Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1512 conjugacy classes of subgroups.
The subgroup lattice has 616 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#92026 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11756827 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D5⋊#833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×D5⋊#100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11752050 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11752049 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11751818 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10617553 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×D4×D15 | C4 | 1 | 1 | yes | characteristic |
| 10 | C2×C5×#237 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×D4×D5 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#6790 | C22 | 1 | 2 | yes | — |
| 13 | C2×D5×#67 | C4 | 1 | 2 | yes | — |
| 14 | C22×#1202 | C4 | 1 | 2 | yes | — |
| 15 | C2×#6779 | C22 | 1 | 2 | yes | — |
| 16 | #92026 | — | 2 | 4 | no | — |
| 17 | #92026 | — | 2 | 4 | no | — |
| 18 | C2×D3×D20 | C4 | 1 | 1 | yes | characteristic |
| 19 | C2×#6773 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6771 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6766 | C4 | 1 | 1 | yes | characteristic |
| 22 | D5⋊#208 | C22 | 1 | 2 | yes | complemented |
| 23 | C3×D5⋊M16 | C22 | 1 | 2 | yes | complemented |
| 24 | #91931 | C22 | 1 | 8 | yes | complemented |
| 25 | #91916 | — | 2 | 4 | no | — |
| 26 | #91914 | — | 2 | 4 | no | — |
| 27 | #91242 | C22 | 1 | 4 | yes | complemented |
| 28 | C3×#4013 | C22 | 1 | 4 | yes | complemented |
| 29 | #91175 | C22 | 1 | 4 | yes | complemented |
| 30 | #91174 | C22 | 1 | 4 | yes | complemented |
| 31 | #78697 | — | 5 | 1 | no | maximal, Hall |
| 32 | C2×#4149 | — | 3 | 1 | no | — |
| 33 | #66260 | — | 3 | 2 | no | — |
| 34 | D5⋊#100 | — | 3 | 4 | no | — |
| 35 | D5⋊#100 | — | 3 | 1 | no | — |
| 36 | D5⋊#100 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #65761 | — | 3 | 4 | no | — |
| 38 | #65761 | — | 3 | 2 | no | — |
| 39 | C23×D15 | C2×C4 | 1 | 2 | yes | — |
| 40 | C23×C3×D5 | C2×C4 | 1 | 2 | yes | — |
| 41 | C22×D3×D5 | C2×C4 | 1 | 2 | yes | — |
| 42 | C2×C3×C5×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×#1220 | C2×C4 | 1 | 2 | yes | — |
| 44 | D4×D15 | — | 2 | 4 | no | — |
| 45 | C2×D60 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×C4×D15 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C2×C5×#67 | C2×C4 | 1 | 2 | yes | — |
| 48 | C22×C5×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 49 | C5×#237 | — | 2 | 4 | no | — |
| 50 | C2×C4×C5×D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×C5×Dic6 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C2×C3×C22⋊D5 | C23 | 1 | 2 | yes | — |
| 53 | C3×D4×D5 | — | 2 | 2 | no | — |
| 54 | C3×D4×D5 | — | 2 | 2 | no | — |
| 55 | C2×C3×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 57 | #6790 | — | 2 | 8 | no | — |
| 58 | D5×#67 | — | 2 | 4 | no | — |
| 59 | D5×#67 | — | 2 | 4 | no | — |
| 60 | C2×#1204 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×#1203 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#1202 | — | 2 | 4 | no | — |
| 63 | C2×#1202 | — | 2 | 4 | no | — |
| 64 | C2×#1202 | C2×C4 | 1 | 2 | yes | — |
| 65 | C2×#1202 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×#1202 | C2×C4 | 1 | 2 | yes | — |
| 67 | C2×#1202 | C2×C4 | 1 | 2 | yes | — |
| 68 | C2×#1201 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C2×#1200 | C23 | 1 | 2 | yes | — |
| 70 | #6779 | — | 2 | 8 | no | — |
| 71 | C2×D5×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 72 | D3×D20 | — | 2 | 4 | no | — |
| 73 | #6773 | D4 | 1 | 4 | yes | — |
| 74 | #6773 | D4 | 1 | 4 | yes | — |
| 75 | #6771 | — | 2 | 2 | no | — |
| 76 | #6771 | — | 2 | 2 | no | — |
| 77 | #6766 | — | 2 | 4 | no | — |
| 78 | #6762 | C23 | 1 | 4 | yes | — |
| 79 | #6758 | — | 2 | 2 | no | — |
| 80 | D5⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 81 | C3×#704 | C23 | 1 | 4 | yes | — |
| 82 | C3×#700 | — | 2 | 2 | no | — |
| 83 | C3×D5⋊C8 | — | 2 | 2 | no | — |
| 84 | #6740 | — | 2 | 8 | no | — |
| 85 | #6738 | — | 2 | 8 | no | — |
| 86 | C2×#1004 | — | 5 | 1 | no | — |
| 87 | #5745 | — | 5 | 2 | no | — |
| 88 | C2×C3×#100 | — | 5 | 1 | no | — |
| 89 | C2×#833 | — | 5 | 1 | no | — |
| 90 | #5132 | — | 5 | 2 | no | — |
| 91 | #4745 | — | 5 | 4 | no | — |
| 92 | D3×#100 | — | 5 | 4 | no | — |
| 93 | C2×C5×#41 | — | 3 | 1 | no | — |
| 94 | #4149 | — | 6 | 4 | no | — |
| 95 | #4149 | — | 6 | 4 | no | — |
| 96 | C2×#713 | — | 3 | 1 | no | — |
| 97 | C2×#713 | — | 3 | 1 | no | — |
| 98 | C2×D4×D5 | — | 3 | 2 | no | — |
| 99 | C2×D4×D5 | — | 3 | 1 | no | — |
| 100 | C2×D4×D5 | — | 3 | 2 | no | — |
| 101 | C2×D4×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 102 | C2×#709 | — | 3 | 2 | no | — |
| 103 | C2×#709 | — | 3 | 1 | no | — |
| 104 | C22×D20 | — | 3 | 2 | no | — |
| 105 | C22×D20 | — | 3 | 1 | no | — |
| 106 | #4133 | — | 6 | 4 | no | — |
| 107 | #4133 | — | 6 | 4 | no | — |
| 108 | D5⋊M16 | — | 3 | 2 | no | — |
| 109 | D5⋊M16 | — | 3 | 8 | no | — |
| 110 | D5⋊M16 | C2×D3 | 1 | 2 | yes | complemented |
| 111 | #4013 | — | 3 | 4 | no | — |
| 112 | #4013 | — | 3 | 4 | no | — |
| 113 | #4013 | C2×D3 | 1 | 4 | yes | complemented |
| 114 | #4005 | — | 3 | 4 | no | — |
| 115 | #2888 | — | 15 | 1 | no | Sylow |
| 116 | C23×C3×C5 | C22×C4 | 1 | 2 | yes | — |
| 117 | C22×D15 | — | 2 | 4 | no | — |
| 118 | C22×D15 | — | 8 | 2 | no | — |
| 119 | C22×D15 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C22×D15 | C22×C4 | 1 | 2 | yes | — |
| 121 | C22×C5×D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | C22×C3×D5 | — | 2 | 2 | no | — |
| 123 | C22×C3×D5 | — | 2 | 2 | no | — |
| 124 | C22×C3×D5 | — | 8 | 2 | no | — |
| 125 | C22×C3×D5 | C22×C4 | 1 | 2 | yes | — |
| 126 | C22×C3×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | C2×D3×D5 | — | 2 | 4 | no | — |
| 128 | C2×D3×D5 | — | 8 | 2 | no | — |
| 129 | C3×C5×D4 | — | 2 | 2 | no | — |
| 130 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | #1220 | — | 2 | 4 | no | — |
| 132 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | D60 | C22⋊C4 | 1 | 4 | yes | — |
| 134 | C4×D15 | — | 2 | 2 | no | — |
| 135 | C5×#67 | — | 2 | 4 | no | — |
| 136 | C2×C5×Dic3 | — | 2 | 4 | no | — |
| 137 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C2×C5×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 139 | C4×C5×D3 | — | 2 | 2 | no | — |
| 140 | C5×Dic6 | C22⋊C4 | 1 | 4 | yes | — |
| 141 | C3×C22⋊D5 | — | 2 | 4 | no | — |
| 142 | C2×C3×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 143 | C3×D20 | — | 2 | 2 | no | — |
| 144 | C3×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 145 | C3×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 146 | #1204 | — | 2 | 2 | no | — |
| 147 | #1203 | — | 2 | 2 | no | — |
| 148 | #1202 | — | 2 | 4 | no | — |
| 149 | #1202 | — | 2 | 1 | no | — |
| 150 | #1202 | — | 2 | 1 | no | — |
| 151 | #1202 | — | 2 | 4 | no | — |
| 152 | #1202 | C22⋊C4 | 1 | 4 | yes | — |
| 153 | #1202 | C22⋊C4 | 1 | 4 | yes | — |
| 154 | #1201 | — | 2 | 1 | no | — |
| 155 | #1201 | — | 2 | 1 | no | — |
| 156 | #1200 | C2×D4 | 1 | 8 | yes | — |
| 157 | D5×Dic3 | — | 2 | 4 | no | — |
| 158 | C3⋊#170 | — | 2 | 4 | no | — |
| 159 | C3×#170 | — | 2 | 4 | no | — |
| 160 | C22×C3×D4 | — | 5 | 1 | no | — |
| 161 | C22×#67 | — | 5 | 2 | no | — |
| 162 | C22×#67 | — | 5 | 2 | no | — |
| 163 | #1004 | — | 10 | 4 | no | — |
| 164 | #1004 | — | 10 | 4 | no | — |
| 165 | C2×#237 | — | 5 | 2 | no | — |
| 166 | C2×#237 | — | 5 | 1 | no | — |
| 167 | C2×#237 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 168 | C2×D3×D4 | — | 5 | 1 | no | — |
| 169 | C2×D3×D4 | — | 5 | 2 | no | — |
| 170 | C2×D3×D4 | — | 5 | 1 | no | — |
| 171 | C2×#235 | — | 5 | 1 | no | — |
| 172 | C2×#235 | — | 5 | 1 | no | — |
| 173 | C2×C3×M16 | — | 5 | 2 | no | — |
| 174 | C2×#208 | — | 5 | 2 | no | — |
| 175 | #907 | — | 10 | 4 | no | — |
| 176 | D3×M16 | — | 5 | 8 | no | — |
| 177 | #901 | — | 10 | 4 | no | — |
| 178 | C3×#100 | — | 5 | 4 | no | — |
| 179 | #833 | — | 5 | 4 | no | — |
| 180 | #824 | — | 5 | 4 | no | — |
| 181 | #823 | — | 5 | 4 | no | — |
| 182 | C23×D5 | — | 3 | 2 | no | — |
| 183 | C23×D5 | — | 3 | 2 | no | — |
| 184 | C23×D5 | C4×D3 | 1 | 2 | yes | — |
| 185 | C5×#41 | — | 6 | 4 | no | — |
| 186 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 187 | C2×C5×D4 | — | 3 | 2 | no | — |
| 188 | C2×C5×D4 | C4×D3 | 1 | 1 | yes | characteristic |
| 189 | C22×C4×C5 | — | 3 | 2 | no | — |
| 190 | C22×C4×C5 | — | 3 | 1 | no | — |
| 191 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 192 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 193 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 194 | C2×C22⋊D5 | C22×D3 | 1 | 2 | yes | — |
| 195 | #713 | — | 3 | 4 | no | — |
| 196 | #713 | — | 3 | 4 | no | — |
| 197 | #713 | — | 6 | 4 | no | — |
| 198 | D4×D5 | — | 2 | 2 | no | — |
| 199 | D4×D5 | — | 2 | 2 | no | — |
| 200 | D4×D5 | — | 6 | 8 | no | — |
| 201 | D4×D5 | — | 6 | 4 | no | — |
| 202 | D4×D5 | — | 6 | 4 | no | — |
| 203 | D4×D5 | — | 6 | 4 | no | — |
| 204 | #709 | — | 6 | 8 | no | — |
| 205 | #709 | — | 6 | 2 | no | — |
| 206 | #709 | — | 6 | 2 | no | — |
| 207 | C2×D20 | — | 3 | 2 | no | — |
| 208 | C2×D20 | — | 3 | 1 | no | — |
| 209 | C2×D20 | — | 3 | 2 | no | — |
| 210 | C2×D20 | — | 3 | 1 | no | — |
| 211 | C2×D20 | — | 3 | 2 | no | — |
| 212 | C2×D20 | — | 6 | 4 | no | — |
| 213 | C2×D20 | — | 6 | 4 | no | — |
| 214 | C2×D20 | — | 6 | 4 | no | — |
| 215 | C2×D20 | C4×D3 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×D5 | — | 3 | 2 | no | — |
| 217 | C2×C4×D5 | — | 3 | 2 | no | — |
| 218 | C2×C4×D5 | — | 3 | 1 | no | — |
| 219 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 220 | C2×Dic10 | — | 3 | 1 | no | — |
| 221 | #704 | — | 3 | 4 | no | — |
| 222 | #704 | C22×D3 | 1 | 4 | yes | — |
| 223 | #700 | — | 2 | 2 | no | — |
| 224 | #700 | — | 6 | 8 | no | — |
| 225 | #700 | — | 6 | 2 | no | — |
| 226 | D5⋊C8 | — | 2 | 2 | no | — |
| 227 | D5⋊C8 | — | 6 | 8 | no | — |
| 228 | D5⋊C8 | — | 6 | 2 | no | — |
| 229 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 230 | #568 | — | 15 | 2 | no | — |
| 231 | #413 | — | 15 | 4 | no | — |
| 232 | #413 | — | 15 | 2 | no | — |
| 233 | C2×#100 | — | 5 | 1 | no | — |
| 234 | C2×#100 | — | 15 | 4 | no | — |
| 235 | C2×#100 | — | 15 | 1 | no | — |
| 236 | C22×C3×C5 | — | 2 | 2 | no | — |
| 237 | C22×C3×C5 | — | 4 | 2 | no | — |
| 238 | C22×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 239 | C2×D15 | — | 2 | 1 | no | — |
| 240 | C2×D15 | — | 4 | 2 | no | — |
| 241 | C2×D15 | — | 4 | 1 | no | — |
| 242 | C2×D15 | — | 8 | 4 | no | — |
| 243 | C2×D15 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 244 | C2×C5×D3 | — | 2 | 1 | no | — |
| 245 | C2×C5×D3 | — | 4 | 1 | no | — |
| 246 | C2×C3×D5 | — | 2 | 2 | no | — |
| 247 | C2×C3×D5 | — | 4 | 1 | no | — |
| 248 | C2×C3×D5 | — | 4 | 2 | no | — |
| 249 | C2×C3×D5 | — | 8 | 2 | no | — |
| 250 | C2×C3×D5 | — | 8 | 2 | no | — |
| 251 | C2×C3×D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 252 | C2×C3×D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 253 | D3×D5 | — | 8 | 4 | no | — |
| 254 | C3×C4×C5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 255 | Dic15 | — | 2 | 1 | no | — |
| 256 | C3×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 257 | C5×Dic3 | — | 2 | 1 | no | — |
| 258 | C5×Dic3 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 259 | C24×C3 | — | 5 | 2 | no | — |
| 260 | C23×D3 | — | 5 | 2 | no | — |
| 261 | C23×D3 | — | 5 | 2 | no | — |
| 262 | C2×C3×D4 | — | 5 | 2 | no | — |
| 263 | C2×C3×D4 | — | 5 | 1 | no | — |
| 264 | C2×C3×D4 | — | 10 | 2 | no | — |
| 265 | C2×C3×D4 | — | 10 | 2 | no | — |
| 266 | C2×C3×D4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 267 | C22×C3×C4 | — | 5 | 1 | no | — |
| 268 | C2×#67 | — | 5 | 2 | no | — |
| 269 | C2×#67 | — | 5 | 1 | no | — |
| 270 | C2×#67 | — | 5 | 2 | no | — |
| 271 | C2×#67 | — | 5 | 1 | no | — |
| 272 | C2×#67 | — | 5 | 2 | no | — |
| 273 | C2×#67 | — | 5 | 2 | no | — |
| 274 | C2×#67 | — | 10 | 4 | no | — |
| 275 | C2×#67 | — | 10 | 4 | no | — |
| 276 | C2×#67 | — | 10 | 4 | no | — |
| 277 | C2×#67 | — | 10 | 4 | no | — |
| 278 | C2×#67 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 279 | C22×Dic3 | — | 5 | 2 | no | — |
| 280 | C22×Dic3 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 281 | #237 | — | 2 | 4 | no | — |
| 282 | #237 | — | 10 | 8 | no | — |
| 283 | #237 | — | 10 | 4 | no | — |
| 284 | D3×D4 | — | 10 | 4 | no | — |
| 285 | D3×D4 | — | 10 | 8 | no | — |
| 286 | D3×D4 | — | 10 | 4 | no | — |
| 287 | #235 | — | 5 | 4 | no | — |
| 288 | #235 | — | 5 | 4 | no | — |
| 289 | #235 | — | 10 | 2 | no | — |
| 290 | #235 | — | 10 | 2 | no | — |
| 291 | C2×D12 | — | 5 | 1 | no | — |
| 292 | C2×D12 | — | 5 | 1 | no | — |
| 293 | C2×C4×D3 | — | 5 | 2 | no | — |
| 294 | C2×C4×D3 | — | 5 | 1 | no | — |
| 295 | C2×C4×D3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 296 | C2×Dic6 | — | 5 | 1 | no | — |
| 297 | C2×Dic6 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 298 | C3×M16 | — | 5 | 4 | no | — |
| 299 | C3×M16 | — | 10 | 2 | no | — |
| 300 | C2×C3×C8 | — | 10 | 2 | no | — |
| 301 | #208 | — | 5 | 4 | no | — |
| 302 | #208 | — | 10 | 2 | no | — |
| 303 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 304 | ΓL(1,𝔽25) | — | 10 | 8 | no | — |
| 305 | D3×C8 | — | 10 | 8 | no | — |
| 306 | C23×C5 | — | 3 | 1 | no | — |
| 307 | C23×C5 | C2×C4×D3 | 1 | 2 | yes | — |
| 308 | C22×D5 | — | 2 | 2 | no | — |
| 309 | C22×D5 | — | 2 | 2 | no | — |
| 310 | C22×D5 | — | 3 | 2 | no | — |
| 311 | C22×D5 | — | 3 | 1 | no | — |
| 312 | C22×D5 | — | 6 | 4 | no | — |
| 313 | C22×D5 | — | 6 | 4 | no | — |
| 314 | C22×D5 | — | 8 | 2 | no | — |
| 315 | C22×D5 | — | 24 | 2 | no | — |
| 316 | C22×D5 | — | 24 | 2 | no | — |
| 317 | C22×D5 | C2×C4×D3 | 1 | 2 | yes | — |
| 318 | C22×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 319 | C5×Q8 | — | 3 | 4 | no | — |
| 320 | C5×D4 | — | 2 | 2 | no | — |
| 321 | C5×D4 | — | 6 | 4 | no | — |
| 322 | C2×C4×C5 | — | 3 | 2 | no | — |
| 323 | C2×C4×C5 | — | 3 | 1 | no | — |
| 324 | C2×C4×C5 | — | 6 | 4 | no | — |
| 325 | C2×C4×C5 | — | 6 | 2 | no | — |
| 326 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 327 | C22⋊D5 | — | 2 | 4 | no | — |
| 328 | C22⋊D5 | — | 6 | 4 | no | — |
| 329 | C22⋊D5 | — | 6 | 1 | no | — |
| 330 | C22⋊D5 | — | 6 | 1 | no | — |
| 331 | C22⋊D5 | — | 6 | 2 | no | — |
| 332 | C2×Dic5 | — | 3 | 1 | no | — |
| 333 | C2×Dic5 | C23×D3 | 1 | 1 | yes | characteristic |
| 334 | D20 | — | 2 | 2 | no | — |
| 335 | D20 | — | 3 | 4 | no | — |
| 336 | D20 | — | 3 | 4 | no | — |
| 337 | D20 | — | 3 | 4 | no | — |
| 338 | D20 | — | 6 | 4 | no | — |
| 339 | D20 | — | 6 | 4 | no | — |
| 340 | D20 | — | 6 | 1 | no | — |
| 341 | D20 | — | 6 | 1 | no | — |
| 342 | C4×D5 | — | 3 | 8 | no | — |
| 343 | C4×D5 | — | 6 | 4 | no | — |
| 344 | C4×D5 | — | 6 | 2 | no | — |
| 345 | C4×D5 | D3×D4 | 1 | 2 | yes | — |
| 346 | C4×D5 | D3×D4 | 1 | 2 | yes | — |
| 347 | Dic10 | — | 6 | 2 | no | — |
| 348 | #170 | — | 2 | 4 | no | — |
| 349 | #170 | — | 6 | 4 | no | — |
| 350 | H(5,𝔽2) | — | 30 | 4 | no | — |
| 351 | H(5,𝔽2) | — | 30 | 4 | no | — |
| 352 | C2×#41 | — | 3 | 1 | no | — |
| 353 | C2×#41 | — | 15 | 1 | no | — |
| 354 | C2×#41 | — | 15 | 2 | no | — |
| 355 | C2×#41 | — | 15 | 1 | no | — |
| 356 | C2×#41 | — | 15 | 1 | no | — |
| 357 | C22×D4 | — | 5 | 1 | no | — |
| 358 | C22×D4 | — | 15 | 1 | no | — |
| 359 | C22×D4 | — | 15 | 2 | no | — |
| 360 | C22×D4 | — | 15 | 2 | no | — |
| 361 | C22×D4 | — | 15 | 2 | no | — |
| 362 | C22×D4 | — | 15 | 1 | no | — |
| 363 | #131 | — | 30 | 4 | no | — |
| 364 | #131 | — | 30 | 4 | no | — |
| 365 | C2×M16 | — | 5 | 2 | no | — |
| 366 | C2×M16 | — | 15 | 8 | no | — |
| 367 | C2×M16 | — | 15 | 2 | no | — |
| 368 | #101 | — | 15 | 4 | no | — |
| 369 | #100 | — | 5 | 4 | no | — |
| 370 | #100 | — | 15 | 4 | no | — |
| 371 | #100 | — | 15 | 4 | no | — |
| 372 | C2×C3×C5 | — | 2 | 1 | no | — |
| 373 | C2×C3×C5 | — | 4 | 2 | no | — |
| 374 | C2×C3×C5 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 375 | D15 | — | 2 | 4 | no | — |
| 376 | D15 | — | 4 | 1 | no | — |
| 377 | C3×D5 | — | 2 | 1 | no | — |
| 378 | C3×D5 | — | 2 | 1 | no | — |
| 379 | C3×D5 | — | 4 | 2 | no | — |
| 380 | C5×D3 | — | 4 | 1 | no | — |
| 381 | C23×C3 | — | 5 | 1 | no | — |
| 382 | C23×C3 | — | 5 | 2 | no | — |
| 383 | C23×C3 | — | 10 | 2 | no | — |
| 384 | C23×C3 | — | 10 | 2 | no | — |
| 385 | C23×C3 | — | 40 | 2 | no | — |
| 386 | C23×C3 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 387 | C22×D3 | — | 5 | 2 | no | — |
| 388 | C22×D3 | — | 5 | 1 | no | — |
| 389 | C22×D3 | — | 10 | 4 | no | — |
| 390 | C22×D3 | — | 10 | 4 | no | — |
| 391 | C22×D3 | — | 40 | 2 | no | — |
| 392 | C22×D3 | — | 40 | 2 | no | — |
| 393 | C22×D3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 394 | C3×D4 | — | 2 | 2 | no | — |
| 395 | C3×D4 | — | 10 | 4 | no | — |
| 396 | C3×D4 | — | 10 | 2 | no | — |
| 397 | C2×C3×C4 | — | 5 | 1 | no | — |
| 398 | C2×C3×C4 | — | 5 | 2 | no | — |
| 399 | C2×C3×C4 | — | 5 | 2 | no | — |
| 400 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 401 | #67 | — | 2 | 4 | no | — |
| 402 | #67 | — | 5 | 4 | no | — |
| 403 | #67 | — | 5 | 4 | no | — |
| 404 | #67 | — | 10 | 4 | no | — |
| 405 | #67 | — | 10 | 1 | no | — |
| 406 | #67 | — | 10 | 1 | no | — |
| 407 | #67 | — | 10 | 1 | no | — |
| 408 | #67 | — | 10 | 1 | no | — |
| 409 | #67 | — | 10 | 4 | no | — |
| 410 | #67 | — | 10 | 4 | no | — |
| 411 | C2×Dic3 | — | 2 | 4 | no | — |
| 412 | C2×Dic3 | — | 5 | 1 | no | — |
| 413 | C2×Dic3 | — | 10 | 4 | no | — |
| 414 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 415 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 416 | D12 | — | 5 | 4 | no | — |
| 417 | D12 | — | 10 | 2 | no | — |
| 418 | C4×D3 | — | 2 | 2 | no | — |
| 419 | C4×D3 | — | 5 | 8 | no | — |
| 420 | C4×D3 | — | 10 | 2 | no | — |
| 421 | Dic6 | — | 10 | 2 | no | — |
| 422 | Dic6 | C22⋊AGL(1,𝔽5) | 1 | 4 | yes | — |
| 423 | C3×C8 | — | 10 | 4 | no | — |
| 424 | C3⋊C8 | — | 10 | 4 | no | — |
| 425 | C22×C5 | — | 2 | 2 | no | — |
| 426 | C22×C5 | — | 4 | 2 | no | — |
| 427 | C22×C5 | — | 6 | 1 | no | — |
| 428 | C22×C5 | — | 12 | 1 | no | — |
| 429 | C22×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 430 | C2×D5 | — | 2 | 2 | no | — |
| 431 | C2×D5 | — | 3 | 4 | no | — |
| 432 | C2×D5 | — | 4 | 1 | no | — |
| 433 | C2×D5 | — | 4 | 2 | no | — |
| 434 | C2×D5 | — | 6 | 1 | no | — |
| 435 | C2×D5 | — | 8 | 2 | no | — |
| 436 | C2×D5 | — | 8 | 2 | no | — |
| 437 | C2×D5 | — | 12 | 2 | no | — |
| 438 | C2×D5 | — | 12 | 1 | no | — |
| 439 | C2×D5 | — | 24 | 4 | no | — |
| 440 | C2×D5 | — | 24 | 4 | no | — |
| 441 | C2×D5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 442 | C2×D5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 443 | C4×C5 | — | 3 | 4 | no | — |
| 444 | C4×C5 | — | 6 | 1 | no | — |
| 445 | C4×C5 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 446 | Dic5 | — | 6 | 1 | no | — |
| 447 | Dic5 | C2×D3×D4 | 1 | 2 | yes | — |
| 448 | C24 | — | 5 | 2 | no | — |
| 449 | C24 | — | 15 | 2 | no | — |
| 450 | C24 | — | 15 | 2 | no | — |
| 451 | #41 | — | 6 | 4 | no | — |
| 452 | #41 | — | 15 | 4 | no | — |
| 453 | #41 | — | 15 | 4 | no | — |
| 454 | #41 | — | 30 | 2 | no | — |
| 455 | #41 | — | 30 | 2 | no | — |
| 456 | #41 | — | 30 | 8 | no | — |
| 457 | #41 | — | 30 | 4 | no | — |
| 458 | C2×Q8 | — | 3 | 1 | no | — |
| 459 | C2×Q8 | — | 15 | 1 | no | — |
| 460 | C2×D4 | — | 3 | 2 | no | — |
| 461 | C2×D4 | — | 5 | 2 | no | — |
| 462 | C2×D4 | — | 5 | 1 | no | — |
| 463 | C2×D4 | — | 10 | 2 | no | — |
| 464 | C2×D4 | — | 10 | 2 | no | — |
| 465 | C2×D4 | — | 15 | 2 | no | — |
| 466 | C2×D4 | — | 15 | 2 | no | — |
| 467 | C2×D4 | — | 15 | 1 | no | — |
| 468 | C2×D4 | — | 15 | 2 | no | — |
| 469 | C2×D4 | — | 15 | 1 | no | — |
| 470 | C2×D4 | — | 15 | 1 | no | — |
| 471 | C2×D4 | — | 15 | 2 | no | — |
| 472 | C2×D4 | — | 15 | 1 | no | — |
| 473 | C2×D4 | — | 30 | 4 | no | — |
| 474 | C2×D4 | — | 30 | 4 | no | — |
| 475 | C2×D4 | — | 30 | 4 | no | — |
| 476 | C2×D4 | — | 30 | 8 | no | — |
| 477 | C2×D4 | — | 30 | 4 | no | — |
| 478 | C2×D4 | — | 30 | 4 | no | — |
| 479 | C2×D4 | — | 30 | 4 | no | — |
| 480 | C2×D4 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 481 | C22×C4 | — | 3 | 2 | no | — |
| 482 | C22×C4 | — | 3 | 1 | no | — |
| 483 | C22×C4 | — | 5 | 1 | no | — |
| 484 | C22×C4 | — | 15 | 2 | no | — |
| 485 | C22×C4 | — | 15 | 2 | no | — |
| 486 | C22×C4 | — | 15 | 1 | no | — |
| 487 | M16 | — | 5 | 4 | no | — |
| 488 | M16 | — | 10 | 2 | no | — |
| 489 | M16 | — | 15 | 4 | no | — |
| 490 | M16 | — | 30 | 8 | no | — |
| 491 | M16 | — | 30 | 2 | no | — |
| 492 | C2×C8 | — | 10 | 2 | no | — |
| 493 | C2×C8 | — | 30 | 8 | no | — |
| 494 | C2×C8 | — | 30 | 2 | no | — |
| 495 | C3×C5 | #2888 | 1 | 1 | yes | characteristic, complemented, Hall |
| 496 | C22×C3 | — | 2 | 2 | no | — |
| 497 | C22×C3 | — | 4 | 2 | no | — |
| 498 | C22×C3 | — | 5 | 1 | no | — |
| 499 | C22×C3 | — | 5 | 1 | no | — |
| 500 | C22×C3 | — | 10 | 2 | no | — |
| 501 | C22×C3 | — | 20 | 1 | no | — |
| 502 | C22×C3 | — | 20 | 2 | no | — |
| 503 | C22×C3 | — | 40 | 2 | no | — |
| 504 | C22×C3 | — | 40 | 2 | no | — |
| 505 | C22×C3 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 506 | C2×D3 | — | 2 | 1 | no | — |
| 507 | C2×D3 | — | 4 | 1 | no | — |
| 508 | C2×D3 | — | 5 | 4 | no | — |
| 509 | C2×D3 | — | 10 | 1 | no | — |
| 510 | C2×D3 | — | 20 | 2 | no | — |
| 511 | C2×D3 | — | 20 | 1 | no | — |
| 512 | C2×D3 | — | 40 | 4 | no | — |
| 513 | C2×D3 | — | 40 | 4 | no | — |
| 514 | C3×C4 | — | 5 | 2 | no | — |
| 515 | C3×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 516 | Dic3 | — | 2 | 1 | no | — |
| 517 | Dic3 | — | 10 | 1 | no | — |
| 518 | Dic3 | C2×C22⋊AGL(1,𝔽5) | 1 | 4 | yes | — |
| 519 | C2×C5 | — | 2 | 1 | no | — |
| 520 | C2×C5 | — | 4 | 2 | no | — |
| 521 | C2×C5 | — | 12 | 1 | no | — |
| 522 | C2×C5 | C2×D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 523 | D5 | — | 2 | 1 | no | — |
| 524 | D5 | — | 2 | 1 | no | — |
| 525 | D5 | — | 4 | 2 | no | — |
| 526 | D5 | — | 6 | 4 | no | — |
| 527 | D5 | — | 12 | 1 | no | — |
| 528 | C23 | — | 3 | 1 | no | — |
| 529 | C23 | — | 5 | 1 | no | — |
| 530 | C23 | — | 5 | 2 | no | — |
| 531 | C23 | — | 10 | 2 | no | — |
| 532 | C23 | — | 10 | 2 | no | — |
| 533 | C23 | — | 15 | 2 | no | — |
| 534 | C23 | — | 15 | 1 | no | — |
| 535 | C23 | — | 30 | 4 | no | — |
| 536 | C23 | — | 30 | 4 | no | — |
| 537 | C23 | — | 40 | 2 | no | — |
| 538 | C23 | — | 120 | 2 | no | — |
| 539 | C23 | — | 120 | 2 | no | — |
| 540 | C23 | C2×D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 541 | Q8 | — | 3 | 4 | no | — |
| 542 | Q8 | — | 30 | 2 | no | — |
| 543 | D4 | — | 2 | 2 | no | — |
| 544 | D4 | — | 6 | 4 | no | — |
| 545 | D4 | — | 10 | 4 | no | — |
| 546 | D4 | — | 10 | 2 | no | — |
| 547 | D4 | — | 15 | 4 | no | — |
| 548 | D4 | — | 15 | 4 | no | — |
| 549 | D4 | — | 15 | 4 | no | — |
| 550 | D4 | — | 30 | 4 | no | — |
| 551 | D4 | — | 30 | 2 | no | — |
| 552 | D4 | — | 30 | 1 | no | — |
| 553 | D4 | — | 30 | 1 | no | — |
| 554 | D4 | — | 30 | 4 | no | — |
| 555 | D4 | — | 30 | 4 | no | — |
| 556 | D4 | — | 30 | 1 | no | — |
| 557 | D4 | — | 30 | 1 | no | — |
| 558 | C2×C4 | — | 3 | 2 | no | — |
| 559 | C2×C4 | — | 3 | 1 | no | — |
| 560 | C2×C4 | — | 5 | 1 | no | — |
| 561 | C2×C4 | — | 5 | 2 | no | — |
| 562 | C2×C4 | — | 5 | 2 | no | — |
| 563 | C2×C4 | — | 6 | 4 | no | — |
| 564 | C2×C4 | — | 6 | 2 | no | — |
| 565 | C2×C4 | — | 15 | 8 | no | — |
| 566 | C2×C4 | — | 15 | 1 | no | — |
| 567 | C2×C4 | — | 30 | 4 | no | — |
| 568 | C2×C4 | — | 30 | 2 | no | — |
| 569 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 570 | C8 | — | 10 | 4 | no | — |
| 571 | C8 | — | 30 | 4 | no | — |
| 572 | C2×C3 | — | 2 | 1 | no | — |
| 573 | C2×C3 | — | 4 | 2 | no | — |
| 574 | C2×C3 | — | 10 | 1 | no | — |
| 575 | C2×C3 | — | 10 | 1 | no | — |
| 576 | C2×C3 | — | 20 | 2 | no | — |
| 577 | C2×C3 | C22×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 578 | D3 | — | 4 | 1 | no | — |
| 579 | D3 | — | 10 | 4 | no | — |
| 580 | D3 | — | 20 | 1 | no | — |
| 581 | C5 | #78697 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 582 | C22 | — | 2 | 2 | no | — |
| 583 | C22 | — | 4 | 2 | no | — |
| 584 | C22 | — | 5 | 1 | no | — |
| 585 | C22 | — | 5 | 1 | no | — |
| 586 | C22 | — | 6 | 1 | no | — |
| 587 | C22 | — | 10 | 2 | no | — |
| 588 | C22 | — | 12 | 1 | no | — |
| 589 | C22 | — | 15 | 4 | no | — |
| 590 | C22 | — | 20 | 1 | no | — |
| 591 | C22 | — | 20 | 2 | no | — |
| 592 | C22 | — | 30 | 1 | no | — |
| 593 | C22 | — | 40 | 2 | no | — |
| 594 | C22 | — | 40 | 2 | no | — |
| 595 | C22 | — | 60 | 2 | no | — |
| 596 | C22 | — | 60 | 1 | no | — |
| 597 | C22 | — | 120 | 4 | no | — |
| 598 | C22 | — | 120 | 4 | no | — |
| 599 | C22 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 600 | C4 | — | 3 | 4 | no | — |
| 601 | C4 | — | 5 | 2 | no | — |
| 602 | C4 | — | 6 | 1 | no | — |
| 603 | C4 | — | 30 | 1 | no | — |
| 604 | C4 | D3×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 605 | C3 | #10617553 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 606 | C2 | — | 2 | 1 | no | — |
| 607 | C2 | — | 4 | 2 | no | — |
| 608 | C2 | — | 10 | 1 | no | — |
| 609 | C2 | — | 10 | 1 | no | — |
| 610 | C2 | — | 12 | 1 | no | — |
| 611 | C2 | — | 20 | 2 | no | — |
| 612 | C2 | — | 30 | 4 | no | — |
| 613 | C2 | — | 60 | 1 | no | — |
| 614 | C2 | C2×D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11756827 | C2 | semidirect |
| 3. D5⋊#833 | C2 | semidirect |
| 4. C3×D5⋊#100 | C2 | semidirect |
| 5. #11752050 | C2 | semidirect |
| 6. #11752049 | C2 | semidirect |
| 7. #11751818 | C2 | semidirect |
| 22. D5⋊#208 | C22 | semidirect |
| 23. C3×D5⋊M16 | C22 | semidirect |
| 24. #91931 | C22 | semidirect |
| 27. #91242 | C22 | semidirect |
| 28. C3×#4013 | C22 | semidirect |
| 29. #91175 | C22 | semidirect |
| 30. #91174 | C22 | semidirect |
| 36. D5⋊#100 | D3 | semidirect |
| 110. D5⋊M16 | C2×D3 | semidirect |
| 113. #4013 | C2×D3 | semidirect |
| 495. C3×C5 | #2888 | semidirect |
| 581. C5 | #78697 | semidirect |
| 605. C3 | #10617553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92026 | 2 |
| #11756827 | 2 |
| D5⋊#833 | 2 |
| C3×D5⋊#100 | 2 |
| #11752050 | 2 |
| #11752049 | 2 |
| #11751818 | 2 |
| #10617553 | 3 |
| #78697 | 5 |