← #72221572
Subgroups — #72221572
Order 2560.
1026 conjugacy classes of subgroups.
The subgroup lattice has 634 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13033560 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D5⋊#1455 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13013609 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13013597 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D5×#2165 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | D5⋊#430 | C4 | 1 | 1 | yes | characteristic |
| 7 | #10617409 | C4 | 1 | 1 | yes | characteristic |
| 8 | #10617407 | — | 2 | 1 | no | — |
| 9 | C4×D5⋊M16 | — | 2 | 1 | no | — |
| 10 | C4×D5×M16 | C22 | 1 | 1 | yes | characteristic |
| 11 | #10604737 | — | 2 | 1 | no | — |
| 12 | #10604737 | C4 | 1 | 2 | yes | complemented |
| 13 | C2×#64862 | — | 2 | 1 | no | — |
| 14 | #10603885 | — | 2 | 1 | no | — |
| 15 | #10603885 | C4 | 1 | 2 | yes | — |
| 16 | #10603864 | — | 2 | 1 | no | — |
| 17 | #10603864 | C4 | 1 | 2 | yes | complemented |
| 18 | #10603851 | — | 2 | 1 | no | — |
| 19 | #10603851 | C22 | 1 | 2 | yes | — |
| 20 | #10603807 | C22 | 1 | 1 | yes | characteristic |
| 21 | #10603806 | — | 2 | 1 | no | — |
| 22 | C8×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 23 | C5×#2165 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #10600657 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | D5×#364 | C22 | 1 | 2 | yes | — |
| 26 | #10600091 | C4 | 1 | 2 | yes | complemented |
| 27 | D5×#349 | — | 2 | 1 | no | — |
| 28 | #10599907 | — | 2 | 1 | no | — |
| 29 | #10599881 | — | 2 | 1 | no | — |
| 30 | D5×#347 | — | 2 | 1 | no | — |
| 31 | #126894 | — | 5 | 1 | no | maximal, Sylow |
| 32 | C2×#4130 | — | 2 | 1 | no | — |
| 33 | C2×D5⋊M16 | — | 2 | 2 | no | — |
| 34 | C2×D5⋊M16 | — | 2 | 1 | no | — |
| 35 | C2×D5×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×D5×M16 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×C42×D5 | D4 | 1 | 1 | yes | characteristic |
| 38 | C4×#704 | — | 2 | 2 | no | — |
| 39 | C4×#704 | — | 2 | 2 | no | — |
| 40 | #65729 | — | 2 | 4 | no | — |
| 41 | #65728 | — | 4 | 2 | no | — |
| 42 | #65727 | — | 2 | 4 | no | — |
| 43 | M16×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 44 | D5⋊#108 | — | 2 | 1 | no | — |
| 45 | D5⋊#108 | C2×C4 | 1 | 2 | yes | — |
| 46 | #65721 | — | 2 | 1 | no | — |
| 47 | #65721 | C2×C4 | 1 | 2 | yes | — |
| 48 | #65718 | — | 2 | 2 | no | — |
| 49 | #65718 | — | 2 | 2 | no | — |
| 50 | C4×#700 | — | 2 | 2 | no | — |
| 51 | C4×#700 | — | 2 | 2 | no | — |
| 52 | #65676 | — | 2 | 2 | no | — |
| 53 | C4×D5⋊C8 | — | 2 | 1 | no | — |
| 54 | C4×D5⋊C8 | — | 2 | 1 | no | — |
| 55 | C4×C5×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | M16×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | M16×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 58 | C4×#681 | Q8 | 1 | 1 | yes | characteristic |
| 59 | D5×M32 | — | 2 | 2 | no | — |
| 60 | #64996 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | #64996 | D4 | 1 | 1 | yes | characteristic |
| 62 | D5×#97 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | D5×#97 | D4 | 1 | 1 | yes | characteristic |
| 64 | C4×#676 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C4×#676 | Q8 | 1 | 1 | yes | characteristic |
| 66 | C4×C8×D5 | D4 | 1 | 1 | yes | characteristic |
| 67 | C4×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 68 | #170⋊C8 | — | 2 | 2 | no | — |
| 69 | #170⋊C8 | — | 2 | 2 | no | — |
| 70 | #64879 | — | 2 | 1 | no | — |
| 71 | #64879 | C2×C4 | 1 | 2 | yes | complemented |
| 72 | C8×#170 | — | 2 | 1 | no | — |
| 73 | C8×#170 | C2×C4 | 1 | 2 | yes | complemented |
| 74 | #64862 | — | 2 | 2 | no | — |
| 75 | #64862 | — | 2 | 2 | no | — |
| 76 | C5×#364 | C2×C4 | 1 | 2 | yes | complemented |
| 77 | C5×#349 | — | 2 | 1 | no | — |
| 78 | C5×#347 | — | 2 | 1 | no | — |
| 79 | #64773 | — | 2 | 1 | no | — |
| 80 | #64734 | — | 2 | 2 | no | — |
| 81 | #64732 | — | 2 | 2 | no | — |
| 82 | #64731 | — | 2 | 2 | no | — |
| 83 | #64686 | — | 2 | 1 | no | — |
| 84 | #64683 | C2×C4 | 1 | 2 | yes | complemented |
| 85 | C2×#2165 | — | 5 | 1 | no | — |
| 86 | #20445 | — | 5 | 1 | no | — |
| 87 | C2×#1455 | — | 5 | 1 | no | — |
| 88 | #7182 | — | 5 | 2 | no | — |
| 89 | #7179 | — | 5 | 2 | no | — |
| 90 | C22×C4×D5 | — | 2 | 1 | no | — |
| 91 | C22×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 92 | C2×C22⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 93 | C2×#704 | — | 2 | 4 | no | — |
| 94 | C2×#704 | — | 4 | 1 | no | — |
| 95 | #4130 | — | 2 | 2 | no | — |
| 96 | #4130 | — | 2 | 2 | no | — |
| 97 | #4130 | — | 4 | 1 | no | — |
| 98 | #4130 | — | 4 | 1 | no | — |
| 99 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 100 | C2×C4×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 101 | D5⋊M16 | — | 2 | 2 | no | — |
| 102 | D5⋊M16 | — | 2 | 2 | no | — |
| 103 | D5⋊M16 | — | 4 | 8 | no | — |
| 104 | D5⋊M16 | — | 4 | 1 | no | — |
| 105 | D5⋊M16 | — | 4 | 1 | no | — |
| 106 | C2×#700 | — | 2 | 2 | no | — |
| 107 | C2×#700 | — | 2 | 4 | no | — |
| 108 | C2×D5⋊C8 | — | 2 | 2 | no | — |
| 109 | C2×D5⋊C8 | — | 2 | 2 | no | — |
| 110 | C2×D5⋊C8 | — | 4 | 1 | no | — |
| 111 | C2×C5×M16 | C42 | 1 | 1 | yes | characteristic |
| 112 | C2×C5×M16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C42×C5 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 114 | C2×C4×Dic5 | — | 2 | 1 | no | — |
| 115 | C2×C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 116 | C2×#681 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C2×#681 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 118 | D5×M16 | — | 2 | 2 | no | — |
| 119 | D5×M16 | — | 2 | 2 | no | — |
| 120 | D5×M16 | — | 2 | 2 | no | — |
| 121 | D5×M16 | — | 2 | 2 | no | — |
| 122 | C2×#676 | C42 | 1 | 1 | yes | characteristic |
| 123 | C2×#676 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C2×#676 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C2×#676 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C2×C8×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C2×C8×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C2×C8×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C2×C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C42×D5 | — | 2 | 1 | no | — |
| 131 | C42×D5 | — | 2 | 1 | no | — |
| 132 | C42×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 133 | C42×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 134 | C42×D5 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 135 | C42×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | #4002 | — | 2 | 4 | no | — |
| 137 | #4002 | — | 2 | 4 | no | — |
| 138 | C4×#170 | — | 2 | 2 | no | — |
| 139 | C4×#170 | — | 2 | 2 | no | — |
| 140 | C4×#170 | — | 2 | 2 | no | — |
| 141 | C4×#170 | — | 2 | 2 | no | — |
| 142 | #3996 | — | 2 | 2 | no | — |
| 143 | #3996 | M16 | 1 | 4 | yes | complemented |
| 144 | #3995 | — | 2 | 2 | no | — |
| 145 | #3995 | — | 2 | 2 | no | — |
| 146 | #3994 | — | 2 | 2 | no | — |
| 147 | #3994 | M16 | 1 | 4 | yes | complemented |
| 148 | #3993 | — | 2 | 2 | no | — |
| 149 | #3993 | — | 2 | 2 | no | — |
| 150 | #3992 | — | 4 | 2 | no | — |
| 151 | #3992 | — | 4 | 2 | no | — |
| 152 | C8×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 153 | C8×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 154 | C5×M32 | — | 2 | 2 | no | — |
| 155 | C5×#97 | C42 | 1 | 1 | yes | characteristic |
| 156 | C5×#97 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 157 | C4×C5×C8 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C4×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 159 | #3947 | C42 | 1 | 1 | yes | characteristic |
| 160 | #3947 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 161 | #3947 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 162 | #3947 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 163 | C8×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 164 | C8×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C8×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 166 | C8×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | #3944 | — | 2 | 2 | no | — |
| 168 | #3935 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 169 | #3935 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 170 | C4×#168 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 171 | C4×#168 | C2×Q8 | 1 | 1 | yes | characteristic |
| 172 | #3930 | — | 4 | 2 | no | — |
| 173 | D5×C16 | — | 4 | 2 | no | — |
| 174 | C2×#430 | — | 5 | 1 | no | — |
| 175 | #2911 | — | 5 | 1 | no | — |
| 176 | #2873 | — | 10 | 1 | no | — |
| 177 | C2×C4×M16 | — | 5 | 1 | no | — |
| 178 | C2×C4×M16 | — | 10 | 1 | no | — |
| 179 | #2165 | — | 5 | 1 | no | — |
| 180 | #2165 | — | 5 | 2 | no | — |
| 181 | #2165 | — | 10 | 1 | no | — |
| 182 | #2165 | — | 10 | 1 | no | — |
| 183 | #2165 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 184 | C2×#364 | — | 5 | 2 | no | — |
| 185 | C2×#349 | — | 10 | 1 | no | — |
| 186 | C2×#347 | — | 10 | 1 | no | — |
| 187 | #1773 | — | 5 | 2 | no | — |
| 188 | #1773 | — | 10 | 1 | no | — |
| 189 | #1772 | — | 5 | 2 | no | — |
| 190 | #1772 | — | 10 | 1 | no | — |
| 191 | C2×#339 | — | 10 | 1 | no | — |
| 192 | #1455 | — | 5 | 2 | no | — |
| 193 | #1455 | — | 5 | 2 | no | — |
| 194 | #1455 | — | 10 | 1 | no | — |
| 195 | #1455 | — | 10 | 1 | no | — |
| 196 | C2×#322 | — | 5 | 1 | no | — |
| 197 | C2×#322 | — | 10 | 1 | no | — |
| 198 | C2×C82 | — | 5 | 1 | no | — |
| 199 | C23×D5 | #104 | 1 | 1 | yes | characteristic |
| 200 | C22×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 201 | C22×C4×C5 | — | 2 | 1 | no | — |
| 202 | C22×C4×C5 | #95 | 1 | 1 | yes | characteristic |
| 203 | C22×Dic5 | — | 2 | 1 | no | — |
| 204 | C22×Dic5 | #104 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×D5 | — | 2 | 1 | no | — |
| 206 | C2×C4×D5 | — | 2 | 1 | no | — |
| 207 | C2×C4×D5 | — | 2 | 1 | no | — |
| 208 | C2×C4×D5 | — | 2 | 1 | no | — |
| 209 | C2×C4×D5 | — | 2 | 1 | no | — |
| 210 | C2×C4×D5 | — | 2 | 1 | no | — |
| 211 | C2×C4×D5 | — | 2 | 1 | no | — |
| 212 | C2×C4×D5 | — | 2 | 1 | no | — |
| 213 | C2×C4×D5 | — | 4 | 4 | no | — |
| 214 | C2×C4×D5 | #95 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×D5 | #104 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×D5 | #104 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 218 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 219 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 220 | #704 | — | 4 | 8 | no | — |
| 221 | #704 | — | 4 | 2 | no | — |
| 222 | #704 | — | 4 | 2 | no | — |
| 223 | C2×#170 | — | 2 | 4 | no | — |
| 224 | C2×#170 | — | 2 | 4 | no | — |
| 225 | C2×#170 | — | 4 | 2 | no | — |
| 226 | C4⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 227 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 228 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 229 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 230 | #700 | — | 2 | 4 | no | — |
| 231 | #700 | — | 4 | 8 | no | — |
| 232 | #700 | — | 4 | 2 | no | — |
| 233 | D5⋊C8 | — | 2 | 8 | no | — |
| 234 | D5⋊C8 | — | 4 | 4 | no | — |
| 235 | D5⋊C8 | — | 4 | 2 | no | — |
| 236 | D5⋊C8 | — | 4 | 2 | no | — |
| 237 | C5×M16 | — | 2 | 2 | no | — |
| 238 | C5×M16 | — | 2 | 2 | no | — |
| 239 | C2×C5×C8 | #95 | 1 | 1 | yes | characteristic |
| 240 | C2×C5×C8 | #95 | 1 | 1 | yes | characteristic |
| 241 | C2×C5×C8 | C2×C42 | 1 | 1 | yes | characteristic |
| 242 | C2×C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 243 | C42×C5 | — | 2 | 1 | no | — |
| 244 | C42×C5 | #95 | 1 | 1 | yes | characteristic |
| 245 | C42×C5 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 246 | C4×Dic5 | — | 2 | 1 | no | — |
| 247 | C4×Dic5 | — | 2 | 1 | no | — |
| 248 | C4×Dic5 | — | 2 | 1 | no | — |
| 249 | C4×Dic5 | — | 2 | 1 | no | — |
| 250 | C4×Dic5 | — | 2 | 1 | no | — |
| 251 | C4×Dic5 | #95 | 1 | 1 | yes | characteristic |
| 252 | C4×Dic5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 253 | #681 | — | 2 | 2 | no | — |
| 254 | #681 | — | 2 | 2 | no | — |
| 255 | C2×#168 | #95 | 1 | 1 | yes | characteristic |
| 256 | C2×#168 | #95 | 1 | 1 | yes | characteristic |
| 257 | C2×#168 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 258 | C2×#168 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 259 | #676 | — | 2 | 2 | no | — |
| 260 | #676 | — | 2 | 2 | no | — |
| 261 | #676 | — | 2 | 2 | no | — |
| 262 | #676 | — | 2 | 2 | no | — |
| 263 | C8×D5 | — | 2 | 1 | no | — |
| 264 | C8×D5 | — | 2 | 1 | no | — |
| 265 | C8×D5 | — | 2 | 1 | no | — |
| 266 | C8×D5 | — | 2 | 1 | no | — |
| 267 | C8×D5 | C2×M16 | 1 | 2 | yes | — |
| 268 | C8×D5 | C2×M16 | 1 | 2 | yes | — |
| 269 | C8×D5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 270 | C8×D5 | #137 | 1 | 2 | yes | — |
| 271 | C5×C16 | — | 4 | 2 | no | — |
| 272 | #672 | — | 4 | 2 | no | — |
| 273 | C22×M16 | — | 5 | 1 | no | — |
| 274 | C22×M16 | — | 5 | 1 | no | — |
| 275 | C22×M16 | — | 10 | 2 | no | — |
| 276 | C22×M16 | — | 10 | 1 | no | — |
| 277 | C2×#117 | — | 10 | 1 | no | — |
| 278 | C22×C42 | — | 5 | 1 | no | — |
| 279 | C2×M32 | — | 10 | 2 | no | — |
| 280 | #430 | — | 10 | 4 | no | — |
| 281 | C2×#108 | — | 5 | 2 | no | — |
| 282 | C2×#108 | — | 10 | 1 | no | — |
| 283 | #428 | — | 10 | 4 | no | — |
| 284 | #427 | — | 5 | 2 | no | — |
| 285 | #427 | — | 10 | 1 | no | — |
| 286 | #405 | — | 10 | 2 | no | — |
| 287 | #405 | — | 10 | 2 | no | — |
| 288 | #405 | — | 20 | 2 | no | — |
| 289 | C4×M16 | — | 5 | 1 | no | — |
| 290 | C4×M16 | — | 5 | 1 | no | — |
| 291 | C4×M16 | — | 5 | 1 | no | — |
| 292 | C4×M16 | — | 5 | 1 | no | — |
| 293 | C4×M16 | — | 5 | 1 | no | — |
| 294 | C4×M16 | — | 5 | 1 | no | — |
| 295 | C4×M16 | — | 5 | 1 | no | — |
| 296 | C4×M16 | — | 10 | 2 | no | — |
| 297 | C4×M16 | — | 10 | 2 | no | — |
| 298 | C4×M16 | — | 10 | 2 | no | — |
| 299 | C4×M16 | — | 10 | 2 | no | — |
| 300 | C4×M16 | — | 20 | 2 | no | — |
| 301 | C4×M16 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 302 | C2×#97 | — | 5 | 1 | no | — |
| 303 | C2×#97 | — | 5 | 1 | no | — |
| 304 | C2×#97 | — | 10 | 2 | no | — |
| 305 | C2×C4×C8 | — | 5 | 1 | no | — |
| 306 | C2×C4×C8 | — | 5 | 1 | no | — |
| 307 | C2×C4×C8 | — | 10 | 1 | no | — |
| 308 | C2×C4×C8 | — | 10 | 1 | no | — |
| 309 | #364 | — | 5 | 2 | no | — |
| 310 | #364 | — | 10 | 2 | no | — |
| 311 | #364 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 312 | #349 | — | 2 | 1 | no | — |
| 313 | #349 | — | 10 | 2 | no | — |
| 314 | #349 | — | 10 | 1 | no | — |
| 315 | #347 | — | 2 | 1 | no | — |
| 316 | #347 | — | 10 | 2 | no | — |
| 317 | #347 | — | 10 | 1 | no | — |
| 318 | #339 | — | 10 | 2 | no | — |
| 319 | #339 | — | 10 | 2 | no | — |
| 320 | #322 | — | 5 | 2 | no | — |
| 321 | #322 | — | 10 | 1 | no | — |
| 322 | #322 | — | 10 | 2 | no | — |
| 323 | #322 | — | 10 | 2 | no | — |
| 324 | C82 | — | 5 | 2 | no | — |
| 325 | C82 | — | 10 | 1 | no | — |
| 326 | C23×C5 | #339 | 1 | 1 | yes | characteristic |
| 327 | C22×D5 | — | 2 | 1 | no | — |
| 328 | C22×D5 | — | 2 | 1 | no | — |
| 329 | C22×D5 | — | 4 | 2 | no | — |
| 330 | C22×D5 | #339 | 1 | 1 | yes | characteristic |
| 331 | C22×D5 | C2×#104 | 1 | 1 | yes | characteristic |
| 332 | C2×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 333 | C2×AGL(1,𝔽5) | — | 16 | 2 | no | — |
| 334 | C2×C4×C5 | — | 2 | 1 | no | — |
| 335 | C2×C4×C5 | — | 2 | 1 | no | — |
| 336 | C2×C4×C5 | — | 2 | 1 | no | — |
| 337 | C2×C4×C5 | — | 2 | 1 | no | — |
| 338 | C2×C4×C5 | — | 4 | 2 | no | — |
| 339 | C2×C4×C5 | #339 | 1 | 1 | yes | characteristic |
| 340 | C2×C4×C5 | C2×#95 | 1 | 1 | yes | characteristic |
| 341 | C2×Dic5 | — | 2 | 1 | no | — |
| 342 | C2×Dic5 | — | 2 | 1 | no | — |
| 343 | C2×Dic5 | — | 2 | 1 | no | — |
| 344 | C2×Dic5 | — | 2 | 1 | no | — |
| 345 | C2×Dic5 | — | 4 | 2 | no | — |
| 346 | C2×Dic5 | #339 | 1 | 1 | yes | characteristic |
| 347 | C2×Dic5 | C2×#104 | 1 | 1 | yes | characteristic |
| 348 | C4×D5 | — | 2 | 4 | no | — |
| 349 | C4×D5 | — | 2 | 1 | no | — |
| 350 | C4×D5 | — | 2 | 1 | no | — |
| 351 | C4×D5 | — | 2 | 1 | no | — |
| 352 | C4×D5 | — | 2 | 1 | no | — |
| 353 | C4×D5 | — | 2 | 1 | no | — |
| 354 | C4×D5 | — | 2 | 1 | no | — |
| 355 | C4×D5 | — | 4 | 2 | no | — |
| 356 | C4×D5 | — | 4 | 2 | no | — |
| 357 | C4×D5 | — | 4 | 2 | no | — |
| 358 | C4×D5 | #407 | 1 | 1 | yes | characteristic |
| 359 | C4×D5 | #407 | 1 | 1 | yes | characteristic |
| 360 | C4×D5 | #418 | 1 | 1 | yes | characteristic |
| 361 | C4×D5 | #419 | 1 | 1 | yes | characteristic |
| 362 | #170 | — | 2 | 8 | no | — |
| 363 | #170 | — | 4 | 4 | no | — |
| 364 | #170 | — | 4 | 4 | no | — |
| 365 | C5×C8 | — | 2 | 1 | no | — |
| 366 | C5×C8 | — | 2 | 1 | no | — |
| 367 | C5×C8 | C4×M16 | 1 | 2 | yes | — |
| 368 | C5×C8 | #417 | 1 | 2 | yes | — |
| 369 | #168 | — | 2 | 1 | no | — |
| 370 | #168 | — | 2 | 1 | no | — |
| 371 | #168 | #423 | 1 | 2 | yes | — |
| 372 | #168 | #428 | 1 | 2 | yes | — |
| 373 | C23×C4 | — | 5 | 1 | no | — |
| 374 | C23×C4 | — | 10 | 1 | no | — |
| 375 | C2×M16 | — | 5 | 1 | no | — |
| 376 | C2×M16 | — | 5 | 1 | no | — |
| 377 | C2×M16 | — | 5 | 1 | no | — |
| 378 | C2×M16 | — | 5 | 1 | no | — |
| 379 | C2×M16 | — | 5 | 1 | no | — |
| 380 | C2×M16 | — | 5 | 1 | no | — |
| 381 | C2×M16 | — | 10 | 2 | no | — |
| 382 | C2×M16 | — | 10 | 2 | no | — |
| 383 | C2×M16 | — | 10 | 2 | no | — |
| 384 | C2×M16 | — | 10 | 2 | no | — |
| 385 | C2×M16 | — | 10 | 4 | no | — |
| 386 | C2×M16 | — | 10 | 4 | no | — |
| 387 | C2×M16 | — | 10 | 2 | no | — |
| 388 | C2×M16 | — | 10 | 2 | no | — |
| 389 | C2×M16 | — | 10 | 2 | no | — |
| 390 | C2×M16 | — | 20 | 8 | no | — |
| 391 | C2×M16 | — | 20 | 1 | no | — |
| 392 | C2×M16 | — | 20 | 1 | no | — |
| 393 | C2×M16 | — | 20 | 1 | no | — |
| 394 | C2×M16 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 395 | C2×M16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 396 | C22×C8 | — | 5 | 1 | no | — |
| 397 | C22×C8 | — | 5 | 1 | no | — |
| 398 | C22×C8 | — | 5 | 1 | no | — |
| 399 | C22×C8 | — | 5 | 1 | no | — |
| 400 | C22×C8 | — | 10 | 2 | no | — |
| 401 | C22×C8 | — | 10 | 2 | no | — |
| 402 | C22×C8 | — | 20 | 1 | no | — |
| 403 | #117 | — | 10 | 2 | no | — |
| 404 | #117 | — | 10 | 2 | no | — |
| 405 | #117 | — | 20 | 1 | no | — |
| 406 | #117 | — | 20 | 1 | no | — |
| 407 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 408 | C2×C22⋊C4 | — | 20 | 1 | no | — |
| 409 | C2×C42 | — | 5 | 1 | no | — |
| 410 | C2×C42 | — | 5 | 1 | no | — |
| 411 | C2×C42 | — | 5 | 1 | no | — |
| 412 | C2×C42 | — | 5 | 1 | no | — |
| 413 | C2×C42 | — | 5 | 1 | no | — |
| 414 | C2×C42 | — | 10 | 1 | no | — |
| 415 | C2×C42 | — | 10 | 1 | no | — |
| 416 | C2×C42 | — | 10 | 1 | no | — |
| 417 | C2×C42 | — | 20 | 1 | no | — |
| 418 | C2×C42 | C4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 419 | M32 | — | 2 | 2 | no | — |
| 420 | M32 | — | 10 | 2 | no | — |
| 421 | M32 | — | 20 | 2 | no | — |
| 422 | C2×C16 | — | 20 | 2 | no | — |
| 423 | #108 | — | 5 | 4 | no | — |
| 424 | #108 | — | 10 | 2 | no | — |
| 425 | #108 | — | 10 | 2 | no | — |
| 426 | #108 | — | 10 | 2 | no | — |
| 427 | #107 | — | 5 | 4 | no | — |
| 428 | #107 | — | 10 | 2 | no | — |
| 429 | #106 | — | 10 | 2 | no | — |
| 430 | #106 | — | 10 | 2 | no | — |
| 431 | #97 | — | 5 | 1 | no | — |
| 432 | #97 | — | 5 | 1 | no | — |
| 433 | #97 | — | 5 | 1 | no | — |
| 434 | #97 | — | 5 | 1 | no | — |
| 435 | #97 | — | 5 | 1 | no | — |
| 436 | #97 | — | 5 | 1 | no | — |
| 437 | #97 | — | 10 | 4 | no | — |
| 438 | #97 | — | 10 | 4 | no | — |
| 439 | #97 | — | 20 | 2 | no | — |
| 440 | #97 | — | 20 | 2 | no | — |
| 441 | #97 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 442 | #97 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 443 | C4×C8 | — | 5 | 1 | no | — |
| 444 | C4×C8 | — | 5 | 1 | no | — |
| 445 | C4×C8 | — | 5 | 1 | no | — |
| 446 | C4×C8 | — | 5 | 1 | no | — |
| 447 | C4×C8 | — | 5 | 1 | no | — |
| 448 | C4×C8 | — | 5 | 1 | no | — |
| 449 | C4×C8 | — | 10 | 2 | no | — |
| 450 | C4×C8 | — | 10 | 2 | no | — |
| 451 | C4×C8 | — | 10 | 2 | no | — |
| 452 | C4×C8 | — | 10 | 2 | no | — |
| 453 | C4×C8 | — | 20 | 2 | no | — |
| 454 | C4×C8 | — | 20 | 2 | no | — |
| 455 | C4×C8 | C4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 456 | C4×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 457 | C22×C5 | — | 2 | 1 | no | — |
| 458 | C22×C5 | — | 4 | 1 | no | — |
| 459 | C22×C5 | C2×#339 | 1 | 1 | yes | characteristic |
| 460 | C2×D5 | — | 2 | 2 | no | — |
| 461 | C2×D5 | — | 2 | 1 | no | — |
| 462 | C2×D5 | — | 4 | 2 | no | — |
| 463 | C2×D5 | — | 4 | 1 | no | — |
| 464 | C2×D5 | — | 8 | 1 | no | — |
| 465 | C2×D5 | #1490 | 1 | 1 | yes | characteristic |
| 466 | C2×D5 | #1491 | 1 | 1 | yes | characteristic |
| 467 | AGL(1,𝔽5) | — | 8 | 4 | no | — |
| 468 | C4×C5 | — | 2 | 2 | no | — |
| 469 | C4×C5 | — | 2 | 1 | no | — |
| 470 | C4×C5 | — | 4 | 1 | no | — |
| 471 | C4×C5 | #1728 | 1 | 1 | yes | characteristic |
| 472 | C4×C5 | #1736 | 1 | 1 | yes | characteristic |
| 473 | Dic5 | — | 2 | 2 | no | — |
| 474 | Dic5 | — | 2 | 1 | no | — |
| 475 | Dic5 | — | 4 | 1 | no | — |
| 476 | Dic5 | #1490 | 1 | 1 | yes | characteristic |
| 477 | Dic5 | #1491 | 1 | 1 | yes | characteristic |
| 478 | C24 | — | 5 | 1 | no | — |
| 479 | C22×C4 | — | 2 | 1 | no | — |
| 480 | C22×C4 | — | 5 | 1 | no | — |
| 481 | C22×C4 | — | 5 | 1 | no | — |
| 482 | C22×C4 | — | 5 | 1 | no | — |
| 483 | C22×C4 | — | 5 | 1 | no | — |
| 484 | C22×C4 | — | 5 | 1 | no | — |
| 485 | C22×C4 | — | 10 | 1 | no | — |
| 486 | C22×C4 | — | 10 | 1 | no | — |
| 487 | C22×C4 | — | 10 | 1 | no | — |
| 488 | C22×C4 | — | 10 | 1 | no | — |
| 489 | C22×C4 | — | 10 | 1 | no | — |
| 490 | C22×C4 | — | 10 | 1 | no | — |
| 491 | C22×C4 | — | 10 | 1 | no | — |
| 492 | C22×C4 | — | 10 | 1 | no | — |
| 493 | C22×C4 | — | 10 | 1 | no | — |
| 494 | C22×C4 | — | 20 | 4 | no | — |
| 495 | C22×C4 | — | 20 | 2 | no | — |
| 496 | C22×C4 | (C2×AGL(1,𝔽5))⋊C4 | 1 | 1 | yes | characteristic |
| 497 | M16 | — | 2 | 2 | no | — |
| 498 | M16 | — | 2 | 2 | no | — |
| 499 | M16 | — | 10 | 2 | no | — |
| 500 | M16 | — | 10 | 2 | no | — |
| 501 | M16 | — | 10 | 2 | no | — |
| 502 | M16 | — | 10 | 2 | no | — |
| 503 | M16 | — | 10 | 2 | no | — |
| 504 | M16 | — | 10 | 2 | no | — |
| 505 | M16 | — | 10 | 4 | no | — |
| 506 | M16 | — | 20 | 8 | no | — |
| 507 | M16 | — | 20 | 8 | no | — |
| 508 | M16 | — | 20 | 2 | no | — |
| 509 | M16 | — | 20 | 2 | no | — |
| 510 | M16 | — | 20 | 2 | no | — |
| 511 | C2×C8 | — | 5 | 1 | no | — |
| 512 | C2×C8 | — | 5 | 1 | no | — |
| 513 | C2×C8 | — | 5 | 2 | no | — |
| 514 | C2×C8 | — | 5 | 2 | no | — |
| 515 | C2×C8 | — | 5 | 2 | no | — |
| 516 | C2×C8 | — | 5 | 2 | no | — |
| 517 | C2×C8 | — | 5 | 1 | no | — |
| 518 | C2×C8 | — | 5 | 1 | no | — |
| 519 | C2×C8 | — | 10 | 1 | no | — |
| 520 | C2×C8 | — | 10 | 1 | no | — |
| 521 | C2×C8 | — | 10 | 1 | no | — |
| 522 | C2×C8 | — | 10 | 1 | no | — |
| 523 | C2×C8 | — | 10 | 4 | no | — |
| 524 | C2×C8 | — | 10 | 8 | no | — |
| 525 | C2×C8 | — | 10 | 4 | no | — |
| 526 | C2×C8 | — | 20 | 2 | no | — |
| 527 | C2×C8 | — | 20 | 4 | no | — |
| 528 | C2×C8 | — | 20 | 2 | no | — |
| 529 | C2×C8 | — | 20 | 2 | no | — |
| 530 | C2×C8 | (C2×AGL(1,𝔽5))⋊C4 | 1 | 1 | yes | characteristic |
| 531 | C2×C8 | (C2×AGL(1,𝔽5))⋊C4 | 1 | 1 | yes | characteristic |
| 532 | C2×C8 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 533 | C2×C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 534 | C4⋊C4 | — | 10 | 4 | no | — |
| 535 | C4⋊C4 | — | 20 | 2 | no | — |
| 536 | C22⋊C4 | — | 20 | 2 | no | — |
| 537 | C22⋊C4 | — | 20 | 2 | no | — |
| 538 | C42 | — | 2 | 1 | no | — |
| 539 | C42 | — | 5 | 1 | no | — |
| 540 | C42 | — | 5 | 1 | no | — |
| 541 | C42 | — | 10 | 1 | no | — |
| 542 | C42 | — | 10 | 1 | no | — |
| 543 | C42 | — | 10 | 1 | no | — |
| 544 | C42 | — | 10 | 1 | no | — |
| 545 | C42 | — | 10 | 1 | no | — |
| 546 | C42 | — | 20 | 2 | no | — |
| 547 | C42 | — | 20 | 2 | no | — |
| 548 | C42 | (C2×AGL(1,𝔽5))⋊C4 | 1 | 1 | yes | characteristic |
| 549 | C42 | C2×C4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 550 | C16 | — | 4 | 2 | no | — |
| 551 | C16 | — | 20 | 2 | no | — |
| 552 | C2×C5 | — | 2 | 1 | no | — |
| 553 | C2×C5 | — | 4 | 1 | no | — |
| 554 | C2×C5 | #7904 | 1 | 1 | yes | characteristic |
| 555 | D5 | — | 2 | 1 | no | — |
| 556 | D5 | — | 4 | 1 | no | — |
| 557 | D5 | #11669 | 1 | 2 | yes | — |
| 558 | C23 | — | 5 | 1 | no | — |
| 559 | C23 | — | 5 | 1 | no | — |
| 560 | C23 | — | 10 | 1 | no | — |
| 561 | C23 | — | 10 | 1 | no | — |
| 562 | C23 | — | 20 | 2 | no | — |
| 563 | C23 | #64900 | 1 | 1 | yes | characteristic |
| 564 | C2×C4 | — | 2 | 1 | no | — |
| 565 | C2×C4 | — | 2 | 1 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 1 | no | — |
| 568 | C2×C4 | — | 4 | 2 | no | — |
| 569 | C2×C4 | — | 5 | 1 | no | — |
| 570 | C2×C4 | — | 5 | 1 | no | — |
| 571 | C2×C4 | — | 5 | 1 | no | — |
| 572 | C2×C4 | — | 5 | 1 | no | — |
| 573 | C2×C4 | — | 5 | 1 | no | — |
| 574 | C2×C4 | — | 5 | 1 | no | — |
| 575 | C2×C4 | — | 10 | 1 | no | — |
| 576 | C2×C4 | — | 10 | 1 | no | — |
| 577 | C2×C4 | — | 10 | 1 | no | — |
| 578 | C2×C4 | — | 10 | 1 | no | — |
| 579 | C2×C4 | — | 10 | 4 | no | — |
| 580 | C2×C4 | — | 10 | 1 | no | — |
| 581 | C2×C4 | — | 10 | 1 | no | — |
| 582 | C2×C4 | — | 10 | 1 | no | — |
| 583 | C2×C4 | — | 10 | 1 | no | — |
| 584 | C2×C4 | — | 10 | 1 | no | — |
| 585 | C2×C4 | — | 10 | 1 | no | — |
| 586 | C2×C4 | — | 20 | 2 | no | — |
| 587 | C2×C4 | — | 20 | 2 | no | — |
| 588 | C2×C4 | — | 20 | 2 | no | — |
| 589 | C2×C4 | — | 20 | 2 | no | — |
| 590 | C2×C4 | — | 20 | 4 | no | — |
| 591 | C2×C4 | — | 80 | 2 | no | — |
| 592 | C2×C4 | #64900 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | C2×(C2×AGL(1,𝔽5))⋊C4 | 1 | 1 | yes | characteristic |
| 594 | C8 | — | 2 | 1 | no | — |
| 595 | C8 | — | 2 | 1 | no | — |
| 596 | C8 | — | 5 | 2 | no | — |
| 597 | C8 | — | 5 | 2 | no | — |
| 598 | C8 | — | 10 | 8 | no | — |
| 599 | C8 | — | 10 | 1 | no | — |
| 600 | C8 | — | 10 | 1 | no | — |
| 601 | C8 | — | 20 | 4 | no | — |
| 602 | C8 | — | 20 | 4 | no | — |
| 603 | C8 | M16×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 604 | C8 | #65793 | 1 | 2 | yes | — |
| 605 | C5 | #126894 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 606 | C22 | — | 2 | 1 | no | — |
| 607 | C22 | — | 4 | 1 | no | — |
| 608 | C22 | — | 5 | 1 | no | — |
| 609 | C22 | — | 5 | 1 | no | — |
| 610 | C22 | — | 10 | 2 | no | — |
| 611 | C22 | — | 10 | 1 | no | — |
| 612 | C22 | — | 20 | 1 | no | — |
| 613 | C22 | — | 20 | 2 | no | — |
| 614 | C22 | — | 40 | 1 | no | — |
| 615 | C22 | C2×#64900 | 1 | 1 | yes | characteristic |
| 616 | C4 | — | 2 | 2 | no | — |
| 617 | C4 | — | 2 | 1 | no | — |
| 618 | C4 | — | 4 | 1 | no | — |
| 619 | C4 | — | 5 | 1 | no | — |
| 620 | C4 | — | 5 | 1 | no | — |
| 621 | C4 | — | 10 | 2 | no | — |
| 622 | C4 | — | 10 | 1 | no | — |
| 623 | C4 | — | 20 | 1 | no | — |
| 624 | C4 | — | 40 | 4 | no | — |
| 625 | C4 | #10604379 | 1 | 1 | yes | characteristic |
| 626 | C4 | #10604753 | 1 | 1 | yes | characteristic |
| 627 | C2 | — | 2 | 1 | no | — |
| 628 | C2 | — | 4 | 1 | no | — |
| 629 | C2 | — | 5 | 2 | no | — |
| 630 | C2 | — | 10 | 1 | no | — |
| 631 | C2 | — | 20 | 1 | no | — |
| 632 | C2 | #13015517 | 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