← #13044373
Subgroups — #13044373
Order 1280.
1800 conjugacy classes of subgroups.
The subgroup lattice has 366 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5×#564 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617348 | C2 | 1 | 3 | yes | maximal |
| 3 | #10617347 | C2 | 1 | 6 | yes | maximal |
| 4 | #10617346 | C2 | 1 | 6 | yes | maximal |
| 5 | #10617345 | C2 | 1 | 6 | yes | maximal |
| 6 | #10617344 | C2 | 1 | 6 | yes | maximal |
| 7 | AGL(1,𝔽5)×#125 | C2 | 1 | 3 | yes | maximal |
| 8 | C5×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | D5×#125 | C22 | 1 | 6 | yes | — |
| 10 | D5×#125 | C22 | 1 | 6 | yes | — |
| 11 | D5×#125 | C22 | 1 | 3 | yes | — |
| 12 | C5⋊#564 | C4 | 1 | 6 | yes | complemented |
| 13 | C5⋊#564 | C4 | 1 | 6 | yes | complemented |
| 14 | C5⋊#564 | C4 | 1 | 3 | yes | complemented |
| 15 | #65712 | C22 | 1 | 6 | yes | — |
| 16 | #65712 | C22 | 1 | 3 | yes | — |
| 17 | #65712 | C22 | 1 | 6 | yes | — |
| 18 | #65712 | C22 | 1 | 6 | yes | — |
| 19 | #65712 | C22 | 1 | 6 | yes | — |
| 20 | #65712 | C22 | 1 | 3 | yes | — |
| 21 | #65711 | C22 | 1 | 6 | yes | — |
| 22 | #65711 | C22 | 1 | 6 | yes | — |
| 23 | #65711 | C22 | 1 | 6 | yes | — |
| 24 | #65711 | C22 | 1 | 6 | yes | — |
| 25 | #65711 | C22 | 1 | 6 | yes | — |
| 26 | #65711 | C22 | 1 | 6 | yes | — |
| 27 | #65711 | C22 | 1 | 6 | yes | — |
| 28 | #65711 | C22 | 1 | 6 | yes | — |
| 29 | #65711 | C22 | 1 | 6 | yes | — |
| 30 | #65711 | C22 | 1 | 6 | yes | — |
| 31 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 32 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 33 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 34 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 35 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 36 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 37 | #65690 | C22 | 1 | 2 | yes | — |
| 38 | #65689 | C22 | 1 | 3 | yes | — |
| 39 | #65688 | C22 | 1 | 2 | yes | — |
| 40 | C4×C4⋊AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 41 | #65686 | C22 | 1 | 6 | yes | — |
| 42 | C42×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 43 | #34530 | — | 5 | 1 | no | maximal, Sylow |
| 44 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 45 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 46 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 47 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 48 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 49 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 50 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 51 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 52 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 53 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 54 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 55 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 56 | C5×#125 | C2×C4 | 1 | 6 | yes | — |
| 57 | C5×#125 | C2×C4 | 1 | 6 | yes | — |
| 58 | C5×#125 | C2×C4 | 1 | 3 | yes | — |
| 59 | D5×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 60 | D5×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 61 | D5×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 62 | D5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 63 | D5×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 64 | D5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 65 | #4036 | C2×C4 | 1 | 6 | yes | — |
| 66 | #4036 | C2×C4 | 1 | 6 | yes | — |
| 67 | #4036 | C2×C4 | 1 | 6 | yes | — |
| 68 | #4036 | C2×C4 | 1 | 6 | yes | — |
| 69 | #4036 | C2×C4 | 1 | 3 | yes | — |
| 70 | #4036 | C2×C4 | 1 | 3 | yes | — |
| 71 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 72 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 73 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 74 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 75 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 76 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 77 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 78 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 79 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 80 | #4035 | C2×C4 | 1 | 6 | yes | — |
| 81 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 82 | C42×D5 | C23 | 1 | 2 | yes | — |
| 83 | C42×D5 | C23 | 1 | 2 | yes | — |
| 84 | #4016 | C2×C4 | 1 | 6 | yes | — |
| 85 | #4016 | C2×C4 | 1 | 6 | yes | — |
| 86 | #4016 | C2×C4 | 1 | 3 | yes | — |
| 87 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 88 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 89 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 90 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 91 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 92 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 93 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 94 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 95 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 96 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 6 | yes | — |
| 97 | C2×#564 | — | 5 | 1 | no | — |
| 98 | #2382 | — | 5 | 3 | no | — |
| 99 | #2371 | — | 5 | 6 | no | — |
| 100 | #2370 | — | 5 | 6 | no | — |
| 101 | #2336 | — | 5 | 6 | no | — |
| 102 | #2330 | — | 5 | 6 | no | — |
| 103 | C4×#125 | — | 5 | 3 | no | — |
| 104 | C22×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 105 | C22×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 106 | C22×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 107 | C22×AGL(1,𝔽5) | C24 | 1 | 3 | yes | — |
| 108 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 109 | C2×C4×D5 | C24 | 1 | 6 | yes | — |
| 110 | C2×C4×D5 | C24 | 1 | 6 | yes | — |
| 111 | C4⋊AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 112 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 113 | C4⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 114 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 115 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 116 | C4⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 117 | C4×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 118 | C4×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 119 | C4×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 120 | C4×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 121 | C4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 122 | C4×AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 123 | C5×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 124 | C5×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 125 | C5×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 126 | C5×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 127 | C5×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 128 | C5×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 129 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C42×C5 | C22×C4 | 1 | 2 | yes | — |
| 131 | C42×C5 | C22×C4 | 1 | 2 | yes | — |
| 132 | C4⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 133 | C4⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 134 | C4⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 135 | C4⋊Dic5 | C22×C4 | 1 | 6 | yes | — |
| 136 | C4⋊Dic5 | C22×C4 | 1 | 3 | yes | — |
| 137 | C4⋊Dic5 | C22×C4 | 1 | 3 | yes | — |
| 138 | #683 | C22×C4 | 1 | 6 | yes | — |
| 139 | #683 | C22×C4 | 1 | 6 | yes | — |
| 140 | #683 | C22×C4 | 1 | 6 | yes | — |
| 141 | #683 | C22×C4 | 1 | 6 | yes | — |
| 142 | #683 | C22×C4 | 1 | 6 | yes | — |
| 143 | #683 | C22×C4 | 1 | 6 | yes | — |
| 144 | #683 | C22×C4 | 1 | 6 | yes | — |
| 145 | #683 | C22×C4 | 1 | 6 | yes | — |
| 146 | #683 | C22×C4 | 1 | 6 | yes | — |
| 147 | #683 | C22×C4 | 1 | 6 | yes | — |
| 148 | C4×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 149 | C4×Dic5 | C22×C4 | 1 | 6 | yes | — |
| 150 | C4×Dic5 | C22×C4 | 1 | 6 | yes | — |
| 151 | #564 | — | 5 | 6 | no | — |
| 152 | #564 | — | 5 | 6 | no | — |
| 153 | #564 | — | 5 | 3 | no | — |
| 154 | #564 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 155 | C2×#125 | — | 5 | 3 | no | — |
| 156 | C2×#125 | — | 5 | 6 | no | — |
| 157 | C2×#125 | — | 5 | 6 | no | — |
| 158 | #389 | — | 5 | 3 | no | — |
| 159 | #389 | — | 5 | 3 | no | — |
| 160 | #389 | — | 5 | 6 | no | — |
| 161 | #389 | — | 5 | 6 | no | — |
| 162 | #389 | — | 5 | 6 | no | — |
| 163 | #389 | — | 5 | 6 | no | — |
| 164 | #387 | — | 5 | 6 | no | — |
| 165 | #387 | — | 5 | 6 | no | — |
| 166 | #387 | — | 5 | 6 | no | — |
| 167 | #387 | — | 5 | 6 | no | — |
| 168 | #387 | — | 5 | 6 | no | — |
| 169 | #387 | — | 5 | 6 | no | — |
| 170 | #387 | — | 5 | 6 | no | — |
| 171 | #387 | — | 5 | 6 | no | — |
| 172 | #387 | — | 5 | 6 | no | — |
| 173 | #387 | — | 5 | 6 | no | — |
| 174 | #384 | — | 5 | 2 | no | — |
| 175 | #383 | — | 5 | 2 | no | — |
| 176 | #382 | — | 5 | 3 | no | — |
| 177 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 178 | C4×C4⋊C4 | — | 5 | 3 | no | — |
| 179 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 180 | C4×C4⋊C4 | — | 5 | 3 | no | — |
| 181 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 182 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 183 | C4×C4⋊C4 | — | 5 | 6 | no | — |
| 184 | #376 | — | 5 | 6 | no | — |
| 185 | C43 | — | 5 | 1 | no | — |
| 186 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 187 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 188 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 189 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 190 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 191 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 192 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 193 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 194 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 195 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 196 | C2×AGL(1,𝔽5) | 2−1+4 | 1 | 6 | yes | — |
| 197 | C2×C4×C5 | C23×C4 | 1 | 3 | yes | — |
| 198 | C2×C4×C5 | C23×C4 | 1 | 6 | yes | — |
| 199 | C2×C4×C5 | C23×C4 | 1 | 6 | yes | — |
| 200 | C2×Dic5 | C23×C4 | 1 | 3 | yes | — |
| 201 | C2×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 202 | C2×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 203 | C4×D5 | — | 2 | 3 | no | — |
| 204 | C4×D5 | — | 2 | 6 | no | — |
| 205 | C4×D5 | — | 2 | 6 | no | — |
| 206 | C4×D5 | — | 2 | 6 | no | — |
| 207 | C4×D5 | — | 2 | 3 | no | — |
| 208 | C4×D5 | — | 2 | 6 | no | — |
| 209 | #125 | — | 5 | 6 | no | — |
| 210 | #125 | — | 5 | 6 | no | — |
| 211 | #125 | — | 5 | 6 | no | — |
| 212 | #125 | — | 5 | 6 | no | — |
| 213 | #125 | — | 5 | 6 | no | — |
| 214 | #125 | — | 5 | 6 | no | — |
| 215 | #125 | — | 5 | 6 | no | — |
| 216 | #125 | — | 5 | 6 | no | — |
| 217 | #125 | — | 5 | 6 | no | — |
| 218 | #125 | — | 5 | 6 | no | — |
| 219 | #125 | — | 5 | 3 | no | — |
| 220 | #125 | — | 5 | 3 | no | — |
| 221 | #125 | — | 5 | 6 | no | — |
| 222 | #125 | — | 5 | 6 | no | — |
| 223 | #125 | — | 5 | 6 | no | — |
| 224 | #125 | — | 5 | 6 | no | — |
| 225 | #125 | — | 5 | 3 | no | — |
| 226 | #125 | — | 5 | 6 | no | — |
| 227 | #125 | — | 5 | 6 | no | — |
| 228 | #125 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 229 | #125 | C2×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 230 | #125 | C2×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 231 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 232 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 233 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 234 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 235 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 236 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 237 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 238 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 239 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 240 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 241 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 242 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 243 | C2×C42 | — | 5 | 1 | no | — |
| 244 | C2×C42 | — | 5 | 2 | no | — |
| 245 | C2×C42 | — | 5 | 2 | no | — |
| 246 | C2×C42 | — | 5 | 3 | no | — |
| 247 | C2×C42 | — | 5 | 6 | no | — |
| 248 | C2×C42 | — | 5 | 3 | no | — |
| 249 | C2×C42 | — | 5 | 6 | no | — |
| 250 | C2×C42 | — | 5 | 6 | no | — |
| 251 | C2×C42 | — | 5 | 6 | no | — |
| 252 | #95 | — | 5 | 6 | no | — |
| 253 | #95 | — | 5 | 6 | no | — |
| 254 | #95 | — | 5 | 6 | no | — |
| 255 | #95 | — | 5 | 6 | no | — |
| 256 | #95 | — | 5 | 6 | no | — |
| 257 | #95 | — | 5 | 6 | no | — |
| 258 | #95 | — | 5 | 6 | no | — |
| 259 | #95 | — | 5 | 6 | no | — |
| 260 | #95 | — | 5 | 6 | no | — |
| 261 | #95 | — | 5 | 6 | no | — |
| 262 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 263 | C2×D5 | C2×2−1+4 | 1 | 3 | yes | — |
| 264 | C2×D5 | #585 | 1 | 3 | yes | — |
| 265 | AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 266 | AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 267 | AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 268 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 269 | C4×C5 | — | 2 | 3 | no | — |
| 270 | C4×C5 | — | 2 | 6 | no | — |
| 271 | C4×C5 | — | 2 | 6 | no | — |
| 272 | Dic5 | — | 2 | 3 | no | — |
| 273 | Dic5 | — | 2 | 6 | no | — |
| 274 | Dic5 | — | 2 | 6 | no | — |
| 275 | C22×C4 | — | 5 | 3 | no | — |
| 276 | C22×C4 | — | 5 | 6 | no | — |
| 277 | C22×C4 | — | 5 | 3 | no | — |
| 278 | C22×C4 | — | 5 | 6 | no | — |
| 279 | C22×C4 | — | 5 | 6 | no | — |
| 280 | C22×C4 | — | 5 | 6 | no | — |
| 281 | C22×C4 | — | 5 | 1 | no | — |
| 282 | C4⋊C4 | — | 5 | 6 | no | — |
| 283 | C4⋊C4 | — | 5 | 6 | no | — |
| 284 | C4⋊C4 | — | 5 | 6 | no | — |
| 285 | C4⋊C4 | — | 5 | 6 | no | — |
| 286 | C4⋊C4 | — | 5 | 6 | no | — |
| 287 | C4⋊C4 | — | 5 | 6 | no | — |
| 288 | C4⋊C4 | — | 5 | 6 | no | — |
| 289 | C4⋊C4 | — | 5 | 6 | no | — |
| 290 | C4⋊C4 | — | 5 | 6 | no | — |
| 291 | C4⋊C4 | — | 5 | 6 | no | — |
| 292 | C4⋊C4 | — | 5 | 3 | no | — |
| 293 | C4⋊C4 | — | 5 | 6 | no | — |
| 294 | C4⋊C4 | — | 5 | 6 | no | — |
| 295 | C4⋊C4 | — | 5 | 3 | no | — |
| 296 | C4⋊C4 | — | 5 | 6 | no | — |
| 297 | C4⋊C4 | — | 5 | 6 | no | — |
| 298 | C4⋊C4 | — | 10 | 12 | no | — |
| 299 | C4⋊C4 | — | 20 | 6 | no | — |
| 300 | C4⋊C4 | — | 20 | 3 | no | — |
| 301 | C4⋊C4 | — | 20 | 6 | no | — |
| 302 | C4⋊C4 | — | 20 | 6 | no | — |
| 303 | C4⋊C4 | — | 20 | 3 | no | — |
| 304 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 305 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 306 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 307 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 308 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 309 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 310 | C42 | — | 5 | 3 | no | — |
| 311 | C42 | — | 5 | 6 | no | — |
| 312 | C42 | — | 5 | 6 | no | — |
| 313 | C42 | — | 10 | 6 | no | — |
| 314 | C42 | — | 10 | 12 | no | — |
| 315 | C42 | — | 20 | 6 | no | — |
| 316 | C42 | — | 20 | 6 | no | — |
| 317 | C42 | — | 20 | 3 | no | — |
| 318 | C42 | — | 20 | 6 | no | — |
| 319 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 320 | C42 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 321 | C42 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 322 | C2×C5 | C4×2−1+4 | 1 | 3 | yes | — |
| 323 | D5 | #3563 | 1 | 3 | yes | — |
| 324 | D5 | #3567 | 1 | 1 | yes | characteristic |
| 325 | C23 | — | 5 | 1 | no | — |
| 326 | C2×C4 | — | 5 | 6 | no | — |
| 327 | C2×C4 | — | 5 | 3 | no | — |
| 328 | C2×C4 | — | 5 | 6 | no | — |
| 329 | C2×C4 | — | 5 | 6 | no | — |
| 330 | C2×C4 | — | 10 | 3 | no | — |
| 331 | C2×C4 | — | 10 | 6 | no | — |
| 332 | C2×C4 | — | 10 | 6 | no | — |
| 333 | C2×C4 | — | 10 | 3 | no | — |
| 334 | C2×C4 | — | 10 | 6 | no | — |
| 335 | C2×C4 | — | 10 | 6 | no | — |
| 336 | C2×C4 | — | 10 | 3 | no | — |
| 337 | C2×C4 | — | 10 | 3 | no | — |
| 338 | C2×C4 | — | 10 | 6 | no | — |
| 339 | C2×C4 | — | 10 | 6 | no | — |
| 340 | C2×C4 | — | 10 | 6 | no | — |
| 341 | C2×C4 | — | 10 | 6 | no | — |
| 342 | C2×C4 | — | 10 | 3 | no | — |
| 343 | C2×C4 | — | 10 | 6 | no | — |
| 344 | C2×C4 | — | 10 | 6 | no | — |
| 345 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 346 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 347 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 348 | C5 | #34530 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 349 | C22 | — | 5 | 3 | no | — |
| 350 | C22 | — | 5 | 3 | no | — |
| 351 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 352 | C4 | — | 2 | 3 | no | — |
| 353 | C4 | — | 2 | 6 | no | — |
| 354 | C4 | — | 2 | 6 | no | — |
| 355 | C4 | — | 10 | 6 | no | — |
| 356 | C4 | — | 10 | 3 | no | — |
| 357 | C4 | — | 10 | 6 | no | — |
| 358 | C4 | — | 10 | 6 | no | — |
| 359 | C4 | — | 20 | 6 | no | — |
| 360 | C4 | — | 20 | 6 | no | — |
| 361 | C4 | — | 20 | 1 | no | — |
| 362 | C2 | — | 5 | 3 | no | — |
| 363 | C2 | — | 5 | 1 | no | — |
| 364 | C2 | AGL(1,𝔽5)×2−1+4 | 1 | 3 | yes | — |
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