Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1330 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 149 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 | D5×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#496 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C5×#1655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10602741 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602119 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10599143 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D5×#329 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C5×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×D5×SD16 | — | 2 | 3 | no | — |
| 10 | C2×D5×D8 | — | 2 | 3 | no | — |
| 11 | D5×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #66017 | — | 2 | 3 | no | — |
| 13 | #66017 | C22 | 1 | 3 | yes | complemented |
| 14 | D5×#124 | — | 2 | 3 | no | — |
| 15 | D5×#124 | C22 | 1 | 3 | yes | — |
| 16 | #65928 | — | 2 | 3 | no | — |
| 17 | D5×#120 | — | 2 | 3 | no | — |
| 18 | C5×#496 | C22 | 1 | 3 | yes | complemented |
| 19 | #65465 | — | 2 | 3 | no | — |
| 20 | #65443 | — | 2 | 3 | no | — |
| 21 | #65363 | C22 | 1 | 3 | yes | complemented |
| 22 | #65347 | C22 | 1 | 3 | yes | complemented |
| 23 | #65001 | C22 | 1 | 3 | yes | complemented |
| 24 | D5×#97 | C22 | 1 | 3 | yes | complemented |
| 25 | C5×#329 | C22 | 1 | 3 | yes | complemented |
| 26 | #64760 | C22 | 1 | 3 | yes | complemented |
| 27 | #64684 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×#1655 | — | 5 | 1 | no | maximal, Sylow |
| 29 | C24×D5 | — | 2 | 1 | no | — |
| 30 | C2×Q8×D5 | D4 | 1 | 3 | yes | — |
| 31 | C2×D4×D5 | — | 2 | 3 | no | — |
| 32 | C2×D4×D5 | — | 2 | 3 | no | — |
| 33 | C2×D4×D5 | D4 | 1 | 3 | yes | — |
| 34 | C2×C5×SD16 | — | 2 | 3 | no | — |
| 35 | C2×C5×D8 | — | 2 | 3 | no | — |
| 36 | C5×#127 | C23 | 1 | 1 | yes | characteristic, complemented |
| 37 | C5×#124 | — | 2 | 3 | no | — |
| 38 | C5×#124 | C23 | 1 | 3 | yes | — |
| 39 | C5×#120 | — | 2 | 3 | no | — |
| 40 | #4099 | — | 2 | 3 | no | — |
| 41 | #4093 | — | 2 | 3 | no | — |
| 42 | #4093 | D4 | 1 | 3 | yes | — |
| 43 | C2×#688 | — | 2 | 3 | no | — |
| 44 | #4086 | — | 2 | 3 | no | — |
| 45 | #4083 | — | 2 | 6 | no | — |
| 46 | #4083 | — | 2 | 3 | no | — |
| 47 | #4082 | — | 2 | 3 | no | — |
| 48 | #4082 | D4 | 1 | 3 | yes | — |
| 49 | C2×#687 | — | 2 | 3 | no | — |
| 50 | C2×#686 | — | 2 | 3 | no | — |
| 51 | C2×#686 | — | 2 | 3 | no | — |
| 52 | D5×SD16 | — | 4 | 12 | no | — |
| 53 | D5×D8 | — | 4 | 12 | no | — |
| 54 | C2×D40 | — | 2 | 3 | no | — |
| 55 | C2×#677 | — | 2 | 3 | no | — |
| 56 | C2×C8×D5 | — | 2 | 3 | no | — |
| 57 | #4031 | — | 2 | 6 | no | — |
| 58 | #4031 | — | 2 | 6 | no | — |
| 59 | #4031 | — | 2 | 6 | no | — |
| 60 | #4028 | — | 2 | 3 | no | — |
| 61 | #4028 | — | 2 | 6 | no | — |
| 62 | D5×C22⋊C4 | — | 2 | 3 | no | — |
| 63 | D5×C22⋊C4 | — | 2 | 6 | no | — |
| 64 | #4021 | — | 2 | 3 | no | — |
| 65 | #4021 | C23 | 1 | 3 | yes | — |
| 66 | #4020 | C23 | 1 | 1 | yes | characteristic, complemented |
| 67 | C42×D5 | — | 2 | 1 | no | — |
| 68 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 69 | C5×#97 | C23 | 1 | 3 | yes | complemented |
| 70 | #3947 | — | 2 | 3 | no | — |
| 71 | #3935 | C23 | 1 | 3 | yes | complemented |
| 72 | C2×H(3,𝔽4) | — | 5 | 1 | no | — |
| 73 | C2×#496 | — | 5 | 3 | no | — |
| 74 | #1655 | — | 5 | 3 | no | — |
| 75 | #1655 | — | 5 | 3 | no | — |
| 76 | #1655 | — | 5 | 1 | no | — |
| 77 | #1655 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 78 | C2×#329 | — | 5 | 3 | no | — |
| 79 | C24×C5 | — | 2 | 1 | no | — |
| 80 | C23×D5 | — | 2 | 3 | no | — |
| 81 | C23×D5 | — | 2 | 3 | no | — |
| 82 | C23×D5 | — | 4 | 1 | no | — |
| 83 | C23×D5 | — | 8 | 6 | no | — |
| 84 | C2×C5×Q8 | C2×D4 | 1 | 3 | yes | — |
| 85 | C2×C5×D4 | — | 2 | 3 | no | — |
| 86 | C2×C5×D4 | — | 2 | 3 | no | — |
| 87 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 88 | C2×C22⋊D5 | — | 2 | 6 | no | — |
| 89 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 90 | C2×C22⋊D5 | — | 4 | 3 | no | — |
| 91 | Q8×D5 | — | 4 | 6 | no | — |
| 92 | D4×D5 | — | 4 | 6 | no | — |
| 93 | D4×D5 | — | 4 | 6 | no | — |
| 94 | D4×D5 | — | 4 | 6 | no | — |
| 95 | D4×D5 | — | 8 | 6 | no | — |
| 96 | C2×D20 | — | 2 | 3 | no | — |
| 97 | C2×D20 | — | 2 | 3 | no | — |
| 98 | C2×D20 | C2×D4 | 1 | 3 | yes | — |
| 99 | C2×C4×D5 | — | 2 | 3 | no | — |
| 100 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 101 | C2×Dic10 | — | 2 | 3 | no | — |
| 102 | C2×Dic10 | C2×D4 | 1 | 3 | yes | — |
| 103 | C5×SD16 | — | 4 | 6 | no | — |
| 104 | C5×D8 | — | 4 | 6 | no | — |
| 105 | C2×C5×C8 | — | 2 | 3 | no | — |
| 106 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 107 | C5×C22⋊C4 | — | 2 | 6 | no | — |
| 108 | C42×C5 | — | 2 | 1 | no | — |
| 109 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 110 | C22⋊Dic5 | — | 2 | 3 | no | — |
| 111 | C22⋊Dic5 | — | 2 | 6 | no | — |
| 112 | #688 | — | 4 | 6 | no | — |
| 113 | #687 | — | 4 | 6 | no | — |
| 114 | #686 | — | 4 | 6 | no | — |
| 115 | #686 | — | 4 | 6 | no | — |
| 116 | #685 | — | 2 | 6 | no | — |
| 117 | #685 | — | 2 | 6 | no | — |
| 118 | #685 | — | 2 | 6 | no | — |
| 119 | C4×Dic5 | — | 2 | 3 | no | — |
| 120 | C4×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 121 | C2×#168 | — | 2 | 3 | no | — |
| 122 | D40 | — | 4 | 6 | no | — |
| 123 | #677 | — | 4 | 6 | no | — |
| 124 | C8×D5 | — | 2 | 12 | no | — |
| 125 | C22×SD16 | — | 10 | 3 | no | — |
| 126 | C22×D8 | — | 10 | 3 | no | — |
| 127 | H(3,𝔽4) | — | 5 | 3 | no | — |
| 128 | H(3,𝔽4) | — | 10 | 3 | no | — |
| 129 | H(3,𝔽4) | — | 10 | 3 | no | — |
| 130 | H(3,𝔽4) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 131 | C2×#127 | — | 5 | 1 | no | — |
| 132 | C2×#124 | — | 5 | 3 | no | — |
| 133 | C2×#124 | — | 10 | 3 | no | — |
| 134 | C2×#120 | — | 10 | 3 | no | — |
| 135 | #496 | — | 5 | 3 | no | — |
| 136 | #496 | — | 5 | 3 | no | — |
| 137 | #496 | — | 5 | 3 | no | — |
| 138 | #496 | — | 10 | 3 | no | — |
| 139 | #496 | — | 10 | 3 | no | — |
| 140 | #496 | C2×D5 | 1 | 3 | yes | complemented |
| 141 | C2×#97 | — | 5 | 3 | no | — |
| 142 | #329 | — | 5 | 3 | no | — |
| 143 | #329 | — | 5 | 6 | no | — |
| 144 | #329 | C2×D5 | 1 | 3 | yes | complemented |
| 145 | C23×C5 | — | 2 | 3 | no | — |
| 146 | C23×C5 | — | 4 | 1 | no | — |
| 147 | C23×C5 | — | 8 | 3 | no | — |
| 148 | C22×D5 | — | 2 | 3 | no | — |
| 149 | C22×D5 | — | 4 | 6 | no | — |
| 150 | C22×D5 | — | 4 | 12 | no | — |
| 151 | C22×D5 | — | 4 | 1 | no | — |
| 152 | C22×D5 | — | 8 | 6 | no | — |
| 153 | C22×D5 | — | 8 | 3 | no | — |
| 154 | C22×D5 | — | 8 | 16 | no | — |
| 155 | C22×D5 | — | 8 | 6 | no | — |
| 156 | C22×D5 | #120 | 1 | 1 | yes | characteristic |
| 157 | C5×Q8 | — | 4 | 3 | no | — |
| 158 | C5×D4 | — | 4 | 3 | no | — |
| 159 | C5×D4 | — | 4 | 3 | no | — |
| 160 | C5×D4 | — | 4 | 3 | no | — |
| 161 | C5×D4 | — | 8 | 3 | no | — |
| 162 | C2×C4×C5 | — | 2 | 3 | no | — |
| 163 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 164 | C22⋊D5 | — | 8 | 3 | no | — |
| 165 | C22⋊D5 | — | 8 | 6 | no | — |
| 166 | C22⋊D5 | — | 8 | 6 | no | — |
| 167 | C2×Dic5 | — | 2 | 3 | no | — |
| 168 | C2×Dic5 | #120 | 1 | 3 | yes | — |
| 169 | D20 | — | 4 | 3 | no | — |
| 170 | D20 | — | 4 | 3 | no | — |
| 171 | D20 | — | 4 | 3 | no | — |
| 172 | D20 | — | 8 | 3 | no | — |
| 173 | C4×D5 | — | 2 | 6 | no | — |
| 174 | C4×D5 | — | 4 | 6 | no | — |
| 175 | Dic10 | — | 4 | 3 | no | — |
| 176 | Dic10 | — | 8 | 3 | no | — |
| 177 | C5×C8 | — | 2 | 6 | no | — |
| 178 | #168 | — | 2 | 6 | no | — |
| 179 | C25 | — | 10 | 1 | no | — |
| 180 | C22×Q8 | — | 5 | 3 | no | — |
| 181 | C22×D4 | — | 5 | 3 | no | — |
| 182 | C22×D4 | — | 10 | 3 | no | — |
| 183 | C22×D4 | — | 10 | 3 | no | — |
| 184 | C2×SD16 | — | 2 | 3 | no | — |
| 185 | C2×SD16 | — | 10 | 3 | no | — |
| 186 | C2×SD16 | — | 10 | 3 | no | — |
| 187 | C2×SD16 | — | 10 | 3 | no | — |
| 188 | C2×SD16 | — | 20 | 12 | no | — |
| 189 | C2×D8 | — | 2 | 3 | no | — |
| 190 | C2×D8 | — | 10 | 3 | no | — |
| 191 | C2×D8 | — | 10 | 3 | no | — |
| 192 | C2×D8 | — | 10 | 3 | no | — |
| 193 | C2×D8 | — | 20 | 12 | no | — |
| 194 | C22×C8 | — | 10 | 3 | no | — |
| 195 | #127 | — | 5 | 1 | no | — |
| 196 | #127 | — | 10 | 3 | no | — |
| 197 | #127 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 198 | #124 | — | 2 | 3 | no | — |
| 199 | #124 | — | 5 | 3 | no | — |
| 200 | #124 | — | 5 | 3 | no | — |
| 201 | #124 | — | 5 | 3 | no | — |
| 202 | #124 | — | 10 | 3 | no | — |
| 203 | #124 | — | 10 | 6 | no | — |
| 204 | #124 | — | 10 | 6 | no | — |
| 205 | #124 | — | 10 | 6 | no | — |
| 206 | #124 | — | 10 | 3 | no | — |
| 207 | #124 | — | 10 | 3 | no | — |
| 208 | #124 | C22×D5 | 1 | 3 | yes | — |
| 209 | #120 | — | 2 | 3 | no | — |
| 210 | #120 | — | 10 | 6 | no | — |
| 211 | #120 | — | 10 | 3 | no | — |
| 212 | #120 | — | 10 | 6 | no | — |
| 213 | #120 | — | 10 | 3 | no | — |
| 214 | #120 | — | 10 | 3 | no | — |
| 215 | C2×C22⋊C4 | — | 10 | 6 | no | — |
| 216 | C2×C22⋊C4 | — | 10 | 3 | no | — |
| 217 | C2×C42 | — | 5 | 1 | no | — |
| 218 | C2×C42 | — | 10 | 1 | no | — |
| 219 | #97 | — | 5 | 3 | no | — |
| 220 | #97 | — | 10 | 3 | no | — |
| 221 | #97 | C22×D5 | 1 | 3 | yes | complemented |
| 222 | C22×C5 | — | 4 | 3 | no | — |
| 223 | C22×C5 | — | 4 | 6 | no | — |
| 224 | C22×C5 | — | 8 | 4 | no | — |
| 225 | C22×C5 | — | 8 | 3 | no | — |
| 226 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 227 | C2×D5 | — | 4 | 3 | no | — |
| 228 | C2×D5 | — | 4 | 6 | no | — |
| 229 | C2×D5 | — | 8 | 12 | no | — |
| 230 | C2×D5 | — | 8 | 12 | no | — |
| 231 | C2×D5 | — | 8 | 3 | no | — |
| 232 | C2×D5 | — | 16 | 4 | no | — |
| 233 | C2×D5 | #453 | 1 | 6 | yes | — |
| 234 | C4×C5 | — | 2 | 3 | no | — |
| 235 | C4×C5 | — | 4 | 3 | no | — |
| 236 | Dic5 | — | 2 | 3 | no | — |
| 237 | Dic5 | — | 4 | 3 | no | — |
| 238 | C24 | — | 2 | 1 | no | — |
| 239 | C24 | — | 10 | 3 | no | — |
| 240 | C24 | — | 10 | 3 | no | — |
| 241 | C24 | — | 20 | 1 | no | — |
| 242 | C24 | — | 40 | 6 | no | — |
| 243 | C2×Q8 | — | 5 | 3 | no | — |
| 244 | C2×Q8 | — | 10 | 3 | no | — |
| 245 | C2×Q8 | — | 20 | 6 | no | — |
| 246 | C2×Q8 | D4×D5 | 1 | 3 | yes | — |
| 247 | C2×D4 | — | 2 | 3 | no | — |
| 248 | C2×D4 | — | 2 | 3 | no | — |
| 249 | C2×D4 | — | 5 | 3 | no | — |
| 250 | C2×D4 | — | 10 | 3 | no | — |
| 251 | C2×D4 | — | 10 | 3 | no | — |
| 252 | C2×D4 | — | 10 | 6 | no | — |
| 253 | C2×D4 | — | 10 | 3 | no | — |
| 254 | C2×D4 | — | 20 | 3 | no | — |
| 255 | C2×D4 | — | 20 | 6 | no | — |
| 256 | C2×D4 | — | 20 | 6 | no | — |
| 257 | C2×D4 | — | 20 | 6 | no | — |
| 258 | C2×D4 | — | 40 | 6 | no | — |
| 259 | C2×D4 | D4×D5 | 1 | 3 | yes | — |
| 260 | C22×C4 | — | 5 | 3 | no | — |
| 261 | C22×C4 | — | 10 | 3 | no | — |
| 262 | SD16 | — | 4 | 6 | no | — |
| 263 | SD16 | — | 20 | 6 | no | — |
| 264 | SD16 | — | 20 | 6 | no | — |
| 265 | SD16 | — | 20 | 6 | no | — |
| 266 | D8 | — | 4 | 6 | no | — |
| 267 | D8 | — | 20 | 6 | no | — |
| 268 | D8 | — | 20 | 6 | no | — |
| 269 | D8 | — | 20 | 6 | no | — |
| 270 | C2×C8 | — | 2 | 3 | no | — |
| 271 | C2×C8 | — | 10 | 12 | no | — |
| 272 | C2×C8 | — | 10 | 3 | no | — |
| 273 | C22⋊C4 | — | 2 | 3 | no | — |
| 274 | C22⋊C4 | — | 2 | 6 | no | — |
| 275 | C22⋊C4 | — | 10 | 6 | no | — |
| 276 | C22⋊C4 | — | 10 | 6 | no | — |
| 277 | C22⋊C4 | — | 10 | 6 | no | — |
| 278 | C22⋊C4 | — | 10 | 3 | no | — |
| 279 | C22⋊C4 | — | 10 | 6 | no | — |
| 280 | C42 | — | 2 | 1 | no | — |
| 281 | C42 | — | 5 | 3 | no | — |
| 282 | C42 | — | 10 | 3 | no | — |
| 283 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 284 | C2×C5 | — | 8 | 3 | no | — |
| 285 | C2×C5 | — | 16 | 1 | no | — |
| 286 | C2×C5 | C2×#453 | 1 | 3 | yes | — |
| 287 | D5 | — | 8 | 3 | no | — |
| 288 | D5 | — | 16 | 1 | no | — |
| 289 | D5 | #1655 | 1 | 4 | yes | direct product factor |
| 290 | C23 | — | 2 | 3 | no | — |
| 291 | C23 | — | 4 | 1 | no | — |
| 292 | C23 | — | 5 | 1 | no | — |
| 293 | C23 | — | 8 | 3 | no | — |
| 294 | C23 | — | 10 | 3 | no | — |
| 295 | C23 | — | 20 | 6 | no | — |
| 296 | C23 | — | 20 | 12 | no | — |
| 297 | C23 | — | 20 | 1 | no | — |
| 298 | C23 | — | 40 | 3 | no | — |
| 299 | C23 | — | 40 | 6 | no | — |
| 300 | C23 | — | 40 | 6 | no | — |
| 301 | C23 | — | 40 | 16 | no | — |
| 302 | Q8 | — | 4 | 3 | no | — |
| 303 | Q8 | — | 20 | 3 | no | — |
| 304 | Q8 | — | 40 | 3 | no | — |
| 305 | D4 | — | 4 | 3 | no | — |
| 306 | D4 | — | 4 | 3 | no | — |
| 307 | D4 | — | 4 | 3 | no | — |
| 308 | D4 | — | 8 | 3 | no | — |
| 309 | D4 | — | 20 | 3 | no | — |
| 310 | D4 | — | 20 | 3 | no | — |
| 311 | D4 | — | 20 | 3 | no | — |
| 312 | D4 | — | 40 | 3 | no | — |
| 313 | D4 | — | 40 | 3 | no | — |
| 314 | D4 | — | 40 | 6 | no | — |
| 315 | D4 | — | 40 | 6 | no | — |
| 316 | C2×C4 | — | 2 | 3 | no | — |
| 317 | C2×C4 | — | 5 | 3 | no | — |
| 318 | C2×C4 | — | 10 | 6 | no | — |
| 319 | C2×C4 | — | 10 | 3 | no | — |
| 320 | C2×C4 | — | 20 | 6 | no | — |
| 321 | C2×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 322 | C8 | — | 2 | 6 | no | — |
| 323 | C8 | — | 10 | 6 | no | — |
| 324 | C5 | C2×#1655 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 325 | C22 | — | 4 | 3 | no | — |
| 326 | C22 | — | 4 | 6 | no | — |
| 327 | C22 | — | 5 | 6 | no | — |
| 328 | C22 | — | 8 | 4 | no | — |
| 329 | C22 | — | 8 | 3 | no | — |
| 330 | C22 | — | 20 | 3 | no | — |
| 331 | C22 | — | 20 | 6 | no | — |
| 332 | C22 | — | 40 | 12 | no | — |
| 333 | C22 | — | 40 | 12 | no | — |
| 334 | C22 | — | 40 | 3 | no | — |
| 335 | C22 | — | 80 | 4 | no | — |
| 336 | C22 | D5×#120 | 1 | 1 | yes | characteristic |
| 337 | C4 | — | 2 | 3 | no | — |
| 338 | C4 | — | 4 | 3 | no | — |
| 339 | C4 | — | 10 | 3 | no | — |
| 340 | C4 | — | 20 | 3 | no | — |
| 341 | C2 | — | 5 | 4 | no | — |
| 342 | C2 | — | 8 | 3 | no | — |
| 343 | C2 | — | 16 | 1 | no | — |
| 344 | C2 | — | 40 | 3 | no | — |
| 345 | C2 | — | 80 | 1 | no | — |
| 346 | C2 | D5×#453 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D5×#120 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#1655 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #1655 | D5 |
| hypocenter | C5 | C2×#1655 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1655 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D5×H(3,𝔽4) | C2 | semidirect |
| 2. D5×#496 | C2 | semidirect |
| 3. C5×#1655 | C2 | semidirect |
| 4. #10602741 | C2 | semidirect |
| 5. #10602119 | C2 | semidirect |
| 6. #10599143 | C2 | semidirect |
| 7. D5×#329 | C2 | semidirect |
| 8. C5×H(3,𝔽4) | C22 | semidirect |
| 11. D5×#127 | C22 | semidirect |
| 13. #66017 | C22 | semidirect |
| 18. C5×#496 | C22 | semidirect |
| 21. #65363 | C22 | semidirect |
| 22. #65347 | C22 | semidirect |
| 23. #65001 | C22 | semidirect |
| 24. D5×#97 | C22 | semidirect |
| 25. C5×#329 | C22 | semidirect |
| 26. #64760 | C22 | semidirect |
| 27. #64684 | C22 | semidirect |
| 36. C5×#127 | C23 | semidirect |
| 66. #4020 | C23 | semidirect |
| 69. C5×#97 | C23 | semidirect |
| 71. #3935 | C23 | semidirect |
| 77. #1655 | D5 | direct (N × H) |
| 130. H(3,𝔽4) | C2×D5 | semidirect |
| 140. #496 | C2×D5 | semidirect |
| 144. #329 | C2×D5 | semidirect |
| 197. #127 | C22×D5 | semidirect |
| 221. #97 | C22×D5 | semidirect |
| 289. D5 | #1655 | direct (N × H) |
| 324. C5 | C2×#1655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×H(3,𝔽4) | 2 |
| D5×#496 | 2 |
| C5×#1655 | 2 |
| #10602741 | 2 |
| #10602119 | 2 |
| #10599143 | 2 |
| D5×#329 | 2 |
| C2×#1655 | 5 |