← C3×#10615211 #14430922
Subgroups — C3×#10615211 #14430922
Order 1920.
724 conjugacy classes of subgroups.
The subgroup lattice has 468 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×C5×#544 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#65850 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#65383 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#65380 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#65352 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C3×#65352 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C3×#65293 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C3×#65288 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C3×#65287 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×C3×#3942 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C3×#65253 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #10615211 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 13 | C22×C3×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 15 | C3×C5×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 16 | C3×C5×#125 | — | 2 | 1 | no | — |
| 17 | C3×C5×#125 | C22 | 1 | 2 | yes | — |
| 18 | C3×C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 19 | C3×C5×#117 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×C5×#117 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C3×C5×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#4072 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×#681 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×C3×#168 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#4033 | — | 2 | 1 | no | — |
| 26 | C3×#4033 | — | 2 | 1 | no | — |
| 27 | C3×#4023 | — | 2 | 2 | no | — |
| 28 | C3×C4×Dic10 | C22 | 1 | 2 | yes | — |
| 29 | C3×C4×Dic10 | C22 | 1 | 2 | yes | — |
| 30 | C3×#3942 | C22 | 1 | 2 | yes | — |
| 31 | C3×#3942 | C22 | 1 | 2 | yes | — |
| 32 | C3×#3942 | C22 | 1 | 2 | yes | — |
| 33 | C3×#3942 | C22 | 1 | 2 | yes | — |
| 34 | C3×#3940 | C22 | 1 | 1 | yes | characteristic |
| 35 | C3×#3940 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#3940 | C22 | 1 | 2 | yes | — |
| 37 | C3×#3939 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×#3939 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×#3939 | C22 | 1 | 2 | yes | — |
| 40 | C3×C4⋊#168 | C22 | 1 | 2 | yes | — |
| 41 | C3×C4⋊#168 | C22 | 1 | 2 | yes | — |
| 42 | C3×#3082 | — | 5 | 1 | no | maximal, Hall |
| 43 | C5×#544 | C2×C3 | 1 | 1 | yes | characteristic |
| 44 | #65850 | C2×C3 | 1 | 1 | yes | characteristic |
| 45 | #65383 | C2×C3 | 1 | 2 | yes | complemented |
| 46 | #65380 | C2×C3 | 1 | 2 | yes | complemented |
| 47 | #65352 | C2×C3 | 1 | 2 | yes | complemented |
| 48 | #65352 | C2×C3 | 1 | 2 | yes | complemented |
| 49 | #65293 | C2×C3 | 1 | 1 | yes | characteristic |
| 50 | #65288 | C2×C3 | 1 | 1 | yes | characteristic |
| 51 | #65287 | C2×C3 | 1 | 1 | yes | characteristic |
| 52 | C2×#3942 | C2×C3 | 1 | 1 | yes | characteristic |
| 53 | #65253 | C2×C3 | 1 | 1 | yes | characteristic |
| 54 | C2×C3×C5×Q8 | — | 2 | 2 | no | — |
| 55 | C22×C3×C4×C5 | — | 2 | 1 | no | — |
| 56 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×C3×Dic5 | — | 2 | 1 | no | — |
| 58 | C2×C3×Dic10 | — | 2 | 1 | no | — |
| 59 | C2×C3×Dic10 | — | 2 | 2 | no | — |
| 60 | C2×C3×Dic10 | Q8 | 1 | 4 | yes | complemented |
| 61 | C2×C3×Dic10 | C23 | 1 | 2 | yes | — |
| 62 | C3×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 63 | C3×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 64 | C3×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 65 | C3×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 66 | C3×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 67 | C3×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 68 | C3×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 69 | C3×C5×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 70 | C3×C5×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 71 | C3×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 72 | C3×C5×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 73 | C3×C42×C5 | — | 2 | 1 | no | — |
| 74 | C3×C42×C5 | C23 | 1 | 2 | yes | — |
| 75 | C3×C22⋊Dic5 | — | 2 | 1 | no | — |
| 76 | C3×C4⋊Dic5 | C23 | 1 | 1 | yes | characteristic |
| 77 | C3×C4⋊Dic5 | C23 | 1 | 1 | yes | characteristic |
| 78 | C3×#683 | — | 2 | 2 | no | — |
| 79 | C3×#683 | — | 2 | 2 | no | — |
| 80 | C3×C4×Dic5 | — | 2 | 2 | no | — |
| 81 | C3×C4×Dic5 | — | 2 | 2 | no | — |
| 82 | C3×C4×Dic5 | — | 2 | 1 | no | — |
| 83 | C3×#681 | — | 2 | 2 | no | — |
| 84 | C2×C3×#168 | — | 2 | 2 | no | — |
| 85 | C2×C3×#168 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C3×#168 | C23 | 1 | 2 | yes | — |
| 87 | C2×C3×#168 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3×#544 | D5 | 1 | 1 | yes | characteristic |
| 89 | C3×#519 | — | 5 | 1 | no | — |
| 90 | C3×#479 | — | 5 | 2 | no | — |
| 91 | C3×#479 | — | 5 | 2 | no | — |
| 92 | C3×#477 | — | 5 | 2 | no | — |
| 93 | C3×#475 | — | 5 | 2 | no | — |
| 94 | C3×#428 | — | 5 | 1 | no | — |
| 95 | C3×#427 | — | 5 | 1 | no | — |
| 96 | C3×#424 | — | 5 | 1 | no | — |
| 97 | C3×#419 | — | 5 | 1 | no | — |
| 98 | C2×C3×#103 | — | 5 | 1 | no | — |
| 99 | C22×Dic10 | C22×C3 | 1 | 1 | yes | characteristic |
| 100 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 101 | C5×C4⋊Q8 | C22×C3 | 1 | 2 | yes | — |
| 102 | C5×#125 | — | 2 | 1 | no | — |
| 103 | C5×#125 | C22×C3 | 1 | 2 | yes | — |
| 104 | C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 105 | C5×#117 | C22×C3 | 1 | 1 | yes | characteristic |
| 106 | C5×#117 | C22×C3 | 1 | 1 | yes | characteristic |
| 107 | C2×C5×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 108 | #4072 | C22×C3 | 1 | 1 | yes | characteristic |
| 109 | C2×#681 | C22×C3 | 1 | 1 | yes | characteristic |
| 110 | C22×#168 | C22×C3 | 1 | 1 | yes | characteristic |
| 111 | #4033 | — | 2 | 1 | no | — |
| 112 | #4033 | — | 2 | 1 | no | — |
| 113 | #4023 | — | 2 | 2 | no | — |
| 114 | C4×Dic10 | C22×C3 | 1 | 2 | yes | — |
| 115 | C4×Dic10 | C22×C3 | 1 | 2 | yes | — |
| 116 | #3942 | C22×C3 | 1 | 2 | yes | — |
| 117 | #3942 | C22×C3 | 1 | 2 | yes | — |
| 118 | #3942 | C22×C3 | 1 | 2 | yes | — |
| 119 | #3942 | C22×C3 | 1 | 2 | yes | — |
| 120 | #3940 | C22×C3 | 1 | 1 | yes | characteristic |
| 121 | #3940 | C22×C3 | 1 | 1 | yes | characteristic |
| 122 | #3940 | C22×C3 | 1 | 2 | yes | — |
| 123 | #3939 | C22×C3 | 1 | 1 | yes | characteristic |
| 124 | #3939 | C22×C3 | 1 | 1 | yes | characteristic |
| 125 | #3939 | C22×C3 | 1 | 2 | yes | — |
| 126 | C4⋊#168 | C22×C3 | 1 | 2 | yes | — |
| 127 | C4⋊#168 | C22×C3 | 1 | 2 | yes | — |
| 128 | #3082 | — | 5 | 1 | no | Sylow |
| 129 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C3×C5×Q8 | — | 8 | 2 | no | — |
| 131 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 132 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 133 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 134 | C2×C3×C4×C5 | — | 8 | 1 | no | — |
| 135 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 136 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×C3×C4×C5 | C2×Q8 | 1 | 2 | yes | — |
| 139 | C2×C3×C4×C5 | #41 | 1 | 2 | yes | — |
| 140 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 141 | C2×C3×Dic5 | — | 2 | 4 | no | — |
| 142 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 143 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 144 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 145 | C3×Dic10 | — | 2 | 4 | no | — |
| 146 | C3×Dic10 | — | 2 | 2 | no | — |
| 147 | C3×Dic10 | C2×Q8 | 1 | 4 | yes | — |
| 148 | C3×#168 | — | 2 | 1 | no | — |
| 149 | C3×#168 | — | 2 | 1 | no | — |
| 150 | C3×#168 | — | 2 | 2 | no | — |
| 151 | C22×C3×Q8 | — | 5 | 1 | no | — |
| 152 | C2×C3×M16 | — | 5 | 1 | no | — |
| 153 | C22×C3×C8 | — | 5 | 1 | no | — |
| 154 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 155 | C3×C4⋊Q8 | C2×D5 | 1 | 2 | yes | — |
| 156 | C3×#125 | — | 2 | 1 | no | — |
| 157 | C3×#125 | C2×D5 | 1 | 2 | yes | — |
| 158 | C3×C22⋊Q8 | — | 2 | 2 | no | — |
| 159 | C3×C4×Q8 | — | 5 | 2 | no | — |
| 160 | C3×C4×Q8 | — | 5 | 2 | no | — |
| 161 | C3×C4×Q8 | — | 10 | 1 | no | — |
| 162 | C3×C4×Q8 | — | 10 | 1 | no | — |
| 163 | C3×#117 | — | 5 | 1 | no | — |
| 164 | C3×#117 | — | 10 | 2 | no | — |
| 165 | C3×#117 | C2×D5 | 1 | 1 | yes | characteristic |
| 166 | C3×#117 | C2×D5 | 1 | 1 | yes | characteristic |
| 167 | C2×C3×C4⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 168 | C3×#107 | — | 5 | 1 | no | — |
| 169 | C3×#107 | — | 5 | 1 | no | — |
| 170 | C3×#107 | — | 5 | 2 | no | — |
| 171 | C3×#106 | — | 5 | 1 | no | — |
| 172 | C3×#106 | — | 5 | 1 | no | — |
| 173 | C3×#106 | — | 5 | 2 | no | — |
| 174 | C3×C4⋊C8 | — | 5 | 2 | no | — |
| 175 | C3×C4⋊C8 | — | 5 | 2 | no | — |
| 176 | C3×#103 | — | 5 | 2 | no | — |
| 177 | C3×#103 | — | 5 | 2 | no | — |
| 178 | C3×#103 | — | 5 | 2 | no | — |
| 179 | C3×#103 | — | 5 | 2 | no | — |
| 180 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 181 | C22×C4×C5 | — | 2 | 1 | no | — |
| 182 | C22×C4×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 183 | C22×Dic5 | — | 2 | 1 | no | — |
| 184 | C2×Dic10 | — | 2 | 1 | no | — |
| 185 | C2×Dic10 | — | 2 | 2 | no | — |
| 186 | C2×Dic10 | C3×Q8 | 1 | 4 | yes | complemented |
| 187 | C2×Dic10 | C23×C3 | 1 | 2 | yes | — |
| 188 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 189 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 190 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 191 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 192 | C5×C4⋊C4 | C3×D4 | 1 | 1 | yes | characteristic |
| 193 | C5×C4⋊C4 | C3×D4 | 1 | 1 | yes | characteristic |
| 194 | C5×C4⋊C4 | C23×C3 | 1 | 2 | yes | — |
| 195 | C5×C4⋊C4 | C23×C3 | 1 | 1 | yes | characteristic |
| 196 | C5×C4⋊C4 | C23×C3 | 1 | 1 | yes | characteristic |
| 197 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 198 | C5×C22⋊C4 | C3×D4 | 1 | 2 | yes | — |
| 199 | C42×C5 | — | 2 | 1 | no | — |
| 200 | C42×C5 | C23×C3 | 1 | 2 | yes | — |
| 201 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 202 | C4⋊Dic5 | C23×C3 | 1 | 1 | yes | characteristic |
| 203 | C4⋊Dic5 | C23×C3 | 1 | 1 | yes | characteristic |
| 204 | #683 | — | 2 | 2 | no | — |
| 205 | #683 | — | 2 | 2 | no | — |
| 206 | C4×Dic5 | — | 2 | 2 | no | — |
| 207 | C4×Dic5 | — | 2 | 2 | no | — |
| 208 | C4×Dic5 | — | 2 | 1 | no | — |
| 209 | #681 | — | 2 | 2 | no | — |
| 210 | C2×#168 | — | 2 | 2 | no | — |
| 211 | C2×#168 | C23×C3 | 1 | 1 | yes | characteristic |
| 212 | C2×#168 | C23×C3 | 1 | 2 | yes | — |
| 213 | C2×#168 | C23×C3 | 1 | 1 | yes | characteristic |
| 214 | #544 | C3×D5 | 1 | 1 | yes | characteristic |
| 215 | #519 | — | 5 | 1 | no | — |
| 216 | #479 | — | 5 | 2 | no | — |
| 217 | #479 | — | 5 | 2 | no | — |
| 218 | #477 | — | 5 | 2 | no | — |
| 219 | #475 | — | 5 | 2 | no | — |
| 220 | #428 | — | 5 | 1 | no | — |
| 221 | #427 | — | 5 | 1 | no | — |
| 222 | #424 | — | 5 | 1 | no | — |
| 223 | #419 | — | 5 | 1 | no | — |
| 224 | C2×#103 | — | 5 | 1 | no | — |
| 225 | C22×C3×C5 | — | 2 | 1 | no | — |
| 226 | C22×C3×C5 | — | 2 | 1 | no | — |
| 227 | C22×C3×C5 | C22⋊Q8 | 1 | 2 | yes | — |
| 228 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 229 | C3×C4×C5 | — | 2 | 2 | no | — |
| 230 | C3×C4×C5 | — | 2 | 2 | no | — |
| 231 | C3×C4×C5 | — | 4 | 2 | no | — |
| 232 | C3×C4×C5 | — | 4 | 1 | no | — |
| 233 | C3×C4×C5 | — | 4 | 1 | no | — |
| 234 | C3×C4×C5 | C22⋊Q8 | 1 | 2 | yes | — |
| 235 | C3×C4×C5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 236 | C3×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 237 | C3×Dic5 | — | 2 | 4 | no | — |
| 238 | C3×Dic5 | — | 4 | 1 | no | — |
| 239 | C3×Dic5 | — | 4 | 1 | no | — |
| 240 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 241 | C2×C3×Q8 | — | 5 | 4 | no | — |
| 242 | C2×C3×Q8 | — | 5 | 2 | no | — |
| 243 | C2×C3×Q8 | — | 10 | 2 | no | — |
| 244 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 245 | C22×C3×C4 | — | 2 | 1 | no | — |
| 246 | C22×C3×C4 | — | 10 | 1 | no | — |
| 247 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 248 | C3×M16 | — | 10 | 2 | no | — |
| 249 | C2×C3×C8 | — | 5 | 1 | no | — |
| 250 | C2×C3×C8 | — | 5 | 2 | no | — |
| 251 | C2×C3×C8 | — | 5 | 1 | no | — |
| 252 | C2×C3×C8 | — | 10 | 2 | no | — |
| 253 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 254 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 255 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 256 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 257 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 258 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 259 | C3×C4⋊C4 | — | 10 | 2 | no | — |
| 260 | C3×C4⋊C4 | — | 10 | 2 | no | — |
| 261 | C3×C4⋊C4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 262 | C3×C4⋊C4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 263 | C3×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 264 | C3×C4⋊C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 265 | C3×C4⋊C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 266 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 267 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 268 | C3×C22⋊C4 | C22⋊D5 | 1 | 2 | yes | — |
| 269 | C3×C42 | — | 2 | 1 | no | — |
| 270 | C3×C42 | — | 10 | 1 | no | — |
| 271 | C3×C42 | — | 10 | 2 | no | — |
| 272 | C3×C42 | — | 10 | 2 | no | — |
| 273 | C3×C42 | C22×D5 | 1 | 2 | yes | — |
| 274 | C23×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 275 | C5×Q8 | — | 8 | 2 | no | — |
| 276 | C2×C4×C5 | — | 2 | 1 | no | — |
| 277 | C2×C4×C5 | — | 2 | 1 | no | — |
| 278 | C2×C4×C5 | — | 2 | 2 | no | — |
| 279 | C2×C4×C5 | — | 8 | 1 | no | — |
| 280 | C2×C4×C5 | C2×C3×D4 | 1 | 2 | yes | — |
| 281 | C2×C4×C5 | C2×C3×D4 | 1 | 2 | yes | — |
| 282 | C2×C4×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 283 | C2×C4×C5 | C2×C3×Q8 | 1 | 2 | yes | — |
| 284 | C2×C4×C5 | C3×#41 | 1 | 2 | yes | — |
| 285 | C2×C4×C5 | C24×C3 | 1 | 1 | yes | characteristic |
| 286 | C2×Dic5 | — | 2 | 4 | no | — |
| 287 | C2×Dic5 | — | 2 | 2 | no | — |
| 288 | C2×Dic5 | — | 2 | 1 | no | — |
| 289 | C2×Dic5 | — | 2 | 1 | no | — |
| 290 | Dic10 | — | 2 | 4 | no | — |
| 291 | Dic10 | — | 2 | 2 | no | — |
| 292 | Dic10 | C2×C3×Q8 | 1 | 4 | yes | — |
| 293 | #168 | — | 2 | 1 | no | — |
| 294 | #168 | — | 2 | 1 | no | — |
| 295 | #168 | — | 2 | 2 | no | — |
| 296 | C22×Q8 | — | 5 | 1 | no | — |
| 297 | C2×M16 | — | 5 | 1 | no | — |
| 298 | C22×C8 | — | 5 | 1 | no | — |
| 299 | C4⋊Q8 | — | 2 | 1 | no | — |
| 300 | C4⋊Q8 | C2×C3×D5 | 1 | 2 | yes | — |
| 301 | #125 | — | 2 | 1 | no | — |
| 302 | #125 | C2×C3×D5 | 1 | 2 | yes | — |
| 303 | C22⋊Q8 | — | 2 | 2 | no | — |
| 304 | C4×Q8 | — | 5 | 2 | no | — |
| 305 | C4×Q8 | — | 5 | 2 | no | — |
| 306 | C4×Q8 | — | 10 | 1 | no | — |
| 307 | C4×Q8 | — | 10 | 1 | no | — |
| 308 | #117 | — | 5 | 1 | no | — |
| 309 | #117 | — | 10 | 2 | no | — |
| 310 | #117 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 311 | #117 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 312 | C2×C4⋊C4 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 313 | #107 | — | 5 | 1 | no | — |
| 314 | #107 | — | 5 | 1 | no | — |
| 315 | #107 | — | 5 | 2 | no | — |
| 316 | #106 | — | 5 | 1 | no | — |
| 317 | #106 | — | 5 | 1 | no | — |
| 318 | #106 | — | 5 | 2 | no | — |
| 319 | C4⋊C8 | — | 5 | 2 | no | — |
| 320 | C4⋊C8 | — | 5 | 2 | no | — |
| 321 | #103 | — | 5 | 2 | no | — |
| 322 | #103 | — | 5 | 2 | no | — |
| 323 | #103 | — | 5 | 2 | no | — |
| 324 | #103 | — | 5 | 2 | no | — |
| 325 | C2×C3×C5 | — | 2 | 2 | no | — |
| 326 | C2×C3×C5 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 327 | C2×C3×C5 | #577 | 1 | 1 | yes | characteristic |
| 328 | C2×C3×C5 | #578 | 1 | 1 | yes | characteristic |
| 329 | C23×C3 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 330 | C3×Q8 | — | 5 | 4 | no | — |
| 331 | C3×Q8 | — | 8 | 2 | no | — |
| 332 | C3×Q8 | — | 10 | 2 | no | — |
| 333 | C3×Q8 | — | 10 | 4 | no | — |
| 334 | C2×C3×C4 | — | 2 | 1 | no | — |
| 335 | C2×C3×C4 | — | 2 | 1 | no | — |
| 336 | C2×C3×C4 | — | 2 | 2 | no | — |
| 337 | C2×C3×C4 | — | 8 | 1 | no | — |
| 338 | C2×C3×C4 | — | 10 | 2 | no | — |
| 339 | C2×C3×C4 | — | 10 | 4 | no | — |
| 340 | C2×C3×C4 | — | 10 | 1 | no | — |
| 341 | C2×C3×C4 | — | 10 | 1 | no | — |
| 342 | C2×C3×C4 | Q8×D5 | 1 | 2 | yes | — |
| 343 | C2×C3×C4 | #713 | 1 | 2 | yes | — |
| 344 | C2×C3×C4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 345 | C2×C3×C4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 346 | C2×C3×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 347 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 348 | C3×C8 | — | 10 | 1 | no | — |
| 349 | C3×C8 | — | 10 | 1 | no | — |
| 350 | C3×C8 | — | 10 | 2 | no | — |
| 351 | C22×C5 | — | 2 | 1 | no | — |
| 352 | C22×C5 | — | 2 | 1 | no | — |
| 353 | C22×C5 | C3×C22⋊Q8 | 1 | 2 | yes | — |
| 354 | C22×C5 | C22×C3×D4 | 1 | 1 | yes | characteristic |
| 355 | C4×C5 | — | 2 | 2 | no | — |
| 356 | C4×C5 | — | 2 | 2 | no | — |
| 357 | C4×C5 | — | 4 | 2 | no | — |
| 358 | C4×C5 | — | 4 | 1 | no | — |
| 359 | C4×C5 | — | 4 | 1 | no | — |
| 360 | C4×C5 | C3×C22⋊Q8 | 1 | 2 | yes | — |
| 361 | C4×C5 | C22×C3×Q8 | 1 | 1 | yes | characteristic |
| 362 | C4×C5 | C2×C3×#41 | 1 | 1 | yes | characteristic |
| 363 | Dic5 | — | 2 | 4 | no | — |
| 364 | Dic5 | — | 4 | 1 | no | — |
| 365 | Dic5 | — | 4 | 1 | no | — |
| 366 | C2×Q8 | — | 2 | 2 | no | — |
| 367 | C2×Q8 | — | 5 | 4 | no | — |
| 368 | C2×Q8 | — | 5 | 2 | no | — |
| 369 | C2×Q8 | — | 10 | 2 | no | — |
| 370 | C2×Q8 | — | 10 | 1 | no | — |
| 371 | C22×C4 | — | 2 | 1 | no | — |
| 372 | C22×C4 | — | 10 | 1 | no | — |
| 373 | C22×C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 374 | M16 | — | 10 | 2 | no | — |
| 375 | C2×C8 | — | 5 | 1 | no | — |
| 376 | C2×C8 | — | 5 | 2 | no | — |
| 377 | C2×C8 | — | 5 | 1 | no | — |
| 378 | C2×C8 | — | 10 | 2 | no | — |
| 379 | C4⋊C4 | — | 2 | 1 | no | — |
| 380 | C4⋊C4 | — | 2 | 2 | no | — |
| 381 | C4⋊C4 | — | 2 | 2 | no | — |
| 382 | C4⋊C4 | — | 2 | 2 | no | — |
| 383 | C4⋊C4 | — | 5 | 1 | no | — |
| 384 | C4⋊C4 | — | 5 | 1 | no | — |
| 385 | C4⋊C4 | — | 10 | 2 | no | — |
| 386 | C4⋊C4 | — | 10 | 2 | no | — |
| 387 | C4⋊C4 | C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 388 | C4⋊C4 | C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 389 | C4⋊C4 | C22×C3×D5 | 1 | 2 | yes | — |
| 390 | C4⋊C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 391 | C4⋊C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 392 | C22⋊C4 | — | 2 | 1 | no | — |
| 393 | C22⋊C4 | — | 10 | 1 | no | — |
| 394 | C22⋊C4 | C3×C22⋊D5 | 1 | 2 | yes | — |
| 395 | C42 | — | 2 | 1 | no | — |
| 396 | C42 | — | 10 | 1 | no | — |
| 397 | C42 | — | 10 | 2 | no | — |
| 398 | C42 | — | 10 | 2 | no | — |
| 399 | C42 | C22×C3×D5 | 1 | 2 | yes | — |
| 400 | C3×C5 | #3082 | 1 | 1 | yes | characteristic, complemented, Hall |
| 401 | C22×C3 | — | 2 | 1 | no | — |
| 402 | C22×C3 | — | 2 | 1 | no | — |
| 403 | C22×C3 | #4092 | 1 | 2 | yes | — |
| 404 | C22×C3 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 405 | C3×C4 | — | 2 | 2 | no | — |
| 406 | C3×C4 | — | 2 | 2 | no | — |
| 407 | C3×C4 | — | 4 | 2 | no | — |
| 408 | C3×C4 | — | 4 | 1 | no | — |
| 409 | C3×C4 | — | 4 | 1 | no | — |
| 410 | C3×C4 | — | 10 | 4 | no | — |
| 411 | C3×C4 | — | 20 | 1 | no | — |
| 412 | C3×C4 | — | 20 | 1 | no | — |
| 413 | C3×C4 | #4092 | 1 | 2 | yes | — |
| 414 | C3×C4 | C2×Q8×D5 | 1 | 1 | yes | characteristic |
| 415 | C3×C4 | C2×#713 | 1 | 1 | yes | characteristic |
| 416 | C2×C5 | — | 2 | 2 | no | — |
| 417 | C2×C5 | C2×C3×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 418 | C2×C5 | C3×#577 | 1 | 1 | yes | characteristic |
| 419 | C2×C5 | C3×#578 | 1 | 1 | yes | characteristic |
| 420 | C23 | C2×C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 421 | Q8 | — | 5 | 4 | no | — |
| 422 | Q8 | — | 8 | 2 | no | — |
| 423 | Q8 | — | 10 | 4 | no | — |
| 424 | Q8 | — | 10 | 2 | no | — |
| 425 | C2×C4 | — | 2 | 1 | no | — |
| 426 | C2×C4 | — | 2 | 1 | no | — |
| 427 | C2×C4 | — | 2 | 2 | no | — |
| 428 | C2×C4 | — | 8 | 1 | no | — |
| 429 | C2×C4 | — | 10 | 4 | no | — |
| 430 | C2×C4 | — | 10 | 2 | no | — |
| 431 | C2×C4 | — | 10 | 1 | no | — |
| 432 | C2×C4 | — | 10 | 1 | no | — |
| 433 | C2×C4 | C3×Q8×D5 | 1 | 2 | yes | — |
| 434 | C2×C4 | C3×#713 | 1 | 2 | yes | — |
| 435 | C2×C4 | C2×C3×C22⋊D5 | 1 | 2 | yes | — |
| 436 | C2×C4 | C2×C3×C22⋊D5 | 1 | 2 | yes | — |
| 437 | C2×C4 | C2×C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 438 | C2×C4 | C23×C3×D5 | 1 | 1 | yes | characteristic |
| 439 | C8 | — | 10 | 1 | no | — |
| 440 | C8 | — | 10 | 1 | no | — |
| 441 | C8 | — | 10 | 2 | no | — |
| 442 | C2×C3 | — | 2 | 2 | no | — |
| 443 | C2×C3 | C2×#4092 | 1 | 1 | yes | characteristic |
| 444 | C2×C3 | #66170 | 1 | 1 | yes | characteristic |
| 445 | C2×C3 | #66172 | 1 | 1 | yes | characteristic |
| 446 | C5 | C3×#3082 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 447 | C22 | — | 2 | 1 | no | — |
| 448 | C22 | — | 2 | 1 | no | — |
| 449 | C22 | C3×#4092 | 1 | 2 | yes | — |
| 450 | C22 | C22×C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 451 | C4 | — | 2 | 2 | no | — |
| 452 | C4 | — | 2 | 2 | no | — |
| 453 | C4 | — | 4 | 2 | no | — |
| 454 | C4 | — | 4 | 1 | no | — |
| 455 | C4 | — | 4 | 1 | no | — |
| 456 | C4 | — | 10 | 4 | no | — |
| 457 | C4 | — | 20 | 1 | no | — |
| 458 | C4 | — | 20 | 1 | no | — |
| 459 | C4 | C3×#4092 | 1 | 2 | yes | — |
| 460 | C4 | C2×C3×Q8×D5 | 1 | 1 | yes | characteristic |
| 461 | C4 | C2×C3×#713 | 1 | 1 | yes | characteristic |
| 462 | C3 | #10615211 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 463 | C2 | — | 2 | 2 | no | — |
| 464 | C2 | C2×C3×#4092 | 1 | 1 | yes | characteristic |
| 465 | C2 | C3×#66170 | 1 | 1 | yes | characteristic |
| 466 | C2 | C3×#66172 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta