Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 59 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 | C5×#2785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10600499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10600496 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10600356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598139 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #65844 | C22 | 1 | 1 | yes | characteristic |
| 9 | C5×#395 | C22 | 1 | 1 | yes | characteristic |
| 10 | C5×#394 | — | 2 | 1 | no | — |
| 11 | C5×#394 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×#393 | — | 2 | 1 | no | — |
| 13 | C5×#388 | — | 2 | 1 | no | — |
| 14 | C5×#388 | — | 2 | 1 | no | — |
| 15 | C5×#388 | — | 2 | 1 | no | — |
| 16 | C5×#382 | — | 2 | 1 | no | — |
| 17 | C5×#382 | C22 | 1 | 1 | yes | characteristic |
| 18 | #65516 | — | 2 | 1 | no | — |
| 19 | #65506 | — | 2 | 1 | no | — |
| 20 | #65255 | — | 2 | 1 | no | — |
| 21 | C2×#3937 | — | 2 | 1 | no | — |
| 22 | #64750 | C22 | 1 | 1 | yes | characteristic |
| 23 | #64748 | C22 | 1 | 1 | yes | characteristic |
| 24 | #64748 | C22 | 1 | 1 | yes | characteristic |
| 25 | #64671 | — | 2 | 1 | no | — |
| 26 | #64671 | — | 2 | 1 | no | — |
| 27 | #12145 | — | 5 | 1 | no | maximal, Sylow |
| 28 | C22×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×C5×D4 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×#709 | — | 2 | 1 | no | — |
| 31 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 32 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 33 | C2×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×C5×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 36 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 37 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 38 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 39 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 40 | C2×C5×C22⋊C4 | — | 2 | 1 | no | — |
| 41 | C2×C42×C5 | — | 2 | 1 | no | — |
| 42 | C2×C42×C5 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#688 | — | 4 | 1 | no | — |
| 44 | C2×#686 | — | 4 | 1 | no | — |
| 45 | #4076 | — | 2 | 1 | no | — |
| 46 | #4076 | — | 2 | 1 | no | — |
| 47 | C2×#681 | — | 2 | 1 | no | — |
| 48 | #4043 | — | 4 | 1 | no | — |
| 49 | #4041 | — | 4 | 1 | no | — |
| 50 | C5×#95 | — | 2 | 1 | no | — |
| 51 | C5×#95 | — | 2 | 1 | no | — |
| 52 | C5×#95 | — | 2 | 1 | no | — |
| 53 | C5×#95 | — | 2 | 1 | no | — |
| 54 | C5×#95 | — | 2 | 1 | no | — |
| 55 | C5×#95 | D4 | 1 | 1 | yes | characteristic |
| 56 | C5×#95 | D4 | 1 | 1 | yes | characteristic |
| 57 | #3967 | — | 4 | 1 | no | — |
| 58 | #3964 | — | 4 | 1 | no | — |
| 59 | C22⋊#168 | — | 2 | 1 | no | — |
| 60 | C22⋊#168 | — | 2 | 1 | no | — |
| 61 | #3942 | — | 4 | 1 | no | — |
| 62 | #3941 | — | 4 | 1 | no | — |
| 63 | #3937 | — | 4 | 2 | no | — |
| 64 | #2785 | D5 | 1 | 1 | yes | characteristic, complemented |
| 65 | #2040 | — | 5 | 1 | no | — |
| 66 | #1604 | — | 5 | 1 | no | — |
| 67 | #1598 | — | 5 | 1 | no | — |
| 68 | #1354 | — | 5 | 1 | no | — |
| 69 | #1345 | — | 5 | 1 | no | — |
| 70 | #1324 | — | 5 | 1 | no | — |
| 71 | C24×C5 | — | 2 | 1 | no | — |
| 72 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 73 | C2×C5×Q8 | — | 8 | 1 | no | — |
| 74 | C2×C5×D4 | — | 4 | 1 | no | — |
| 75 | C2×C5×D4 | — | 8 | 1 | no | — |
| 76 | C22×C4×C5 | — | 2 | 1 | no | — |
| 77 | C22×C4×C5 | — | 2 | 1 | no | — |
| 78 | C22×C4×C5 | — | 2 | 1 | no | — |
| 79 | C22×C4×C5 | — | 2 | 1 | no | — |
| 80 | C22×C4×C5 | — | 2 | 1 | no | — |
| 81 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 85 | #709 | — | 4 | 1 | no | — |
| 86 | #709 | — | 4 | 1 | no | — |
| 87 | #709 | — | 4 | 1 | no | — |
| 88 | #709 | — | 4 | 1 | no | — |
| 89 | C2×D20 | — | 2 | 1 | no | — |
| 90 | C2×D20 | — | 2 | 1 | no | — |
| 91 | C2×D20 | — | 2 | 1 | no | — |
| 92 | C2×C4×D5 | — | 4 | 1 | no | — |
| 93 | C2×Dic10 | — | 2 | 1 | no | — |
| 94 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 95 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 96 | C5×C4⋊C4 | — | 8 | 1 | no | — |
| 97 | C5×C4⋊C4 | — | 8 | 1 | no | — |
| 98 | C5×C22⋊C4 | — | 4 | 2 | no | — |
| 99 | C5×C22⋊C4 | — | 4 | 2 | no | — |
| 100 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 101 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 102 | C5×C22⋊C4 | — | 8 | 1 | no | — |
| 103 | C5×C22⋊C4 | — | 8 | 1 | no | — |
| 104 | C5×C22⋊C4 | — | 8 | 1 | no | — |
| 105 | C42×C5 | — | 2 | 1 | no | — |
| 106 | C42×C5 | — | 2 | 1 | no | — |
| 107 | C42×C5 | — | 4 | 2 | no | — |
| 108 | #688 | — | 8 | 2 | no | — |
| 109 | #686 | — | 8 | 2 | no | — |
| 110 | #685 | — | 4 | 1 | no | — |
| 111 | #685 | — | 4 | 1 | no | — |
| 112 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 113 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 114 | #681 | — | 4 | 1 | no | — |
| 115 | #681 | — | 4 | 1 | no | — |
| 116 | C2×#168 | — | 4 | 1 | no | — |
| 117 | C2×#168 | — | 4 | 1 | no | — |
| 118 | C2×#168 | — | 4 | 1 | no | — |
| 119 | #537 | — | 5 | 1 | no | — |
| 120 | #448 | — | 10 | 1 | no | — |
| 121 | #447 | — | 10 | 1 | no | — |
| 122 | C2×#104 | — | 10 | 1 | no | — |
| 123 | #417 | — | 10 | 1 | no | — |
| 124 | #395 | C2×D5 | 1 | 1 | yes | characteristic |
| 125 | #394 | — | 2 | 1 | no | — |
| 126 | #394 | C2×D5 | 1 | 1 | yes | characteristic |
| 127 | #393 | — | 2 | 1 | no | — |
| 128 | #388 | — | 2 | 1 | no | — |
| 129 | #388 | — | 2 | 1 | no | — |
| 130 | #388 | — | 2 | 1 | no | — |
| 131 | #382 | — | 2 | 1 | no | — |
| 132 | #382 | C2×D5 | 1 | 1 | yes | characteristic |
| 133 | #343 | — | 5 | 1 | no | — |
| 134 | #327 | — | 10 | 1 | no | — |
| 135 | #327 | — | 10 | 1 | no | — |
| 136 | #324 | — | 5 | 1 | no | — |
| 137 | #324 | — | 5 | 1 | no | — |
| 138 | C23×C5 | — | 4 | 1 | no | — |
| 139 | C23×C5 | — | 4 | 1 | no | — |
| 140 | C23×C5 | — | 4 | 1 | no | — |
| 141 | C23×C5 | — | 4 | 1 | no | — |
| 142 | C23×C5 | — | 4 | 1 | no | — |
| 143 | C23×C5 | — | 4 | 1 | no | — |
| 144 | C23×C5 | — | 4 | 1 | no | — |
| 145 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 146 | C22×D5 | — | 4 | 1 | no | — |
| 147 | C5×Q8 | — | 4 | 2 | no | — |
| 148 | C5×Q8 | — | 8 | 1 | no | — |
| 149 | C5×D4 | — | 4 | 2 | no | — |
| 150 | C5×D4 | — | 8 | 1 | no | — |
| 151 | C2×C4×C5 | — | 2 | 1 | no | — |
| 152 | C2×C4×C5 | — | 2 | 1 | no | — |
| 153 | C2×C4×C5 | — | 2 | 2 | no | — |
| 154 | C2×C4×C5 | — | 2 | 1 | no | — |
| 155 | C2×C4×C5 | — | 2 | 1 | no | — |
| 156 | C2×C4×C5 | — | 4 | 1 | no | — |
| 157 | C2×C4×C5 | — | 4 | 1 | no | — |
| 158 | C2×C4×C5 | — | 4 | 1 | no | — |
| 159 | C2×C4×C5 | — | 4 | 1 | no | — |
| 160 | C2×C4×C5 | — | 4 | 1 | no | — |
| 161 | C2×C4×C5 | — | 4 | 1 | no | — |
| 162 | C2×C4×C5 | — | 4 | 1 | no | — |
| 163 | C2×C4×C5 | — | 4 | 1 | no | — |
| 164 | C2×C4×C5 | — | 4 | 1 | no | — |
| 165 | C2×C4×C5 | — | 4 | 1 | no | — |
| 166 | C2×C4×C5 | — | 4 | 1 | no | — |
| 167 | C2×C4×C5 | — | 4 | 1 | no | — |
| 168 | C2×C4×C5 | — | 4 | 1 | no | — |
| 169 | C2×C4×C5 | — | 4 | 1 | no | — |
| 170 | C2×C4×C5 | — | 4 | 1 | no | — |
| 171 | C2×C4×C5 | — | 4 | 1 | no | — |
| 172 | C2×C4×C5 | #135 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 174 | C22⋊D5 | — | 8 | 1 | no | — |
| 175 | C22⋊D5 | — | 8 | 1 | no | — |
| 176 | C2×Dic5 | — | 4 | 1 | no | — |
| 177 | D20 | — | 4 | 1 | no | — |
| 178 | D20 | — | 4 | 1 | no | — |
| 179 | D20 | — | 8 | 1 | no | — |
| 180 | D20 | — | 8 | 1 | no | — |
| 181 | C4×D5 | — | 8 | 1 | no | — |
| 182 | C4×D5 | — | 8 | 1 | no | — |
| 183 | Dic10 | — | 4 | 1 | no | — |
| 184 | Dic10 | — | 4 | 1 | no | — |
| 185 | #168 | — | 8 | 1 | no | — |
| 186 | #168 | — | 8 | 1 | no | — |
| 187 | #168 | — | 8 | 1 | no | — |
| 188 | C2×#41 | — | 10 | 1 | no | — |
| 189 | C22×Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 190 | C22×D4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 191 | C2×SD16 | — | 20 | 1 | no | — |
| 192 | C2×D8 | — | 20 | 1 | no | — |
| 193 | C2×M16 | — | 10 | 1 | no | — |
| 194 | C22⋊Q8 | — | 20 | 1 | no | — |
| 195 | #121 | — | 10 | 1 | no | — |
| 196 | #121 | — | 10 | 1 | no | — |
| 197 | #121 | — | 20 | 1 | no | — |
| 198 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 199 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 200 | C2×C4⋊C4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 201 | C2×C4⋊C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 202 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 203 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 204 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 205 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 206 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 207 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 208 | C2×C42 | — | 2 | 1 | no | — |
| 209 | C2×C42 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 210 | #104 | — | 20 | 2 | no | — |
| 211 | #103 | — | 20 | 1 | no | — |
| 212 | #103 | — | 20 | 1 | no | — |
| 213 | #102 | — | 20 | 1 | no | — |
| 214 | #102 | — | 20 | 1 | no | — |
| 215 | C22⋊C8 | — | 10 | 1 | no | — |
| 216 | C22⋊C8 | — | 10 | 1 | no | — |
| 217 | #95 | — | 2 | 1 | no | — |
| 218 | #95 | — | 2 | 1 | no | — |
| 219 | #95 | — | 2 | 1 | no | — |
| 220 | #95 | — | 2 | 1 | no | — |
| 221 | #95 | — | 2 | 1 | no | — |
| 222 | #95 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 223 | #95 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 224 | C22×C5 | — | 2 | 1 | no | — |
| 225 | C22×C5 | — | 2 | 1 | no | — |
| 226 | C22×C5 | — | 8 | 1 | no | — |
| 227 | C22×C5 | — | 8 | 1 | no | — |
| 228 | C22×C5 | — | 8 | 1 | no | — |
| 229 | C22×C5 | — | 8 | 1 | no | — |
| 230 | C22×C5 | — | 8 | 1 | no | — |
| 231 | C22×C5 | — | 8 | 1 | no | — |
| 232 | C22×C5 | — | 8 | 1 | no | — |
| 233 | C22×C5 | #449 | 1 | 1 | yes | characteristic |
| 234 | C22×C5 | #454 | 1 | 1 | yes | characteristic |
| 235 | C22×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 236 | C2×D5 | — | 8 | 1 | no | — |
| 237 | C2×D5 | — | 8 | 1 | no | — |
| 238 | C2×D5 | — | 8 | 1 | no | — |
| 239 | C4×C5 | — | 2 | 1 | no | — |
| 240 | C4×C5 | — | 2 | 1 | no | — |
| 241 | C4×C5 | — | 4 | 2 | no | — |
| 242 | C4×C5 | — | 4 | 1 | no | — |
| 243 | C4×C5 | — | 4 | 1 | no | — |
| 244 | C4×C5 | — | 8 | 1 | no | — |
| 245 | C4×C5 | — | 8 | 1 | no | — |
| 246 | C4×C5 | — | 8 | 1 | no | — |
| 247 | C4×C5 | — | 8 | 1 | no | — |
| 248 | Dic5 | — | 8 | 1 | no | — |
| 249 | C24 | — | 2 | 1 | no | — |
| 250 | #41 | — | 20 | 1 | no | — |
| 251 | #41 | — | 20 | 1 | no | — |
| 252 | #41 | — | 20 | 1 | no | — |
| 253 | #41 | — | 20 | 1 | no | — |
| 254 | C2×Q8 | — | 4 | 1 | no | — |
| 255 | C2×Q8 | — | 8 | 1 | no | — |
| 256 | C2×Q8 | — | 10 | 1 | no | — |
| 257 | C2×D4 | — | 4 | 1 | no | — |
| 258 | C2×D4 | — | 8 | 1 | no | — |
| 259 | C2×D4 | — | 10 | 1 | no | — |
| 260 | C2×D4 | — | 10 | 1 | no | — |
| 261 | C2×D4 | — | 10 | 1 | no | — |
| 262 | C2×D4 | — | 20 | 1 | no | — |
| 263 | C22×C4 | — | 2 | 1 | no | — |
| 264 | C22×C4 | — | 2 | 1 | no | — |
| 265 | C22×C4 | — | 2 | 1 | no | — |
| 266 | C22×C4 | — | 2 | 1 | no | — |
| 267 | C22×C4 | — | 2 | 1 | no | — |
| 268 | C22×C4 | — | 20 | 1 | no | — |
| 269 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 270 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 271 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 272 | SD16 | — | 40 | 2 | no | — |
| 273 | D8 | — | 40 | 2 | no | — |
| 274 | M16 | — | 20 | 1 | no | — |
| 275 | M16 | — | 20 | 1 | no | — |
| 276 | C2×C8 | — | 20 | 1 | no | — |
| 277 | C2×C8 | — | 20 | 1 | no | — |
| 278 | C2×C8 | — | 20 | 1 | no | — |
| 279 | C4⋊C4 | — | 4 | 1 | no | — |
| 280 | C4⋊C4 | — | 4 | 1 | no | — |
| 281 | C4⋊C4 | — | 8 | 1 | no | — |
| 282 | C4⋊C4 | — | 8 | 1 | no | — |
| 283 | C4⋊C4 | — | 10 | 1 | no | — |
| 284 | C4⋊C4 | — | 10 | 1 | no | — |
| 285 | C22⋊C4 | — | 4 | 2 | no | — |
| 286 | C22⋊C4 | — | 4 | 2 | no | — |
| 287 | C22⋊C4 | — | 4 | 1 | no | — |
| 288 | C22⋊C4 | — | 4 | 1 | no | — |
| 289 | C22⋊C4 | — | 8 | 1 | no | — |
| 290 | C22⋊C4 | — | 8 | 1 | no | — |
| 291 | C22⋊C4 | — | 8 | 1 | no | — |
| 292 | C22⋊C4 | — | 20 | 1 | no | — |
| 293 | C22⋊C4 | — | 20 | 1 | no | — |
| 294 | C42 | — | 2 | 1 | no | — |
| 295 | C42 | — | 2 | 1 | no | — |
| 296 | C42 | — | 4 | 2 | no | — |
| 297 | C2×C5 | — | 2 | 1 | no | — |
| 298 | C2×C5 | — | 2 | 1 | no | — |
| 299 | C2×C5 | — | 16 | 1 | no | — |
| 300 | C2×C5 | #1597 | 1 | 1 | yes | characteristic |
| 301 | C2×C5 | #2199 | 1 | 1 | yes | characteristic |
| 302 | C2×C5 | #2204 | 1 | 1 | yes | characteristic |
| 303 | D5 | — | 16 | 1 | no | — |
| 304 | C23 | — | 4 | 1 | no | — |
| 305 | C23 | — | 4 | 1 | no | — |
| 306 | C23 | — | 4 | 1 | no | — |
| 307 | C23 | — | 4 | 1 | no | — |
| 308 | C23 | — | 4 | 1 | no | — |
| 309 | C23 | — | 4 | 1 | no | — |
| 310 | C23 | — | 4 | 1 | no | — |
| 311 | C23 | — | 20 | 1 | no | — |
| 312 | C23 | #4099 | 1 | 1 | yes | characteristic |
| 313 | Q8 | — | 4 | 2 | no | — |
| 314 | Q8 | — | 8 | 1 | no | — |
| 315 | Q8 | — | 20 | 1 | no | — |
| 316 | Q8 | — | 20 | 1 | no | — |
| 317 | D4 | — | 4 | 2 | no | — |
| 318 | D4 | — | 8 | 1 | no | — |
| 319 | D4 | — | 20 | 1 | no | — |
| 320 | D4 | — | 20 | 1 | no | — |
| 321 | D4 | — | 40 | 1 | no | — |
| 322 | D4 | — | 40 | 1 | no | — |
| 323 | D4 | — | 40 | 1 | no | — |
| 324 | D4 | — | 40 | 1 | no | — |
| 325 | C2×C4 | — | 2 | 1 | no | — |
| 326 | C2×C4 | — | 2 | 1 | no | — |
| 327 | C2×C4 | — | 2 | 2 | no | — |
| 328 | C2×C4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 2 | 1 | no | — |
| 330 | C2×C4 | — | 4 | 1 | no | — |
| 331 | C2×C4 | — | 4 | 1 | no | — |
| 332 | C2×C4 | — | 4 | 1 | no | — |
| 333 | C2×C4 | — | 4 | 1 | no | — |
| 334 | C2×C4 | — | 4 | 1 | no | — |
| 335 | C2×C4 | — | 4 | 1 | no | — |
| 336 | C2×C4 | — | 4 | 1 | no | — |
| 337 | C2×C4 | — | 4 | 1 | no | — |
| 338 | C2×C4 | — | 4 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 1 | no | — |
| 340 | C2×C4 | — | 4 | 1 | no | — |
| 341 | C2×C4 | — | 4 | 1 | no | — |
| 342 | C2×C4 | — | 4 | 1 | no | — |
| 343 | C2×C4 | — | 4 | 1 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 4 | 1 | no | — |
| 346 | C2×C4 | — | 20 | 1 | no | — |
| 347 | C2×C4 | — | 40 | 1 | no | — |
| 348 | C2×C4 | — | 40 | 1 | no | — |
| 349 | C2×C4 | #4095 | 1 | 1 | yes | characteristic |
| 350 | C2×C4 | #4096 | 1 | 1 | yes | characteristic |
| 351 | C8 | — | 40 | 1 | no | — |
| 352 | C8 | — | 40 | 1 | no | — |
| 353 | C8 | — | 40 | 1 | no | — |
| 354 | C5 | #12145 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 355 | C22 | — | 2 | 1 | no | — |
| 356 | C22 | — | 2 | 1 | no | — |
| 357 | C22 | — | 8 | 1 | no | — |
| 358 | C22 | — | 8 | 1 | no | — |
| 359 | C22 | — | 8 | 1 | no | — |
| 360 | C22 | — | 8 | 1 | no | — |
| 361 | C22 | — | 8 | 1 | no | — |
| 362 | C22 | — | 8 | 1 | no | — |
| 363 | C22 | — | 8 | 1 | no | — |
| 364 | C22 | — | 40 | 1 | no | — |
| 365 | C22 | — | 40 | 1 | no | — |
| 366 | C22 | — | 40 | 1 | no | — |
| 367 | C22 | #65527 | 1 | 1 | yes | characteristic |
| 368 | C22 | #65533 | 1 | 1 | yes | characteristic |
| 369 | C22 | #65534 | 1 | 1 | yes | characteristic |
| 370 | C4 | — | 2 | 1 | no | — |
| 371 | C4 | — | 2 | 1 | no | — |
| 372 | C4 | — | 4 | 2 | no | — |
| 373 | C4 | — | 4 | 1 | no | — |
| 374 | C4 | — | 4 | 1 | no | — |
| 375 | C4 | — | 8 | 1 | no | — |
| 376 | C4 | — | 8 | 1 | no | — |
| 377 | C4 | — | 8 | 1 | no | — |
| 378 | C4 | — | 8 | 1 | no | — |
| 379 | C4 | — | 40 | 1 | no | — |
| 380 | C2 | — | 2 | 1 | no | — |
| 381 | C2 | — | 2 | 1 | no | — |
| 382 | C2 | — | 16 | 1 | no | — |
| 383 | C2 | — | 80 | 1 | no | — |
| 384 | C2 | #10602681 | 1 | 1 | yes | characteristic |
| 385 | C2 | #10602723 | 1 | 1 | yes | characteristic |
| 386 | C2 | #10602743 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2785 | C2 | semidirect |
| 2. #10600499 | C2 | semidirect |
| 4. #10600356 | C2 | semidirect |
| 5. #10598139 | C2 | semidirect |
| 6. #10598138 | C2 | semidirect |
| 7. #10598123 | C2 | semidirect |
| 64. #2785 | D5 | semidirect |
| 354. C5 | #12145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2785 | 2 |
| #10600499 | 2 |
| #10600496 | 2 |
| #10600356 | 2 |
| #10598139 | 2 |
| #10598138 | 2 |
| #10598123 | 2 |
| #12145 | 5 |