Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1078 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #10618988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10613581 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10613575 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#1655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602742 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602119 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10602119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10599146 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10599145 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10599142 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10599138 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C5×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#4062 | — | 2 | 1 | no | — |
| 14 | C2×#4058 | — | 2 | 1 | no | — |
| 15 | #66050 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #66017 | C22 | 1 | 2 | yes | — |
| 17 | #66017 | C22 | 1 | 1 | yes | characteristic |
| 18 | #66008 | — | 2 | 1 | no | — |
| 19 | #66008 | — | 2 | 2 | no | — |
| 20 | #66004 | — | 2 | 2 | no | — |
| 21 | #66004 | — | 2 | 1 | no | — |
| 22 | #66002 | C22 | 1 | 1 | yes | characteristic |
| 23 | #66002 | C22 | 1 | 2 | yes | — |
| 24 | #65926 | — | 2 | 1 | no | — |
| 25 | #65926 | — | 2 | 2 | no | — |
| 26 | #65924 | — | 2 | 2 | no | — |
| 27 | #65924 | — | 2 | 1 | no | — |
| 28 | C5×#496 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C5×#496 | C22 | 1 | 2 | yes | complemented |
| 30 | #65461 | — | 2 | 2 | no | — |
| 31 | #65456 | — | 2 | 1 | no | — |
| 32 | #65451 | — | 2 | 2 | no | — |
| 33 | #65447 | — | 2 | 2 | no | — |
| 34 | #65443 | — | 2 | 1 | no | — |
| 35 | #65439 | — | 2 | 2 | no | — |
| 36 | #65363 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #65363 | C22 | 1 | 2 | yes | complemented |
| 38 | #65349 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #65344 | C22 | 1 | 2 | yes | complemented |
| 40 | #65004 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #65003 | C22 | 1 | 2 | yes | complemented |
| 42 | #64994 | C22 | 1 | 2 | yes | complemented |
| 43 | D5×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C5×#329 | C22 | 1 | 2 | yes | complemented |
| 45 | C5×#329 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #64760 | C22 | 1 | 2 | yes | complemented |
| 47 | #64760 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #64684 | C22 | 1 | 2 | yes | complemented |
| 49 | #64684 | C22 | 1 | 2 | yes | complemented |
| 50 | #64684 | C22 | 1 | 2 | yes | complemented |
| 51 | #19052 | — | 5 | 1 | no | maximal, Sylow |
| 52 | C22×C22⋊D5 | — | 2 | 2 | no | — |
| 53 | C22×C22⋊D5 | — | 2 | 1 | no | — |
| 54 | C2×#713 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×#713 | D4 | 1 | 2 | yes | — |
| 56 | C2×#711 | — | 2 | 1 | no | — |
| 57 | C2×#711 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×#711 | D4 | 1 | 2 | yes | — |
| 59 | C2×D4×D5 | — | 2 | 2 | no | — |
| 60 | C2×D4×D5 | — | 2 | 1 | no | — |
| 61 | C2×C5×SD16 | — | 2 | 1 | no | — |
| 62 | C2×C5×SD16 | — | 2 | 2 | no | — |
| 63 | C2×C5×D8 | — | 2 | 1 | no | — |
| 64 | C2×C5×D8 | — | 2 | 2 | no | — |
| 65 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 66 | C5×#124 | — | 2 | 2 | no | — |
| 67 | C5×#124 | — | 2 | 1 | no | — |
| 68 | C5×#124 | C23 | 1 | 2 | yes | — |
| 69 | C5×#124 | C23 | 1 | 1 | yes | characteristic |
| 70 | C5×#120 | — | 2 | 2 | no | — |
| 71 | C5×#120 | — | 2 | 1 | no | — |
| 72 | #4099 | — | 2 | 1 | no | — |
| 73 | #4093 | — | 2 | 2 | no | — |
| 74 | #4093 | — | 2 | 1 | no | — |
| 75 | #4090 | D4 | 1 | 2 | yes | — |
| 76 | #4090 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#689 | — | 2 | 1 | no | — |
| 78 | #4086 | — | 2 | 1 | no | — |
| 79 | #4086 | — | 2 | 2 | no | — |
| 80 | #4086 | D4 | 1 | 2 | yes | — |
| 81 | #4086 | D4 | 1 | 1 | yes | characteristic |
| 82 | #4085 | — | 2 | 2 | no | — |
| 83 | #4085 | — | 2 | 2 | no | — |
| 84 | #4085 | — | 2 | 2 | no | — |
| 85 | #4084 | — | 2 | 2 | no | — |
| 86 | #4083 | — | 2 | 2 | no | — |
| 87 | #4083 | — | 2 | 1 | no | — |
| 88 | #4082 | — | 2 | 1 | no | — |
| 89 | D4×Dic5 | — | 2 | 2 | no | — |
| 90 | C2×#687 | — | 2 | 1 | no | — |
| 91 | C2×#687 | — | 2 | 1 | no | — |
| 92 | C2×#687 | — | 2 | 2 | no | — |
| 93 | C2×#686 | — | 2 | 1 | no | — |
| 94 | C2×#686 | — | 2 | 2 | no | — |
| 95 | #4062 | — | 4 | 4 | no | — |
| 96 | #4058 | — | 4 | 4 | no | — |
| 97 | C2×Dic20 | — | 2 | 1 | no | — |
| 98 | C2×#677 | — | 2 | 1 | no | — |
| 99 | C2×C8×D5 | — | 2 | 1 | no | — |
| 100 | #4031 | — | 2 | 2 | no | — |
| 101 | #4031 | — | 2 | 2 | no | — |
| 102 | #4031 | — | 2 | 2 | no | — |
| 103 | #4030 | — | 2 | 2 | no | — |
| 104 | #4030 | — | 2 | 2 | no | — |
| 105 | #4030 | — | 2 | 2 | no | — |
| 106 | #4030 | — | 2 | 2 | no | — |
| 107 | #4030 | — | 2 | 2 | no | — |
| 108 | #4030 | — | 2 | 2 | no | — |
| 109 | #4028 | — | 2 | 2 | no | — |
| 110 | #4028 | — | 2 | 1 | no | — |
| 111 | #4028 | — | 2 | 2 | no | — |
| 112 | #4028 | — | 2 | 2 | no | — |
| 113 | #4028 | — | 2 | 2 | no | — |
| 114 | #4027 | — | 2 | 2 | no | — |
| 115 | #4027 | — | 2 | 2 | no | — |
| 116 | #4027 | — | 2 | 2 | no | — |
| 117 | #4023 | — | 2 | 2 | no | — |
| 118 | #4023 | — | 2 | 1 | no | — |
| 119 | #4021 | C23 | 1 | 2 | yes | — |
| 120 | #4021 | C23 | 1 | 1 | yes | characteristic |
| 121 | #4020 | — | 2 | 1 | no | — |
| 122 | #4018 | — | 2 | 2 | no | — |
| 123 | #4018 | — | 2 | 1 | no | — |
| 124 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 125 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 126 | C5×#97 | C23 | 1 | 1 | yes | characteristic |
| 127 | C5×#97 | C23 | 1 | 2 | yes | — |
| 128 | #3967 | — | 2 | 2 | no | — |
| 129 | #3964 | — | 2 | 2 | no | — |
| 130 | #3953 | — | 2 | 2 | no | — |
| 131 | #3952 | — | 2 | 2 | no | — |
| 132 | #3948 | — | 2 | 2 | no | — |
| 133 | #3947 | — | 2 | 1 | no | — |
| 134 | #3946 | — | 2 | 2 | no | — |
| 135 | #3935 | C23 | 1 | 2 | yes | — |
| 136 | #3935 | C23 | 1 | 1 | yes | characteristic |
| 137 | #3549 | — | 5 | 1 | no | — |
| 138 | #3214 | — | 5 | 2 | no | — |
| 139 | #3150 | — | 5 | 1 | no | — |
| 140 | #1659 | — | 5 | 2 | no | — |
| 141 | #1659 | — | 5 | 1 | no | — |
| 142 | #1659 | — | 5 | 1 | no | — |
| 143 | #1655 | — | 5 | 1 | no | — |
| 144 | #1655 | — | 5 | 2 | no | — |
| 145 | #1655 | D5 | 1 | 1 | yes | characteristic, complemented |
| 146 | #1536 | — | 5 | 1 | no | — |
| 147 | #1530 | — | 5 | 2 | no | — |
| 148 | C24×C5 | — | 2 | 1 | no | — |
| 149 | C23×D5 | — | 2 | 2 | no | — |
| 150 | C23×D5 | — | 2 | 1 | no | — |
| 151 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 152 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×C5×D4 | — | 2 | 1 | no | — |
| 154 | C2×C5×D4 | — | 2 | 2 | no | — |
| 155 | C2×C5×D4 | — | 2 | 1 | no | — |
| 156 | C2×C5×D4 | — | 2 | 2 | no | — |
| 157 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C5×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 160 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 161 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 162 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 163 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 164 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 165 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 166 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 167 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 168 | C2×C22⋊D5 | — | 8 | 4 | no | — |
| 169 | C2×C22⋊D5 | — | 8 | 2 | no | — |
| 170 | C22×Dic5 | — | 2 | 2 | no | — |
| 171 | C22×Dic5 | — | 2 | 1 | no | — |
| 172 | C22×Dic5 | — | 4 | 1 | no | — |
| 173 | #713 | — | 4 | 2 | no | — |
| 174 | #713 | — | 8 | 2 | no | — |
| 175 | #711 | — | 4 | 2 | no | — |
| 176 | #711 | — | 4 | 2 | no | — |
| 177 | #711 | — | 4 | 2 | no | — |
| 178 | #711 | — | 8 | 2 | no | — |
| 179 | D4×D5 | — | 8 | 4 | no | — |
| 180 | D4×D5 | — | 8 | 2 | no | — |
| 181 | C2×D20 | — | 2 | 1 | no | — |
| 182 | C2×D20 | — | 2 | 2 | no | — |
| 183 | C2×D20 | — | 2 | 1 | no | — |
| 184 | C2×D20 | — | 2 | 2 | no | — |
| 185 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 186 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×D5 | — | 2 | 2 | no | — |
| 188 | C2×C4×D5 | — | 2 | 1 | no | — |
| 189 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 191 | C2×Dic10 | — | 2 | 1 | no | — |
| 192 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 193 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C5×SD16 | — | 4 | 2 | no | — |
| 195 | C5×SD16 | — | 8 | 2 | no | — |
| 196 | C5×D8 | — | 4 | 2 | no | — |
| 197 | C5×D8 | — | 8 | 2 | no | — |
| 198 | C2×C5×C8 | — | 2 | 1 | no | — |
| 199 | C2×C5×C8 | — | 2 | 2 | no | — |
| 200 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 201 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 202 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 203 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 204 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 205 | C42×C5 | — | 2 | 1 | no | — |
| 206 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 207 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 208 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 209 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 210 | #689 | — | 4 | 2 | no | — |
| 211 | #687 | — | 4 | 2 | no | — |
| 212 | #687 | — | 4 | 2 | no | — |
| 213 | #687 | — | 8 | 2 | no | — |
| 214 | #686 | — | 4 | 2 | no | — |
| 215 | #686 | — | 8 | 2 | no | — |
| 216 | #685 | — | 2 | 2 | no | — |
| 217 | #685 | — | 2 | 2 | no | — |
| 218 | #685 | — | 2 | 2 | no | — |
| 219 | #685 | — | 2 | 2 | no | — |
| 220 | #685 | — | 2 | 2 | no | — |
| 221 | #685 | — | 2 | 2 | no | — |
| 222 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 223 | #683 | — | 2 | 2 | no | — |
| 224 | #683 | — | 2 | 2 | no | — |
| 225 | #683 | — | 2 | 2 | no | — |
| 226 | C4×Dic5 | — | 2 | 2 | no | — |
| 227 | C4×Dic5 | — | 2 | 1 | no | — |
| 228 | C4×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 229 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×#168 | — | 2 | 1 | no | — |
| 231 | C2×#168 | — | 2 | 2 | no | — |
| 232 | Dic20 | — | 4 | 2 | no | — |
| 233 | #677 | — | 4 | 2 | no | — |
| 234 | C8×D5 | — | 2 | 4 | no | — |
| 235 | C2×#135 | — | 10 | 1 | no | — |
| 236 | C2×#135 | — | 10 | 1 | no | — |
| 237 | H(3,𝔽4) | — | 5 | 1 | no | — |
| 238 | H(3,𝔽4) | — | 5 | 2 | no | — |
| 239 | H(3,𝔽4) | C2×D5 | 1 | 1 | yes | characteristic |
| 240 | #555 | — | 10 | 2 | no | — |
| 241 | #555 | — | 10 | 1 | no | — |
| 242 | D42 | — | 10 | 2 | no | — |
| 243 | D42 | — | 10 | 1 | no | — |
| 244 | #535 | — | 10 | 1 | no | — |
| 245 | #535 | — | 10 | 2 | no | — |
| 246 | #535 | — | 10 | 1 | no | — |
| 247 | #535 | — | 10 | 2 | no | — |
| 248 | #532 | — | 5 | 1 | no | — |
| 249 | #532 | — | 5 | 2 | no | — |
| 250 | #532 | — | 5 | 1 | no | — |
| 251 | #497 | — | 5 | 1 | no | — |
| 252 | #497 | — | 5 | 1 | no | — |
| 253 | #497 | — | 10 | 1 | no | — |
| 254 | #496 | — | 5 | 1 | no | — |
| 255 | #496 | — | 5 | 2 | no | — |
| 256 | #496 | — | 10 | 1 | no | — |
| 257 | #496 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 258 | #496 | C2×D5 | 1 | 2 | yes | complemented |
| 259 | #489 | — | 5 | 2 | no | — |
| 260 | #489 | — | 5 | 2 | no | — |
| 261 | #461 | — | 10 | 2 | no | — |
| 262 | #459 | — | 10 | 2 | no | — |
| 263 | #449 | — | 10 | 2 | no | — |
| 264 | #449 | — | 10 | 2 | no | — |
| 265 | #432 | — | 5 | 2 | no | — |
| 266 | C2×#97 | — | 5 | 1 | no | — |
| 267 | #329 | — | 5 | 1 | no | — |
| 268 | #329 | — | 5 | 2 | no | — |
| 269 | #329 | — | 5 | 2 | no | — |
| 270 | #329 | — | 5 | 2 | no | — |
| 271 | #329 | — | 5 | 2 | no | — |
| 272 | #329 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 273 | #329 | C2×D5 | 1 | 2 | yes | complemented |
| 274 | C23×C5 | — | 2 | 1 | no | — |
| 275 | C23×C5 | — | 2 | 2 | no | — |
| 276 | C23×C5 | — | 4 | 1 | no | — |
| 277 | C23×C5 | — | 8 | 1 | no | — |
| 278 | C23×C5 | — | 8 | 2 | no | — |
| 279 | C22×D5 | — | 2 | 1 | no | — |
| 280 | C22×D5 | — | 2 | 2 | no | — |
| 281 | C22×D5 | — | 8 | 2 | no | — |
| 282 | C22×D5 | — | 8 | 2 | no | — |
| 283 | C22×D5 | — | 8 | 2 | no | — |
| 284 | C22×D5 | — | 8 | 1 | no | — |
| 285 | C22×D5 | — | 8 | 2 | no | — |
| 286 | C22×D5 | #120 | 1 | 1 | yes | characteristic |
| 287 | C5×Q8 | — | 4 | 1 | no | — |
| 288 | C5×Q8 | — | 4 | 2 | no | — |
| 289 | C5×D4 | — | 4 | 1 | no | — |
| 290 | C5×D4 | — | 4 | 2 | no | — |
| 291 | C5×D4 | — | 4 | 1 | no | — |
| 292 | C5×D4 | — | 4 | 2 | no | — |
| 293 | C5×D4 | — | 4 | 1 | no | — |
| 294 | C5×D4 | — | 4 | 2 | no | — |
| 295 | C5×D4 | — | 8 | 1 | no | — |
| 296 | C5×D4 | — | 8 | 2 | no | — |
| 297 | C2×C4×C5 | — | 2 | 1 | no | — |
| 298 | C2×C4×C5 | — | 2 | 2 | no | — |
| 299 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 300 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C22⋊D5 | — | 4 | 4 | no | — |
| 302 | C22⋊D5 | — | 4 | 4 | no | — |
| 303 | C22⋊D5 | — | 4 | 4 | no | — |
| 304 | C22⋊D5 | — | 8 | 1 | no | — |
| 305 | C22⋊D5 | — | 8 | 2 | no | — |
| 306 | C22⋊D5 | — | 8 | 2 | no | — |
| 307 | C22⋊D5 | — | 8 | 2 | no | — |
| 308 | C22⋊D5 | — | 8 | 2 | no | — |
| 309 | C22⋊D5 | — | 8 | 2 | no | — |
| 310 | C2×Dic5 | — | 2 | 1 | no | — |
| 311 | C2×Dic5 | — | 2 | 2 | no | — |
| 312 | C2×Dic5 | — | 4 | 4 | no | — |
| 313 | C2×Dic5 | — | 4 | 2 | no | — |
| 314 | C2×Dic5 | — | 4 | 1 | no | — |
| 315 | C2×Dic5 | — | 8 | 2 | no | — |
| 316 | C2×Dic5 | #120 | 1 | 2 | yes | — |
| 317 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 318 | D20 | — | 4 | 1 | no | — |
| 319 | D20 | — | 4 | 2 | no | — |
| 320 | D20 | — | 8 | 1 | no | — |
| 321 | D20 | — | 8 | 2 | no | — |
| 322 | D20 | — | 8 | 1 | no | — |
| 323 | D20 | — | 8 | 2 | no | — |
| 324 | C4×D5 | — | 2 | 2 | no | — |
| 325 | C4×D5 | — | 4 | 2 | no | — |
| 326 | C4×D5 | — | 4 | 4 | no | — |
| 327 | C4×D5 | — | 4 | 2 | no | — |
| 328 | Dic10 | — | 4 | 1 | no | — |
| 329 | Dic10 | — | 4 | 2 | no | — |
| 330 | Dic10 | — | 4 | 1 | no | — |
| 331 | Dic10 | — | 4 | 1 | no | — |
| 332 | C5×C8 | — | 2 | 2 | no | — |
| 333 | C5×C8 | — | 4 | 2 | no | — |
| 334 | #168 | — | 2 | 2 | no | — |
| 335 | #168 | — | 4 | 2 | no | — |
| 336 | C2×#41 | — | 5 | 1 | no | — |
| 337 | C2×#41 | — | 5 | 2 | no | — |
| 338 | C2×#41 | — | 5 | 1 | no | — |
| 339 | C2×#41 | — | 5 | 2 | no | — |
| 340 | C2×#41 | — | 10 | 1 | no | — |
| 341 | C22×D4 | — | 10 | 1 | no | — |
| 342 | C22×D4 | — | 10 | 2 | no | — |
| 343 | C22×D4 | — | 10 | 1 | no | — |
| 344 | C22×D4 | — | 10 | 2 | no | — |
| 345 | #135 | — | 20 | 4 | no | — |
| 346 | #135 | — | 20 | 4 | no | — |
| 347 | C2×Q16 | — | 10 | 1 | no | — |
| 348 | C2×Q16 | — | 10 | 1 | no | — |
| 349 | C2×SD16 | — | 2 | 1 | no | — |
| 350 | C2×SD16 | — | 2 | 2 | no | — |
| 351 | C2×SD16 | — | 10 | 1 | no | — |
| 352 | C2×SD16 | — | 10 | 1 | no | — |
| 353 | C2×SD16 | — | 10 | 1 | no | — |
| 354 | C2×SD16 | — | 10 | 2 | no | — |
| 355 | C2×D8 | — | 2 | 1 | no | — |
| 356 | C2×D8 | — | 2 | 2 | no | — |
| 357 | C2×D8 | — | 10 | 1 | no | — |
| 358 | C2×D8 | — | 10 | 2 | no | — |
| 359 | C22×C8 | — | 10 | 1 | no | — |
| 360 | C4⋊Q8 | — | 5 | 2 | no | — |
| 361 | C4⋊Q8 | — | 5 | 1 | no | — |
| 362 | C4⋊Q8 | — | 5 | 1 | no | — |
| 363 | #127 | — | 5 | 2 | no | — |
| 364 | #127 | — | 5 | 1 | no | — |
| 365 | #127 | — | 10 | 1 | no | — |
| 366 | #127 | — | 10 | 1 | no | — |
| 367 | #127 | — | 10 | 2 | no | — |
| 368 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 369 | #124 | — | 2 | 2 | no | — |
| 370 | #124 | — | 2 | 1 | no | — |
| 371 | #124 | — | 5 | 2 | no | — |
| 372 | #124 | — | 5 | 1 | no | — |
| 373 | #124 | — | 10 | 1 | no | — |
| 374 | #124 | — | 10 | 2 | no | — |
| 375 | #124 | — | 10 | 2 | no | — |
| 376 | #124 | — | 10 | 2 | no | — |
| 377 | #124 | — | 10 | 2 | no | — |
| 378 | #124 | — | 10 | 1 | no | — |
| 379 | #124 | C22×D5 | 1 | 2 | yes | — |
| 380 | #124 | C22×D5 | 1 | 1 | yes | characteristic |
| 381 | #121 | — | 10 | 2 | no | — |
| 382 | #121 | — | 10 | 2 | no | — |
| 383 | #121 | — | 10 | 2 | no | — |
| 384 | #121 | — | 10 | 2 | no | — |
| 385 | #121 | — | 10 | 2 | no | — |
| 386 | #121 | — | 10 | 2 | no | — |
| 387 | #121 | — | 10 | 2 | no | — |
| 388 | #121 | — | 10 | 2 | no | — |
| 389 | #121 | — | 10 | 2 | no | — |
| 390 | #121 | — | 10 | 2 | no | — |
| 391 | #120 | — | 2 | 2 | no | — |
| 392 | #120 | — | 2 | 1 | no | — |
| 393 | #120 | — | 10 | 2 | no | — |
| 394 | #120 | — | 10 | 2 | no | — |
| 395 | #120 | — | 10 | 2 | no | — |
| 396 | #120 | — | 10 | 2 | no | — |
| 397 | #120 | — | 10 | 1 | no | — |
| 398 | #120 | — | 10 | 1 | no | — |
| 399 | #120 | — | 10 | 2 | no | — |
| 400 | #120 | — | 10 | 1 | no | — |
| 401 | C4×D4 | — | 10 | 2 | no | — |
| 402 | C4×D4 | — | 10 | 2 | no | — |
| 403 | C4×D4 | — | 10 | 2 | no | — |
| 404 | C4×D4 | — | 10 | 2 | no | — |
| 405 | #117 | — | 10 | 1 | no | — |
| 406 | #117 | — | 10 | 2 | no | — |
| 407 | #117 | — | 10 | 1 | no | — |
| 408 | #117 | — | 10 | 2 | no | — |
| 409 | C2×C42 | — | 5 | 1 | no | — |
| 410 | C4⋊C8 | — | 10 | 2 | no | — |
| 411 | #103 | — | 10 | 2 | no | — |
| 412 | #103 | — | 10 | 2 | no | — |
| 413 | #102 | — | 10 | 2 | no | — |
| 414 | #102 | — | 10 | 2 | no | — |
| 415 | C22⋊C8 | — | 10 | 2 | no | — |
| 416 | #97 | — | 5 | 1 | no | — |
| 417 | #97 | — | 5 | 2 | no | — |
| 418 | #97 | — | 10 | 1 | no | — |
| 419 | #97 | C22×D5 | 1 | 1 | yes | characteristic |
| 420 | #97 | C22×D5 | 1 | 2 | yes | — |
| 421 | C22×C5 | — | 4 | 1 | no | — |
| 422 | C22×C5 | — | 4 | 2 | no | — |
| 423 | C22×C5 | — | 4 | 2 | no | — |
| 424 | C22×C5 | — | 4 | 2 | no | — |
| 425 | C22×C5 | — | 4 | 2 | no | — |
| 426 | C22×C5 | — | 8 | 1 | no | — |
| 427 | C22×C5 | — | 8 | 2 | no | — |
| 428 | C22×C5 | — | 16 | 2 | no | — |
| 429 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 430 | C2×D5 | — | 2 | 1 | no | — |
| 431 | C2×D5 | — | 2 | 2 | no | — |
| 432 | C2×D5 | — | 4 | 1 | no | — |
| 433 | C2×D5 | — | 4 | 2 | no | — |
| 434 | C2×D5 | — | 4 | 2 | no | — |
| 435 | C2×D5 | — | 4 | 2 | no | — |
| 436 | C2×D5 | — | 4 | 2 | no | — |
| 437 | C2×D5 | — | 16 | 4 | no | — |
| 438 | C2×D5 | — | 16 | 2 | no | — |
| 439 | C4×C5 | — | 2 | 1 | no | — |
| 440 | C4×C5 | — | 2 | 2 | no | — |
| 441 | C4×C5 | — | 4 | 1 | no | — |
| 442 | C4×C5 | — | 4 | 2 | no | — |
| 443 | Dic5 | — | 2 | 2 | no | — |
| 444 | Dic5 | — | 4 | 1 | no | — |
| 445 | Dic5 | — | 4 | 2 | no | — |
| 446 | Dic5 | — | 8 | 1 | no | — |
| 447 | Dic5 | #453 | 1 | 2 | yes | — |
| 448 | C24 | — | 2 | 1 | no | — |
| 449 | C24 | — | 10 | 1 | no | — |
| 450 | C24 | — | 10 | 2 | no | — |
| 451 | #41 | — | 20 | 2 | no | — |
| 452 | #41 | — | 20 | 2 | no | — |
| 453 | #41 | — | 20 | 2 | no | — |
| 454 | #41 | — | 20 | 2 | no | — |
| 455 | #41 | — | 40 | 2 | no | — |
| 456 | #41 | — | 40 | 2 | no | — |
| 457 | C2×Q8 | — | 5 | 2 | no | — |
| 458 | C2×Q8 | — | 5 | 1 | no | — |
| 459 | C2×Q8 | — | 10 | 1 | no | — |
| 460 | C2×Q8 | D4×D5 | 1 | 2 | yes | — |
| 461 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 462 | C2×D4 | — | 2 | 1 | no | — |
| 463 | C2×D4 | — | 2 | 2 | no | — |
| 464 | C2×D4 | — | 2 | 2 | no | — |
| 465 | C2×D4 | — | 2 | 1 | no | — |
| 466 | C2×D4 | — | 5 | 2 | no | — |
| 467 | C2×D4 | — | 5 | 1 | no | — |
| 468 | C2×D4 | — | 10 | 1 | no | — |
| 469 | C2×D4 | — | 10 | 2 | no | — |
| 470 | C2×D4 | — | 10 | 1 | no | — |
| 471 | C2×D4 | — | 10 | 2 | no | — |
| 472 | C2×D4 | — | 10 | 2 | no | — |
| 473 | C2×D4 | — | 10 | 2 | no | — |
| 474 | C2×D4 | — | 10 | 2 | no | — |
| 475 | C2×D4 | — | 10 | 1 | no | — |
| 476 | C2×D4 | — | 10 | 2 | no | — |
| 477 | C2×D4 | — | 10 | 2 | no | — |
| 478 | C2×D4 | — | 10 | 2 | no | — |
| 479 | C2×D4 | — | 10 | 2 | no | — |
| 480 | C2×D4 | — | 20 | 1 | no | — |
| 481 | C2×D4 | — | 40 | 2 | no | — |
| 482 | C2×D4 | — | 40 | 4 | no | — |
| 483 | C2×D4 | — | 40 | 2 | no | — |
| 484 | C2×D4 | — | 40 | 4 | no | — |
| 485 | C2×D4 | D4×D5 | 1 | 2 | yes | — |
| 486 | C2×D4 | D4×D5 | 1 | 1 | yes | characteristic |
| 487 | C22×C4 | — | 5 | 1 | no | — |
| 488 | C22×C4 | — | 5 | 2 | no | — |
| 489 | C22×C4 | — | 10 | 1 | no | — |
| 490 | C22×C4 | — | 10 | 2 | no | — |
| 491 | C22×C4 | — | 10 | 1 | no | — |
| 492 | C22×C4 | — | 10 | 2 | no | — |
| 493 | C22×C4 | — | 20 | 1 | no | — |
| 494 | Q16 | — | 20 | 2 | no | — |
| 495 | Q16 | — | 20 | 2 | no | — |
| 496 | SD16 | — | 4 | 2 | no | — |
| 497 | SD16 | — | 8 | 2 | no | — |
| 498 | SD16 | — | 20 | 2 | no | — |
| 499 | SD16 | — | 20 | 2 | no | — |
| 500 | SD16 | — | 20 | 2 | no | — |
| 501 | SD16 | — | 40 | 2 | no | — |
| 502 | D8 | — | 4 | 2 | no | — |
| 503 | D8 | — | 8 | 2 | no | — |
| 504 | D8 | — | 20 | 2 | no | — |
| 505 | D8 | — | 40 | 2 | no | — |
| 506 | C2×C8 | — | 2 | 1 | no | — |
| 507 | C2×C8 | — | 2 | 2 | no | — |
| 508 | C2×C8 | — | 10 | 4 | no | — |
| 509 | C2×C8 | — | 10 | 1 | no | — |
| 510 | C2×C8 | — | 10 | 2 | no | — |
| 511 | C4⋊C4 | — | 10 | 2 | no | — |
| 512 | C4⋊C4 | — | 10 | 2 | no | — |
| 513 | C4⋊C4 | — | 10 | 2 | no | — |
| 514 | C4⋊C4 | — | 10 | 2 | no | — |
| 515 | C22⋊C4 | — | 2 | 2 | no | — |
| 516 | C22⋊C4 | — | 2 | 1 | no | — |
| 517 | C22⋊C4 | — | 2 | 2 | no | — |
| 518 | C22⋊C4 | — | 2 | 2 | no | — |
| 519 | C22⋊C4 | — | 2 | 2 | no | — |
| 520 | C22⋊C4 | — | 10 | 2 | no | — |
| 521 | C22⋊C4 | — | 10 | 2 | no | — |
| 522 | C22⋊C4 | — | 10 | 2 | no | — |
| 523 | C22⋊C4 | — | 10 | 2 | no | — |
| 524 | C22⋊C4 | — | 10 | 1 | no | — |
| 525 | C22⋊C4 | — | 10 | 2 | no | — |
| 526 | C22⋊C4 | — | 10 | 2 | no | — |
| 527 | C22⋊C4 | — | 10 | 2 | no | — |
| 528 | C22⋊C4 | — | 20 | 2 | no | — |
| 529 | C42 | — | 2 | 1 | no | — |
| 530 | C42 | — | 5 | 1 | no | — |
| 531 | C42 | — | 5 | 2 | no | — |
| 532 | C42 | — | 10 | 1 | no | — |
| 533 | C42 | — | 10 | 2 | no | — |
| 534 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 535 | C2×C5 | — | 8 | 1 | no | — |
| 536 | C2×C5 | — | 8 | 2 | no | — |
| 537 | C2×C5 | — | 16 | 1 | no | — |
| 538 | C2×C5 | C2×#453 | 1 | 1 | yes | characteristic |
| 539 | C2×C5 | #3019 | 1 | 2 | yes | — |
| 540 | D5 | — | 4 | 1 | no | — |
| 541 | D5 | — | 8 | 1 | no | — |
| 542 | D5 | — | 8 | 2 | no | — |
| 543 | C23 | — | 2 | 1 | no | — |
| 544 | C23 | — | 2 | 2 | no | — |
| 545 | C23 | — | 4 | 1 | no | — |
| 546 | C23 | — | 5 | 1 | no | — |
| 547 | C23 | — | 8 | 1 | no | — |
| 548 | C23 | — | 8 | 2 | no | — |
| 549 | C23 | — | 10 | 1 | no | — |
| 550 | C23 | — | 10 | 2 | no | — |
| 551 | C23 | — | 40 | 1 | no | — |
| 552 | C23 | — | 40 | 2 | no | — |
| 553 | C23 | — | 40 | 2 | no | — |
| 554 | C23 | — | 40 | 2 | no | — |
| 555 | C23 | — | 40 | 2 | no | — |
| 556 | Q8 | — | 4 | 1 | no | — |
| 557 | Q8 | — | 4 | 2 | no | — |
| 558 | Q8 | — | 20 | 1 | no | — |
| 559 | Q8 | — | 20 | 2 | no | — |
| 560 | Q8 | — | 20 | 1 | no | — |
| 561 | Q8 | — | 20 | 1 | no | — |
| 562 | D4 | — | 4 | 1 | no | — |
| 563 | D4 | — | 4 | 2 | no | — |
| 564 | D4 | — | 4 | 1 | no | — |
| 565 | D4 | — | 4 | 2 | no | — |
| 566 | D4 | — | 4 | 1 | no | — |
| 567 | D4 | — | 4 | 2 | no | — |
| 568 | D4 | — | 8 | 1 | no | — |
| 569 | D4 | — | 8 | 2 | no | — |
| 570 | D4 | — | 20 | 1 | no | — |
| 571 | D4 | — | 20 | 2 | no | — |
| 572 | D4 | — | 20 | 4 | no | — |
| 573 | D4 | — | 20 | 4 | no | — |
| 574 | D4 | — | 20 | 4 | no | — |
| 575 | D4 | — | 40 | 1 | no | — |
| 576 | D4 | — | 40 | 2 | no | — |
| 577 | D4 | — | 40 | 1 | no | — |
| 578 | D4 | — | 40 | 2 | no | — |
| 579 | D4 | — | 40 | 1 | no | — |
| 580 | D4 | — | 40 | 2 | no | — |
| 581 | D4 | — | 40 | 2 | no | — |
| 582 | D4 | — | 40 | 2 | no | — |
| 583 | D4 | — | 40 | 2 | no | — |
| 584 | D4 | — | 40 | 2 | no | — |
| 585 | C2×C4 | — | 2 | 1 | no | — |
| 586 | C2×C4 | — | 2 | 2 | no | — |
| 587 | C2×C4 | — | 5 | 1 | no | — |
| 588 | C2×C4 | — | 5 | 2 | no | — |
| 589 | C2×C4 | — | 10 | 2 | no | — |
| 590 | C2×C4 | — | 10 | 1 | no | — |
| 591 | C2×C4 | — | 10 | 2 | no | — |
| 592 | C2×C4 | — | 20 | 2 | no | — |
| 593 | C2×C4 | — | 20 | 2 | no | — |
| 594 | C2×C4 | — | 20 | 4 | no | — |
| 595 | C2×C4 | — | 20 | 2 | no | — |
| 596 | C2×C4 | — | 20 | 4 | no | — |
| 597 | C2×C4 | — | 20 | 1 | no | — |
| 598 | C2×C4 | — | 40 | 2 | no | — |
| 599 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 600 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 601 | C8 | — | 2 | 2 | no | — |
| 602 | C8 | — | 4 | 2 | no | — |
| 603 | C8 | — | 10 | 2 | no | — |
| 604 | C8 | — | 20 | 2 | no | — |
| 605 | C5 | #19052 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 606 | C22 | — | 4 | 1 | no | — |
| 607 | C22 | — | 4 | 2 | no | — |
| 608 | C22 | — | 4 | 2 | no | — |
| 609 | C22 | — | 4 | 2 | no | — |
| 610 | C22 | — | 4 | 2 | no | — |
| 611 | C22 | — | 8 | 1 | no | — |
| 612 | C22 | — | 8 | 2 | no | — |
| 613 | C22 | — | 10 | 1 | no | — |
| 614 | C22 | — | 10 | 2 | no | — |
| 615 | C22 | — | 16 | 2 | no | — |
| 616 | C22 | — | 20 | 1 | no | — |
| 617 | C22 | — | 20 | 2 | no | — |
| 618 | C22 | — | 20 | 2 | no | — |
| 619 | C22 | — | 20 | 2 | no | — |
| 620 | C22 | — | 20 | 2 | no | — |
| 621 | C22 | — | 80 | 2 | no | — |
| 622 | C22 | — | 80 | 4 | no | — |
| 623 | C22 | D5×#120 | 1 | 1 | yes | characteristic |
| 624 | C4 | — | 2 | 1 | no | — |
| 625 | C4 | — | 2 | 2 | no | — |
| 626 | C4 | — | 4 | 1 | no | — |
| 627 | C4 | — | 4 | 2 | no | — |
| 628 | C4 | — | 5 | 2 | no | — |
| 629 | C4 | — | 10 | 2 | no | — |
| 630 | C4 | — | 20 | 1 | no | — |
| 631 | C4 | — | 20 | 2 | no | — |
| 632 | C4 | — | 40 | 1 | no | — |
| 633 | C2 | — | 8 | 1 | no | — |
| 634 | C2 | — | 8 | 2 | no | — |
| 635 | C2 | — | 16 | 1 | no | — |
| 636 | C2 | — | 20 | 1 | no | — |
| 637 | C2 | — | 40 | 1 | no | — |
| 638 | C2 | — | 40 | 2 | no | — |
| 639 | C2 | D5×#453 | 1 | 1 | yes | characteristic |
| 640 | C2 | #10612009 | 1 | 2 | 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 | #19052 |
| 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. #10618988 | C2 | semidirect |
| 2. #10613581 | C2 | semidirect |
| 3. #10613575 | C2 | semidirect |
| 4. C5×#1655 | C2 | semidirect |
| 5. #10602742 | C2 | semidirect |
| 6. #10602119 | C2 | semidirect |
| 7. #10602119 | C2 | semidirect |
| 8. #10599146 | C2 | semidirect |
| 9. #10599145 | C2 | semidirect |
| 10. #10599142 | C2 | semidirect |
| 11. #10599138 | C2 | semidirect |
| 15. #66050 | C22 | semidirect |
| 28. C5×#496 | C22 | semidirect |
| 29. C5×#496 | C22 | semidirect |
| 36. #65363 | C22 | semidirect |
| 37. #65363 | C22 | semidirect |
| 38. #65349 | C22 | semidirect |
| 39. #65344 | C22 | semidirect |
| 40. #65004 | C22 | semidirect |
| 41. #65003 | C22 | semidirect |
| 42. #64994 | C22 | semidirect |
| 43. D5×#97 | C22 | semidirect |
| 44. C5×#329 | C22 | semidirect |
| 45. C5×#329 | C22 | semidirect |
| 46. #64760 | C22 | semidirect |
| 47. #64760 | C22 | semidirect |
| 48. #64684 | C22 | semidirect |
| 49. #64684 | C22 | semidirect |
| 50. #64684 | C22 | semidirect |
| 145. #1655 | D5 | semidirect |
| 257. #496 | C2×D5 | semidirect |
| 258. #496 | C2×D5 | semidirect |
| 272. #329 | C2×D5 | semidirect |
| 273. #329 | C2×D5 | semidirect |
| 605. C5 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618988 | 2 |
| #10613581 | 2 |
| #10613575 | 2 |
| C5×#1655 | 2 |
| #10602742 | 2 |
| #10602119 | 2 |
| #10599146 | 2 |
| #10599145 | 2 |
| #10599142 | 2 |
| #10599138 | 2 |
| #19052 | 5 |