Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
632 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #10617364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10612008 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10605018 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10604602 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598574 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #66285 | C22 | 1 | 1 | yes | characteristic |
| 7 | #66107 | — | 2 | 1 | no | — |
| 8 | #66050 | C22 | 1 | 1 | yes | characteristic |
| 9 | #65777 | — | 2 | 2 | no | — |
| 10 | #65777 | C22 | 1 | 2 | yes | — |
| 11 | #65775 | — | 2 | 1 | no | — |
| 12 | #65775 | — | 2 | 2 | no | — |
| 13 | #65775 | C22 | 1 | 2 | yes | — |
| 14 | #65774 | — | 2 | 2 | no | — |
| 15 | D4×#170 | — | 2 | 2 | no | — |
| 16 | #65680 | — | 2 | 1 | no | — |
| 17 | C5×#453 | C4 | 1 | 1 | yes | characteristic |
| 18 | #65531 | C4 | 1 | 1 | yes | characteristic |
| 19 | #65490 | — | 2 | 1 | no | — |
| 20 | #65366 | C4 | 1 | 1 | yes | characteristic |
| 21 | #65115 | — | 2 | 1 | no | — |
| 22 | D5×#104 | — | 2 | 1 | no | — |
| 23 | #65035 | C4 | 1 | 1 | yes | characteristic |
| 24 | #65034 | C22 | 1 | 1 | yes | characteristic |
| 25 | #64923 | — | 2 | 1 | no | — |
| 26 | #64855 | — | 2 | 1 | no | — |
| 27 | #13051 | — | 5 | 1 | no | maximal, Sylow |
| 28 | C5×H(5,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #4150 | — | 2 | 1 | no | — |
| 30 | #4150 | — | 4 | 1 | no | — |
| 31 | D5×#41 | — | 2 | 1 | no | — |
| 32 | D5×#41 | — | 4 | 1 | no | — |
| 33 | #4144 | — | 2 | 2 | no | — |
| 34 | #4144 | — | 4 | 1 | no | — |
| 35 | #4144 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#711 | — | 2 | 2 | no | — |
| 37 | C2×#711 | — | 4 | 1 | no | — |
| 38 | C2×#711 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×#711 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#704 | — | 2 | 1 | no | — |
| 41 | C2×#704 | — | 2 | 2 | no | — |
| 42 | C2×#704 | D4 | 1 | 2 | yes | — |
| 43 | C22×#170 | — | 2 | 1 | no | — |
| 44 | C22×#170 | D4 | 1 | 2 | yes | — |
| 45 | C5×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 46 | C5×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #4097 | — | 2 | 1 | no | — |
| 48 | #4084 | — | 2 | 2 | no | — |
| 49 | #4082 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #4082 | D4 | 1 | 1 | yes | characteristic |
| 51 | D4×Dic5 | — | 2 | 2 | no | — |
| 52 | #4078 | — | 2 | 1 | no | — |
| 53 | #4062 | — | 4 | 1 | no | — |
| 54 | #4061 | — | 4 | 1 | no | — |
| 55 | #4058 | — | 4 | 1 | no | — |
| 56 | #4057 | — | 4 | 1 | no | — |
| 57 | #4055 | — | 2 | 1 | no | — |
| 58 | D5×M16 | — | 2 | 1 | no | — |
| 59 | C42×D5 | D4 | 1 | 1 | yes | characteristic |
| 60 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 61 | #4013 | — | 2 | 2 | no | — |
| 62 | #4013 | — | 4 | 2 | no | — |
| 63 | C22⋊#170 | — | 2 | 2 | no | — |
| 64 | C22⋊#170 | — | 2 | 2 | no | — |
| 65 | C22⋊#170 | — | 4 | 2 | no | — |
| 66 | #4005 | — | 2 | 2 | no | — |
| 67 | #4005 | — | 4 | 2 | no | — |
| 68 | #4003 | — | 2 | 2 | no | — |
| 69 | #4003 | — | 4 | 2 | no | — |
| 70 | C4⋊#170 | — | 2 | 1 | no | — |
| 71 | C4⋊#170 | — | 2 | 1 | no | — |
| 72 | C4×#170 | — | 2 | 2 | no | — |
| 73 | C5×#104 | — | 2 | 1 | no | — |
| 74 | C5×#100 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #3969 | — | 2 | 1 | no | — |
| 76 | #3965 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | #3957 | — | 2 | 1 | no | — |
| 78 | #3956 | — | 2 | 1 | no | — |
| 79 | #3937 | — | 2 | 1 | no | — |
| 80 | #3018 | — | 5 | 1 | no | — |
| 81 | #2979 | — | 5 | 1 | no | — |
| 82 | #2132 | — | 5 | 1 | no | — |
| 83 | #1791 | — | 5 | 2 | no | — |
| 84 | #1392 | — | 5 | 2 | no | — |
| 85 | C5×#41 | — | 2 | 1 | no | — |
| 86 | C5×#41 | — | 4 | 1 | no | — |
| 87 | C2×C5×D4 | — | 2 | 2 | no | — |
| 88 | C2×C5×D4 | — | 2 | 2 | no | — |
| 89 | C2×C5×D4 | — | 4 | 1 | no | — |
| 90 | C2×C5×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 91 | C2×C5×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 93 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 94 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 95 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 96 | C2×C22⋊D5 | #41 | 1 | 2 | yes | — |
| 97 | C22×Dic5 | — | 2 | 2 | no | — |
| 98 | C22×Dic5 | — | 2 | 1 | no | — |
| 99 | C22×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 100 | #713 | — | 2 | 1 | no | — |
| 101 | Q8×D5 | — | 2 | 1 | no | — |
| 102 | Q8×D5 | — | 4 | 1 | no | — |
| 103 | #711 | — | 2 | 1 | no | — |
| 104 | #711 | — | 4 | 1 | no | — |
| 105 | #711 | — | 4 | 1 | no | — |
| 106 | #711 | — | 4 | 1 | no | — |
| 107 | #711 | — | 4 | 1 | no | — |
| 108 | #711 | — | 4 | 1 | no | — |
| 109 | #711 | — | 4 | 2 | no | — |
| 110 | #711 | — | 4 | 2 | no | — |
| 111 | #711 | — | 4 | 2 | no | — |
| 112 | #711 | — | 4 | 1 | no | — |
| 113 | #711 | — | 4 | 1 | no | — |
| 114 | #711 | — | 4 | 2 | no | — |
| 115 | D4×D5 | — | 2 | 1 | no | — |
| 116 | D4×D5 | — | 4 | 1 | no | — |
| 117 | D4×D5 | — | 4 | 2 | no | — |
| 118 | D4×D5 | — | 4 | 1 | no | — |
| 119 | #709 | — | 2 | 1 | no | — |
| 120 | #709 | — | 4 | 1 | no | — |
| 121 | #709 | — | 4 | 1 | no | — |
| 122 | #709 | — | 4 | 2 | no | — |
| 123 | C2×C4×D5 | — | 2 | 2 | no | — |
| 124 | C2×C4×D5 | — | 2 | 1 | no | — |
| 125 | C2×C4×D5 | — | 4 | 1 | no | — |
| 126 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×Dic10 | — | 2 | 2 | no | — |
| 128 | C2×Dic10 | — | 4 | 1 | no | — |
| 129 | C2×Dic10 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 130 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | #704 | — | 4 | 2 | no | — |
| 132 | #704 | — | 4 | 2 | no | — |
| 133 | #704 | — | 4 | 2 | no | — |
| 134 | #704 | — | 8 | 1 | no | — |
| 135 | C2×#170 | — | 2 | 2 | no | — |
| 136 | C2×#170 | — | 2 | 2 | no | — |
| 137 | C2×#170 | — | 4 | 2 | no | — |
| 138 | C2×#170 | — | 4 | 2 | no | — |
| 139 | C2×#170 | — | 8 | 1 | no | — |
| 140 | C5×SD16 | — | 4 | 1 | no | — |
| 141 | C5×D8 | — | 4 | 1 | no | — |
| 142 | C5×M16 | — | 2 | 1 | no | — |
| 143 | C42×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 144 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 145 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 146 | #689 | — | 4 | 1 | no | — |
| 147 | #687 | — | 4 | 1 | no | — |
| 148 | #687 | — | 4 | 1 | no | — |
| 149 | #686 | — | 4 | 1 | no | — |
| 150 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 151 | C4×Dic5 | — | 2 | 1 | no | — |
| 152 | C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 153 | #681 | — | 2 | 1 | no | — |
| 154 | Dic20 | — | 4 | 1 | no | — |
| 155 | #677 | — | 4 | 1 | no | — |
| 156 | #676 | — | 4 | 1 | no | — |
| 157 | C8×D5 | — | 4 | 1 | no | — |
| 158 | #585 | — | 5 | 1 | no | — |
| 159 | #575 | — | 10 | 1 | no | — |
| 160 | #532 | — | 5 | 1 | no | — |
| 161 | #456 | — | 10 | 1 | no | — |
| 162 | #455 | — | 5 | 1 | no | — |
| 163 | #455 | — | 5 | 1 | no | — |
| 164 | #454 | — | 10 | 1 | no | — |
| 165 | #453 | — | 5 | 1 | no | — |
| 166 | #453 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 167 | #436 | — | 10 | 2 | no | — |
| 168 | C8×D4 | — | 10 | 2 | no | — |
| 169 | #431 | — | 10 | 1 | no | — |
| 170 | C2×#104 | — | 10 | 1 | no | — |
| 171 | #413 | — | 5 | 1 | no | — |
| 172 | #413 | — | 5 | 2 | no | — |
| 173 | #413 | — | 10 | 2 | no | — |
| 174 | #408 | — | 5 | 2 | no | — |
| 175 | #408 | — | 10 | 1 | no | — |
| 176 | #408 | — | 10 | 2 | no | — |
| 177 | #356 | — | 10 | 1 | no | — |
| 178 | #355 | — | 10 | 1 | no | — |
| 179 | C23×C5 | — | 2 | 2 | no | — |
| 180 | C23×C5 | — | 2 | 1 | no | — |
| 181 | C23×C5 | C4×D4 | 1 | 2 | yes | — |
| 182 | C22×D5 | — | 2 | 2 | no | — |
| 183 | C22×D5 | — | 4 | 1 | no | — |
| 184 | C22×D5 | #123 | 1 | 1 | yes | characteristic |
| 185 | C5×Q8 | — | 2 | 1 | no | — |
| 186 | C5×D4 | — | 2 | 1 | no | — |
| 187 | C5×D4 | — | 4 | 1 | no | — |
| 188 | C5×D4 | — | 4 | 1 | no | — |
| 189 | C5×D4 | — | 4 | 4 | no | — |
| 190 | C5×D4 | — | 4 | 2 | no | — |
| 191 | C5×D4 | — | 4 | 1 | no | — |
| 192 | C2×C4×C5 | — | 2 | 1 | no | — |
| 193 | C2×C4×C5 | — | 2 | 2 | no | — |
| 194 | C2×C4×C5 | — | 4 | 1 | no | — |
| 195 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 196 | C22⋊D5 | — | 4 | 2 | no | — |
| 197 | C22⋊D5 | — | 4 | 2 | no | — |
| 198 | C22⋊D5 | — | 4 | 1 | no | — |
| 199 | C22⋊D5 | — | 4 | 2 | no | — |
| 200 | C22⋊D5 | — | 4 | 1 | no | — |
| 201 | C22⋊D5 | — | 4 | 1 | no | — |
| 202 | C22⋊D5 | — | 8 | 1 | no | — |
| 203 | C2×Dic5 | — | 2 | 2 | no | — |
| 204 | C2×Dic5 | — | 2 | 2 | no | — |
| 205 | C2×Dic5 | — | 2 | 2 | no | — |
| 206 | C2×Dic5 | — | 2 | 1 | no | — |
| 207 | C2×Dic5 | — | 2 | 1 | no | — |
| 208 | C2×Dic5 | — | 4 | 2 | no | — |
| 209 | C2×Dic5 | — | 4 | 1 | no | — |
| 210 | C2×Dic5 | — | 4 | 1 | no | — |
| 211 | C2×Dic5 | — | 4 | 1 | no | — |
| 212 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 213 | C2×Dic5 | #121 | 1 | 2 | yes | — |
| 214 | D20 | — | 2 | 1 | no | — |
| 215 | D20 | — | 4 | 1 | no | — |
| 216 | C4×D5 | — | 2 | 1 | no | — |
| 217 | C4×D5 | — | 2 | 1 | no | — |
| 218 | C4×D5 | — | 4 | 2 | no | — |
| 219 | C4×D5 | — | 4 | 2 | no | — |
| 220 | C4×D5 | — | 4 | 1 | no | — |
| 221 | C4×D5 | — | 4 | 1 | no | — |
| 222 | C4×D5 | — | 4 | 1 | no | — |
| 223 | Dic10 | — | 2 | 1 | no | — |
| 224 | Dic10 | — | 4 | 1 | no | — |
| 225 | Dic10 | — | 4 | 2 | no | — |
| 226 | Dic10 | — | 4 | 1 | no | — |
| 227 | Dic10 | — | 4 | 1 | no | — |
| 228 | #170 | — | 4 | 2 | no | — |
| 229 | #170 | — | 4 | 2 | no | — |
| 230 | #170 | — | 8 | 2 | no | — |
| 231 | C5×C8 | — | 4 | 1 | no | — |
| 232 | #168 | — | 4 | 1 | no | — |
| 233 | 2−1+4 | — | 10 | 1 | no | — |
| 234 | 2−1+4 | — | 20 | 1 | no | — |
| 235 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 236 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 237 | H(5,𝔽2) | — | 20 | 1 | no | — |
| 238 | H(5,𝔽2) | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 239 | C2×#41 | — | 5 | 1 | no | — |
| 240 | C2×#41 | — | 5 | 1 | no | — |
| 241 | C2×#41 | — | 10 | 2 | no | — |
| 242 | C2×#41 | — | 10 | 1 | no | — |
| 243 | C2×#41 | — | 20 | 1 | no | — |
| 244 | C2×#41 | — | 20 | 1 | no | — |
| 245 | #137 | — | 10 | 1 | no | — |
| 246 | #137 | — | 10 | 1 | no | — |
| 247 | #137 | — | 20 | 1 | no | — |
| 248 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 249 | AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 250 | AGL(1,ℤ/8) | — | 20 | 1 | no | — |
| 251 | #135 | — | 20 | 1 | no | — |
| 252 | #135 | — | 20 | 1 | no | — |
| 253 | C2×M16 | — | 5 | 2 | no | — |
| 254 | C2×M16 | — | 10 | 1 | no | — |
| 255 | C2×M16 | — | 10 | 1 | no | — |
| 256 | C2×M16 | — | 10 | 2 | no | — |
| 257 | C22×C8 | — | 5 | 2 | no | — |
| 258 | C22×C8 | — | 10 | 1 | no | — |
| 259 | C4⋊Q8 | — | 5 | 1 | no | — |
| 260 | #127 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 261 | #124 | — | 5 | 1 | no | — |
| 262 | #124 | — | 5 | 1 | no | — |
| 263 | #121 | — | 10 | 2 | no | — |
| 264 | C4×D4 | — | 10 | 2 | no | — |
| 265 | C2×C42 | — | 5 | 1 | no | — |
| 266 | C4⋊C8 | — | 10 | 1 | no | — |
| 267 | C4⋊C8 | — | 10 | 1 | no | — |
| 268 | #104 | — | 2 | 1 | no | — |
| 269 | #104 | — | 10 | 1 | no | — |
| 270 | #104 | — | 10 | 1 | no | — |
| 271 | #104 | — | 10 | 1 | no | — |
| 272 | #101 | — | 10 | 1 | no | — |
| 273 | #101 | — | 10 | 2 | no | — |
| 274 | #101 | — | 20 | 2 | no | — |
| 275 | #100 | — | 5 | 1 | no | — |
| 276 | #100 | — | 10 | 2 | no | — |
| 277 | #100 | — | 20 | 2 | no | — |
| 278 | #100 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 279 | C22⋊C8 | — | 10 | 2 | no | — |
| 280 | C22⋊C8 | — | 10 | 2 | no | — |
| 281 | C22⋊C8 | — | 10 | 2 | no | — |
| 282 | C22⋊C8 | — | 20 | 2 | no | — |
| 283 | C22⋊C8 | — | 20 | 2 | no | — |
| 284 | C4×C8 | — | 10 | 2 | no | — |
| 285 | C22×C5 | — | 2 | 2 | no | — |
| 286 | C22×C5 | — | 4 | 2 | no | — |
| 287 | C22×C5 | — | 4 | 2 | no | — |
| 288 | C22×C5 | — | 4 | 1 | no | — |
| 289 | C22×C5 | — | 4 | 1 | no | — |
| 290 | C22×C5 | — | 8 | 2 | no | — |
| 291 | C22×C5 | #386 | 1 | 1 | yes | characteristic |
| 292 | C2×D5 | — | 2 | 1 | no | — |
| 293 | C2×D5 | — | 4 | 1 | no | — |
| 294 | C2×D5 | — | 4 | 1 | no | — |
| 295 | C2×D5 | — | 8 | 2 | no | — |
| 296 | C2×D5 | — | 16 | 1 | no | — |
| 297 | C4×C5 | — | 2 | 2 | no | — |
| 298 | C4×C5 | — | 2 | 1 | no | — |
| 299 | C4×C5 | — | 4 | 1 | no | — |
| 300 | Dic5 | — | 2 | 2 | no | — |
| 301 | Dic5 | — | 4 | 1 | no | — |
| 302 | Dic5 | — | 4 | 1 | no | — |
| 303 | Dic5 | — | 4 | 1 | no | — |
| 304 | Dic5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 305 | Dic5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 306 | #41 | — | 2 | 1 | no | — |
| 307 | #41 | — | 4 | 1 | no | — |
| 308 | #41 | — | 10 | 1 | no | — |
| 309 | #41 | — | 10 | 1 | no | — |
| 310 | #41 | — | 10 | 1 | no | — |
| 311 | #41 | — | 20 | 2 | no | — |
| 312 | #41 | — | 20 | 1 | no | — |
| 313 | #41 | — | 20 | 1 | no | — |
| 314 | #41 | — | 20 | 1 | no | — |
| 315 | #41 | — | 20 | 2 | no | — |
| 316 | #41 | — | 20 | 1 | no | — |
| 317 | #41 | — | 20 | 1 | no | — |
| 318 | #41 | — | 20 | 1 | no | — |
| 319 | #41 | — | 20 | 2 | no | — |
| 320 | #41 | — | 20 | 2 | no | — |
| 321 | #41 | — | 20 | 2 | no | — |
| 322 | #41 | — | 20 | 1 | no | — |
| 323 | #41 | — | 20 | 1 | no | — |
| 324 | #41 | — | 20 | 1 | no | — |
| 325 | C2×Q8 | — | 5 | 1 | no | — |
| 326 | C2×Q8 | — | 5 | 1 | no | — |
| 327 | C2×Q8 | — | 10 | 2 | no | — |
| 328 | C2×Q8 | — | 10 | 1 | no | — |
| 329 | C2×Q8 | — | 20 | 1 | no | — |
| 330 | C2×Q8 | — | 20 | 1 | no | — |
| 331 | C2×D4 | — | 2 | 2 | no | — |
| 332 | C2×D4 | — | 2 | 2 | no | — |
| 333 | C2×D4 | — | 4 | 1 | no | — |
| 334 | C2×D4 | — | 5 | 2 | no | — |
| 335 | C2×D4 | — | 10 | 1 | no | — |
| 336 | C2×D4 | — | 10 | 2 | no | — |
| 337 | C2×D4 | — | 10 | 2 | no | — |
| 338 | C2×D4 | — | 10 | 1 | no | — |
| 339 | C2×D4 | — | 20 | 1 | no | — |
| 340 | C2×D4 | — | 20 | 1 | no | — |
| 341 | C2×D4 | — | 20 | 2 | no | — |
| 342 | C2×D4 | — | 20 | 2 | no | — |
| 343 | C2×D4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 344 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 345 | C22×C4 | — | 5 | 2 | no | — |
| 346 | C22×C4 | — | 5 | 1 | no | — |
| 347 | C22×C4 | — | 10 | 1 | no | — |
| 348 | C22×C4 | — | 10 | 2 | no | — |
| 349 | C22×C4 | — | 10 | 1 | no | — |
| 350 | C22×C4 | — | 10 | 2 | no | — |
| 351 | C22×C4 | — | 20 | 1 | no | — |
| 352 | Q16 | — | 20 | 1 | no | — |
| 353 | Q16 | — | 20 | 1 | no | — |
| 354 | SD16 | — | 4 | 1 | no | — |
| 355 | SD16 | — | 20 | 1 | no | — |
| 356 | SD16 | — | 20 | 1 | no | — |
| 357 | SD16 | — | 20 | 1 | no | — |
| 358 | D8 | — | 4 | 1 | no | — |
| 359 | D8 | — | 20 | 1 | no | — |
| 360 | M16 | — | 2 | 1 | no | — |
| 361 | M16 | — | 10 | 1 | no | — |
| 362 | M16 | — | 20 | 1 | no | — |
| 363 | M16 | — | 20 | 2 | no | — |
| 364 | M16 | — | 20 | 2 | no | — |
| 365 | M16 | — | 20 | 2 | no | — |
| 366 | M16 | — | 40 | 1 | no | — |
| 367 | C2×C8 | — | 10 | 2 | no | — |
| 368 | C2×C8 | — | 10 | 2 | no | — |
| 369 | C2×C8 | — | 20 | 1 | no | — |
| 370 | C2×C8 | — | 20 | 2 | no | — |
| 371 | C2×C8 | — | 20 | 2 | no | — |
| 372 | C2×C8 | — | 40 | 1 | no | — |
| 373 | C4⋊C4 | — | 10 | 2 | no | — |
| 374 | C22⋊C4 | — | 10 | 2 | no | — |
| 375 | C22⋊C4 | — | 10 | 2 | no | — |
| 376 | C42 | — | 5 | 1 | no | — |
| 377 | C42 | — | 10 | 1 | no | — |
| 378 | C42 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 379 | C2×C5 | — | 2 | 1 | no | — |
| 380 | C2×C5 | — | 4 | 2 | no | — |
| 381 | C2×C5 | — | 8 | 1 | no | — |
| 382 | C2×C5 | — | 8 | 1 | no | — |
| 383 | C2×C5 | #1889 | 1 | 1 | yes | characteristic |
| 384 | D5 | — | 4 | 1 | no | — |
| 385 | D5 | — | 8 | 1 | no | — |
| 386 | C23 | — | 2 | 2 | no | — |
| 387 | C23 | — | 2 | 1 | no | — |
| 388 | C23 | — | 5 | 1 | no | — |
| 389 | C23 | — | 10 | 2 | no | — |
| 390 | C23 | — | 20 | 1 | no | — |
| 391 | C23 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 392 | Q8 | — | 2 | 1 | no | — |
| 393 | Q8 | — | 10 | 1 | no | — |
| 394 | Q8 | — | 20 | 1 | no | — |
| 395 | Q8 | — | 20 | 1 | no | — |
| 396 | Q8 | — | 20 | 1 | no | — |
| 397 | Q8 | — | 20 | 2 | no | — |
| 398 | D4 | — | 2 | 1 | no | — |
| 399 | D4 | — | 4 | 1 | no | — |
| 400 | D4 | — | 4 | 1 | no | — |
| 401 | D4 | — | 4 | 4 | no | — |
| 402 | D4 | — | 4 | 2 | no | — |
| 403 | D4 | — | 4 | 1 | no | — |
| 404 | D4 | — | 10 | 1 | no | — |
| 405 | D4 | — | 20 | 1 | no | — |
| 406 | D4 | — | 20 | 1 | no | — |
| 407 | D4 | — | 20 | 2 | no | — |
| 408 | D4 | — | 20 | 2 | no | — |
| 409 | D4 | — | 20 | 2 | no | — |
| 410 | D4 | — | 20 | 1 | no | — |
| 411 | D4 | — | 20 | 1 | no | — |
| 412 | D4 | — | 40 | 1 | no | — |
| 413 | C2×C4 | — | 2 | 1 | no | — |
| 414 | C2×C4 | — | 2 | 2 | no | — |
| 415 | C2×C4 | — | 4 | 1 | no | — |
| 416 | C2×C4 | — | 5 | 1 | no | — |
| 417 | C2×C4 | — | 5 | 2 | no | — |
| 418 | C2×C4 | — | 10 | 1 | no | — |
| 419 | C2×C4 | — | 10 | 1 | no | — |
| 420 | C2×C4 | — | 10 | 2 | no | — |
| 421 | C2×C4 | — | 10 | 2 | no | — |
| 422 | C2×C4 | — | 10 | 2 | no | — |
| 423 | C2×C4 | — | 10 | 1 | no | — |
| 424 | C2×C4 | — | 10 | 1 | no | — |
| 425 | C2×C4 | — | 20 | 2 | no | — |
| 426 | C2×C4 | — | 20 | 1 | no | — |
| 427 | C2×C4 | — | 20 | 1 | no | — |
| 428 | C2×C4 | — | 20 | 2 | no | — |
| 429 | C2×C4 | — | 20 | 1 | no | — |
| 430 | C2×C4 | — | 20 | 1 | no | — |
| 431 | C2×C4 | — | 20 | 1 | no | — |
| 432 | C2×C4 | — | 20 | 1 | no | — |
| 433 | C2×C4 | — | 20 | 2 | no | — |
| 434 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 435 | C8 | — | 4 | 1 | no | — |
| 436 | C8 | — | 20 | 1 | no | — |
| 437 | C8 | — | 20 | 2 | no | — |
| 438 | C8 | — | 20 | 2 | no | — |
| 439 | C8 | — | 40 | 2 | no | — |
| 440 | C5 | #13051 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 441 | C22 | — | 2 | 2 | no | — |
| 442 | C22 | — | 4 | 2 | no | — |
| 443 | C22 | — | 4 | 2 | no | — |
| 444 | C22 | — | 4 | 1 | no | — |
| 445 | C22 | — | 4 | 1 | no | — |
| 446 | C22 | — | 8 | 2 | no | — |
| 447 | C22 | — | 10 | 1 | no | — |
| 448 | C22 | — | 20 | 1 | no | — |
| 449 | C22 | — | 20 | 1 | no | — |
| 450 | C22 | — | 40 | 2 | no | — |
| 451 | C22 | — | 80 | 1 | no | — |
| 452 | C22 | #65779 | 1 | 1 | yes | characteristic |
| 453 | C4 | — | 2 | 2 | no | — |
| 454 | C4 | — | 2 | 1 | no | — |
| 455 | C4 | — | 4 | 1 | no | — |
| 456 | C4 | — | 5 | 1 | no | — |
| 457 | C4 | — | 5 | 1 | no | — |
| 458 | C4 | — | 10 | 2 | no | — |
| 459 | C4 | — | 20 | 1 | no | — |
| 460 | C4 | — | 20 | 1 | no | — |
| 461 | C4 | — | 20 | 1 | no | — |
| 462 | C2 | — | 2 | 1 | no | — |
| 463 | C2 | — | 4 | 2 | no | — |
| 464 | C2 | — | 8 | 1 | no | — |
| 465 | C2 | — | 8 | 1 | no | — |
| 466 | C2 | — | 20 | 1 | no | — |
| 467 | C2 | — | 40 | 1 | no | — |
| 468 | C2 | #10604461 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617364 | C2 | semidirect |
| 3. #10605018 | C2 | semidirect |
| 4. #10604602 | C2 | semidirect |
| 5. #10598574 | C2 | semidirect |
| 440. C5 | #13051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617364 | 2 |
| #10612008 | 2 |
| #10605018 | 2 |
| #10604602 | 2 |
| #10598574 | 2 |
| #13051 | 5 |