Finite Group DatabasebetaFinite Group DatabasebetaOrder 2560.
1034 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13042037 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13027411 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D5⋊#1359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13013610 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D5×#1721 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10617428 | — | 2 | 2 | no | — |
| 7 | D5×#493 | — | 2 | 1 | no | — |
| 8 | D5×#493 | C22 | 1 | 1 | yes | characteristic |
| 9 | D5×#492 | C22 | 1 | 1 | yes | characteristic |
| 10 | D5×#486 | — | 2 | 1 | no | — |
| 11 | #10604828 | — | 2 | 2 | no | — |
| 12 | D5⋊#361 | — | 2 | 2 | no | — |
| 13 | #10604786 | — | 2 | 2 | no | — |
| 14 | #10604670 | — | 2 | 1 | no | — |
| 15 | #10604614 | — | 2 | 1 | no | — |
| 16 | #10603851 | C22 | 1 | 2 | yes | — |
| 17 | D5⋊#364 | C22 | 1 | 2 | yes | — |
| 18 | C5×#1721 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #10602073 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #10602072 | — | 2 | 1 | no | — |
| 21 | #10602055 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #10601987 | — | 2 | 1 | no | — |
| 23 | #10598887 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | D5×#322 | C22 | 1 | 1 | yes | characteristic |
| 25 | #10598757 | — | 2 | 1 | no | — |
| 26 | #10598751 | — | 2 | 1 | no | — |
| 27 | #137556 | — | 5 | 1 | no | maximal, Sylow |
| 28 | #66262 | — | 2 | 1 | no | — |
| 29 | #66258 | — | 2 | 1 | no | — |
| 30 | C2×D5×SD16 | — | 2 | 2 | no | — |
| 31 | C2×D5×D8 | — | 2 | 2 | no | — |
| 32 | C2×D5×D8 | — | 4 | 2 | no | — |
| 33 | D5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 34 | D5×#127 | — | 2 | 1 | no | — |
| 35 | D5×#127 | D4 | 1 | 1 | yes | characteristic |
| 36 | D5⋊#101 | — | 2 | 1 | no | — |
| 37 | #65782 | — | 2 | 2 | no | — |
| 38 | D5⋊#100 | — | 2 | 1 | no | — |
| 39 | #65767 | — | 2 | 2 | no | — |
| 40 | #65735 | — | 4 | 4 | no | — |
| 41 | SD16×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 42 | D5⋊#108 | D4 | 1 | 2 | yes | — |
| 43 | #65721 | D4 | 1 | 2 | yes | — |
| 44 | #65718 | — | 2 | 2 | no | — |
| 45 | D5⋊M32 | — | 2 | 2 | no | — |
| 46 | C5×#493 | — | 2 | 1 | no | — |
| 47 | C5×#493 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 48 | C5×#492 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C5×#486 | — | 2 | 1 | no | — |
| 50 | #65464 | — | 2 | 2 | no | — |
| 51 | #65440 | — | 2 | 2 | no | — |
| 52 | #65440 | — | 4 | 2 | no | — |
| 53 | #65377 | — | 2 | 1 | no | — |
| 54 | #65374 | D4 | 1 | 1 | yes | characteristic |
| 55 | #65365 | D4 | 1 | 1 | yes | characteristic |
| 56 | #65362 | — | 2 | 1 | no | — |
| 57 | #65362 | — | 2 | 1 | no | — |
| 58 | #65362 | — | 2 | 1 | no | — |
| 59 | #65359 | — | 2 | 1 | no | — |
| 60 | D5×#102 | — | 4 | 2 | no | — |
| 61 | #65049 | — | 4 | 2 | no | — |
| 62 | #64984 | — | 2 | 1 | no | — |
| 63 | #64984 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 64 | #64983 | — | 2 | 1 | no | — |
| 65 | #64982 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C4×C8×D5 | — | 2 | 1 | no | — |
| 67 | C4×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 68 | #64906 | — | 4 | 4 | no | — |
| 69 | #64904 | — | 4 | 4 | no | — |
| 70 | #64889 | — | 2 | 2 | no | — |
| 71 | #64862 | — | 2 | 2 | no | — |
| 72 | #64861 | — | 2 | 2 | no | — |
| 73 | C5×#322 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 74 | #64675 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 75 | #64674 | — | 2 | 1 | no | — |
| 76 | #23198 | — | 5 | 1 | no | — |
| 77 | C2×#1721 | — | 5 | 1 | no | — |
| 78 | #13261 | — | 5 | 2 | no | — |
| 79 | C2×#1359 | — | 5 | 1 | no | — |
| 80 | #7182 | — | 5 | 2 | no | — |
| 81 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 82 | C2×D4×D5 | — | 2 | 1 | no | — |
| 83 | C2×D4×D5 | — | 4 | 1 | no | — |
| 84 | C2×D4×D5 | — | 4 | 1 | no | — |
| 85 | C2×D4×D5 | — | 4 | 1 | no | — |
| 86 | C2×D4×D5 | — | 4 | 1 | no | — |
| 87 | C2×C22⋊AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 88 | Q8×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 89 | D4×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 90 | #4130 | — | 2 | 2 | no | — |
| 91 | #4130 | — | 8 | 1 | no | — |
| 92 | D5⋊M16 | — | 2 | 2 | no | — |
| 93 | C2×C5×SD16 | — | 2 | 2 | no | — |
| 94 | C2×C5×D8 | — | 2 | 2 | no | — |
| 95 | C2×C5×D8 | — | 4 | 2 | no | — |
| 96 | C5×C4⋊Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C5×#127 | — | 2 | 1 | no | — |
| 98 | C5×#127 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 99 | #4090 | — | 2 | 1 | no | — |
| 100 | C2×#688 | — | 2 | 2 | no | — |
| 101 | #4086 | — | 2 | 1 | no | — |
| 102 | #4086 | — | 4 | 1 | no | — |
| 103 | #4086 | — | 4 | 1 | no | — |
| 104 | #4086 | — | 4 | 1 | no | — |
| 105 | #4086 | — | 4 | 1 | no | — |
| 106 | C2×#687 | — | 2 | 2 | no | — |
| 107 | C2×#686 | — | 4 | 2 | no | — |
| 108 | C2×#686 | — | 4 | 2 | no | — |
| 109 | C2×#686 | — | 4 | 2 | no | — |
| 110 | D5×SD16 | — | 4 | 2 | no | — |
| 111 | D5×SD16 | — | 4 | 2 | no | — |
| 112 | D5×SD16 | — | 4 | 2 | no | — |
| 113 | D5×SD16 | — | 4 | 2 | no | — |
| 114 | D5×D8 | — | 4 | 2 | no | — |
| 115 | D5×D8 | — | 4 | 2 | no | — |
| 116 | D5×D8 | — | 4 | 2 | no | — |
| 117 | D5×D8 | — | 4 | 2 | no | — |
| 118 | D5×D8 | — | 8 | 8 | no | — |
| 119 | C2×D40 | — | 2 | 2 | no | — |
| 120 | C2×D40 | — | 4 | 2 | no | — |
| 121 | C2×#677 | — | 2 | 2 | no | — |
| 122 | C2×C8×D5 | — | 2 | 2 | no | — |
| 123 | C2×C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 124 | D5×C4⋊C4 | — | 4 | 1 | no | — |
| 125 | #4034 | — | 4 | 1 | no | — |
| 126 | #4020 | — | 2 | 1 | no | — |
| 127 | #4020 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C42×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | #4015 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 130 | #4013 | — | 8 | 1 | no | — |
| 131 | #4009 | — | 4 | 4 | no | — |
| 132 | #4007 | — | 4 | 4 | no | — |
| 133 | #4005 | — | 8 | 1 | no | — |
| 134 | #3998 | — | 4 | 2 | no | — |
| 135 | #3996 | — | 2 | 2 | no | — |
| 136 | #3995 | — | 2 | 2 | no | — |
| 137 | #3994 | D8 | 1 | 4 | yes | complemented |
| 138 | #3993 | — | 2 | 2 | no | — |
| 139 | #3992 | — | 4 | 2 | no | — |
| 140 | C8×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 141 | #3990 | — | 4 | 2 | no | — |
| 142 | D5⋊C16 | — | 4 | 2 | no | — |
| 143 | C5×#102 | — | 4 | 2 | no | — |
| 144 | C4×C5×C8 | — | 2 | 1 | no | — |
| 145 | C4×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 146 | #3964 | — | 4 | 2 | no | — |
| 147 | #3953 | — | 4 | 2 | no | — |
| 148 | C8×Dic5 | — | 2 | 2 | no | — |
| 149 | C8×Dic5 | #41 | 1 | 2 | yes | — |
| 150 | #3941 | — | 4 | 2 | no | — |
| 151 | C4×#168 | — | 2 | 1 | no | — |
| 152 | C4×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×#493 | — | 5 | 1 | no | — |
| 154 | C2×#493 | — | 10 | 1 | no | — |
| 155 | C2×#492 | — | 5 | 1 | no | — |
| 156 | C2×#486 | — | 10 | 1 | no | — |
| 157 | #2949 | — | 10 | 2 | no | — |
| 158 | C2×#364 | — | 5 | 2 | no | — |
| 159 | C2×#361 | — | 10 | 2 | no | — |
| 160 | #2140 | — | 10 | 2 | no | — |
| 161 | #1977 | — | 10 | 2 | no | — |
| 162 | #1887 | — | 10 | 1 | no | — |
| 163 | #1886 | — | 10 | 1 | no | — |
| 164 | #1772 | — | 5 | 2 | no | — |
| 165 | #1721 | — | 5 | 1 | no | — |
| 166 | #1721 | — | 5 | 1 | no | — |
| 167 | #1721 | — | 5 | 1 | no | — |
| 168 | #1721 | — | 10 | 1 | no | — |
| 169 | #1721 | — | 10 | 1 | no | — |
| 170 | #1721 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 171 | C2×#322 | — | 5 | 1 | no | — |
| 172 | #1359 | — | 10 | 1 | no | — |
| 173 | #1359 | — | 10 | 1 | no | — |
| 174 | C23×D5 | — | 4 | 1 | no | — |
| 175 | C23×D5 | — | 8 | 1 | no | — |
| 176 | C22×AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 177 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 178 | C2×C5×D4 | — | 2 | 1 | no | — |
| 179 | C2×C5×D4 | — | 4 | 1 | no | — |
| 180 | C2×C5×D4 | — | 4 | 1 | no | — |
| 181 | C2×C5×D4 | — | 4 | 1 | no | — |
| 182 | C2×C5×D4 | — | 4 | 1 | no | — |
| 183 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 184 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 185 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 186 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 187 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 188 | Q8×D5 | — | 4 | 2 | no | — |
| 189 | Q8×D5 | — | 4 | 2 | no | — |
| 190 | D4×D5 | — | 4 | 2 | no | — |
| 191 | D4×D5 | — | 4 | 2 | no | — |
| 192 | D4×D5 | — | 8 | 4 | no | — |
| 193 | D4×D5 | — | 8 | 4 | no | — |
| 194 | D4×D5 | — | 8 | 4 | no | — |
| 195 | D4×D5 | — | 8 | 2 | no | — |
| 196 | D4×D5 | — | 8 | 2 | no | — |
| 197 | C2×D20 | — | 2 | 1 | no | — |
| 198 | C2×D20 | — | 4 | 1 | no | — |
| 199 | C2×D20 | — | 4 | 1 | no | — |
| 200 | C2×D20 | — | 4 | 1 | no | — |
| 201 | C2×D20 | — | 4 | 1 | no | — |
| 202 | C2×C4×D5 | — | 2 | 1 | no | — |
| 203 | C2×C4×D5 | — | 4 | 1 | no | — |
| 204 | C2×C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 205 | C2×Dic10 | — | 2 | 1 | no | — |
| 206 | C2×Dic10 | — | 4 | 1 | no | — |
| 207 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 208 | C22⋊AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 209 | #704 | — | 4 | 2 | no | — |
| 210 | C4⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 211 | C4⋊AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 212 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 213 | C4×AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 214 | #700 | — | 4 | 2 | no | — |
| 215 | D5⋊C8 | — | 4 | 2 | no | — |
| 216 | C5×SD16 | — | 4 | 2 | no | — |
| 217 | C5×SD16 | — | 4 | 2 | no | — |
| 218 | C5×D8 | — | 4 | 2 | no | — |
| 219 | C5×D8 | — | 4 | 2 | no | — |
| 220 | C5×D8 | — | 8 | 4 | no | — |
| 221 | C2×C5×C8 | — | 2 | 2 | no | — |
| 222 | C2×C5×C8 | C4×D4 | 1 | 2 | yes | — |
| 223 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 224 | C42×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 225 | #688 | — | 4 | 2 | no | — |
| 226 | #688 | — | 4 | 2 | no | — |
| 227 | #687 | — | 4 | 2 | no | — |
| 228 | #687 | — | 4 | 2 | no | — |
| 229 | #686 | — | 8 | 4 | no | — |
| 230 | #686 | — | 8 | 4 | no | — |
| 231 | #686 | — | 8 | 2 | no | — |
| 232 | #686 | — | 8 | 2 | no | — |
| 233 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 234 | #683 | — | 8 | 1 | no | — |
| 235 | C4×Dic5 | — | 2 | 1 | no | — |
| 236 | C4×Dic5 | #123 | 1 | 1 | yes | characteristic |
| 237 | C2×#168 | — | 2 | 2 | no | — |
| 238 | C2×#168 | #121 | 1 | 2 | yes | — |
| 239 | D40 | — | 4 | 2 | no | — |
| 240 | D40 | — | 4 | 2 | no | — |
| 241 | D40 | — | 8 | 4 | no | — |
| 242 | #677 | — | 4 | 2 | no | — |
| 243 | #677 | — | 4 | 2 | no | — |
| 244 | C8×D5 | — | 4 | 4 | no | — |
| 245 | C8×D5 | C2×D8 | 1 | 2 | yes | — |
| 246 | C8×D5 | #135 | 1 | 2 | yes | — |
| 247 | C8×D5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 248 | C8×D5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 249 | #674 | — | 8 | 2 | no | — |
| 250 | C22×SD16 | — | 10 | 2 | no | — |
| 251 | C22×D8 | — | 10 | 2 | no | — |
| 252 | C22×D8 | — | 20 | 2 | no | — |
| 253 | C2×C4⋊Q8 | — | 5 | 1 | no | — |
| 254 | C2×#127 | — | 5 | 1 | no | — |
| 255 | C2×#127 | — | 10 | 1 | no | — |
| 256 | #519 | — | 10 | 1 | no | — |
| 257 | #518 | — | 10 | 1 | no | — |
| 258 | C2×M32 | — | 10 | 2 | no | — |
| 259 | #493 | — | 2 | 1 | no | — |
| 260 | #493 | — | 5 | 1 | no | — |
| 261 | #493 | — | 10 | 1 | no | — |
| 262 | #493 | — | 10 | 1 | no | — |
| 263 | #493 | — | 10 | 2 | no | — |
| 264 | #493 | — | 10 | 1 | no | — |
| 265 | #493 | — | 10 | 1 | no | — |
| 266 | #493 | — | 20 | 2 | no | — |
| 267 | #493 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 268 | #492 | — | 5 | 1 | no | — |
| 269 | #492 | — | 5 | 1 | no | — |
| 270 | #492 | — | 5 | 1 | no | — |
| 271 | #492 | — | 10 | 2 | no | — |
| 272 | #492 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 273 | #486 | — | 2 | 1 | no | — |
| 274 | #486 | — | 10 | 1 | no | — |
| 275 | #486 | — | 10 | 1 | no | — |
| 276 | #486 | — | 10 | 1 | no | — |
| 277 | #486 | — | 20 | 2 | no | — |
| 278 | #440 | — | 20 | 4 | no | — |
| 279 | C4×SD16 | — | 20 | 4 | no | — |
| 280 | C2×#108 | — | 5 | 2 | no | — |
| 281 | #427 | — | 5 | 2 | no | — |
| 282 | #419 | — | 10 | 2 | no | — |
| 283 | #418 | — | 10 | 2 | no | — |
| 284 | C2×#102 | — | 20 | 2 | no | — |
| 285 | C2×#101 | — | 10 | 1 | no | — |
| 286 | C2×#100 | — | 10 | 1 | no | — |
| 287 | #405 | — | 10 | 2 | no | — |
| 288 | C2×C4×C8 | — | 5 | 1 | no | — |
| 289 | C2×C4×C8 | — | 10 | 1 | no | — |
| 290 | #364 | — | 10 | 2 | no | — |
| 291 | #364 | — | 10 | 2 | no | — |
| 292 | #361 | — | 20 | 4 | no | — |
| 293 | #357 | — | 20 | 4 | no | — |
| 294 | #339 | — | 10 | 2 | no | — |
| 295 | #322 | — | 5 | 1 | no | — |
| 296 | #322 | — | 10 | 1 | no | — |
| 297 | #322 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 298 | C23×C5 | — | 4 | 1 | no | — |
| 299 | C23×C5 | — | 8 | 1 | no | — |
| 300 | C22×D5 | — | 4 | 1 | no | — |
| 301 | C22×D5 | — | 8 | 1 | no | — |
| 302 | C22×D5 | — | 8 | 1 | no | — |
| 303 | C22×D5 | — | 8 | 1 | no | — |
| 304 | C22×D5 | — | 16 | 2 | no | — |
| 305 | C22×D5 | — | 16 | 2 | no | — |
| 306 | C22×D5 | — | 16 | 2 | no | — |
| 307 | C22×D5 | — | 16 | 1 | no | — |
| 308 | C22×D5 | — | 16 | 1 | no | — |
| 309 | C22×D5 | #453 | 1 | 1 | yes | characteristic |
| 310 | C2×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 311 | C2×AGL(1,𝔽5) | — | 32 | 2 | no | — |
| 312 | C5×Q8 | — | 4 | 2 | no | — |
| 313 | C5×D4 | — | 4 | 2 | no | — |
| 314 | C5×D4 | — | 8 | 2 | no | — |
| 315 | C5×D4 | — | 8 | 2 | no | — |
| 316 | C5×D4 | — | 8 | 2 | no | — |
| 317 | C5×D4 | — | 8 | 2 | no | — |
| 318 | C2×C4×C5 | — | 2 | 1 | no | — |
| 319 | C2×C4×C5 | — | 4 | 1 | no | — |
| 320 | C2×C4×C5 | #386 | 1 | 1 | yes | characteristic |
| 321 | C22⋊D5 | — | 8 | 2 | no | — |
| 322 | C22⋊D5 | — | 16 | 2 | no | — |
| 323 | C22⋊D5 | — | 16 | 2 | no | — |
| 324 | C22⋊D5 | — | 16 | 2 | no | — |
| 325 | C22⋊D5 | — | 16 | 2 | no | — |
| 326 | C2×Dic5 | — | 2 | 1 | no | — |
| 327 | C2×Dic5 | — | 4 | 1 | no | — |
| 328 | C2×Dic5 | #453 | 1 | 1 | yes | characteristic |
| 329 | D20 | — | 4 | 2 | no | — |
| 330 | D20 | — | 8 | 2 | no | — |
| 331 | D20 | — | 8 | 2 | no | — |
| 332 | D20 | — | 8 | 2 | no | — |
| 333 | D20 | — | 8 | 2 | no | — |
| 334 | C4×D5 | — | 2 | 4 | no | — |
| 335 | C4×D5 | — | 8 | 1 | no | — |
| 336 | C4×D5 | — | 8 | 1 | no | — |
| 337 | C4×D5 | #447 | 1 | 2 | yes | — |
| 338 | C4×D5 | #449 | 1 | 2 | yes | — |
| 339 | Dic10 | — | 4 | 2 | no | — |
| 340 | Dic10 | — | 8 | 2 | no | — |
| 341 | #170 | — | 8 | 2 | no | — |
| 342 | C5×C8 | — | 4 | 2 | no | — |
| 343 | C5×C8 | C4×D8 | 1 | 2 | yes | — |
| 344 | C5×C8 | #442 | 1 | 2 | yes | — |
| 345 | #168 | — | 4 | 2 | no | — |
| 346 | #168 | #459 | 1 | 2 | yes | — |
| 347 | #168 | #463 | 1 | 2 | yes | — |
| 348 | C22×Q8 | — | 10 | 1 | no | — |
| 349 | C22×D4 | — | 10 | 1 | no | — |
| 350 | C22×D4 | — | 20 | 1 | no | — |
| 351 | C22×D4 | — | 20 | 1 | no | — |
| 352 | C22×D4 | — | 20 | 1 | no | — |
| 353 | C22×D4 | — | 20 | 1 | no | — |
| 354 | C2×SD16 | — | 2 | 2 | no | — |
| 355 | C2×SD16 | — | 10 | 2 | no | — |
| 356 | C2×SD16 | — | 10 | 2 | no | — |
| 357 | C2×SD16 | — | 10 | 2 | no | — |
| 358 | C2×SD16 | — | 20 | 2 | no | — |
| 359 | C2×SD16 | — | 20 | 2 | no | — |
| 360 | C2×SD16 | — | 20 | 2 | no | — |
| 361 | C2×SD16 | — | 20 | 2 | no | — |
| 362 | C2×D8 | — | 2 | 2 | no | — |
| 363 | C2×D8 | — | 4 | 2 | no | — |
| 364 | C2×D8 | — | 10 | 2 | no | — |
| 365 | C2×D8 | — | 20 | 2 | no | — |
| 366 | C2×D8 | — | 20 | 2 | no | — |
| 367 | C2×D8 | — | 20 | 2 | no | — |
| 368 | C2×D8 | — | 20 | 2 | no | — |
| 369 | C2×D8 | — | 20 | 2 | no | — |
| 370 | C2×D8 | — | 20 | 2 | no | — |
| 371 | C2×D8 | — | 20 | 2 | no | — |
| 372 | C2×D8 | — | 20 | 2 | no | — |
| 373 | C2×D8 | — | 40 | 8 | no | — |
| 374 | C2×M16 | — | 10 | 2 | no | — |
| 375 | C22×C8 | — | 5 | 2 | no | — |
| 376 | C22×C8 | — | 10 | 2 | no | — |
| 377 | C4⋊Q8 | — | 5 | 1 | no | — |
| 378 | C4⋊Q8 | — | 10 | 1 | no | — |
| 379 | C4⋊Q8 | — | 20 | 1 | no | — |
| 380 | C4⋊Q8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 381 | #127 | — | 2 | 1 | no | — |
| 382 | #127 | — | 5 | 1 | no | — |
| 383 | #127 | — | 10 | 1 | no | — |
| 384 | #127 | — | 10 | 1 | no | — |
| 385 | #127 | — | 20 | 1 | no | — |
| 386 | #127 | — | 20 | 1 | no | — |
| 387 | #127 | — | 20 | 1 | no | — |
| 388 | #127 | — | 20 | 1 | no | — |
| 389 | #127 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 390 | C4×Q8 | — | 20 | 4 | no | — |
| 391 | C4×D4 | — | 20 | 4 | no | — |
| 392 | #117 | — | 10 | 2 | no | — |
| 393 | #117 | — | 40 | 1 | no | — |
| 394 | C2×C4⋊C4 | — | 20 | 1 | no | — |
| 395 | C2×C22⋊C4 | — | 40 | 1 | no | — |
| 396 | C2×C42 | — | 5 | 1 | no | — |
| 397 | M32 | — | 20 | 2 | no | — |
| 398 | M32 | — | 20 | 2 | no | — |
| 399 | C2×C16 | — | 20 | 2 | no | — |
| 400 | #108 | — | 10 | 2 | no | — |
| 401 | #108 | — | 10 | 2 | no | — |
| 402 | #107 | — | 5 | 4 | no | — |
| 403 | #106 | — | 10 | 2 | no | — |
| 404 | #103 | — | 20 | 4 | no | — |
| 405 | #102 | — | 4 | 2 | no | — |
| 406 | #102 | — | 20 | 2 | no | — |
| 407 | #102 | — | 20 | 4 | no | — |
| 408 | #102 | — | 20 | 2 | no | — |
| 409 | #102 | — | 20 | 2 | no | — |
| 410 | #101 | — | 40 | 1 | no | — |
| 411 | #100 | — | 40 | 1 | no | — |
| 412 | #97 | — | 20 | 2 | no | — |
| 413 | C4×C8 | — | 2 | 1 | no | — |
| 414 | C4×C8 | — | 5 | 2 | no | — |
| 415 | C4×C8 | — | 5 | 1 | no | — |
| 416 | C4×C8 | — | 10 | 2 | no | — |
| 417 | C4×C8 | — | 10 | 1 | no | — |
| 418 | C4×C8 | — | 20 | 2 | no | — |
| 419 | C4×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 420 | C22×C5 | — | 8 | 1 | no | — |
| 421 | C22×C5 | — | 16 | 1 | no | — |
| 422 | C22×C5 | — | 16 | 1 | no | — |
| 423 | C22×C5 | — | 16 | 1 | no | — |
| 424 | C22×C5 | — | 16 | 1 | no | — |
| 425 | C22×C5 | #1887 | 1 | 1 | yes | characteristic |
| 426 | C2×D5 | — | 2 | 2 | no | — |
| 427 | C2×D5 | — | 8 | 1 | no | — |
| 428 | C2×D5 | — | 16 | 2 | no | — |
| 429 | C2×D5 | — | 16 | 1 | no | — |
| 430 | C2×D5 | — | 16 | 1 | no | — |
| 431 | C2×D5 | — | 16 | 1 | no | — |
| 432 | C2×D5 | — | 16 | 1 | no | — |
| 433 | C2×D5 | — | 32 | 1 | no | — |
| 434 | C2×D5 | — | 32 | 2 | no | — |
| 435 | C2×D5 | — | 32 | 2 | no | — |
| 436 | C2×D5 | #1619 | 1 | 1 | yes | characteristic |
| 437 | C2×D5 | #1620 | 1 | 1 | yes | characteristic |
| 438 | AGL(1,𝔽5) | — | 8 | 4 | no | — |
| 439 | C4×C5 | — | 2 | 2 | no | — |
| 440 | C4×C5 | — | 8 | 1 | no | — |
| 441 | C4×C5 | #1879 | 1 | 2 | yes | — |
| 442 | Dic5 | — | 2 | 2 | no | — |
| 443 | Dic5 | — | 8 | 1 | no | — |
| 444 | Dic5 | #1621 | 1 | 2 | yes | — |
| 445 | C24 | — | 20 | 1 | no | — |
| 446 | C24 | — | 40 | 1 | no | — |
| 447 | C2×Q8 | — | 2 | 1 | no | — |
| 448 | C2×Q8 | — | 10 | 1 | no | — |
| 449 | C2×Q8 | — | 20 | 1 | no | — |
| 450 | C2×Q8 | — | 20 | 2 | no | — |
| 451 | C2×Q8 | — | 20 | 2 | no | — |
| 452 | C2×D4 | — | 2 | 1 | no | — |
| 453 | C2×D4 | — | 4 | 1 | no | — |
| 454 | C2×D4 | — | 4 | 1 | no | — |
| 455 | C2×D4 | — | 4 | 1 | no | — |
| 456 | C2×D4 | — | 4 | 1 | no | — |
| 457 | C2×D4 | — | 10 | 1 | no | — |
| 458 | C2×D4 | — | 20 | 1 | no | — |
| 459 | C2×D4 | — | 20 | 1 | no | — |
| 460 | C2×D4 | — | 20 | 1 | no | — |
| 461 | C2×D4 | — | 20 | 2 | no | — |
| 462 | C2×D4 | — | 20 | 2 | no | — |
| 463 | C2×D4 | — | 20 | 1 | no | — |
| 464 | C2×D4 | — | 20 | 1 | no | — |
| 465 | C2×D4 | — | 40 | 2 | no | — |
| 466 | C2×D4 | — | 40 | 2 | no | — |
| 467 | C2×D4 | — | 40 | 1 | no | — |
| 468 | C2×D4 | — | 40 | 4 | no | — |
| 469 | C2×D4 | — | 40 | 4 | no | — |
| 470 | C2×D4 | — | 40 | 4 | no | — |
| 471 | C2×D4 | — | 40 | 1 | no | — |
| 472 | C2×D4 | — | 40 | 1 | no | — |
| 473 | C2×D4 | — | 40 | 1 | no | — |
| 474 | C22×C4 | — | 5 | 1 | no | — |
| 475 | C22×C4 | — | 10 | 1 | no | — |
| 476 | C22×C4 | — | 20 | 1 | no | — |
| 477 | C22×C4 | — | 40 | 2 | no | — |
| 478 | SD16 | — | 4 | 2 | no | — |
| 479 | SD16 | — | 4 | 2 | no | — |
| 480 | SD16 | — | 20 | 2 | no | — |
| 481 | SD16 | — | 20 | 2 | no | — |
| 482 | SD16 | — | 20 | 2 | no | — |
| 483 | SD16 | — | 20 | 2 | no | — |
| 484 | SD16 | — | 20 | 2 | no | — |
| 485 | SD16 | — | 20 | 2 | no | — |
| 486 | D8 | — | 4 | 2 | no | — |
| 487 | D8 | — | 4 | 2 | no | — |
| 488 | D8 | — | 8 | 4 | no | — |
| 489 | D8 | — | 20 | 2 | no | — |
| 490 | D8 | — | 20 | 2 | no | — |
| 491 | D8 | — | 40 | 4 | no | — |
| 492 | D8 | — | 40 | 2 | no | — |
| 493 | D8 | — | 40 | 2 | no | — |
| 494 | D8 | — | 40 | 4 | no | — |
| 495 | D8 | — | 40 | 4 | no | — |
| 496 | M16 | — | 20 | 2 | no | — |
| 497 | M16 | — | 20 | 2 | no | — |
| 498 | C2×C8 | — | 2 | 2 | no | — |
| 499 | C2×C8 | — | 5 | 2 | no | — |
| 500 | C2×C8 | — | 5 | 2 | no | — |
| 501 | C2×C8 | — | 5 | 2 | no | — |
| 502 | C2×C8 | — | 5 | 2 | no | — |
| 503 | C2×C8 | — | 5 | 2 | no | — |
| 504 | C2×C8 | — | 10 | 2 | no | — |
| 505 | C2×C8 | — | 20 | 4 | no | — |
| 506 | C2×C8 | — | 20 | 2 | no | — |
| 507 | C2×C8 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 508 | C4⋊C4 | — | 4 | 1 | no | — |
| 509 | C4⋊C4 | — | 10 | 4 | no | — |
| 510 | C4⋊C4 | — | 20 | 1 | no | — |
| 511 | C4⋊C4 | — | 40 | 1 | no | — |
| 512 | C4⋊C4 | — | 40 | 2 | no | — |
| 513 | C22⋊C4 | — | 20 | 2 | no | — |
| 514 | C22⋊C4 | — | 40 | 2 | no | — |
| 515 | C42 | — | 5 | 1 | no | — |
| 516 | C42 | — | 10 | 1 | no | — |
| 517 | C42 | — | 20 | 2 | no | — |
| 518 | C42 | — | 40 | 2 | no | — |
| 519 | C42 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 520 | C16 | — | 40 | 2 | no | — |
| 521 | C2×C5 | — | 2 | 1 | no | — |
| 522 | C2×C5 | — | 16 | 1 | no | — |
| 523 | C2×C5 | — | 32 | 1 | no | — |
| 524 | C2×C5 | #9061 | 1 | 1 | yes | characteristic |
| 525 | D5 | — | 2 | 1 | no | — |
| 526 | D5 | — | 16 | 1 | no | — |
| 527 | D5 | — | 32 | 1 | no | — |
| 528 | D5 | #12314 | 1 | 2 | yes | — |
| 529 | C23 | — | 4 | 1 | no | — |
| 530 | C23 | — | 5 | 1 | no | — |
| 531 | C23 | — | 8 | 1 | no | — |
| 532 | C23 | — | 20 | 1 | no | — |
| 533 | C23 | — | 40 | 1 | no | — |
| 534 | C23 | — | 40 | 1 | no | — |
| 535 | C23 | — | 40 | 1 | no | — |
| 536 | C23 | — | 80 | 1 | no | — |
| 537 | C23 | — | 80 | 1 | no | — |
| 538 | C23 | — | 80 | 2 | no | — |
| 539 | C23 | — | 80 | 2 | no | — |
| 540 | C23 | — | 80 | 2 | no | — |
| 541 | Q8 | — | 4 | 2 | no | — |
| 542 | Q8 | — | 20 | 2 | no | — |
| 543 | Q8 | — | 40 | 2 | no | — |
| 544 | D4 | — | 4 | 2 | no | — |
| 545 | D4 | — | 8 | 2 | no | — |
| 546 | D4 | — | 8 | 2 | no | — |
| 547 | D4 | — | 8 | 2 | no | — |
| 548 | D4 | — | 8 | 2 | no | — |
| 549 | D4 | — | 20 | 2 | no | — |
| 550 | D4 | — | 40 | 2 | no | — |
| 551 | D4 | — | 40 | 2 | no | — |
| 552 | D4 | — | 40 | 2 | no | — |
| 553 | D4 | — | 40 | 2 | no | — |
| 554 | D4 | — | 40 | 2 | no | — |
| 555 | D4 | — | 80 | 2 | no | — |
| 556 | D4 | — | 80 | 2 | no | — |
| 557 | D4 | — | 80 | 2 | no | — |
| 558 | D4 | — | 80 | 2 | no | — |
| 559 | C2×C4 | — | 2 | 1 | no | — |
| 560 | C2×C4 | — | 4 | 1 | no | — |
| 561 | C2×C4 | — | 5 | 1 | no | — |
| 562 | C2×C4 | — | 5 | 2 | no | — |
| 563 | C2×C4 | — | 5 | 2 | no | — |
| 564 | C2×C4 | — | 10 | 4 | no | — |
| 565 | C2×C4 | — | 10 | 1 | no | — |
| 566 | C2×C4 | — | 20 | 4 | no | — |
| 567 | C2×C4 | — | 20 | 1 | no | — |
| 568 | C2×C4 | — | 40 | 1 | no | — |
| 569 | C2×C4 | — | 40 | 1 | no | — |
| 570 | C2×C4 | — | 160 | 2 | no | — |
| 571 | C2×C4 | #65779 | 1 | 1 | yes | characteristic |
| 572 | C8 | — | 4 | 2 | no | — |
| 573 | C8 | — | 5 | 2 | no | — |
| 574 | C8 | — | 5 | 2 | no | — |
| 575 | C8 | — | 20 | 2 | no | — |
| 576 | C8 | — | 40 | 2 | no | — |
| 577 | C8 | D8×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 578 | C8 | #65731 | 1 | 2 | yes | — |
| 579 | C5 | #137556 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 580 | C22 | — | 5 | 1 | no | — |
| 581 | C22 | — | 5 | 1 | no | — |
| 582 | C22 | — | 8 | 1 | no | — |
| 583 | C22 | — | 10 | 2 | no | — |
| 584 | C22 | — | 16 | 1 | no | — |
| 585 | C22 | — | 16 | 1 | no | — |
| 586 | C22 | — | 16 | 1 | no | — |
| 587 | C22 | — | 16 | 1 | no | — |
| 588 | C22 | — | 40 | 1 | no | — |
| 589 | C22 | — | 80 | 1 | no | — |
| 590 | C22 | — | 80 | 1 | no | — |
| 591 | C22 | — | 80 | 1 | no | — |
| 592 | C22 | — | 80 | 2 | no | — |
| 593 | C22 | — | 80 | 1 | no | — |
| 594 | C22 | — | 160 | 2 | no | — |
| 595 | C22 | — | 160 | 1 | no | — |
| 596 | C22 | — | 160 | 2 | no | — |
| 597 | C22 | #10604614 | 1 | 1 | yes | characteristic |
| 598 | C4 | — | 2 | 2 | no | — |
| 599 | C4 | — | 5 | 2 | no | — |
| 600 | C4 | — | 8 | 1 | no | — |
| 601 | C4 | — | 10 | 2 | no | — |
| 602 | C4 | — | 40 | 4 | no | — |
| 603 | C4 | — | 40 | 1 | no | — |
| 604 | C4 | #10604799 | 1 | 2 | yes | — |
| 605 | C2 | — | 2 | 1 | no | — |
| 606 | C2 | — | 5 | 2 | no | — |
| 607 | C2 | — | 10 | 1 | no | — |
| 608 | C2 | — | 16 | 1 | no | — |
| 609 | C2 | — | 32 | 1 | no | — |
| 610 | C2 | — | 80 | 1 | no | — |
| 611 | C2 | — | 160 | 1 | no | — |
| 612 | C2 | #13019420 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13042037 | C2 | semidirect |
| 2. #13027411 | C2 | semidirect |
| 3. D5⋊#1359 | C2 | semidirect |
| 4. #13013610 | C2 | semidirect |
| 18. C5×#1721 | C4 | semidirect |
| 19. #10602073 | C4 | semidirect |
| 21. #10602055 | C4 | semidirect |
| 23. #10598887 | C4 | semidirect |
| 47. C5×#493 | C2×C4 | semidirect |
| 63. #64984 | C2×C4 | semidirect |
| 73. C5×#322 | C2×C4 | semidirect |
| 74. #64675 | C2×C4 | semidirect |
| 137. #3994 | D8 | semidirect |
| 170. #1721 | AGL(1,𝔽5) | semidirect |
| 267. #493 | C2×AGL(1,𝔽5) | semidirect |
| 297. #322 | C2×AGL(1,𝔽5) | semidirect |
| 579. C5 | #137556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13042037 | 2 |
| #13027411 | 2 |
| D5⋊#1359 | 2 |
| #13013610 | 2 |
| D5×#1721 | 2 |
| #137556 | 5 |