← #72242159
Subgroups — #72242159
Order 2560.
404 conjugacy classes of subgroups.
The subgroup lattice has 372 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13027805 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13027533 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13026042 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13026036 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13014405 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13014402 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | D5×#1426 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10604107 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#64849 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#64844 | C22 | 1 | 1 | yes | characteristic |
| 11 | D5⋊M64 | C22 | 1 | 1 | yes | characteristic |
| 12 | #10604089 | — | 2 | 1 | no | — |
| 13 | AGL(1,𝔽5)×#107 | — | 2 | 1 | no | — |
| 14 | D5×M64 | C22 | 1 | 1 | yes | characteristic |
| 15 | D5×#368 | C22 | 1 | 1 | yes | characteristic |
| 16 | D5×#367 | C22 | 1 | 1 | yes | characteristic |
| 17 | #10598626 | — | 2 | 1 | no | — |
| 18 | #10598619 | — | 2 | 1 | no | — |
| 19 | #10598490 | C4 | 1 | 2 | yes | complemented |
| 20 | #10598489 | C4 | 1 | 2 | yes | complemented |
| 21 | #10598488 | C4 | 1 | 2 | yes | complemented |
| 22 | #10598487 | C4 | 1 | 2 | yes | complemented |
| 23 | C5×#1426 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #10598092 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | #10598073 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #10598070 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #152000 | — | 5 | 1 | no | maximal, Sylow |
| 28 | #65728 | — | 4 | 1 | no | — |
| 29 | #65721 | — | 2 | 1 | no | — |
| 30 | C2×#3994 | — | 2 | 1 | no | — |
| 31 | C2×C8×AGL(1,𝔽5) | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×D5⋊C16 | D4 | 1 | 1 | yes | characteristic |
| 33 | C4⋊C4×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 34 | C2×D5×C16 | C23 | 1 | 1 | yes | characteristic |
| 35 | D5×#108 | — | 2 | 1 | no | — |
| 36 | D5×#107 | — | 2 | 1 | no | — |
| 37 | #64900 | — | 4 | 1 | no | — |
| 38 | #64877 | — | 2 | 1 | no | — |
| 39 | #64874 | — | 4 | 1 | no | — |
| 40 | #64850 | — | 2 | 1 | no | — |
| 41 | #64849 | — | 2 | 1 | no | — |
| 42 | #64849 | C2×C4 | 1 | 2 | yes | — |
| 43 | #64849 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #64849 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #64844 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | #64844 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #64844 | Q8 | 1 | 1 | yes | characteristic |
| 48 | #64844 | Q8 | 1 | 1 | yes | characteristic |
| 49 | #64842 | C2×C4 | 1 | 2 | yes | — |
| 50 | D5⋊C32 | — | 2 | 1 | no | — |
| 51 | C5×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C5×#368 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C5×#367 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | #64726 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | #64725 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | #64719 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #64713 | — | 2 | 1 | no | — |
| 58 | #64710 | — | 2 | 1 | no | — |
| 59 | #64667 | C2×C4 | 1 | 2 | yes | — |
| 60 | D5×C32 | C2×C4 | 1 | 2 | yes | — |
| 61 | C2×#1426 | — | 5 | 1 | no | — |
| 62 | #13634 | — | 5 | 1 | no | — |
| 63 | C2×#1398 | — | 5 | 1 | no | — |
| 64 | #12674 | — | 5 | 1 | no | — |
| 65 | #12671 | — | 5 | 1 | no | — |
| 66 | #7478 | — | 5 | 1 | no | — |
| 67 | #7477 | — | 5 | 1 | no | — |
| 68 | #4130 | — | 4 | 1 | no | — |
| 69 | C2×C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 70 | C2×C4×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 71 | C2×C4×AGL(1,𝔽5) | D8 | 1 | 1 | yes | characteristic |
| 72 | C2×D5⋊C8 | D8 | 1 | 1 | yes | characteristic |
| 73 | D5×M16 | — | 4 | 1 | no | — |
| 74 | C2×C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | D5×C4⋊C4 | — | 4 | 1 | no | — |
| 76 | (C2×AGL(1,𝔽5))⋊C4 | — | 8 | 1 | no | — |
| 77 | C2×#674 | — | 2 | 1 | no | — |
| 78 | #3994 | — | 2 | 2 | no | — |
| 79 | #3994 | — | 2 | 1 | no | — |
| 80 | #3994 | — | 2 | 1 | no | — |
| 81 | #3994 | — | 4 | 1 | no | — |
| 82 | #3993 | — | 4 | 1 | no | — |
| 83 | #3992 | — | 8 | 1 | no | — |
| 84 | C8×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 85 | C8×AGL(1,𝔽5) | C4⋊C4 | 1 | 1 | yes | characteristic |
| 86 | C8×AGL(1,𝔽5) | C4⋊C4 | 1 | 1 | yes | characteristic |
| 87 | C8×AGL(1,𝔽5) | Q16 | 1 | 1 | yes | characteristic |
| 88 | C8×AGL(1,𝔽5) | Q16 | 1 | 1 | yes | characteristic |
| 89 | D5⋊C16 | — | 2 | 1 | no | — |
| 90 | D5⋊C16 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 91 | D5⋊C16 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 92 | C2×C5×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | C5×#108 | — | 2 | 1 | no | — |
| 94 | C5×#107 | — | 2 | 1 | no | — |
| 95 | #3954 | — | 4 | 1 | no | — |
| 96 | #3951 | — | 2 | 1 | no | — |
| 97 | #3950 | — | 2 | 1 | no | — |
| 98 | C2×#672 | #41 | 1 | 1 | yes | characteristic |
| 99 | #3939 | — | 4 | 1 | no | — |
| 100 | D5×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | D5×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | D5×C16 | C2×Q8 | 1 | 1 | yes | characteristic |
| 103 | D5×C16 | #41 | 1 | 1 | yes | characteristic |
| 104 | #3928 | — | 2 | 2 | no | — |
| 105 | C5×C32 | C42 | 1 | 2 | yes | complemented |
| 106 | #3926 | C42 | 1 | 2 | yes | complemented |
| 107 | C2×M64 | — | 5 | 1 | no | — |
| 108 | C2×M64 | — | 5 | 1 | no | — |
| 109 | C2×#368 | — | 5 | 1 | no | — |
| 110 | #2158 | — | 5 | 1 | no | — |
| 111 | C2×#367 | — | 5 | 1 | no | — |
| 112 | C2×#366 | — | 5 | 1 | no | — |
| 113 | C2×#346 | — | 5 | 1 | no | — |
| 114 | C4×#107 | — | 10 | 1 | no | — |
| 115 | #1772 | — | 10 | 1 | no | — |
| 116 | #1426 | — | 5 | 1 | no | — |
| 117 | #1426 | — | 5 | 1 | no | — |
| 118 | #1426 | — | 5 | 1 | no | — |
| 119 | #1426 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 120 | #1424 | — | 5 | 2 | no | — |
| 121 | #1423 | — | 5 | 2 | no | — |
| 122 | #1398 | — | 5 | 2 | no | — |
| 123 | #1398 | — | 5 | 2 | no | — |
| 124 | #1382 | — | 10 | 1 | no | — |
| 125 | #1380 | — | 10 | 1 | no | — |
| 126 | C22×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 127 | C22×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 128 | C2×C4×D5 | — | 8 | 1 | no | — |
| 129 | C2×C4×D5 | C2×D8 | 1 | 1 | yes | characteristic |
| 130 | C22⋊AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 131 | C2×#170 | — | 2 | 1 | no | — |
| 132 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 133 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 134 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 135 | C4⋊AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 136 | C4×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 137 | C4×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 138 | C4×AGL(1,𝔽5) | — | 16 | 2 | no | — |
| 139 | C4×AGL(1,𝔽5) | #107 | 1 | 1 | yes | characteristic |
| 140 | C4×AGL(1,𝔽5) | #107 | 1 | 1 | yes | characteristic |
| 141 | D5⋊C8 | — | 2 | 1 | no | — |
| 142 | D5⋊C8 | #107 | 1 | 1 | yes | characteristic |
| 143 | D5⋊C8 | #107 | 1 | 1 | yes | characteristic |
| 144 | C5×M16 | — | 4 | 1 | no | — |
| 145 | C2×C5×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 146 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 147 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 148 | #683 | — | 8 | 1 | no | — |
| 149 | #681 | — | 4 | 1 | no | — |
| 150 | C2×#168 | #135 | 1 | 1 | yes | characteristic |
| 151 | #676 | — | 8 | 1 | no | — |
| 152 | C8×D5 | — | 8 | 1 | no | — |
| 153 | C8×D5 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 154 | C8×D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 155 | C8×D5 | C2×Q16 | 1 | 1 | yes | characteristic |
| 156 | C8×D5 | #135 | 1 | 1 | yes | characteristic |
| 157 | #674 | — | 2 | 1 | no | — |
| 158 | #674 | — | 2 | 1 | no | — |
| 159 | C5×C16 | C2×C42 | 1 | 1 | yes | characteristic |
| 160 | C5×C16 | C4×Q8 | 1 | 1 | yes | characteristic |
| 161 | #672 | #117 | 1 | 1 | yes | characteristic |
| 162 | #672 | C4×Q8 | 1 | 1 | yes | characteristic |
| 163 | C22×C16 | — | 5 | 1 | no | — |
| 164 | C22×C16 | — | 5 | 1 | no | — |
| 165 | C2×#108 | — | 10 | 1 | no | — |
| 166 | #427 | — | 10 | 1 | no | — |
| 167 | C2×#107 | — | 10 | 1 | no | — |
| 168 | C2×#107 | — | 10 | 1 | no | — |
| 169 | #405 | — | 20 | 1 | no | — |
| 170 | C2×C4×C8 | — | 5 | 1 | no | — |
| 171 | C4×C4⋊C4 | — | 20 | 1 | no | — |
| 172 | M64 | — | 5 | 1 | no | — |
| 173 | M64 | — | 5 | 2 | no | — |
| 174 | M64 | — | 5 | 2 | no | — |
| 175 | M64 | — | 10 | 1 | no | — |
| 176 | M64 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 177 | C2×C32 | — | 5 | 2 | no | — |
| 178 | C2×C32 | — | 10 | 1 | no | — |
| 179 | #368 | — | 5 | 1 | no | — |
| 180 | #368 | — | 10 | 1 | no | — |
| 181 | #368 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 182 | #367 | — | 5 | 1 | no | — |
| 183 | #367 | — | 10 | 1 | no | — |
| 184 | #367 | — | 10 | 1 | no | — |
| 185 | #367 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 186 | #366 | — | 5 | 2 | no | — |
| 187 | #366 | — | 5 | 1 | no | — |
| 188 | #366 | — | 5 | 1 | no | — |
| 189 | #366 | — | 10 | 1 | no | — |
| 190 | #346 | — | 5 | 1 | no | — |
| 191 | #346 | — | 5 | 1 | no | — |
| 192 | #346 | — | 5 | 1 | no | — |
| 193 | #346 | — | 5 | 1 | no | — |
| 194 | #340 | — | 20 | 1 | no | — |
| 195 | #339 | — | 20 | 1 | no | — |
| 196 | C22×D5 | #509 | 1 | 1 | yes | characteristic |
| 197 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 198 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 199 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 200 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 201 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 202 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 203 | C2×AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 204 | C2×AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 205 | C2×AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 206 | C2×C4×C5 | — | 8 | 1 | no | — |
| 207 | C2×C4×C5 | C4×D8 | 1 | 1 | yes | characteristic |
| 208 | C2×Dic5 | — | 8 | 1 | no | — |
| 209 | C2×Dic5 | #510 | 1 | 1 | yes | characteristic |
| 210 | C4×D5 | — | 16 | 1 | no | — |
| 211 | C4×D5 | — | 16 | 1 | no | — |
| 212 | C4×D5 | C2×#107 | 1 | 1 | yes | characteristic |
| 213 | C4×D5 | C4×D8 | 1 | 1 | yes | characteristic |
| 214 | C4×D5 | #509 | 1 | 1 | yes | characteristic |
| 215 | C4×D5 | #510 | 1 | 1 | yes | characteristic |
| 216 | #170 | — | 2 | 1 | no | — |
| 217 | #170 | — | 2 | 1 | no | — |
| 218 | C5×C8 | — | 8 | 1 | no | — |
| 219 | C5×C8 | C4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 220 | C5×C8 | C4×Q16 | 1 | 1 | yes | characteristic |
| 221 | #168 | — | 8 | 1 | no | — |
| 222 | #168 | #427 | 1 | 1 | yes | characteristic |
| 223 | #168 | C4×Q16 | 1 | 1 | yes | characteristic |
| 224 | C2×M16 | — | 20 | 1 | no | — |
| 225 | C22×C8 | — | 5 | 1 | no | — |
| 226 | C22×C8 | — | 5 | 1 | no | — |
| 227 | #117 | — | 20 | 1 | no | — |
| 228 | C2×C4⋊C4 | — | 20 | 1 | no | — |
| 229 | C2×C4⋊C4 | — | 20 | 1 | no | — |
| 230 | C2×C42 | — | 5 | 1 | no | — |
| 231 | C2×C42 | — | 40 | 1 | no | — |
| 232 | C2×C16 | — | 5 | 1 | no | — |
| 233 | C2×C16 | — | 5 | 1 | no | — |
| 234 | C2×C16 | — | 5 | 1 | no | — |
| 235 | C2×C16 | — | 5 | 1 | no | — |
| 236 | C2×C16 | — | 5 | 1 | no | — |
| 237 | C2×C16 | — | 5 | 1 | no | — |
| 238 | C2×C16 | — | 5 | 1 | no | — |
| 239 | C2×C16 | — | 10 | 1 | no | — |
| 240 | C2×C16 | — | 10 | 1 | no | — |
| 241 | C2×C16 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 242 | #108 | — | 2 | 1 | no | — |
| 243 | #108 | — | 10 | 1 | no | — |
| 244 | #108 | — | 20 | 1 | no | — |
| 245 | #107 | — | 2 | 1 | no | — |
| 246 | #107 | — | 10 | 2 | no | — |
| 247 | #107 | — | 10 | 1 | no | — |
| 248 | #107 | — | 10 | 1 | no | — |
| 249 | #107 | — | 10 | 1 | no | — |
| 250 | #107 | — | 20 | 1 | no | — |
| 251 | #107 | — | 20 | 1 | no | — |
| 252 | #106 | — | 20 | 1 | no | — |
| 253 | #97 | — | 40 | 1 | no | — |
| 254 | C4×C8 | — | 5 | 1 | no | — |
| 255 | C4×C8 | — | 5 | 1 | no | — |
| 256 | C4×C8 | — | 5 | 1 | no | — |
| 257 | C4×C8 | — | 5 | 1 | no | — |
| 258 | C4×C8 | — | 40 | 1 | no | — |
| 259 | #95 | — | 40 | 1 | no | — |
| 260 | C32 | — | 5 | 2 | no | — |
| 261 | C32 | — | 10 | 2 | no | — |
| 262 | C32 | C4×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 263 | C22×C5 | #2175 | 1 | 1 | yes | characteristic |
| 264 | C2×D5 | — | 2 | 1 | no | — |
| 265 | C2×D5 | — | 2 | 1 | no | — |
| 266 | C2×D5 | #2159 | 1 | 1 | yes | characteristic |
| 267 | C2×D5 | #2177 | 1 | 1 | yes | characteristic |
| 268 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 269 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 270 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 271 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 272 | AGL(1,𝔽5) | — | 16 | 2 | no | — |
| 273 | C4×C5 | — | 16 | 1 | no | — |
| 274 | C4×C5 | C4×#107 | 1 | 1 | yes | characteristic |
| 275 | C4×C5 | #2175 | 1 | 1 | yes | characteristic |
| 276 | Dic5 | — | 16 | 1 | no | — |
| 277 | Dic5 | #2159 | 1 | 1 | yes | characteristic |
| 278 | Dic5 | #2176 | 1 | 1 | yes | characteristic |
| 279 | C22×C4 | — | 5 | 1 | no | — |
| 280 | C22×C4 | — | 10 | 1 | no | — |
| 281 | C22×C4 | — | 40 | 1 | no | — |
| 282 | C22×C4 | — | 40 | 1 | no | — |
| 283 | M16 | — | 4 | 1 | no | — |
| 284 | M16 | — | 20 | 1 | no | — |
| 285 | M16 | — | 40 | 1 | no | — |
| 286 | C2×C8 | — | 5 | 1 | no | — |
| 287 | C2×C8 | — | 5 | 1 | no | — |
| 288 | C2×C8 | — | 5 | 1 | no | — |
| 289 | C2×C8 | — | 5 | 1 | no | — |
| 290 | C2×C8 | — | 5 | 1 | no | — |
| 291 | C2×C8 | — | 5 | 1 | no | — |
| 292 | C2×C8 | — | 5 | 1 | no | — |
| 293 | C2×C8 | — | 10 | 1 | no | — |
| 294 | C2×C8 | — | 10 | 1 | no | — |
| 295 | C2×C8 | — | 40 | 1 | no | — |
| 296 | C2×C8 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 297 | C4⋊C4 | — | 4 | 1 | no | — |
| 298 | C4⋊C4 | — | 20 | 1 | no | — |
| 299 | C4⋊C4 | — | 20 | 1 | no | — |
| 300 | C4⋊C4 | — | 20 | 2 | no | — |
| 301 | C4⋊C4 | — | 20 | 1 | no | — |
| 302 | C4⋊C4 | — | 40 | 1 | no | — |
| 303 | C4⋊C4 | — | 40 | 1 | no | — |
| 304 | C22⋊C4 | — | 40 | 1 | no | — |
| 305 | C42 | — | 5 | 1 | no | — |
| 306 | C42 | — | 5 | 1 | no | — |
| 307 | C42 | — | 10 | 1 | no | — |
| 308 | C42 | — | 40 | 1 | no | — |
| 309 | C42 | — | 80 | 2 | no | — |
| 310 | C16 | — | 5 | 1 | no | — |
| 311 | C16 | — | 5 | 1 | no | — |
| 312 | C16 | — | 10 | 1 | no | — |
| 313 | C16 | — | 10 | 1 | no | — |
| 314 | C16 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 315 | C16 | Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 316 | C2×C5 | — | 2 | 1 | no | — |
| 317 | C2×C5 | #12674 | 1 | 1 | yes | characteristic |
| 318 | D5 | — | 2 | 1 | no | — |
| 319 | D5 | #13657 | 1 | 1 | yes | characteristic |
| 320 | D5 | #13658 | 1 | 1 | yes | characteristic |
| 321 | C23 | — | 5 | 1 | no | — |
| 322 | C2×C4 | — | 5 | 1 | no | — |
| 323 | C2×C4 | — | 5 | 1 | no | — |
| 324 | C2×C4 | — | 5 | 1 | no | — |
| 325 | C2×C4 | — | 5 | 1 | no | — |
| 326 | C2×C4 | — | 5 | 1 | no | — |
| 327 | C2×C4 | — | 8 | 1 | no | — |
| 328 | C2×C4 | — | 10 | 1 | no | — |
| 329 | C2×C4 | — | 10 | 1 | no | — |
| 330 | C2×C4 | — | 20 | 1 | no | — |
| 331 | C2×C4 | — | 20 | 1 | no | — |
| 332 | C2×C4 | — | 40 | 1 | no | — |
| 333 | C2×C4 | — | 40 | 1 | no | — |
| 334 | C2×C4 | — | 40 | 2 | no | — |
| 335 | C2×C4 | — | 40 | 1 | no | — |
| 336 | C2×C4 | — | 80 | 1 | no | — |
| 337 | C2×C4 | — | 80 | 1 | no | — |
| 338 | C2×C4 | — | 80 | 1 | no | — |
| 339 | C2×C4 | — | 80 | 1 | no | — |
| 340 | C2×C4 | D8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 341 | C8 | — | 5 | 1 | no | — |
| 342 | C8 | — | 5 | 1 | no | — |
| 343 | C8 | — | 8 | 1 | no | — |
| 344 | C8 | — | 10 | 1 | no | — |
| 345 | C8 | — | 10 | 1 | no | — |
| 346 | C8 | — | 40 | 1 | no | — |
| 347 | C8 | C4⋊C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 348 | C8 | Q16×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 349 | C5 | #152000 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 350 | C22 | — | 5 | 1 | no | — |
| 351 | C22 | — | 5 | 1 | no | — |
| 352 | C22 | — | 10 | 1 | no | — |
| 353 | C22 | — | 10 | 1 | no | — |
| 354 | C22 | #10604127 | 1 | 1 | yes | characteristic |
| 355 | C4 | — | 5 | 1 | no | — |
| 356 | C4 | — | 5 | 1 | no | — |
| 357 | C4 | — | 16 | 1 | no | — |
| 358 | C4 | — | 20 | 1 | no | — |
| 359 | C4 | — | 20 | 1 | no | — |
| 360 | C4 | — | 80 | 1 | no | — |
| 361 | C4 | — | 80 | 2 | no | — |
| 362 | C4 | — | 80 | 1 | no | — |
| 363 | C4 | — | 80 | 1 | no | — |
| 364 | C4 | AGL(1,𝔽5)×#107 | 1 | 1 | yes | characteristic |
| 365 | C4 | #10604127 | 1 | 1 | yes | characteristic |
| 366 | C2 | — | 2 | 1 | no | — |
| 367 | C2 | — | 5 | 1 | no | — |
| 368 | C2 | — | 5 | 1 | no | — |
| 369 | C2 | — | 10 | 1 | no | — |
| 370 | C2 | #13026042 | 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