4 | yes | — |
| 56 | #91410 | C22 | 1 | 4 | yes | complemented |
| 57 | #91406 | C22 | 1 | 4 | yes | complemented |
| 58 | #91406 | C22 | 1 | 4 | yes | complemented |
| 59 | C4×#1200 | C22 | 1 | 2 | yes | complemented |
| 60 | #91400 | C22 | 1 | 4 | yes | complemented |
| 61 | #91383 | C22 | 1 | 2 | yes | complemented |
| 62 | #91379 | C22 | 1 | 4 | yes | complemented |
| 63 | #91374 | C22 | 1 | 2 | yes | complemented |
| 64 | #91372 | C22 | 1 | 4 | yes | complemented |
| 65 | #91367 | C22 | 1 | 4 | yes | complemented |
| 66 | #91355 | C22 | 1 | 4 | yes | complemented |
| 67 | #91344 | C22 | 1 | 2 | yes | complemented |
| 68 | #87115 | — | 5 | 1 | no | maximal, Hall |
| 69 | C5×H(3,𝔽4) | — | 3 | 1 | no | — |
| 70 | #66018 | — | 3 | 4 | no | — |
| 71 | #66018 | — | 3 | 2 | no | — |
| 72 | #66014 | — | 3 | 4 | no | — |
| 73 | #66014 | — | 3 | 2 | no | — |
| 74 | #66006 | — | 3 | 2 | no | — |
| 75 | #66006 | D3 | 1 | 1 | yes | characteristic, complemented |
| 76 | #66002 | — | 3 | 2 | no | — |
| 77 | #66002 | — | 3 | 1 | no | — |
| 78 | #65929 | — | 3 | 2 | no | — |
| 79 | #65929 | — | 3 | 4 | no | — |
| 80 | #65920 | — | 3 | 2 | no | — |
| 81 | #65920 | — | 3 | 4 | no | — |
| 82 | C23×C5×D3 | C23 | 1 | 2 | yes | — |
| 83 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×C3×C5×D4 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×#1220 | C23 | 1 | 4 | yes | — |
| 86 | C2×#1220 | C23 | 1 | 2 | yes | — |
| 87 | C22×Dic15 | C23 | 1 | 2 | yes | — |
| 88 | #6821 | — | 4 | 2 | no | — |
| 89 | #6819 | — | 4 | 2 | no | — |
| 90 | C2×D60 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×D60 | C23 | 1 | 2 | yes | — |
| 92 | C2×C4×D15 | C23 | 1 | 2 | yes | — |
| 93 | C2×C4×D15 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×D15 | C23 | 1 | 2 | yes | — |
| 95 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C5×#67 | C23 | 1 | 4 | yes | — |
| 97 | C2×C5×D12 | C23 | 1 | 2 | yes | — |
| 98 | C2×C5×D12 | C23 | 1 | 2 | yes | — |
| 99 | C2×C5×Dic6 | C23 | 1 | 2 | yes | — |
| 100 | C22×C3×Dic5 | C23 | 1 | 2 | yes | — |
| 101 | C2×C3×Dic10 | C23 | 1 | 2 | yes | — |
| 102 | C2×#1203 | C23 | 1 | 4 | yes | — |
| 103 | C2×#1203 | C23 | 1 | 4 | yes | — |
| 104 | C2×#1203 | C23 | 1 | 4 | yes | — |
| 105 | C2×#1200 | C23 | 1 | 4 | yes | — |
| 106 | C2×D3×Dic5 | — | 4 | 4 | no | — |
| 107 | C2×D3×Dic5 | C23 | 1 | 4 | yes | — |
| 108 | C2×D3×Dic5 | C23 | 1 | 4 | yes | — |
| 109 | #6768 | — | 4 | 4 | no | — |
| 110 | C3×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 111 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 112 | #6714 | C23 | 1 | 4 | yes | — |
| 113 | #6712 | C23 | 1 | 4 | yes | — |
| 114 | C4×Dic15 | C23 | 1 | 2 | yes | — |
| 115 | C4×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 116 | C5×#217 | C23 | 1 | 2 | yes | — |
| 117 | C5×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 118 | C5×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 119 | C5×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 120 | C4×C5×Dic3 | C23 | 1 | 2 | yes | — |
| 121 | C3×C22⋊Dic5 | C23 | 1 | 2 | yes | — |
| 122 | C3×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 123 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 124 | C3×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 125 | C3×#683 | C23 | 1 | 4 | yes | — |
| 126 | C3×#683 | C23 | 1 | 4 | yes | — |
| 127 | C3×#683 | C23 | 1 | 4 | yes | — |
| 128 | C3×C4×Dic5 | C23 | 1 | 2 | yes | — |
| 129 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 130 | Dic3⋊Dic5 | C23 | 1 | 4 | yes | — |
| 131 | #6669 | C23 | 1 | 4 | yes | — |
| 132 | #6668 | C23 | 1 | 4 | yes | — |
| 133 | #6667 | C23 | 1 | 4 | yes | — |
| 134 | #6667 | C23 | 1 | 4 | yes | — |
| 135 | (C2×D3)⋊Dic5 | C23 | 1 | 4 | yes | — |
| 136 | (C2×D3)⋊Dic5 | C23 | 1 | 4 | yes | — |
| 137 | (C2×D3)⋊Dic5 | C23 | 1 | 4 | yes | — |
| 138 | Dic3×Dic5 | C23 | 1 | 4 | yes | — |
| 139 | C3×#563 | — | 5 | 1 | no | — |
| 140 | #5735 | — | 5 | 2 | no | — |
| 141 | #5725 | — | 5 | 2 | no | — |
| 142 | #5711 | — | 5 | 4 | no | — |
| 143 | #5706 | — | 5 | 4 | no | — |
| 144 | #5700 | — | 5 | 2 | no | — |
| 145 | #5691 | — | 5 | 2 | no | — |
| 146 | #5683 | D5 | 1 | 1 | yes | characteristic, complemented |
| 147 | #5668 | — | 5 | 1 | no | — |
| 148 | #5666 | — | 5 | 2 | no | — |
| 149 | #5656 | — | 5 | 2 | no | — |
| 150 | #5647 | — | 5 | 4 | no | — |
| 151 | #5627 | — | 5 | 4 | no | — |
| 152 | C23×Dic5 | — | 3 | 2 | no | — |
| 153 | C2×#713 | — | 3 | 1 | no | — |
| 154 | C2×#711 | — | 3 | 1 | no | — |
| 155 | C2×#711 | — | 3 | 2 | no | — |
| 156 | C5×#124 | — | 3 | 2 | no | — |
| 157 | C5×#124 | — | 3 | 4 | no | — |
| 158 | C5×#124 | — | 3 | 2 | no | — |
| 159 | C5×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 160 | C5×#120 | — | 3 | 2 | no | — |
| 161 | C5×#120 | — | 3 | 4 | no | — |
| 162 | #4099 | — | 3 | 4 | no | — |
| 163 | #4099 | — | 3 | 2 | no | — |
| 164 | #4092 | — | 3 | 2 | no | — |
| 165 | #4092 | — | 3 | 4 | no | — |
| 166 | Q8×Dic5 | — | 3 | 2 | no | — |
| 167 | #4090 | — | 3 | 1 | no | — |
| 168 | #4090 | C2×D3 | 1 | 2 | yes | complemented |
| 169 | #4086 | — | 3 | 1 | no | — |
| 170 | #4086 | — | 3 | 2 | no | — |
| 171 | #4085 | — | 3 | 4 | no | — |
| 172 | #4085 | — | 3 | 4 | no | — |
| 173 | #4085 | — | 3 | 4 | no | — |
| 174 | #4084 | — | 3 | 4 | no | — |
| 175 | #4084 | — | 3 | 2 | no | — |
| 176 | #4081 | — | 3 | 4 | no | — |
| 177 | #4081 | C2×D3 | 1 | 2 | yes | — |
| 178 | D4×Dic5 | — | 3 | 4 | no | — |
| 179 | D4×Dic5 | — | 3 | 2 | no | — |
| 180 | #4032 | — | 3 | 2 | no | — |
| 181 | #4032 | — | 3 | 4 | no | — |
| 182 | #4030 | — | 3 | 4 | no | — |
| 183 | #4030 | — | 3 | 4 | no | — |
| 184 | #4030 | — | 3 | 4 | no | — |
| 185 | #4029 | — | 3 | 4 | no | — |
| 186 | #4029 | — | 3 | 4 | no | — |
| 187 | #4029 | — | 3 | 4 | no | — |
| 188 | #4027 | — | 3 | 4 | no | — |
| 189 | #4027 | — | 3 | 4 | no | — |
| 190 | #4027 | — | 3 | 4 | no | — |
| 191 | #4025 | — | 3 | 4 | no | — |
| 192 | #4025 | — | 3 | 4 | no | — |
| 193 | #4025 | C2×D3 | 1 | 4 | yes | complemented |
| 194 | #4024 | — | 3 | 4 | no | — |
| 195 | #4024 | — | 3 | 4 | no | — |
| 196 | #4024 | C2×D3 | 1 | 4 | yes | complemented |
| 197 | #4023 | — | 3 | 2 | no | — |
| 198 | #4023 | — | 3 | 4 | no | — |
| 199 | #4021 | — | 3 | 2 | no | — |
| 200 | #4021 | — | 3 | 1 | no | — |
| 201 | C42×D5 | — | 3 | 1 | no | — |
| 202 | C42×D5 | — | 3 | 2 | no | — |
| 203 | #4016 | — | 3 | 4 | no | — |
| 204 | #4016 | C2×D3 | 1 | 2 | yes | complemented |
| 205 | #3529 | — | 15 | 1 | no | Sylow |
| 206 | C23×C3×C5 | C24 | 1 | 2 | yes | — |
| 207 | C22×D15 | C24 | 1 | 1 | yes | characteristic |
| 208 | C22×D15 | C24 | 1 | 2 | yes | — |
| 209 | C22×C5×D3 | — | 4 | 2 | no | — |
| 210 | C22×C5×D3 | — | 4 | 4 | no | — |
| 211 | C22×C5×D3 | C24 | 1 | 4 | yes | — |
| 212 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 213 | C3×C5×D4 | — | 4 | 1 | no | — |
| 214 | C2×C3×C4×C5 | C24 | 1 | 2 | yes | — |
| 215 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 216 | C2×C3×C4×C5 | C24 | 1 | 2 | yes | — |
| 217 | #1220 | — | 4 | 2 | no | — |
| 218 | #1220 | — | 4 | 4 | no | — |
| 219 | C2×Dic15 | — | 2 | 4 | no | — |
| 220 | C2×Dic15 | C24 | 1 | 2 | yes | — |
| 221 | C2×Dic15 | C24 | 1 | 2 | yes | — |
| 222 | C2×Dic15 | C24 | 1 | 1 | yes | characteristic |
| 223 | D60 | — | 4 | 2 | no | — |
| 224 | D60 | — | 4 | 1 | no | — |
| 225 | C4×D15 | — | 2 | 4 | no | — |
| 226 | C4×D15 | — | 2 | 2 | no | — |
| 227 | C4×D15 | — | 4 | 2 | no | — |
| 228 | Dic30 | — | 4 | 1 | no | — |
| 229 | C5×#67 | — | 4 | 4 | no | — |
| 230 | C2×C5×Dic3 | C24 | 1 | 4 | yes | — |
| 231 | C5×D12 | — | 4 | 2 | no | — |
| 232 | C5×D12 | — | 4 | 2 | no | — |
| 233 | C5×Dic6 | — | 4 | 2 | no | — |
| 234 | C2×C3×Dic5 | — | 4 | 2 | no | — |
| 235 | C2×C3×Dic5 | C24 | 1 | 4 | yes | — |
| 236 | C2×C3×Dic5 | C24 | 1 | 4 | yes | — |
| 237 | C3×Dic10 | — | 4 | 2 | no | — |
| 238 | #1203 | — | 4 | 4 | no | — |
| 239 | #1203 | — | 4 | 4 | no | — |
| 240 | #1203 | — | 4 | 4 | no | — |
| 241 | #1200 | — | 4 | 4 | no | — |
| 242 | D3×Dic5 | — | 2 | 8 | no | — |
| 243 | D3×Dic5 | — | 4 | 4 | no | — |
| 244 | C2×#239 | — | 5 | 1 | no | — |
| 245 | C2×#239 | — | 5 | 2 | no | — |
| 246 | C2×#237 | — | 5 | 1 | no | — |
| 247 | C22×C4×D3 | — | 5 | 2 | no | — |
| 248 | C3×C4⋊Q8 | — | 5 | 2 | no | — |
| 249 | C3×#126 | — | 5 | 4 | no | — |
| 250 | C3×#125 | — | 5 | 2 | no | — |
| 251 | C3×#124 | C2×D5 | 1 | 1 | yes | characteristic |
| 252 | C3×#123 | — | 5 | 2 | no | — |
| 253 | C3×C22⋊Q8 | — | 5 | 4 | no | — |
| 254 | #947 | — | 5 | 2 | no | — |
| 255 | #947 | C2×D5 | 1 | 2 | yes | — |
| 256 | #946 | — | 5 | 4 | no | — |
| 257 | #944 | — | 5 | 1 | no | — |
| 258 | #940 | — | 5 | 1 | no | — |
| 259 | #937 | C2×D5 | 1 | 2 | yes | — |
| 260 | #930 | — | 5 | 4 | no | — |
| 261 | #929 | — | 5 | 2 | no | — |
| 262 | #898 | — | 5 | 4 | no | — |
| 263 | #897 | — | 5 | 2 | no | — |
| 264 | #896 | — | 5 | 4 | no | — |
| 265 | #896 | — | 5 | 4 | no | — |
| 266 | #895 | — | 5 | 4 | no | — |
| 267 | #895 | — | 5 | 2 | no | — |
| 268 | #895 | — | 5 | 4 | no | — |
| 269 | #895 | — | 5 | 4 | no | — |
| 270 | #894 | — | 5 | 4 | no | — |
| 271 | #894 | — | 5 | 4 | no | — |
| 272 | #894 | — | 5 | 4 | no | — |
| 273 | #894 | — | 5 | 4 | no | — |
| 274 | #893 | — | 5 | 2 | no | — |
| 275 | #893 | — | 5 | 4 | no | — |
| 276 | #893 | — | 5 | 4 | no | — |
| 277 | #892 | — | 5 | 4 | no | — |
| 278 | #889 | — | 5 | 4 | no | — |
| 279 | #887 | — | 5 | 2 | no | — |
| 280 | #885 | C2×D5 | 1 | 4 | yes | — |
| 281 | #884 | — | 5 | 4 | no | — |
| 282 | #884 | — | 5 | 4 | no | — |
| 283 | #884 | — | 5 | 4 | no | — |
| 284 | #883 | — | 5 | 4 | no | — |
| 285 | #882 | — | 5 | 2 | no | — |
| 286 | #882 | — | 5 | 4 | no | — |
| 287 | #882 | C2×D5 | 1 | 4 | yes | — |
| 288 | #67⋊C4 | — | 5 | 4 | no | — |
| 289 | #67⋊C4 | — | 5 | 4 | no | — |
| 290 | #877 | — | 5 | 2 | no | — |
| 291 | #876 | — | 5 | 4 | no | — |
| 292 | #875 | — | 5 | 1 | no | — |
| 293 | #875 | C2×D5 | 1 | 2 | yes | — |
| 294 | #874 | — | 5 | 2 | no | — |
| 295 | C42×D3 | — | 5 | 1 | no | — |
| 296 | C42×D3 | — | 5 | 2 | no | — |
| 297 | C24×C5 | — | 3 | 2 | no | — |
| 298 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 299 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 300 | C2×C5×D4 | — | 3 | 4 | no | — |
| 301 | C2×C5×D4 | — | 3 | 2 | no | — |
| 302 | C2×C5×D4 | — | 3 | 2 | no | — |
| 303 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 304 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 305 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 306 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 307 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 308 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 309 | C22×Dic5 | — | 3 | 2 | no | — |
| 310 | C22×Dic5 | — | 3 | 4 | no | — |
| 311 | C22×Dic5 | — | 3 | 4 | no | — |
| 312 | C22×Dic5 | — | 12 | 4 | no | — |
| 313 | C22×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 314 | #713 | — | 12 | 2 | no | — |
| 315 | #711 | — | 12 | 4 | no | — |
| 316 | #711 | — | 12 | 2 | no | — |
| 317 | C2×D20 | — | 3 | 1 | no | — |
| 318 | C2×D20 | — | 3 | 2 | no | — |
| 319 | C2×C4×D5 | — | 3 | 1 | no | — |
| 320 | C2×C4×D5 | — | 3 | 2 | no | — |
| 321 | C2×C4×D5 | — | 3 | 2 | no | — |
| 322 | C2×C4×D5 | — | 3 | 4 | no | — |
| 323 | C2×Dic10 | — | 3 | 1 | no | — |
| 324 | C2×Dic10 | C22×D3 | 1 | 2 | yes | — |
| 325 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 326 | C5×C22⋊C4 | — | 3 | 4 | no | — |
| 327 | C5×C22⋊C4 | — | 3 | 4 | no | — |
| 328 | C5×C22⋊C4 | — | 3 | 4 | no | — |
| 329 | C5×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 330 | C42×C5 | — | 3 | 2 | no | — |
| 331 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 332 | C22⋊Dic5 | — | 3 | 4 | no | — |
| 333 | C22⋊Dic5 | — | 3 | 4 | no | — |
| 334 | C22⋊Dic5 | — | 3 | 4 | no | — |
| 335 | C22⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 336 | C22⋊Dic5 | C22×D3 | 1 | 4 | yes | — |
| 337 | #685 | — | 3 | 4 | no | — |
| 338 | #685 | — | 3 | 4 | no | — |
| 339 | #685 | — | 3 | 4 | no | — |
| 340 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 341 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 342 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 343 | C4⋊Dic5 | C22×D3 | 1 | 2 | yes | — |
| 344 | #683 | — | 3 | 4 | no | — |
| 345 | #683 | — | 3 | 4 | no | — |
| 346 | #683 | — | 3 | 4 | no | — |
| 347 | #683 | C22×D3 | 1 | 4 | yes | — |
| 348 | #683 | C22×D3 | 1 | 4 | yes | — |
| 349 | #683 | C22×D3 | 1 | 4 | yes | — |
| 350 | C4×Dic5 | — | 3 | 2 | no | — |
| 351 | C4×Dic5 | — | 3 | 1 | no | — |
| 352 | C4×Dic5 | — | 3 | 4 | no | — |
| 353 | C4×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 354 | #563 | — | 5 | 1 | no | — |
| 355 | #563 | — | 15 | 2 | no | — |
| 356 | #562 | — | 15 | 4 | no | — |
| 357 | #562 | — | 15 | 2 | no | — |
| 358 | H(3,𝔽4) | — | 3 | 1 | no | — |
| 359 | #560 | — | 15 | 2 | no | — |
| 360 | #560 | — | 15 | 4 | no | — |
| 361 | #532 | — | 15 | 2 | no | — |
| 362 | #532 | — | 15 | 1 | no | — |
| 363 | #529 | — | 15 | 2 | no | — |
| 364 | #529 | — | 15 | 4 | no | — |
| 365 | #525 | — | 15 | 4 | no | — |
| 366 | #525 | — | 15 | 2 | no | — |
| 367 | C22×C3×C5 | — | 2 | 2 | no | — |
| 368 | C22×C3×C5 | — | 2 | 4 | no | — |
| 369 | C22×C3×C5 | C25 | 1 | 1 | yes | characteristic |
| 370 | C2×D15 | — | 2 | 2 | no | — |
| 371 | C2×D15 | — | 2 | 1 | no | — |
| 372 | C2×D15 | — | 2 | 4 | no | — |
| 373 | C2×D15 | — | 2 | 2 | no | — |
| 374 | C2×C5×D3 | — | 2 | 4 | no | — |
| 375 | C2×C5×D3 | — | 2 | 4 | no | — |
| 376 | C2×C5×D3 | — | 2 | 4 | no | — |
| 377 | C2×C5×D3 | — | 4 | 8 | no | — |
| 378 | C3×C4×C5 | — | 2 | 2 | no | — |
| 379 | C3×C4×C5 | — | 2 | 1 | no | — |
| 380 | C3×C4×C5 | — | 2 | 2 | no | — |
| 381 | Dic15 | — | 2 | 2 | no | — |
| 382 | Dic15 | — | 2 | 2 | no | — |
| 383 | Dic15 | H(5,𝔽2) | 1 | 2 | yes | — |
| 384 | C3×Dic5 | — | 2 | 4 | no | — |
| 385 | C3×Dic5 | — | 2 | 4 | no | — |
| 386 | C5×Dic3 | — | 2 | 4 | no | — |
| 387 | C23×D3 | C22×D5 | 1 | 2 | yes | — |
| 388 | C2×C3×Q8 | — | 5 | 2 | no | — |
| 389 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 390 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 391 | C22×C3×C4 | — | 5 | 2 | no | — |
| 392 | C2×#67 | — | 5 | 4 | no | — |
| 393 | C2×#67 | — | 5 | 2 | no | — |
| 394 | C2×#67 | C22×D5 | 1 | 4 | yes | — |
| 395 | C22×Dic3 | — | 5 | 2 | no | — |
| 396 | #239 | — | 20 | 4 | no | — |
| 397 | #239 | — | 20 | 2 | no | — |
| 398 | #237 | — | 20 | 2 | no | — |
| 399 | C2×D12 | — | 5 | 4 | no | — |
| 400 | C2×D12 | — | 5 | 4 | no | — |
| 401 | C2×D12 | — | 5 | 4 | no | — |
| 402 | C2×D12 | — | 5 | 2 | no | — |
| 403 | C2×D12 | — | 5 | 1 | no | — |
| 404 | C2×D12 | C22×D5 | 1 | 2 | yes | — |
| 405 | C2×D12 | C22×D5 | 1 | 2 | yes | — |
| 406 | C2×C4×D3 | — | 5 | 4 | no | — |
| 407 | C2×C4×D3 | — | 5 | 2 | no | — |
| 408 | C2×C4×D3 | — | 5 | 1 | no | — |
| 409 | C2×C4×D3 | — | 5 | 4 | no | — |
| 410 | C2×C4×D3 | — | 5 | 2 | no | — |
| 411 | C2×C4×D3 | — | 5 | 4 | no | — |
| 412 | C2×C4×D3 | — | 20 | 4 | no | — |
| 413 | C2×Dic6 | — | 5 | 1 | no | — |
| 414 | C2×Dic6 | C22×D5 | 1 | 2 | yes | — |
| 415 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 416 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 417 | C3×C4⋊C4 | — | 5 | 4 | no | — |
| 418 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 419 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 420 | C3×C22⋊C4 | — | 5 | 2 | no | — |
| 421 | C3×C22⋊C4 | — | 5 | 4 | no | — |
| 422 | C3×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 423 | C3×C42 | — | 5 | 2 | no | — |
| 424 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 425 | #217 | C22×D5 | 1 | 2 | yes | — |
| 426 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 427 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 428 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 429 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 430 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 431 | (C2×D3)⋊C4 | — | 5 | 4 | no | — |
| 432 | (C2×D3)⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 433 | (C2×D3)⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 434 | (C2×D3)⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 435 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 436 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 437 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 438 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 439 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 440 | C4×Dic3 | — | 5 | 2 | no | — |
| 441 | C4×Dic3 | — | 5 | 1 | no | — |
| 442 | C4×Dic3 | — | 5 | 4 | no | — |
| 443 | C4×Dic3 | C22×D5 | 1 | 2 | yes | — |
| 444 | C23×C5 | — | 3 | 4 | no | — |
| 445 | C23×C5 | — | 12 | 2 | no | — |
| 446 | C23×C5 | — | 12 | 4 | no | — |
| 447 | C23×C5 | C23×D3 | 1 | 2 | yes | — |
| 448 | C22×D5 | — | 3 | 2 | no | — |
| 449 | C22×D5 | — | 3 | 1 | no | — |
| 450 | C5×Q8 | — | 4 | 1 | no | — |
| 451 | C5×Q8 | — | 12 | 2 | no | — |
| 452 | C5×D4 | — | 4 | 1 | no | — |
| 453 | C5×D4 | — | 12 | 2 | no | — |
| 454 | C5×D4 | — | 12 | 2 | no | — |
| 455 | C5×D4 | — | 12 | 4 | no | — |
| 456 | C2×C4×C5 | — | 3 | 4 | no | — |
| 457 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 458 | C2×C4×C5 | C23×D3 | 1 | 2 | yes | — |
| 459 | C2×C4×C5 | C23×D3 | 1 | 2 | yes | — |
| 460 | C22⋊D5 | — | 12 | 4 | no | — |
| 461 | C22⋊D5 | — | 12 | 4 | no | — |
| 462 | C22⋊D5 | — | 12 | 4 | no | — |
| 463 | C22⋊D5 | — | 12 | 2 | no | — |
| 464 | C22⋊D5 | — | 12 | 4 | no | — |
| 465 | C2×Dic5 | — | 3 | 1 | no | — |
| 466 | C2×Dic5 | — | 3 | 2 | no | — |
| 467 | C2×Dic5 | — | 3 | 2 | no | — |
| 468 | C2×Dic5 | — | 4 | 2 | no | — |
| 469 | C2×Dic5 | — | 6 | 8 | no | — |
| 470 | C2×Dic5 | — | 6 | 4 | no | — |
| 471 | C2×Dic5 | — | 12 | 4 | no | — |
| 472 | C2×Dic5 | C23×D3 | 1 | 4 | yes | — |
| 473 | C2×Dic5 | C23×D3 | 1 | 4 | yes | — |
| 474 | D20 | — | 12 | 2 | no | — |
| 475 | D20 | — | 12 | 1 | no | — |
| 476 | C4×D5 | — | 6 | 4 | no | — |
| 477 | C4×D5 | — | 6 | 2 | no | — |
| 478 | C4×D5 | — | 12 | 4 | no | — |
| 479 | C4×D5 | — | 12 | 2 | no | — |
| 480 | Dic10 | — | 4 | 2 | no | — |
| 481 | Dic10 | — | 12 | 1 | no | — |
| 482 | C2×#41 | — | 15 | 2 | no | — |
| 483 | C2×#41 | — | 15 | 1 | no | — |
| 484 | C2×#41 | — | 15 | 1 | no | — |
| 485 | C23×C4 | — | 15 | 2 | no | — |
| 486 | C4⋊Q8 | — | 5 | 2 | no | — |
| 487 | C4⋊Q8 | — | 15 | 1 | no | — |
| 488 | #127 | — | 15 | 2 | no | — |
| 489 | #127 | — | 15 | 1 | no | — |
| 490 | #126 | — | 5 | 4 | no | — |
| 491 | #126 | — | 15 | 4 | no | — |
| 492 | #126 | — | 15 | 4 | no | — |
| 493 | #125 | — | 5 | 2 | no | — |
| 494 | #125 | — | 15 | 4 | no | — |
| 495 | #124 | — | 3 | 2 | no | — |
| 496 | #124 | — | 3 | 4 | no | — |
| 497 | #124 | — | 3 | 2 | no | — |
| 498 | #124 | — | 15 | 2 | no | — |
| 499 | #124 | — | 15 | 1 | no | — |
| 500 | #124 | D3×D5 | 1 | 1 | yes | characteristic |
| 501 | #123 | — | 5 | 2 | no | — |
| 502 | #123 | — | 15 | 4 | no | — |
| 503 | #123 | — | 15 | 4 | no | — |
| 504 | #123 | — | 15 | 4 | no | — |
| 505 | #123 | — | 15 | 4 | no | — |
| 506 | #123 | — | 15 | 2 | no | — |
| 507 | #123 | — | 15 | 4 | no | — |
| 508 | C22⋊Q8 | — | 5 | 4 | no | — |
| 509 | C22⋊Q8 | — | 15 | 4 | no | — |
| 510 | C22⋊Q8 | — | 15 | 4 | no | — |
| 511 | C22⋊Q8 | — | 15 | 4 | no | — |
| 512 | C22⋊Q8 | — | 15 | 2 | no | — |
| 513 | #121 | — | 15 | 4 | no | — |
| 514 | #121 | — | 15 | 4 | no | — |
| 515 | #121 | — | 15 | 4 | no | — |
| 516 | #121 | — | 15 | 4 | no | — |
| 517 | #121 | — | 15 | 4 | no | — |
| 518 | #121 | — | 15 | 2 | no | — |
| 519 | #121 | — | 15 | 4 | no | — |
| 520 | #121 | — | 15 | 4 | no | — |
| 521 | #120 | — | 3 | 2 | no | — |
| 522 | #120 | — | 3 | 4 | no | — |
| 523 | #120 | — | 15 | 2 | no | — |
| 524 | #120 | — | 15 | 4 | no | — |
| 525 | C4×Q8 | — | 15 | 2 | no | — |
| 526 | C4×D4 | — | 15 | 4 | no | — |
| 527 | C4×D4 | — | 15 | 4 | no | — |
| 528 | C4×D4 | — | 15 | 4 | no | — |
| 529 | C4×D4 | — | 15 | 2 | no | — |
| 530 | C4×D4 | — | 15 | 4 | no | — |
| 531 | #117 | — | 15 | 2 | no | — |
| 532 | #117 | — | 15 | 4 | no | — |
| 533 | C2×C42 | — | 15 | 2 | no | — |
| 534 | C2×C42 | — | 15 | 1 | no | — |
| 535 | C2×C3×C5 | — | 4 | 2 | no | — |
| 536 | C2×C3×C5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 537 | C2×C3×C5 | #585 | 1 | 2 | yes | — |
| 538 | D15 | — | 4 | 2 | no | — |
| 539 | D15 | — | 4 | 1 | no | — |
| 540 | C5×D3 | — | 4 | 4 | no | — |
| 541 | C23×C3 | C23×D5 | 1 | 2 | yes | — |
| 542 | C22×D3 | — | 4 | 2 | no | — |
| 543 | C22×D3 | — | 4 | 4 | no | — |
| 544 | C22×D3 | — | 5 | 2 | no | — |
| 545 | C22×D3 | — | 5 | 1 | no | — |
| 546 | C22×D3 | C23×D5 | 1 | 4 | yes | — |
| 547 | C3×Q8 | — | 4 | 1 | no | — |
| 548 | C3×Q8 | — | 20 | 2 | no | — |
| 549 | C3×D4 | — | 4 | 1 | no | — |
| 550 | C2×C3×C4 | — | 5 | 4 | no | — |
| 551 | C2×C3×C4 | — | 5 | 4 | no | — |
| 552 | C2×C3×C4 | — | 20 | 2 | no | — |
| 553 | C2×C3×C4 | C23×D5 | 1 | 2 | yes | — |
| 554 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 555 | C2×C3×C4 | C23×D5 | 1 | 2 | yes | — |
| 556 | #67 | — | 4 | 4 | no | — |
| 557 | #67 | — | 20 | 2 | no | — |
| 558 | #67 | — | 20 | 4 | no | — |
| 559 | C2×Dic3 | — | 5 | 1 | no | — |
| 560 | C2×Dic3 | — | 5 | 2 | no | — |
| 561 | C2×Dic3 | — | 5 | 2 | no | — |
| 562 | C2×Dic3 | — | 10 | 4 | no | — |
| 563 | C2×Dic3 | C23×D5 | 1 | 4 | yes | — |
| 564 | D12 | — | 4 | 2 | no | — |
| 565 | D12 | — | 4 | 2 | no | — |
| 566 | D12 | — | 20 | 1 | no | — |
| 567 | D12 | — | 20 | 2 | no | — |
| 568 | D12 | — | 20 | 4 | no | — |
| 569 | D12 | — | 20 | 4 | no | — |
| 570 | D12 | — | 20 | 4 | no | — |
| 571 | C4×D3 | — | 10 | 2 | no | — |
| 572 | C4×D3 | — | 10 | 4 | no | — |
| 573 | C4×D3 | — | 10 | 8 | no | — |
| 574 | C4×D3 | — | 20 | 4 | no | — |
| 575 | C4×D3 | — | 20 | 2 | no | — |
| 576 | C4×D3 | — | 20 | 4 | no | — |
| 577 | Dic6 | — | 4 | 2 | no | — |
| 578 | Dic6 | — | 20 | 1 | no | — |
| 579 | C22×C5 | — | 2 | 2 | no | — |
| 580 | C22×C5 | — | 2 | 4 | no | — |
| 581 | C22×C5 | — | 6 | 4 | no | — |
| 582 | C22×C5 | — | 6 | 4 | no | — |
| 583 | C22×C5 | — | 6 | 4 | no | — |
| 584 | C22×C5 | — | 12 | 8 | no | — |
| 585 | C22×C5 | C24×D3 | 1 | 1 | yes | characteristic |
| 586 | C2×D5 | — | 6 | 2 | no | — |
| 587 | C2×D5 | — | 6 | 1 | no | — |
| 588 | C2×D5 | — | 6 | 4 | no | — |
| 589 | C2×D5 | — | 6 | 2 | no | — |
| 590 | C4×C5 | — | 2 | 2 | no | — |
| 591 | C4×C5 | — | 2 | 1 | no | — |
| 592 | C4×C5 | — | 2 | 2 | no | — |
| 593 | C4×C5 | — | 6 | 4 | no | — |
| 594 | Dic5 | — | 2 | 4 | no | — |
| 595 | Dic5 | — | 2 | 4 | no | — |
| 596 | Dic5 | — | 3 | 2 | no | — |
| 597 | Dic5 | — | 6 | 2 | no | — |
| 598 | Dic5 | — | 6 | 2 | no | — |
| 599 | C24 | — | 3 | 2 | no | — |
| 600 | #41 | — | 60 | 2 | no | — |
| 601 | #41 | — | 60 | 4 | no | — |
| 602 | #41 | — | 60 | 2 | no | — |
| 603 | C2×Q8 | — | 3 | 2 | no | — |
| 604 | C2×Q8 | — | 5 | 2 | no | — |
| 605 | C2×Q8 | — | 15 | 1 | no | — |
| 606 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 607 | C2×D4 | — | 3 | 4 | no | — |
| 608 | C2×D4 | — | 3 | 2 | no | — |
| 609 | C2×D4 | — | 3 | 2 | no | — |
| 610 | C2×D4 | — | 15 | 4 | no | — |
| 611 | C2×D4 | — | 15 | 4 | no | — |
| 612 | C2×D4 | — | 15 | 4 | no | — |
| 613 | C2×D4 | — | 15 | 4 | no | — |
| 614 | C2×D4 | — | 15 | 2 | no | — |
| 615 | C2×D4 | — | 15 | 2 | no | — |
| 616 | C2×D4 | — | 15 | 1 | no | — |
| 617 | C2×D4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 618 | C22×C4 | — | 5 | 2 | no | — |
| 619 | C22×C4 | — | 15 | 4 | no | — |
| 620 | C22×C4 | — | 15 | 4 | no | — |
| 621 | C22×C4 | — | 15 | 4 | no | — |
| 622 | C22×C4 | — | 15 | 2 | no | — |
| 623 | C22×C4 | — | 15 | 2 | no | — |
| 624 | C22×C4 | — | 15 | 1 | no | — |
| 625 | C22×C4 | — | 15 | 2 | no | — |
| 626 | C22×C4 | — | 60 | 4 | no | — |
| 627 | C4⋊C4 | — | 5 | 4 | no | — |
| 628 | C4⋊C4 | — | 5 | 4 | no | — |
| 629 | C4⋊C4 | — | 5 | 4 | no | — |
| 630 | C4⋊C4 | — | 5 | 2 | no | — |
| 631 | C4⋊C4 | — | 5 | 2 | no | — |
| 632 | C4⋊C4 | — | 15 | 4 | no | — |
| 633 | C4⋊C4 | — | 15 | 4 | no | — |
| 634 | C4⋊C4 | — | 15 | 4 | no | — |
| 635 | C4⋊C4 | — | 15 | 4 | no | — |
| 636 | C4⋊C4 | — | 15 | 4 | no | — |
| 637 | C22⋊C4 | — | 3 | 2 | no | — |
| 638 | C22⋊C4 | — | 3 | 4 | no | — |
| 639 | C22⋊C4 | — | 3 | 4 | no | — |
| 640 | C22⋊C4 | — | 3 | 4 | no | — |
| 641 | C22⋊C4 | — | 5 | 2 | no | — |
| 642 | C22⋊C4 | — | 5 | 4 | no | — |
| 643 | C22⋊C4 | — | 15 | 4 | no | — |
| 644 | C22⋊C4 | — | 15 | 4 | no | — |
| 645 | C22⋊C4 | — | 15 | 4 | no | — |
| 646 | C22⋊C4 | — | 15 | 4 | no | — |
| 647 | C22⋊C4 | — | 15 | 4 | no | — |
| 648 | C22⋊C4 | — | 15 | 4 | no | — |
| 649 | C22⋊C4 | C2×D3×D5 | 1 | 4 | yes | — |
| 650 | C42 | — | 3 | 2 | no | — |
| 651 | C42 | — | 5 | 2 | no | — |
| 652 | C42 | — | 15 | 4 | no | — |
| 653 | C42 | — | 15 | 2 | no | — |
| 654 | C42 | — | 15 | 1 | no | — |
| 655 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 656 | C3×C5 | #3529 | 1 | 1 | yes | characteristic, complemented, Hall |
| 657 | C22×C3 | — | 2 | 2 | no | — |
| 658 | C22×C3 | — | 2 | 4 | no | — |
| 659 | C22×C3 | C24×D5 | 1 | 1 | yes | characteristic |
| 660 | C2×D3 | — | 2 | 4 | no | — |
| 661 | C2×D3 | — | 2 | 4 | no | — |
| 662 | C2×D3 | — | 2 | 4 | no | — |
| 663 | C2×D3 | — | 4 | 8 | no | — |
| 664 | C2×D3 | — | 10 | 2 | no | — |
| 665 | C2×D3 | — | 10 | 1 | no | — |
| 666 | C2×D3 | — | 10 | 2 | no | — |
| 667 | C2×D3 | — | 10 | 4 | no | — |
| 668 | C3×C4 | — | 2 | 1 | no | — |
| 669 | C3×C4 | — | 2 | 2 | no | — |
| 670 | C3×C4 | — | 2 | 2 | no | — |
| 671 | C3×C4 | — | 10 | 4 | no | — |
| 672 | C3×C4 | — | 10 | 4 | no | — |
| 673 | Dic3 | — | 2 | 4 | no | — |
| 674 | Dic3 | — | 5 | 2 | no | — |
| 675 | Dic3 | — | 10 | 2 | no | — |
| 676 | Dic3 | — | 10 | 2 | no | — |
| 677 | C2×C5 | — | 4 | 2 | no | — |
| 678 | C2×C5 | — | 12 | 4 | no | — |
| 679 | C2×C5 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 680 | C2×C5 | #5968 | 1 | 2 | yes | — |
| 681 | D5 | — | 12 | 2 | no | — |
| 682 | D5 | — | 12 | 1 | no | — |
| 683 | C23 | — | 3 | 4 | no | — |
| 684 | C23 | — | 12 | 2 | no | — |
| 685 | C23 | — | 12 | 4 | no | — |
| 686 | C23 | — | 15 | 1 | no | — |
| 687 | C23 | — | 15 | 2 | no | — |
| 688 | C23 | C22×D3×D5 | 1 | 2 | yes | — |
| 689 | Q8 | — | 4 | 1 | no | — |
| 690 | Q8 | — | 12 | 2 | no | — |
| 691 | Q8 | — | 20 | 2 | no | — |
| 692 | Q8 | — | 60 | 1 | no | — |
| 693 | D4 | — | 4 | 1 | no | — |
| 694 | D4 | — | 12 | 2 | no | — |
| 695 | D4 | — | 12 | 2 | no | — |
| 696 | D4 | — | 12 | 4 | no | — |
| 697 | D4 | — | 60 | 1 | no | — |
| 698 | D4 | — | 60 | 2 | no | — |
| 699 | D4 | — | 60 | 4 | no | — |
| 700 | D4 | — | 60 | 4 | no | — |
| 701 | D4 | — | 60 | 4 | no | — |
| 702 | D4 | — | 60 | 2 | no | — |
| 703 | D4 | — | 60 | 4 | no | — |
| 704 | C2×C4 | — | 3 | 4 | no | — |
| 705 | C2×C4 | — | 5 | 4 | no | — |
| 706 | C2×C4 | — | 5 | 4 | no | — |
| 707 | C2×C4 | — | 15 | 1 | no | — |
| 708 | C2×C4 | — | 15 | 2 | no | — |
| 709 | C2×C4 | — | 15 | 2 | no | — |
| 710 | C2×C4 | — | 20 | 2 | no | — |
| 711 | C2×C4 | — | 30 | 2 | no | — |
| 712 | C2×C4 | — | 30 | 4 | no | — |
| 713 | C2×C4 | — | 30 | 8 | no | — |
| 714 | C2×C4 | — | 30 | 4 | no | — |
| 715 | C2×C4 | — | 60 | 2 | no | — |
| 716 | C2×C4 | — | 60 | 4 | no | — |
| 717 | C2×C4 | — | 60 | 4 | no | — |
| 718 | C2×C4 | C22×D3×D5 | 1 | 2 | yes | — |
| 719 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | C22×D3×D5 | 1 | 2 | yes | — |
| 721 | C2×C3 | — | 4 | 2 | no | — |
| 722 | C2×C3 | D5×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 723 | C2×C3 | #66285 | 1 | 2 | yes | — |
| 724 | D3 | — | 4 | 4 | no | — |
| 725 | D3 | — | 20 | 2 | no | — |
| 726 | D3 | — | 20 | 1 | no | — |
| 727 | C5 | #87115 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 728 | C22 | — | 2 | 4 | no | — |
| 729 | C22 | — | 2 | 2 | no | — |
| 730 | C22 | — | 6 | 4 | no | — |
| 731 | C22 | — | 6 | 4 | no | — |
| 732 | C22 | — | 6 | 4 | no | — |
| 733 | C22 | — | 12 | 8 | no | — |
| 734 | C22 | — | 30 | 2 | no | — |
| 735 | C22 | — | 30 | 4 | no | — |
| 736 | C22 | — | 30 | 2 | no | — |
| 737 | C22 | — | 30 | 1 | no | — |
| 738 | C22 | C23×D3×D5 | 1 | 1 | yes | characteristic |
| 739 | C4 | — | 2 | 2 | no | — |
| 740 | C4 | — | 2 | 1 | no | — |
| 741 | C4 | — | 2 | 2 | no | — |
| 742 | C4 | — | 6 | 4 | no | — |
| 743 | C4 | — | 10 | 4 | no | — |
| 744 | C4 | — | 10 | 4 | no | — |
| 745 | C4 | — | 15 | 2 | no | — |
| 746 | C4 | — | 30 | 2 | no | — |
| 747 | C4 | — | 30 | 2 | no | — |
| 748 | C3 | #10618986 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 749 | C2 | — | 4 | 2 | no | — |
| 750 | C2 | — | 12 | 4 | no | — |
| 751 | C2 | — | 60 | 1 | no | — |
| 752 | C2 | — | 60 | 2 | no | — |
| 753 | C2 | #11757030 | 1 | 1 | yes | characteristic |
| 754 | C2 | #11757064 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#124 | C22 |
| hypercenter | #124 | D3×D5 |
| hypocenter | C3×C5 | #3529 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756427 | C2 | semidirect |
| 2. C5×#5683 | C2 | semidirect |
| 3. C3×#66006 | C2 | semidirect |
| 4. #11755216 | C2 | semidirect |
| 5. #11755170 | C2 | semidirect |
| 6. #11754999 | C2 | semidirect |
| 7. #11754824 | C2 | semidirect |
| 8. #11753185 | C2 | semidirect |
| 9. #11753059 | C2 | semidirect |
| 10. #11752996 | C2 | semidirect |
| 11. #11752842 | C2 | semidirect |
| 12. #11752656 | C2 | semidirect |
| 13. #11752628 | C2 | semidirect |
| 15. C2×#6821 | C22 | semidirect |
| 17. C22×D3×Dic5 | C22 | semidirect |
| 20. #91833 | C22 | semidirect |
| 22. #91773 | C22 | semidirect |
| 23. #91770 | C22 | semidirect |
| 24. #91764 | C22 | semidirect |
| 25. C42×D15 | C22 | semidirect |
| 31. C3×#4090 | C22 | semidirect |
| 33. C3×#4025 | C22 | semidirect |
| 34. C3×#4024 | C22 | semidirect |
| 35. C3×#4016 | C22 | semidirect |
| 36. #91570 | C22 | semidirect |
| 37. #91570 | C22 | semidirect |
| 39. #91562 | C22 | semidirect |
| 43. #91546 | C22 | semidirect |
| 44. #91532 | C22 | semidirect |
| 47. #91438 | C22 | semidirect |
| 49. #91432 | C22 | semidirect |
| 50. #91427 | C22 | semidirect |
| 51. #91424 | C22 | semidirect |
| 53. #91420 | C22 | semidirect |
| 54. #91420 | C22 | semidirect |
| 56. #91410 | C22 | semidirect |
| 57. #91406 | C22 | semidirect |
| 58. #91406 | C22 | semidirect |
| 59. C4×#1200 | C22 | semidirect |
| 60. #91400 | C22 | semidirect |
| 61. #91383 | C22 | semidirect |
| 62. #91379 | C22 | semidirect |
| 63. #91374 | C22 | semidirect |
| 64. #91372 | C22 | semidirect |
| 65. #91367 | C22 | semidirect |
| 66. #91355 | C22 | semidirect |
| 67. #91344 | C22 | semidirect |
| 75. #66006 | D3 | semidirect |
| 146. #5683 | D5 | semidirect |
| 168. #4090 | C2×D3 | semidirect |
| 193. #4025 | C2×D3 | semidirect |
| 196. #4024 | C2×D3 | semidirect |
| 204. #4016 | C2×D3 | semidirect |
| 656. C3×C5 | #3529 | semidirect |
| 727. C5 | #87115 | semidirect |
| 748. C3 | #10618986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756427 | 2 |
| C5×#5683 | 2 |
| C3×#66006 | 2 |
| #11755216 | 2 |
| #11755170 | 2 |
| #11754999 | 2 |
| #11754824 | 2 |
| #11753185 | 2 |
| #11753059 | 2 |
| #11752996 | 2 |
| #11752842 | 2 |
| #11752656 | 2 |
| #11752628 | 2 |
| #10618986 | 3 |
| #87115 | 5 |