Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
814 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 159 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 | #10613508 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10613508 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10613493 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10613296 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C5×#1721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602071 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10602068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10602049 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10601984 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10598888 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10598868 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#4061 | — | 2 | 2 | no | — |
| 13 | D5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66050 | C22 | 1 | 2 | yes | — |
| 15 | #66050 | C22 | 1 | 1 | yes | characteristic |
| 16 | C5×#493 | C22 | 1 | 1 | yes | characteristic |
| 17 | C5×#493 | C22 | 1 | 2 | yes | — |
| 18 | C5×#492 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×#486 | C22 | 1 | 2 | yes | — |
| 20 | #65456 | — | 2 | 2 | no | — |
| 21 | #65448 | — | 2 | 2 | no | — |
| 22 | #65448 | — | 2 | 4 | no | — |
| 23 | #65441 | — | 2 | 4 | no | — |
| 24 | #65441 | — | 2 | 2 | no | — |
| 25 | #65382 | C22 | 1 | 2 | yes | — |
| 26 | #65381 | C22 | 1 | 1 | yes | characteristic |
| 27 | #65365 | C22 | 1 | 1 | yes | characteristic |
| 28 | #65359 | C22 | 1 | 2 | yes | — |
| 29 | #65359 | C22 | 1 | 2 | yes | — |
| 30 | #65359 | C22 | 1 | 2 | yes | — |
| 31 | #65359 | C22 | 1 | 2 | yes | — |
| 32 | #65060 | — | 2 | 4 | no | — |
| 33 | #65054 | — | 2 | 4 | no | — |
| 34 | #64988 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×#676 | C22 | 1 | 2 | yes | — |
| 36 | C4×#676 | C22 | 1 | 1 | yes | characteristic |
| 37 | #64970 | C22 | 1 | 2 | yes | — |
| 38 | #64969 | C22 | 1 | 2 | yes | — |
| 39 | #64969 | C22 | 1 | 1 | yes | characteristic |
| 40 | C5×#322 | C22 | 1 | 1 | yes | characteristic |
| 41 | #64674 | C22 | 1 | 2 | yes | — |
| 42 | C8×#168 | C22 | 1 | 1 | yes | characteristic |
| 43 | #19750 | — | 5 | 1 | no | maximal, Sylow |
| 44 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 45 | C2×#711 | — | 2 | 2 | no | — |
| 46 | C2×#711 | — | 2 | 1 | no | — |
| 47 | C2×C5×SD16 | — | 2 | 2 | no | — |
| 48 | C2×C5×D8 | — | 2 | 4 | no | — |
| 49 | C2×C5×D8 | — | 2 | 2 | no | — |
| 50 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 51 | C5×#127 | C23 | 1 | 2 | yes | — |
| 52 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 53 | #4090 | — | 2 | 1 | no | — |
| 54 | C2×#689 | — | 2 | 2 | no | — |
| 55 | #4084 | — | 2 | 2 | no | — |
| 56 | #4084 | — | 2 | 2 | no | — |
| 57 | #4084 | — | 2 | 2 | no | — |
| 58 | #4082 | — | 2 | 2 | no | — |
| 59 | #4082 | — | 2 | 1 | no | — |
| 60 | D4×Dic5 | — | 2 | 2 | no | — |
| 61 | D4×Dic5 | — | 2 | 2 | no | — |
| 62 | D4×Dic5 | — | 2 | 2 | no | — |
| 63 | C2×#687 | — | 2 | 2 | no | — |
| 64 | #4061 | — | 4 | 8 | no | — |
| 65 | C2×Dic20 | — | 2 | 2 | no | — |
| 66 | C2×#676 | D4 | 1 | 2 | yes | — |
| 67 | C2×#676 | D4 | 1 | 4 | yes | — |
| 68 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 69 | #4034 | — | 2 | 2 | no | — |
| 70 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 71 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 72 | #4015 | C23 | 1 | 2 | yes | — |
| 73 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 74 | C5×#102 | — | 2 | 4 | no | — |
| 75 | C4×C5×C8 | C23 | 1 | 2 | yes | — |
| 76 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 77 | #3964 | — | 2 | 4 | no | — |
| 78 | #3964 | — | 2 | 4 | no | — |
| 79 | #3964 | — | 2 | 4 | no | — |
| 80 | #3964 | — | 2 | 4 | no | — |
| 81 | #3949 | — | 2 | 4 | no | — |
| 82 | #3949 | — | 2 | 2 | no | — |
| 83 | #3948 | — | 2 | 4 | no | — |
| 84 | #3947 | D4 | 1 | 4 | yes | — |
| 85 | #3947 | D4 | 1 | 2 | yes | — |
| 86 | #3942 | — | 2 | 4 | no | — |
| 87 | C4×#168 | C23 | 1 | 2 | yes | — |
| 88 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 89 | #3184 | — | 5 | 1 | no | — |
| 90 | #3184 | — | 5 | 2 | no | — |
| 91 | #3152 | — | 5 | 1 | no | — |
| 92 | #3141 | — | 5 | 2 | no | — |
| 93 | #1721 | D5 | 1 | 1 | yes | characteristic, complemented |
| 94 | #1720 | — | 5 | 2 | no | — |
| 95 | #1717 | — | 5 | 2 | no | — |
| 96 | #1716 | — | 5 | 1 | no | — |
| 97 | #1709 | — | 5 | 1 | no | — |
| 98 | #1708 | — | 5 | 1 | no | — |
| 99 | #1455 | — | 5 | 1 | no | — |
| 100 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 101 | C2×C5×D4 | — | 2 | 2 | no | — |
| 102 | C2×C5×D4 | — | 2 | 2 | no | — |
| 103 | C2×C5×D4 | — | 2 | 2 | no | — |
| 104 | C2×C5×D4 | — | 2 | 1 | no | — |
| 105 | C2×C5×D4 | — | 2 | 2 | no | — |
| 106 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 107 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 108 | C22×Dic5 | — | 4 | 2 | no | — |
| 109 | C22×Dic5 | — | 4 | 1 | no | — |
| 110 | Q8×D5 | — | 4 | 4 | no | — |
| 111 | #711 | — | 4 | 8 | no | — |
| 112 | #711 | — | 4 | 4 | no | — |
| 113 | C2×C4×D5 | — | 4 | 1 | no | — |
| 114 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 116 | C2×Dic10 | — | 2 | 2 | no | — |
| 117 | C2×Dic10 | — | 2 | 1 | no | — |
| 118 | C2×Dic10 | — | 2 | 1 | no | — |
| 119 | C2×Dic10 | — | 4 | 1 | no | — |
| 120 | C5×SD16 | — | 4 | 4 | no | — |
| 121 | C5×D8 | — | 4 | 8 | no | — |
| 122 | C5×D8 | — | 4 | 4 | no | — |
| 123 | C2×C5×C8 | C2×D4 | 1 | 4 | yes | — |
| 124 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 125 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 126 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 127 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 128 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 129 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 130 | #689 | — | 4 | 4 | no | — |
| 131 | #687 | — | 4 | 4 | no | — |
| 132 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 133 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 134 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 135 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 136 | #683 | — | 4 | 2 | no | — |
| 137 | C4×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 138 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×#168 | C2×D4 | 1 | 4 | yes | — |
| 140 | C2×#168 | C2×D4 | 1 | 2 | yes | — |
| 141 | Dic20 | — | 4 | 4 | no | — |
| 142 | #676 | — | 2 | 4 | no | — |
| 143 | #676 | — | 4 | 4 | no | — |
| 144 | C2×#137 | — | 10 | 2 | no | — |
| 145 | #532 | — | 5 | 2 | no | — |
| 146 | #532 | — | 5 | 1 | no | — |
| 147 | C2×C4⋊Q8 | — | 5 | 1 | no | — |
| 148 | #498 | — | 5 | 1 | no | — |
| 149 | #498 | — | 5 | 2 | no | — |
| 150 | #497 | — | 10 | 2 | no | — |
| 151 | #494 | — | 5 | 1 | no | — |
| 152 | #494 | — | 5 | 1 | no | — |
| 153 | #493 | C2×D5 | 1 | 1 | yes | characteristic |
| 154 | #493 | C2×D5 | 1 | 2 | yes | — |
| 155 | #492 | — | 5 | 1 | no | — |
| 156 | #492 | C2×D5 | 1 | 1 | yes | characteristic |
| 157 | #489 | — | 10 | 4 | no | — |
| 158 | #487 | — | 5 | 2 | no | — |
| 159 | #487 | — | 5 | 2 | no | — |
| 160 | #486 | — | 5 | 2 | no | — |
| 161 | #486 | — | 5 | 2 | no | — |
| 162 | #486 | — | 5 | 2 | no | — |
| 163 | #486 | — | 5 | 2 | no | — |
| 164 | #486 | C2×D5 | 1 | 2 | yes | — |
| 165 | #469 | — | 10 | 2 | no | — |
| 166 | #469 | — | 10 | 4 | no | — |
| 167 | #442 | — | 10 | 4 | no | — |
| 168 | #442 | — | 10 | 2 | no | — |
| 169 | #417 | — | 10 | 4 | no | — |
| 170 | C4×M16 | — | 5 | 2 | no | — |
| 171 | C4×M16 | — | 5 | 1 | no | — |
| 172 | #322 | — | 5 | 2 | no | — |
| 173 | #322 | C2×D5 | 1 | 1 | yes | characteristic |
| 174 | C82 | — | 5 | 1 | no | — |
| 175 | C23×C5 | — | 4 | 1 | no | — |
| 176 | C23×C5 | — | 4 | 2 | no | — |
| 177 | C22×D5 | #127 | 1 | 1 | yes | characteristic |
| 178 | C5×Q8 | — | 4 | 2 | no | — |
| 179 | C5×D4 | — | 4 | 2 | no | — |
| 180 | C5×D4 | — | 4 | 4 | no | — |
| 181 | C5×D4 | — | 4 | 4 | no | — |
| 182 | C5×D4 | — | 4 | 4 | no | — |
| 183 | C5×D4 | — | 4 | 4 | no | — |
| 184 | C2×C4×C5 | — | 4 | 1 | no | — |
| 185 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 187 | C22⋊D5 | — | 8 | 2 | no | — |
| 188 | C22⋊D5 | — | 8 | 4 | no | — |
| 189 | C2×Dic5 | — | 4 | 1 | no | — |
| 190 | C2×Dic5 | — | 4 | 1 | no | — |
| 191 | C2×Dic5 | — | 4 | 2 | no | — |
| 192 | C2×Dic5 | — | 8 | 2 | no | — |
| 193 | C2×Dic5 | — | 8 | 4 | no | — |
| 194 | C2×Dic5 | #127 | 1 | 2 | yes | — |
| 195 | C2×Dic5 | #127 | 1 | 1 | yes | characteristic |
| 196 | C4×D5 | — | 2 | 2 | no | — |
| 197 | C4×D5 | — | 2 | 4 | no | — |
| 198 | C4×D5 | — | 8 | 2 | no | — |
| 199 | Dic10 | — | 4 | 2 | no | — |
| 200 | Dic10 | — | 4 | 2 | no | — |
| 201 | Dic10 | — | 4 | 4 | no | — |
| 202 | Dic10 | — | 8 | 2 | no | — |
| 203 | C5×C8 | — | 2 | 4 | no | — |
| 204 | C5×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 205 | #168 | — | 2 | 2 | no | — |
| 206 | #168 | — | 2 | 4 | no | — |
| 207 | C2×#41 | — | 10 | 1 | no | — |
| 208 | C2×#41 | — | 10 | 2 | no | — |
| 209 | C22×Q8 | — | 10 | 1 | no | — |
| 210 | #137 | — | 20 | 8 | no | — |
| 211 | C2×Q16 | — | 10 | 2 | no | — |
| 212 | C2×Q16 | — | 10 | 2 | no | — |
| 213 | C2×SD16 | — | 2 | 2 | no | — |
| 214 | C2×SD16 | — | 10 | 2 | no | — |
| 215 | C2×D8 | — | 2 | 4 | no | — |
| 216 | C2×D8 | — | 2 | 2 | no | — |
| 217 | C2×M16 | — | 5 | 2 | no | — |
| 218 | C2×M16 | — | 5 | 4 | no | — |
| 219 | C4⋊Q8 | — | 5 | 1 | no | — |
| 220 | C4⋊Q8 | — | 5 | 2 | no | — |
| 221 | C4⋊Q8 | — | 5 | 1 | no | — |
| 222 | C4⋊Q8 | — | 10 | 2 | no | — |
| 223 | C4⋊Q8 | — | 10 | 1 | no | — |
| 224 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 225 | #127 | C22×D5 | 1 | 2 | yes | — |
| 226 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 227 | #124 | — | 10 | 2 | no | — |
| 228 | #124 | — | 10 | 1 | no | — |
| 229 | #121 | — | 10 | 2 | no | — |
| 230 | #121 | — | 10 | 2 | no | — |
| 231 | #121 | — | 10 | 2 | no | — |
| 232 | C4×D4 | — | 10 | 2 | no | — |
| 233 | C4×D4 | — | 10 | 2 | no | — |
| 234 | C4×D4 | — | 10 | 2 | no | — |
| 235 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 236 | C2×C42 | — | 5 | 1 | no | — |
| 237 | #106 | — | 10 | 4 | no | — |
| 238 | #106 | — | 10 | 2 | no | — |
| 239 | #103 | — | 10 | 4 | no | — |
| 240 | #103 | — | 10 | 4 | no | — |
| 241 | #102 | — | 2 | 4 | no | — |
| 242 | #102 | — | 10 | 4 | no | — |
| 243 | #102 | — | 10 | 4 | no | — |
| 244 | #102 | — | 10 | 4 | no | — |
| 245 | #102 | — | 10 | 4 | no | — |
| 246 | #97 | — | 5 | 4 | no | — |
| 247 | #97 | — | 5 | 2 | no | — |
| 248 | C4×C8 | — | 5 | 2 | no | — |
| 249 | C4×C8 | — | 5 | 1 | no | — |
| 250 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 251 | C4×C8 | C22×D5 | 1 | 2 | yes | — |
| 252 | C22×C5 | — | 8 | 1 | no | — |
| 253 | C22×C5 | — | 8 | 2 | no | — |
| 254 | C22×C5 | — | 8 | 2 | no | — |
| 255 | C22×C5 | — | 8 | 2 | no | — |
| 256 | C22×C5 | — | 8 | 2 | no | — |
| 257 | C22×C5 | C2×#127 | 1 | 1 | yes | characteristic |
| 258 | C2×D5 | — | 2 | 1 | no | — |
| 259 | C2×D5 | — | 2 | 2 | no | — |
| 260 | C4×C5 | — | 8 | 1 | no | — |
| 261 | C4×C5 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 262 | C4×C5 | #575 | 1 | 4 | yes | — |
| 263 | Dic5 | — | 2 | 1 | no | — |
| 264 | Dic5 | — | 2 | 2 | no | — |
| 265 | Dic5 | — | 8 | 1 | no | — |
| 266 | Dic5 | — | 8 | 1 | no | — |
| 267 | Dic5 | — | 8 | 2 | no | — |
| 268 | #41 | — | 20 | 4 | no | — |
| 269 | #41 | — | 20 | 8 | no | — |
| 270 | C2×Q8 | — | 2 | 1 | no | — |
| 271 | C2×Q8 | — | 10 | 2 | no | — |
| 272 | C2×Q8 | — | 10 | 1 | no | — |
| 273 | C2×Q8 | — | 10 | 1 | no | — |
| 274 | C2×Q8 | — | 20 | 1 | no | — |
| 275 | C2×Q8 | — | 20 | 4 | no | — |
| 276 | C2×D4 | — | 2 | 2 | no | — |
| 277 | C2×D4 | — | 2 | 2 | no | — |
| 278 | C2×D4 | — | 2 | 2 | no | — |
| 279 | C2×D4 | — | 2 | 2 | no | — |
| 280 | C2×D4 | — | 2 | 1 | no | — |
| 281 | C2×D4 | — | 20 | 1 | no | — |
| 282 | C2×D4 | — | 20 | 2 | no | — |
| 283 | C22×C4 | — | 5 | 2 | no | — |
| 284 | C22×C4 | — | 5 | 1 | no | — |
| 285 | C22×C4 | — | 20 | 1 | no | — |
| 286 | C22×C4 | — | 20 | 2 | no | — |
| 287 | C22×C4 | — | 20 | 1 | no | — |
| 288 | Q16 | — | 20 | 4 | no | — |
| 289 | Q16 | — | 20 | 4 | no | — |
| 290 | SD16 | — | 4 | 4 | no | — |
| 291 | SD16 | — | 20 | 4 | no | — |
| 292 | D8 | — | 4 | 8 | no | — |
| 293 | D8 | — | 4 | 4 | no | — |
| 294 | M16 | — | 10 | 4 | no | — |
| 295 | M16 | — | 20 | 4 | no | — |
| 296 | C2×C8 | — | 5 | 4 | no | — |
| 297 | C2×C8 | — | 5 | 2 | no | — |
| 298 | C2×C8 | D4×D5 | 1 | 4 | yes | — |
| 299 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 300 | C4⋊C4 | — | 2 | 2 | no | — |
| 301 | C4⋊C4 | — | 10 | 2 | no | — |
| 302 | C4⋊C4 | — | 10 | 2 | no | — |
| 303 | C4⋊C4 | — | 10 | 2 | no | — |
| 304 | C4⋊C4 | — | 10 | 2 | no | — |
| 305 | C4⋊C4 | — | 20 | 2 | no | — |
| 306 | C22⋊C4 | — | 20 | 2 | no | — |
| 307 | C22⋊C4 | — | 20 | 2 | no | — |
| 308 | C22⋊C4 | — | 20 | 2 | no | — |
| 309 | C42 | — | 5 | 1 | no | — |
| 310 | C42 | — | 5 | 2 | no | — |
| 311 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 312 | C2×C5 | — | 16 | 1 | no | — |
| 313 | C2×C5 | — | 16 | 2 | no | — |
| 314 | C2×C5 | #3151 | 1 | 1 | yes | characteristic |
| 315 | C2×C5 | #3153 | 1 | 2 | yes | — |
| 316 | D5 | — | 4 | 1 | no | — |
| 317 | C23 | — | 4 | 1 | no | — |
| 318 | C23 | — | 4 | 2 | no | — |
| 319 | C23 | — | 5 | 1 | no | — |
| 320 | Q8 | — | 4 | 2 | no | — |
| 321 | Q8 | — | 20 | 2 | no | — |
| 322 | Q8 | — | 20 | 2 | no | — |
| 323 | Q8 | — | 20 | 4 | no | — |
| 324 | Q8 | — | 40 | 2 | no | — |
| 325 | D4 | — | 4 | 4 | no | — |
| 326 | D4 | — | 4 | 2 | no | — |
| 327 | D4 | — | 4 | 4 | no | — |
| 328 | D4 | — | 4 | 4 | no | — |
| 329 | D4 | — | 4 | 4 | no | — |
| 330 | D4 | — | 40 | 2 | no | — |
| 331 | D4 | — | 40 | 4 | no | — |
| 332 | C2×C4 | — | 4 | 1 | no | — |
| 333 | C2×C4 | — | 5 | 2 | no | — |
| 334 | C2×C4 | — | 5 | 1 | no | — |
| 335 | C2×C4 | — | 10 | 2 | no | — |
| 336 | C2×C4 | — | 10 | 4 | no | — |
| 337 | C2×C4 | — | 20 | 1 | no | — |
| 338 | C2×C4 | — | 20 | 2 | no | — |
| 339 | C2×C4 | — | 20 | 1 | no | — |
| 340 | C2×C4 | — | 40 | 2 | no | — |
| 341 | C2×C4 | — | 40 | 2 | no | — |
| 342 | C2×C4 | — | 40 | 4 | no | — |
| 343 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 345 | C8 | — | 2 | 4 | no | — |
| 346 | C8 | — | 10 | 2 | no | — |
| 347 | C8 | — | 10 | 4 | no | — |
| 348 | C8 | #4057 | 1 | 4 | yes | — |
| 349 | C5 | #19750 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 350 | C22 | — | 8 | 1 | no | — |
| 351 | C22 | — | 8 | 2 | no | — |
| 352 | C22 | — | 8 | 2 | no | — |
| 353 | C22 | — | 8 | 2 | no | — |
| 354 | C22 | — | 8 | 2 | no | — |
| 355 | C22 | — | 10 | 1 | no | — |
| 356 | C22 | — | 10 | 2 | no | — |
| 357 | C22 | D5×#127 | 1 | 1 | yes | characteristic |
| 358 | C4 | — | 8 | 1 | no | — |
| 359 | C4 | — | 10 | 1 | no | — |
| 360 | C4 | — | 10 | 2 | no | — |
| 361 | C4 | — | 40 | 1 | no | — |
| 362 | C4 | — | 40 | 1 | no | — |
| 363 | C4 | — | 40 | 2 | no | — |
| 364 | C4 | C2×#4057 | 1 | 2 | yes | — |
| 365 | C4 | #66107 | 1 | 4 | yes | — |
| 366 | C2 | — | 16 | 1 | no | — |
| 367 | C2 | — | 16 | 2 | no | — |
| 368 | C2 | — | 20 | 1 | no | — |
| 369 | C2 | #10613514 | 1 | 1 | yes | characteristic |
| 370 | C2 | #10613577 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D5×#127 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#1721 | C2 |
| socle | C22×C5 | C2×#127 |
| hypercenter | #1721 | D5 |
| hypocenter | C5 | #19750 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1721 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10613508 | C2 | semidirect |
| 2. #10613508 | C2 | semidirect |
| 3. #10613493 | C2 | semidirect |
| 4. #10613296 | C2 | semidirect |
| 5. C5×#1721 | C2 | semidirect |
| 6. #10602071 | C2 | semidirect |
| 7. #10602068 | C2 | semidirect |
| 8. #10602049 | C2 | semidirect |
| 9. #10601984 | C2 | semidirect |
| 10. #10598888 | C2 | semidirect |
| 11. #10598868 | C2 | semidirect |
| 93. #1721 | D5 | semidirect |
| 349. C5 | #19750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613508 | 2 |
| #10613493 | 2 |
| #10613296 | 2 |
| C5×#1721 | 2 |
| #10602071 | 2 |
| #10602068 | 2 |
| #10602049 | 2 |
| #10601984 | 2 |
| #10598888 | 2 |
| #10598868 | 2 |
| #19750 | 5 |