Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1150 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 171 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 | C2×#66017 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C5×#497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#65378 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#64760 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602122 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 6 | C2×#64684 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C22×C5×Q16 | — | 2 | 1 | no | — |
| 8 | C22×C5×SD16 | — | 2 | 1 | no | — |
| 9 | C2×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C5×#124 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#4093 | — | 2 | 1 | no | — |
| 12 | C2×#4083 | — | 2 | 1 | no | — |
| 13 | #66017 | — | 2 | 4 | no | — |
| 14 | #66017 | — | 2 | 2 | no | — |
| 15 | #66017 | C22 | 1 | 4 | yes | — |
| 16 | C2×#4031 | — | 2 | 2 | no | — |
| 17 | C2×#4028 | — | 2 | 2 | no | — |
| 18 | C2×#4021 | C22 | 1 | 2 | yes | — |
| 19 | C5×#497 | — | 2 | 2 | no | — |
| 20 | C5×#497 | C22 | 1 | 4 | yes | complemented |
| 21 | C2×C5×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #65378 | — | 2 | 4 | no | — |
| 23 | #65378 | C22 | 1 | 8 | yes | complemented |
| 24 | C2×#3942 | — | 2 | 2 | no | — |
| 25 | C2×#3941 | — | 2 | 2 | no | — |
| 26 | C2×#3935 | C22 | 1 | 2 | yes | complemented |
| 27 | #64760 | C22 | 1 | 4 | yes | complemented |
| 28 | #64684 | C22 | 1 | 8 | yes | complemented |
| 29 | C2×#1659 | — | 5 | 1 | no | maximal, Sylow |
| 30 | C24×D5 | — | 2 | 1 | no | — |
| 31 | C22×C5×Q8 | — | 2 | 1 | no | — |
| 32 | C22×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 33 | C22×C5×D4 | D4 | 1 | 1 | yes | characteristic |
| 34 | C22×C22⋊D5 | — | 2 | 2 | no | — |
| 35 | C22×D20 | — | 2 | 1 | no | — |
| 36 | C22×D20 | D4 | 1 | 2 | yes | — |
| 37 | C22×Dic10 | D4 | 1 | 2 | yes | — |
| 38 | C2×C5×Q16 | — | 2 | 4 | no | — |
| 39 | C2×C5×Q16 | — | 4 | 4 | no | — |
| 40 | C2×C5×SD16 | — | 2 | 4 | no | — |
| 41 | C2×C5×SD16 | — | 4 | 4 | no | — |
| 42 | C22×C5×C8 | — | 2 | 1 | no | — |
| 43 | C5×C4⋊Q8 | — | 2 | 2 | no | — |
| 44 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 45 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | complemented |
| 46 | C5×#124 | — | 2 | 2 | no | — |
| 47 | C5×#124 | D4 | 1 | 2 | yes | — |
| 48 | C5×#124 | C23 | 1 | 2 | yes | — |
| 49 | C2×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 50 | C2×C5×C22⋊C4 | — | 2 | 2 | no | — |
| 51 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C22⋊Dic5 | — | 2 | 1 | no | — |
| 53 | #4093 | — | 2 | 4 | no | — |
| 54 | #4093 | — | 2 | 4 | no | — |
| 55 | #4083 | — | 2 | 4 | no | — |
| 56 | #4083 | — | 2 | 4 | no | — |
| 57 | C2×#685 | — | 2 | 2 | no | — |
| 58 | C2×#685 | — | 2 | 2 | no | — |
| 59 | C2×#685 | — | 2 | 2 | no | — |
| 60 | C2×C4×Dic5 | — | 2 | 1 | no | — |
| 61 | C22×#168 | — | 2 | 2 | no | — |
| 62 | #4031 | — | 2 | 8 | no | — |
| 63 | #4031 | — | 2 | 8 | no | — |
| 64 | #4028 | — | 2 | 8 | no | — |
| 65 | #4028 | — | 2 | 8 | no | — |
| 66 | #4021 | — | 2 | 2 | no | — |
| 67 | #4021 | — | 2 | 2 | no | — |
| 68 | #4021 | D4 | 1 | 4 | yes | — |
| 69 | #4021 | C23 | 1 | 4 | yes | — |
| 70 | C5×#97 | — | 2 | 1 | no | — |
| 71 | C5×#97 | C23 | 1 | 2 | yes | complemented |
| 72 | #3942 | — | 2 | 8 | no | — |
| 73 | #3941 | — | 2 | 8 | no | — |
| 74 | #3935 | — | 2 | 2 | no | — |
| 75 | #3935 | C23 | 1 | 4 | yes | complemented |
| 76 | C2×H(3,𝔽4) | — | 5 | 1 | no | — |
| 77 | C2×#497 | D5 | 1 | 1 | yes | characteristic, complemented |
| 78 | C2×#489 | — | 5 | 2 | no | — |
| 79 | #1659 | — | 5 | 8 | no | — |
| 80 | C2×#329 | — | 5 | 2 | no | — |
| 81 | C2×#329 | — | 5 | 1 | no | — |
| 82 | C24×C5 | — | 2 | 1 | no | — |
| 83 | C23×D5 | — | 2 | 2 | no | — |
| 84 | C23×D5 | — | 2 | 4 | no | — |
| 85 | C23×D5 | — | 8 | 2 | no | — |
| 86 | C23×D5 | — | 8 | 4 | no | — |
| 87 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 88 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 89 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 90 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 91 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 92 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 93 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×C5×D4 | — | 2 | 1 | no | — |
| 95 | C2×C5×D4 | — | 4 | 2 | no | — |
| 96 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 97 | C22×C4×C5 | — | 2 | 1 | no | — |
| 98 | C22×C4×C5 | — | 4 | 1 | no | — |
| 99 | C22×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 100 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×C22⋊D5 | — | 2 | 8 | no | — |
| 102 | C2×C22⋊D5 | — | 8 | 4 | no | — |
| 103 | C22×Dic5 | — | 2 | 2 | no | — |
| 104 | C2×D20 | — | 2 | 4 | no | — |
| 105 | C2×D20 | — | 2 | 2 | no | — |
| 106 | C2×D20 | — | 4 | 4 | no | — |
| 107 | C2×D20 | — | 8 | 2 | no | — |
| 108 | C2×D20 | C2×D4 | 1 | 4 | yes | — |
| 109 | C2×Dic10 | — | 2 | 2 | no | — |
| 110 | C2×Dic10 | — | 4 | 4 | no | — |
| 111 | C2×Dic10 | C2×D4 | 1 | 4 | yes | — |
| 112 | C5×Q16 | — | 4 | 8 | no | — |
| 113 | C5×SD16 | — | 4 | 8 | no | — |
| 114 | C2×C5×C8 | — | 2 | 4 | no | — |
| 115 | C2×C5×C8 | — | 2 | 2 | no | — |
| 116 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 117 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 118 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 119 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 120 | C42×C5 | C2×D4 | 1 | 2 | yes | — |
| 121 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 123 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 124 | #685 | — | 2 | 8 | no | — |
| 125 | #685 | — | 2 | 4 | no | — |
| 126 | #685 | — | 2 | 4 | no | — |
| 127 | #685 | — | 2 | 4 | no | — |
| 128 | #685 | — | 2 | 4 | no | — |
| 129 | C4×Dic5 | — | 2 | 4 | no | — |
| 130 | C2×#168 | — | 2 | 4 | no | — |
| 131 | C2×#168 | — | 4 | 4 | no | — |
| 132 | C22×Q16 | — | 2 | 1 | no | — |
| 133 | C22×SD16 | — | 2 | 1 | no | — |
| 134 | H(3,𝔽4) | — | 5 | 4 | no | — |
| 135 | H(3,𝔽4) | — | 10 | 4 | no | — |
| 136 | H(3,𝔽4) | — | 10 | 2 | no | — |
| 137 | C2×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 138 | C2×#124 | — | 5 | 2 | no | — |
| 139 | C2×#124 | — | 10 | 2 | no | — |
| 140 | C2×#124 | — | 10 | 1 | no | — |
| 141 | C2×#124 | C2×D5 | 1 | 1 | yes | characteristic |
| 142 | C2×#120 | — | 10 | 2 | no | — |
| 143 | C2×#120 | — | 10 | 1 | no | — |
| 144 | #497 | — | 2 | 2 | no | — |
| 145 | #497 | C2×D5 | 1 | 4 | yes | complemented |
| 146 | #489 | — | 5 | 8 | no | — |
| 147 | #489 | — | 10 | 4 | no | — |
| 148 | C2×#103 | — | 10 | 2 | no | — |
| 149 | C2×#102 | — | 10 | 2 | no | — |
| 150 | C2×#97 | — | 5 | 2 | no | — |
| 151 | C2×#97 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 152 | #329 | — | 5 | 4 | no | — |
| 153 | #329 | — | 5 | 8 | no | — |
| 154 | C23×C5 | — | 2 | 2 | no | — |
| 155 | C23×C5 | — | 4 | 2 | no | — |
| 156 | C23×C5 | — | 4 | 4 | no | — |
| 157 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 158 | C22×D5 | — | 2 | 4 | no | — |
| 159 | C22×D5 | — | 4 | 4 | no | — |
| 160 | C22×D5 | — | 4 | 4 | no | — |
| 161 | C22×D5 | — | 4 | 4 | no | — |
| 162 | C22×D5 | — | 8 | 4 | no | — |
| 163 | C22×D5 | — | 8 | 8 | no | — |
| 164 | C22×D5 | — | 8 | 16 | no | — |
| 165 | C5×Q8 | — | 4 | 2 | no | — |
| 166 | C5×Q8 | — | 4 | 2 | no | — |
| 167 | C5×Q8 | — | 4 | 2 | no | — |
| 168 | C5×Q8 | — | 8 | 1 | no | — |
| 169 | C5×Q8 | — | 8 | 2 | no | — |
| 170 | C5×D4 | — | 4 | 2 | no | — |
| 171 | C5×D4 | — | 8 | 1 | no | — |
| 172 | C2×C4×C5 | — | 2 | 2 | no | — |
| 173 | C2×C4×C5 | — | 2 | 4 | no | — |
| 174 | C2×C4×C5 | — | 2 | 2 | no | — |
| 175 | C2×C4×C5 | — | 4 | 2 | no | — |
| 176 | C2×C4×C5 | — | 4 | 2 | no | — |
| 177 | C2×C4×C5 | — | 8 | 2 | no | — |
| 178 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C5 | #120 | 1 | 2 | yes | — |
| 180 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 181 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 182 | C22⋊D5 | — | 8 | 8 | no | — |
| 183 | C2×Dic5 | — | 2 | 4 | no | — |
| 184 | C2×Dic5 | — | 4 | 4 | no | — |
| 185 | D20 | — | 4 | 4 | no | — |
| 186 | D20 | — | 8 | 2 | no | — |
| 187 | D20 | — | 8 | 4 | no | — |
| 188 | Dic10 | — | 4 | 4 | no | — |
| 189 | Dic10 | — | 8 | 2 | no | — |
| 190 | C5×C8 | — | 2 | 4 | no | — |
| 191 | #168 | — | 4 | 4 | no | — |
| 192 | C25 | — | 10 | 1 | no | — |
| 193 | C22×Q8 | — | 2 | 1 | no | — |
| 194 | C22×Q8 | — | 5 | 2 | no | — |
| 195 | C22×Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 196 | C22×D4 | — | 5 | 2 | no | — |
| 197 | C22×D4 | — | 10 | 1 | no | — |
| 198 | C22×D4 | — | 10 | 2 | no | — |
| 199 | C22×D4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 200 | C2×Q16 | — | 2 | 4 | no | — |
| 201 | C2×Q16 | — | 4 | 4 | no | — |
| 202 | C2×SD16 | — | 2 | 4 | no | — |
| 203 | C2×SD16 | — | 4 | 4 | no | — |
| 204 | C22×C8 | — | 2 | 1 | no | — |
| 205 | C22×C8 | — | 10 | 2 | no | — |
| 206 | C4⋊Q8 | — | 2 | 2 | no | — |
| 207 | C4⋊Q8 | — | 2 | 1 | no | — |
| 208 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | complemented |
| 209 | #124 | — | 2 | 2 | no | — |
| 210 | #124 | — | 5 | 4 | no | — |
| 211 | #124 | — | 5 | 4 | no | — |
| 212 | #124 | — | 10 | 8 | no | — |
| 213 | #124 | — | 10 | 8 | no | — |
| 214 | #124 | — | 10 | 4 | no | — |
| 215 | #124 | — | 10 | 4 | no | — |
| 216 | #124 | — | 10 | 2 | no | — |
| 217 | #124 | — | 10 | 2 | no | — |
| 218 | #124 | C22⋊D5 | 1 | 2 | yes | — |
| 219 | #124 | C22×D5 | 1 | 2 | yes | — |
| 220 | #120 | — | 10 | 8 | no | — |
| 221 | #120 | — | 10 | 8 | no | — |
| 222 | #120 | — | 10 | 4 | no | — |
| 223 | #120 | — | 10 | 4 | no | — |
| 224 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 225 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 226 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 227 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 228 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 229 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 230 | C2×C42 | — | 10 | 1 | no | — |
| 231 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 232 | #103 | — | 10 | 8 | no | — |
| 233 | #102 | — | 10 | 8 | no | — |
| 234 | #97 | — | 2 | 1 | no | — |
| 235 | #97 | — | 5 | 4 | no | — |
| 236 | #97 | — | 10 | 2 | no | — |
| 237 | #97 | C22×D5 | 1 | 2 | yes | complemented |
| 238 | C22×C5 | — | 4 | 2 | no | — |
| 239 | C22×C5 | — | 4 | 4 | no | — |
| 240 | C22×C5 | — | 8 | 4 | no | — |
| 241 | C22×C5 | #453 | 1 | 2 | yes | — |
| 242 | C22×C5 | #455 | 1 | 4 | yes | — |
| 243 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 244 | C2×D5 | — | 4 | 4 | no | — |
| 245 | C2×D5 | — | 4 | 4 | no | — |
| 246 | C2×D5 | — | 4 | 4 | no | — |
| 247 | C2×D5 | — | 8 | 16 | no | — |
| 248 | C2×D5 | — | 8 | 8 | no | — |
| 249 | C4×C5 | — | 2 | 1 | no | — |
| 250 | C4×C5 | — | 2 | 1 | no | — |
| 251 | C4×C5 | — | 2 | 2 | no | — |
| 252 | C4×C5 | — | 2 | 2 | no | — |
| 253 | C4×C5 | — | 4 | 2 | no | — |
| 254 | C4×C5 | — | 8 | 2 | no | — |
| 255 | Dic5 | — | 4 | 4 | no | — |
| 256 | C24 | — | 2 | 1 | no | — |
| 257 | C24 | — | 10 | 4 | no | — |
| 258 | C24 | — | 10 | 2 | no | — |
| 259 | C24 | — | 40 | 2 | no | — |
| 260 | C24 | — | 40 | 4 | no | — |
| 261 | C2×Q8 | — | 2 | 1 | no | — |
| 262 | C2×Q8 | — | 2 | 2 | no | — |
| 263 | C2×Q8 | — | 4 | 2 | no | — |
| 264 | C2×Q8 | — | 4 | 2 | no | — |
| 265 | C2×Q8 | — | 4 | 2 | no | — |
| 266 | C2×Q8 | — | 4 | 1 | no | — |
| 267 | C2×Q8 | — | 5 | 4 | no | — |
| 268 | C2×Q8 | — | 10 | 2 | no | — |
| 269 | C2×Q8 | — | 20 | 4 | no | — |
| 270 | C2×Q8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 271 | C2×D4 | — | 2 | 1 | no | — |
| 272 | C2×D4 | — | 4 | 2 | no | — |
| 273 | C2×D4 | — | 5 | 4 | no | — |
| 274 | C2×D4 | — | 10 | 4 | no | — |
| 275 | C2×D4 | — | 10 | 8 | no | — |
| 276 | C2×D4 | — | 10 | 2 | no | — |
| 277 | C2×D4 | — | 20 | 4 | no | — |
| 278 | C2×D4 | — | 40 | 2 | no | — |
| 279 | C2×D4 | — | 40 | 4 | no | — |
| 280 | C2×D4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 281 | C22×C4 | — | 2 | 1 | no | — |
| 282 | C22×C4 | — | 4 | 1 | no | — |
| 283 | C22×C4 | — | 10 | 2 | no | — |
| 284 | C22×C4 | D4×D5 | 1 | 2 | yes | — |
| 285 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 286 | Q16 | — | 4 | 8 | no | — |
| 287 | SD16 | — | 4 | 8 | no | — |
| 288 | C2×C8 | — | 2 | 4 | no | — |
| 289 | C2×C8 | — | 2 | 2 | no | — |
| 290 | C2×C8 | — | 10 | 4 | no | — |
| 291 | C2×C8 | — | 20 | 4 | no | — |
| 292 | C4⋊C4 | — | 2 | 4 | no | — |
| 293 | C4⋊C4 | — | 4 | 2 | no | — |
| 294 | C22⋊C4 | — | 2 | 4 | no | — |
| 295 | C22⋊C4 | — | 2 | 4 | no | — |
| 296 | C22⋊C4 | — | 10 | 8 | no | — |
| 297 | C22⋊C4 | — | 10 | 4 | no | — |
| 298 | C22⋊C4 | — | 10 | 4 | no | — |
| 299 | C22⋊C4 | — | 10 | 4 | no | — |
| 300 | C22⋊C4 | — | 10 | 4 | no | — |
| 301 | C22⋊C4 | — | 10 | 4 | no | — |
| 302 | C42 | — | 10 | 4 | no | — |
| 303 | C42 | D4×D5 | 1 | 2 | yes | — |
| 304 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 305 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 306 | C2×C5 | — | 8 | 2 | no | — |
| 307 | C2×C5 | #1659 | 1 | 4 | yes | complemented |
| 308 | C2×C5 | C2×#453 | 1 | 1 | yes | characteristic |
| 309 | C2×C5 | C2×#455 | 1 | 2 | yes | — |
| 310 | D5 | — | 8 | 4 | no | — |
| 311 | C23 | — | 2 | 2 | no | — |
| 312 | C23 | — | 4 | 2 | no | — |
| 313 | C23 | — | 4 | 4 | no | — |
| 314 | C23 | — | 10 | 4 | no | — |
| 315 | C23 | — | 20 | 4 | no | — |
| 316 | C23 | — | 20 | 4 | no | — |
| 317 | C23 | — | 20 | 4 | no | — |
| 318 | C23 | — | 40 | 4 | no | — |
| 319 | C23 | — | 40 | 8 | no | — |
| 320 | C23 | — | 40 | 16 | no | — |
| 321 | C23 | #4083 | 1 | 1 | yes | characteristic |
| 322 | Q8 | — | 4 | 2 | no | — |
| 323 | Q8 | — | 4 | 2 | no | — |
| 324 | Q8 | — | 4 | 2 | no | — |
| 325 | Q8 | — | 8 | 1 | no | — |
| 326 | Q8 | — | 8 | 2 | no | — |
| 327 | Q8 | — | 20 | 4 | no | — |
| 328 | Q8 | — | 40 | 2 | no | — |
| 329 | D4 | — | 4 | 2 | no | — |
| 330 | D4 | — | 8 | 1 | no | — |
| 331 | D4 | — | 20 | 4 | no | — |
| 332 | D4 | — | 40 | 2 | no | — |
| 333 | D4 | — | 40 | 4 | no | — |
| 334 | D4 | — | 40 | 8 | no | — |
| 335 | C2×C4 | — | 2 | 2 | no | — |
| 336 | C2×C4 | — | 2 | 4 | no | — |
| 337 | C2×C4 | — | 2 | 2 | no | — |
| 338 | C2×C4 | — | 4 | 2 | no | — |
| 339 | C2×C4 | — | 4 | 2 | no | — |
| 340 | C2×C4 | — | 8 | 2 | no | — |
| 341 | C2×C4 | — | 10 | 4 | no | — |
| 342 | C2×C4 | — | 20 | 4 | no | — |
| 343 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | #4083 | 1 | 2 | yes | — |
| 345 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 346 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 347 | C8 | — | 2 | 4 | no | — |
| 348 | C8 | — | 20 | 4 | no | — |
| 349 | C5 | C2×#1659 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 350 | C22 | — | 4 | 2 | no | — |
| 351 | C22 | — | 4 | 4 | no | — |
| 352 | C22 | — | 8 | 4 | no | — |
| 353 | C22 | — | 20 | 4 | no | — |
| 354 | C22 | — | 20 | 4 | no | — |
| 355 | C22 | — | 20 | 4 | no | — |
| 356 | C22 | — | 40 | 16 | no | — |
| 357 | C22 | — | 40 | 8 | no | — |
| 358 | C22 | #65366 | 1 | 2 | yes | — |
| 359 | C22 | #65491 | 1 | 4 | yes | — |
| 360 | C22 | C2×#4083 | 1 | 1 | yes | characteristic |
| 361 | C4 | — | 2 | 1 | no | — |
| 362 | C4 | — | 2 | 1 | no | — |
| 363 | C4 | — | 2 | 2 | no | — |
| 364 | C4 | — | 2 | 2 | no | — |
| 365 | C4 | — | 4 | 2 | no | — |
| 366 | C4 | — | 8 | 2 | no | — |
| 367 | C4 | — | 20 | 4 | no | — |
| 368 | C2 | — | 8 | 2 | no | — |
| 369 | C2 | — | 40 | 4 | no | — |
| 370 | C2 | #10602122 | 1 | 4 | yes | direct product factor |
| 371 | C2 | C2×#65366 | 1 | 1 | yes | characteristic |
| 372 | C2 | C2×#65491 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#497 | C2 | semidirect |
| 3. C2×#65378 | C2 | semidirect |
| 4. C2×#64760 | C2 | semidirect |
| 5. #10602122 | C2 | direct (N × H) |
| 6. C2×#64684 | C2 | semidirect |
| 9. C2×C5×C4⋊Q8 | C22 | semidirect |
| 20. C5×#497 | C22 | semidirect |
| 21. C2×C5×#97 | C22 | semidirect |
| 23. #65378 | C22 | semidirect |
| 26. C2×#3935 | C22 | semidirect |
| 27. #64760 | C22 | semidirect |
| 28. #64684 | C22 | semidirect |
| 45. C5×C4⋊Q8 | C23 | semidirect |
| 71. C5×#97 | C23 | semidirect |
| 75. #3935 | C23 | semidirect |
| 77. C2×#497 | D5 | semidirect |
| 137. C2×C4⋊Q8 | C2×D5 | semidirect |
| 145. #497 | C2×D5 | semidirect |
| 151. C2×#97 | C2×D5 | semidirect |
| 208. C4⋊Q8 | C22×D5 | semidirect |
| 237. #97 | C22×D5 | semidirect |
| 307. C2×C5 | #1659 | semidirect |
| 349. C5 | C2×#1659 | semidirect |
| 370. C2 | #10602122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66017 | 2 |
| C2×C5×#497 | 2 |
| C2×#65378 | 2 |
| C2×#64760 | 2 |
| #10602122 | 2 |
| C2×#64684 | 2 |
| C2×#1659 | 5 |