Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
908 conjugacy classes of subgroups.
The subgroup lattice has 742 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618922 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10613287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10612119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10612094 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#1626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601821 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10601821 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10599232 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10599220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10599063 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #10599042 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10599034 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #10599022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C5×#557 | C22 | 1 | 1 | yes | characteristic |
| 17 | #66065 | — | 2 | 1 | no | — |
| 18 | #66062 | C22 | 1 | 1 | yes | characteristic |
| 19 | #66060 | — | 2 | 1 | no | — |
| 20 | #66060 | C22 | 1 | 1 | yes | characteristic |
| 21 | #66050 | C22 | 1 | 1 | yes | characteristic |
| 22 | #66029 | — | 2 | 1 | no | — |
| 23 | #66027 | — | 2 | 2 | no | — |
| 24 | #66026 | — | 2 | 2 | no | — |
| 25 | D5×#125 | — | 2 | 1 | no | — |
| 26 | #65915 | — | 2 | 1 | no | — |
| 27 | #65915 | — | 2 | 1 | no | — |
| 28 | #65914 | — | 2 | 1 | no | — |
| 29 | #65914 | C22 | 1 | 1 | yes | characteristic |
| 30 | #65913 | C22 | 1 | 1 | yes | characteristic |
| 31 | #65913 | C22 | 1 | 1 | yes | characteristic |
| 32 | #65908 | — | 2 | 1 | no | — |
| 33 | C4×#713 | C22 | 1 | 1 | yes | characteristic |
| 34 | C5×#486 | C22 | 1 | 1 | yes | characteristic |
| 35 | C5×#460 | C22 | 1 | 1 | yes | characteristic |
| 36 | C5×#460 | C22 | 1 | 1 | yes | characteristic |
| 37 | #65462 | — | 2 | 1 | no | — |
| 38 | #65461 | — | 2 | 1 | no | — |
| 39 | #65457 | — | 2 | 1 | no | — |
| 40 | #65453 | — | 2 | 1 | no | — |
| 41 | #65368 | C22 | 1 | 1 | yes | characteristic |
| 42 | #65365 | C22 | 1 | 1 | yes | characteristic |
| 43 | #65361 | C22 | 1 | 1 | yes | characteristic |
| 44 | #65361 | C22 | 1 | 1 | yes | characteristic |
| 45 | #65320 | C22 | 1 | 1 | yes | characteristic |
| 46 | #65309 | C22 | 1 | 1 | yes | characteristic |
| 47 | #65135 | C22 | 1 | 1 | yes | characteristic |
| 48 | #65130 | C22 | 1 | 1 | yes | characteristic |
| 49 | #65124 | C22 | 1 | 1 | yes | characteristic |
| 50 | #65122 | C22 | 1 | 1 | yes | characteristic |
| 51 | #65074 | — | 2 | 1 | no | — |
| 52 | #65073 | — | 2 | 1 | no | — |
| 53 | #65070 | — | 2 | 1 | no | — |
| 54 | #65067 | — | 2 | 2 | no | — |
| 55 | #65057 | — | 2 | 1 | no | — |
| 56 | #65047 | — | 2 | 2 | no | — |
| 57 | C4×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 58 | #64970 | C22 | 1 | 1 | yes | characteristic |
| 59 | C5×#332 | C22 | 1 | 1 | yes | characteristic |
| 60 | C5×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 61 | C5×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 62 | #64767 | C22 | 1 | 1 | yes | characteristic |
| 63 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 64 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 65 | #64703 | C22 | 1 | 1 | yes | characteristic |
| 66 | #64703 | C22 | 1 | 1 | yes | characteristic |
| 67 | #64701 | C22 | 1 | 1 | yes | characteristic |
| 68 | #64701 | C22 | 1 | 1 | yes | characteristic |
| 69 | #64679 | C22 | 1 | 1 | yes | characteristic |
| 70 | #64679 | C22 | 1 | 1 | yes | characteristic |
| 71 | #18660 | — | 5 | 1 | no | maximal, Sylow |
| 72 | C2×#713 | — | 2 | 1 | no | — |
| 73 | C2×#713 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×#711 | — | 2 | 1 | no | — |
| 75 | C2×C5×SD16 | — | 2 | 1 | no | — |
| 76 | C2×C5×SD16 | — | 2 | 1 | no | — |
| 77 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 78 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 79 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 80 | C5×#125 | — | 2 | 1 | no | — |
| 81 | C5×#125 | — | 2 | 2 | no | — |
| 82 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 83 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 84 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 86 | #4093 | D4 | 1 | 1 | yes | characteristic |
| 87 | #4092 | — | 2 | 1 | no | — |
| 88 | #4092 | — | 2 | 1 | no | — |
| 89 | #4092 | — | 2 | 1 | no | — |
| 90 | #4092 | — | 2 | 1 | no | — |
| 91 | #4092 | D4 | 1 | 1 | yes | characteristic |
| 92 | Q8×Dic5 | — | 2 | 1 | no | — |
| 93 | Q8×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×#689 | — | 2 | 1 | no | — |
| 95 | #4084 | — | 2 | 1 | no | — |
| 96 | #4084 | — | 2 | 1 | no | — |
| 97 | #4082 | — | 2 | 1 | no | — |
| 98 | D4×Dic5 | — | 2 | 1 | no | — |
| 99 | D4×Dic5 | — | 2 | 1 | no | — |
| 100 | C2×#687 | — | 2 | 2 | no | — |
| 101 | C2×#686 | — | 2 | 1 | no | — |
| 102 | C2×#686 | — | 2 | 1 | no | — |
| 103 | C2×#677 | — | 2 | 1 | no | — |
| 104 | C2×C8×D5 | — | 2 | 1 | no | — |
| 105 | #4044 | — | 2 | 2 | no | — |
| 106 | #4044 | — | 2 | 2 | no | — |
| 107 | #4044 | — | 2 | 1 | no | — |
| 108 | #4043 | D4 | 1 | 2 | yes | — |
| 109 | #4042 | — | 2 | 2 | no | — |
| 110 | #4042 | — | 2 | 2 | no | — |
| 111 | #4041 | — | 2 | 2 | no | — |
| 112 | #4041 | — | 2 | 1 | no | — |
| 113 | #4041 | D4 | 1 | 1 | yes | characteristic |
| 114 | #4040 | — | 2 | 2 | no | — |
| 115 | #4040 | — | 2 | 2 | no | — |
| 116 | #4040 | — | 2 | 2 | no | — |
| 117 | #4040 | — | 2 | 1 | no | — |
| 118 | #4040 | — | 2 | 2 | no | — |
| 119 | #4039 | — | 2 | 2 | no | — |
| 120 | #4039 | — | 2 | 1 | no | — |
| 121 | #4039 | D4 | 1 | 1 | yes | characteristic |
| 122 | #4038 | — | 2 | 1 | no | — |
| 123 | #4038 | — | 2 | 1 | no | — |
| 124 | #4038 | D4 | 1 | 1 | yes | characteristic |
| 125 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 126 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 127 | D5×C4⋊C4 | — | 2 | 1 | no | — |
| 128 | D5×C4⋊C4 | — | 2 | 1 | no | — |
| 129 | D5×C4⋊C4 | — | 2 | 1 | no | — |
| 130 | #4036 | — | 2 | 1 | no | — |
| 131 | #4036 | D4 | 1 | 1 | yes | characteristic |
| 132 | #4035 | — | 2 | 2 | no | — |
| 133 | #4035 | — | 2 | 2 | no | — |
| 134 | #4035 | — | 2 | 2 | no | — |
| 135 | #4033 | D4 | 1 | 2 | yes | — |
| 136 | #4022 | — | 2 | 2 | no | — |
| 137 | C4×D20 | — | 2 | 2 | no | — |
| 138 | C4×D20 | — | 2 | 1 | no | — |
| 139 | C4×D20 | — | 2 | 1 | no | — |
| 140 | C4×D20 | — | 2 | 1 | no | — |
| 141 | C4×D20 | — | 2 | 1 | no | — |
| 142 | C4×D20 | C23 | 1 | 1 | yes | characteristic |
| 143 | C4×D20 | C23 | 1 | 1 | yes | characteristic |
| 144 | #4018 | — | 2 | 2 | no | — |
| 145 | #4018 | — | 2 | 2 | no | — |
| 146 | #4018 | — | 2 | 1 | no | — |
| 147 | C42×D5 | — | 2 | 1 | no | — |
| 148 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 149 | #4016 | — | 2 | 1 | no | — |
| 150 | #4016 | — | 2 | 1 | no | — |
| 151 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 152 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 153 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 154 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 155 | C5×#102 | — | 2 | 2 | no | — |
| 156 | C5×#102 | — | 2 | 1 | no | — |
| 157 | C5×#102 | — | 2 | 1 | no | — |
| 158 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 159 | #3967 | — | 2 | 1 | no | — |
| 160 | #3964 | — | 2 | 1 | no | — |
| 161 | #3964 | — | 2 | 1 | no | — |
| 162 | #3953 | — | 2 | 1 | no | — |
| 163 | #3952 | — | 2 | 1 | no | — |
| 164 | #3952 | — | 2 | 1 | no | — |
| 165 | #3950 | — | 2 | 1 | no | — |
| 166 | #3948 | — | 2 | 2 | no | — |
| 167 | #3948 | — | 2 | 1 | no | — |
| 168 | #3947 | — | 2 | 1 | no | — |
| 169 | C8×Dic5 | — | 2 | 1 | no | — |
| 170 | C8×Dic5 | — | 2 | 1 | no | — |
| 171 | #3942 | — | 2 | 1 | no | — |
| 172 | #3940 | — | 2 | 2 | no | — |
| 173 | #3940 | — | 2 | 1 | no | — |
| 174 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 175 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 176 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 177 | #3515 | — | 5 | 1 | no | — |
| 178 | #3212 | — | 5 | 1 | no | — |
| 179 | #3167 | — | 5 | 1 | no | — |
| 180 | #3115 | — | 5 | 1 | no | — |
| 181 | #1654 | — | 5 | 1 | no | — |
| 182 | #1653 | — | 5 | 1 | no | — |
| 183 | #1644 | — | 5 | 1 | no | — |
| 184 | #1643 | — | 5 | 1 | no | — |
| 185 | #1626 | D5 | 1 | 1 | yes | characteristic, complemented |
| 186 | #1625 | — | 5 | 1 | no | — |
| 187 | #1622 | — | 5 | 1 | no | — |
| 188 | #1622 | — | 5 | 1 | no | — |
| 189 | #1554 | — | 5 | 1 | no | — |
| 190 | #1494 | — | 5 | 1 | no | — |
| 191 | #1476 | — | 5 | 1 | no | — |
| 192 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 193 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C5×D4 | — | 2 | 1 | no | — |
| 196 | C2×C5×D4 | — | 2 | 1 | no | — |
| 197 | C2×C5×D4 | — | 2 | 1 | no | — |
| 198 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 199 | C22×Dic5 | — | 4 | 1 | no | — |
| 200 | #713 | — | 2 | 2 | no | — |
| 201 | #713 | — | 4 | 1 | no | — |
| 202 | #713 | — | 4 | 2 | no | — |
| 203 | #713 | — | 4 | 2 | no | — |
| 204 | #711 | — | 8 | 1 | no | — |
| 205 | #711 | — | 8 | 1 | no | — |
| 206 | C2×D20 | — | 2 | 2 | no | — |
| 207 | C2×D20 | — | 2 | 1 | no | — |
| 208 | C2×D20 | — | 2 | 1 | no | — |
| 209 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×D5 | — | 2 | 2 | no | — |
| 212 | C2×C4×D5 | — | 2 | 1 | no | — |
| 213 | C2×C4×D5 | — | 2 | 1 | no | — |
| 214 | C2×C4×D5 | — | 2 | 1 | no | — |
| 215 | C2×C4×D5 | — | 2 | 2 | no | — |
| 216 | C2×C4×D5 | — | 2 | 2 | no | — |
| 217 | C2×C4×D5 | — | 2 | 1 | no | — |
| 218 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×Dic10 | — | 2 | 1 | no | — |
| 222 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 223 | C5×SD16 | — | 4 | 2 | no | — |
| 224 | C5×SD16 | — | 8 | 1 | no | — |
| 225 | C2×C5×C8 | — | 2 | 1 | no | — |
| 226 | C2×C5×C8 | — | 2 | 1 | no | — |
| 227 | C2×C5×C8 | — | 2 | 1 | no | — |
| 228 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 229 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 230 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 231 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 232 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 233 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 234 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 237 | C42×C5 | — | 2 | 2 | no | — |
| 238 | C42×C5 | — | 2 | 1 | no | — |
| 239 | C42×C5 | — | 2 | 1 | no | — |
| 240 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 241 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 242 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 243 | #689 | — | 8 | 1 | no | — |
| 244 | #687 | — | 4 | 4 | no | — |
| 245 | #686 | — | 4 | 2 | no | — |
| 246 | #686 | — | 8 | 1 | no | — |
| 247 | #685 | — | 2 | 2 | no | — |
| 248 | #685 | — | 2 | 2 | no | — |
| 249 | #685 | — | 2 | 2 | no | — |
| 250 | #685 | — | 2 | 1 | no | — |
| 251 | #685 | — | 2 | 1 | no | — |
| 252 | #685 | — | 2 | 2 | no | — |
| 253 | #685 | — | 2 | 1 | no | — |
| 254 | #685 | — | 2 | 1 | no | — |
| 255 | #685 | — | 2 | 1 | no | — |
| 256 | #685 | — | 2 | 1 | no | — |
| 257 | #685 | — | 2 | 1 | no | — |
| 258 | #685 | — | 2 | 1 | no | — |
| 259 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 260 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 261 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 262 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 263 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 264 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 265 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 266 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | #683 | — | 2 | 2 | no | — |
| 269 | #683 | — | 2 | 2 | no | — |
| 270 | #683 | — | 2 | 2 | no | — |
| 271 | #683 | — | 2 | 2 | no | — |
| 272 | #683 | — | 2 | 2 | no | — |
| 273 | #683 | — | 2 | 1 | no | — |
| 274 | #683 | — | 2 | 2 | no | — |
| 275 | #683 | — | 2 | 1 | no | — |
| 276 | C4×Dic5 | — | 2 | 1 | no | — |
| 277 | C4×Dic5 | — | 2 | 1 | no | — |
| 278 | C4×Dic5 | — | 2 | 2 | no | — |
| 279 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C4×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×#168 | — | 2 | 1 | no | — |
| 283 | C2×#168 | — | 2 | 1 | no | — |
| 284 | C2×#168 | — | 2 | 1 | no | — |
| 285 | #677 | — | 8 | 1 | no | — |
| 286 | C8×D5 | — | 4 | 2 | no | — |
| 287 | #557 | C2×D5 | 1 | 1 | yes | characteristic |
| 288 | #554 | — | 5 | 1 | no | — |
| 289 | #554 | — | 5 | 1 | no | — |
| 290 | #553 | — | 10 | 1 | no | — |
| 291 | #552 | — | 10 | 1 | no | — |
| 292 | #552 | — | 10 | 1 | no | — |
| 293 | #552 | — | 10 | 2 | no | — |
| 294 | #547 | — | 5 | 1 | no | — |
| 295 | #547 | — | 10 | 1 | no | — |
| 296 | #541 | — | 10 | 1 | no | — |
| 297 | #539 | — | 10 | 2 | no | — |
| 298 | #533 | — | 5 | 1 | no | — |
| 299 | #532 | — | 5 | 1 | no | — |
| 300 | #529 | — | 5 | 1 | no | — |
| 301 | #529 | — | 10 | 1 | no | — |
| 302 | C2×#125 | — | 10 | 1 | no | — |
| 303 | #520 | — | 10 | 1 | no | — |
| 304 | C4×#41 | — | 5 | 1 | no | — |
| 305 | #498 | — | 5 | 1 | no | — |
| 306 | #495 | — | 10 | 1 | no | — |
| 307 | #492 | — | 5 | 1 | no | — |
| 308 | #488 | — | 10 | 1 | no | — |
| 309 | #487 | — | 5 | 1 | no | — |
| 310 | #486 | C2×D5 | 1 | 1 | yes | characteristic |
| 311 | #482 | — | 10 | 1 | no | — |
| 312 | #475 | — | 5 | 1 | no | — |
| 313 | #474 | — | 5 | 1 | no | — |
| 314 | #465 | — | 10 | 2 | no | — |
| 315 | #462 | — | 5 | 1 | no | — |
| 316 | #461 | — | 5 | 1 | no | — |
| 317 | #460 | C2×D5 | 1 | 1 | yes | characteristic |
| 318 | #460 | C2×D5 | 1 | 1 | yes | characteristic |
| 319 | #459 | — | 5 | 1 | no | — |
| 320 | #459 | — | 5 | 1 | no | — |
| 321 | #452 | — | 10 | 1 | no | — |
| 322 | #449 | — | 10 | 1 | no | — |
| 323 | #449 | — | 10 | 1 | no | — |
| 324 | #442 | — | 10 | 1 | no | — |
| 325 | #440 | — | 10 | 1 | no | — |
| 326 | C4×SD16 | — | 10 | 2 | no | — |
| 327 | #432 | — | 5 | 1 | no | — |
| 328 | #431 | — | 5 | 1 | no | — |
| 329 | C2×C4×C8 | — | 5 | 1 | no | — |
| 330 | #333 | — | 5 | 1 | no | — |
| 331 | #333 | — | 5 | 1 | no | — |
| 332 | #332 | — | 5 | 1 | no | — |
| 333 | #332 | C2×D5 | 1 | 1 | yes | characteristic |
| 334 | Q8⋊C8 | — | 5 | 1 | no | — |
| 335 | Q8⋊C8 | — | 5 | 1 | no | — |
| 336 | Q8⋊C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 337 | Q8⋊C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 338 | D4⋊C8 | — | 5 | 1 | no | — |
| 339 | D4⋊C8 | — | 5 | 1 | no | — |
| 340 | D4⋊C8 | — | 5 | 1 | no | — |
| 341 | D4⋊C8 | — | 5 | 1 | no | — |
| 342 | C23×C5 | — | 4 | 1 | no | — |
| 343 | C22×D5 | — | 2 | 1 | no | — |
| 344 | C22×D5 | — | 2 | 1 | no | — |
| 345 | C22×D5 | #120 | 1 | 1 | yes | characteristic |
| 346 | C5×Q8 | — | 2 | 1 | no | — |
| 347 | C5×Q8 | — | 2 | 1 | no | — |
| 348 | C5×Q8 | — | 2 | 1 | no | — |
| 349 | C5×Q8 | — | 2 | 1 | no | — |
| 350 | C5×Q8 | — | 4 | 1 | no | — |
| 351 | C5×Q8 | — | 4 | 1 | no | — |
| 352 | C5×D4 | — | 4 | 2 | no | — |
| 353 | C5×D4 | — | 4 | 1 | no | — |
| 354 | C5×D4 | — | 4 | 1 | no | — |
| 355 | C5×D4 | — | 4 | 1 | no | — |
| 356 | C5×D4 | — | 4 | 1 | no | — |
| 357 | C2×C4×C5 | — | 2 | 1 | no | — |
| 358 | C2×C4×C5 | — | 2 | 2 | no | — |
| 359 | C2×C4×C5 | — | 2 | 1 | no | — |
| 360 | C2×C4×C5 | — | 2 | 1 | no | — |
| 361 | C2×C4×C5 | — | 2 | 1 | no | — |
| 362 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 363 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 364 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 365 | C22⋊D5 | — | 8 | 2 | no | — |
| 366 | C2×Dic5 | — | 2 | 1 | no | — |
| 367 | C2×Dic5 | — | 2 | 2 | no | — |
| 368 | C2×Dic5 | — | 2 | 1 | no | — |
| 369 | C2×Dic5 | — | 4 | 1 | no | — |
| 370 | C2×Dic5 | — | 8 | 2 | no | — |
| 371 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 372 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 373 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 374 | D20 | — | 2 | 1 | no | — |
| 375 | D20 | — | 2 | 1 | no | — |
| 376 | D20 | — | 2 | 1 | no | — |
| 377 | D20 | — | 4 | 2 | no | — |
| 378 | D20 | — | 4 | 4 | no | — |
| 379 | D20 | — | 8 | 1 | no | — |
| 380 | D20 | #135 | 1 | 2 | yes | — |
| 381 | C4×D5 | — | 2 | 1 | no | — |
| 382 | C4×D5 | — | 2 | 1 | no | — |
| 383 | C4×D5 | — | 2 | 1 | no | — |
| 384 | C4×D5 | — | 2 | 1 | no | — |
| 385 | C4×D5 | — | 4 | 1 | no | — |
| 386 | C4×D5 | — | 4 | 2 | no | — |
| 387 | C4×D5 | — | 4 | 4 | no | — |
| 388 | C4×D5 | — | 4 | 1 | no | — |
| 389 | C4×D5 | — | 4 | 1 | no | — |
| 390 | C4×D5 | — | 4 | 1 | no | — |
| 391 | C4×D5 | — | 4 | 1 | no | — |
| 392 | C4×D5 | — | 8 | 1 | no | — |
| 393 | C4×D5 | — | 8 | 2 | no | — |
| 394 | C4×D5 | — | 8 | 2 | no | — |
| 395 | Dic10 | — | 4 | 2 | no | — |
| 396 | Dic10 | — | 4 | 1 | no | — |
| 397 | Dic10 | — | 4 | 1 | no | — |
| 398 | C5×C8 | — | 4 | 1 | no | — |
| 399 | C5×C8 | — | 4 | 1 | no | — |
| 400 | C5×C8 | — | 4 | 1 | no | — |
| 401 | #168 | — | 2 | 2 | no | — |
| 402 | #168 | — | 4 | 1 | no | — |
| 403 | #168 | — | 4 | 1 | no | — |
| 404 | C2×#41 | — | 5 | 1 | no | — |
| 405 | C2×#41 | — | 10 | 1 | no | — |
| 406 | C2×#41 | — | 10 | 1 | no | — |
| 407 | C2×Q16 | — | 10 | 1 | no | — |
| 408 | C2×SD16 | — | 2 | 1 | no | — |
| 409 | C2×SD16 | — | 2 | 1 | no | — |
| 410 | C2×SD16 | — | 10 | 1 | no | — |
| 411 | C2×SD16 | — | 10 | 2 | no | — |
| 412 | C2×D8 | — | 10 | 1 | no | — |
| 413 | C2×D8 | — | 10 | 1 | no | — |
| 414 | C22×C8 | — | 10 | 1 | no | — |
| 415 | C4⋊Q8 | — | 2 | 1 | no | — |
| 416 | C4⋊Q8 | — | 5 | 1 | no | — |
| 417 | C4⋊Q8 | — | 5 | 1 | no | — |
| 418 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 419 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 420 | #126 | — | 10 | 2 | no | — |
| 421 | #126 | — | 10 | 1 | no | — |
| 422 | #126 | — | 10 | 2 | no | — |
| 423 | #126 | — | 10 | 2 | no | — |
| 424 | #125 | — | 2 | 1 | no | — |
| 425 | #125 | — | 2 | 2 | no | — |
| 426 | #125 | — | 5 | 1 | no | — |
| 427 | #125 | — | 10 | 1 | no | — |
| 428 | #125 | — | 10 | 1 | no | — |
| 429 | #125 | — | 10 | 1 | no | — |
| 430 | #125 | — | 10 | 2 | no | — |
| 431 | #125 | — | 10 | 2 | no | — |
| 432 | #125 | — | 10 | 2 | no | — |
| 433 | #124 | — | 5 | 1 | no | — |
| 434 | #124 | — | 10 | 1 | no | — |
| 435 | #123 | — | 10 | 1 | no | — |
| 436 | #123 | — | 10 | 2 | no | — |
| 437 | #123 | — | 10 | 2 | no | — |
| 438 | #123 | — | 10 | 2 | no | — |
| 439 | #123 | — | 10 | 2 | no | — |
| 440 | C22⋊Q8 | — | 5 | 1 | no | — |
| 441 | C22⋊Q8 | — | 5 | 2 | no | — |
| 442 | C22⋊Q8 | — | 10 | 2 | no | — |
| 443 | C22⋊Q8 | — | 10 | 2 | no | — |
| 444 | C22⋊Q8 | — | 10 | 1 | no | — |
| 445 | C22⋊Q8 | — | 10 | 1 | no | — |
| 446 | C22⋊Q8 | — | 10 | 1 | no | — |
| 447 | C22⋊Q8 | — | 10 | 1 | no | — |
| 448 | #121 | — | 5 | 1 | no | — |
| 449 | #121 | — | 10 | 1 | no | — |
| 450 | #121 | — | 10 | 2 | no | — |
| 451 | #121 | — | 10 | 1 | no | — |
| 452 | #121 | — | 10 | 1 | no | — |
| 453 | C4×Q8 | — | 2 | 1 | no | — |
| 454 | C4×Q8 | — | 2 | 1 | no | — |
| 455 | C4×Q8 | — | 5 | 1 | no | — |
| 456 | C4×Q8 | — | 5 | 2 | no | — |
| 457 | C4×Q8 | — | 10 | 1 | no | — |
| 458 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 459 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 460 | C4×D4 | — | 5 | 1 | no | — |
| 461 | C4×D4 | — | 5 | 1 | no | — |
| 462 | C4×D4 | — | 5 | 1 | no | — |
| 463 | C4×D4 | — | 10 | 1 | no | — |
| 464 | C4×D4 | — | 10 | 1 | no | — |
| 465 | C4×D4 | — | 10 | 1 | no | — |
| 466 | C4×D4 | — | 10 | 1 | no | — |
| 467 | C4×D4 | — | 10 | 2 | no | — |
| 468 | C4×D4 | — | 10 | 1 | no | — |
| 469 | C4×D4 | — | 10 | 1 | no | — |
| 470 | C4×D4 | — | 10 | 1 | no | — |
| 471 | C4×D4 | — | 10 | 2 | no | — |
| 472 | #117 | — | 5 | 1 | no | — |
| 473 | #117 | — | 10 | 1 | no | — |
| 474 | #117 | — | 10 | 2 | no | — |
| 475 | #117 | — | 10 | 2 | no | — |
| 476 | #117 | — | 10 | 1 | no | — |
| 477 | #117 | — | 10 | 1 | no | — |
| 478 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 479 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 480 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 481 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 482 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 483 | C2×C42 | — | 5 | 1 | no | — |
| 484 | C2×C42 | — | 10 | 1 | no | — |
| 485 | #107 | — | 10 | 1 | no | — |
| 486 | #106 | — | 10 | 2 | no | — |
| 487 | #106 | — | 10 | 1 | no | — |
| 488 | C4⋊C8 | — | 5 | 1 | no | — |
| 489 | C4⋊C8 | — | 5 | 1 | no | — |
| 490 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 491 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 492 | #103 | — | 10 | 1 | no | — |
| 493 | #103 | — | 10 | 2 | no | — |
| 494 | #103 | — | 10 | 1 | no | — |
| 495 | #103 | — | 10 | 1 | no | — |
| 496 | #102 | — | 2 | 2 | no | — |
| 497 | #102 | — | 2 | 1 | no | — |
| 498 | #102 | — | 2 | 1 | no | — |
| 499 | #102 | — | 10 | 1 | no | — |
| 500 | #102 | — | 10 | 1 | no | — |
| 501 | #102 | — | 10 | 1 | no | — |
| 502 | C22⋊C8 | — | 10 | 1 | no | — |
| 503 | C22⋊C8 | — | 10 | 1 | no | — |
| 504 | #97 | — | 10 | 1 | no | — |
| 505 | C4×C8 | — | 5 | 1 | no | — |
| 506 | C4×C8 | — | 10 | 1 | no | — |
| 507 | C4×C8 | — | 10 | 1 | no | — |
| 508 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 509 | C22×C5 | — | 8 | 1 | no | — |
| 510 | C22×C5 | — | 8 | 1 | no | — |
| 511 | C22×C5 | — | 8 | 1 | no | — |
| 512 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 513 | C2×D5 | — | 2 | 1 | no | — |
| 514 | C2×D5 | — | 2 | 2 | no | — |
| 515 | C2×D5 | — | 2 | 1 | no | — |
| 516 | C2×D5 | — | 2 | 1 | no | — |
| 517 | C2×D5 | — | 4 | 1 | no | — |
| 518 | C2×D5 | — | 4 | 1 | no | — |
| 519 | C2×D5 | — | 4 | 1 | no | — |
| 520 | C2×D5 | — | 4 | 1 | no | — |
| 521 | C2×D5 | — | 4 | 1 | no | — |
| 522 | C4×C5 | — | 2 | 1 | no | — |
| 523 | C4×C5 | — | 4 | 1 | no | — |
| 524 | C4×C5 | — | 4 | 2 | no | — |
| 525 | C4×C5 | — | 4 | 1 | no | — |
| 526 | C4×C5 | — | 4 | 1 | no | — |
| 527 | C4×C5 | — | 4 | 1 | no | — |
| 528 | C4×C5 | C2×#135 | 1 | 1 | yes | characteristic |
| 529 | C4×C5 | #575 | 1 | 1 | yes | characteristic |
| 530 | C4×C5 | #577 | 1 | 1 | yes | characteristic |
| 531 | C4×C5 | #577 | 1 | 1 | yes | characteristic |
| 532 | Dic5 | — | 2 | 1 | no | — |
| 533 | Dic5 | — | 2 | 1 | no | — |
| 534 | Dic5 | — | 2 | 1 | no | — |
| 535 | Dic5 | — | 4 | 1 | no | — |
| 536 | Dic5 | — | 4 | 1 | no | — |
| 537 | Dic5 | — | 4 | 2 | no | — |
| 538 | Dic5 | — | 8 | 1 | no | — |
| 539 | #41 | — | 10 | 2 | no | — |
| 540 | #41 | — | 20 | 1 | no | — |
| 541 | #41 | — | 20 | 2 | no | — |
| 542 | #41 | — | 20 | 2 | no | — |
| 543 | #41 | — | 40 | 1 | no | — |
| 544 | #41 | — | 40 | 1 | no | — |
| 545 | C2×Q8 | — | 2 | 1 | no | — |
| 546 | C2×Q8 | — | 5 | 2 | no | — |
| 547 | C2×Q8 | — | 10 | 1 | no | — |
| 548 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 549 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 550 | C2×D4 | — | 2 | 1 | no | — |
| 551 | C2×D4 | — | 2 | 1 | no | — |
| 552 | C2×D4 | — | 2 | 1 | no | — |
| 553 | C2×D4 | — | 5 | 1 | no | — |
| 554 | C2×D4 | — | 5 | 1 | no | — |
| 555 | C2×D4 | — | 10 | 1 | no | — |
| 556 | C2×D4 | — | 10 | 2 | no | — |
| 557 | C2×D4 | — | 10 | 1 | no | — |
| 558 | C2×D4 | — | 20 | 1 | no | — |
| 559 | C22×C4 | — | 5 | 1 | no | — |
| 560 | C22×C4 | — | 5 | 1 | no | — |
| 561 | C22×C4 | — | 5 | 1 | no | — |
| 562 | C22×C4 | — | 10 | 1 | no | — |
| 563 | C22×C4 | — | 10 | 1 | no | — |
| 564 | C22×C4 | — | 10 | 2 | no | — |
| 565 | C22×C4 | — | 10 | 2 | no | — |
| 566 | C22×C4 | — | 10 | 2 | no | — |
| 567 | C22×C4 | — | 10 | 1 | no | — |
| 568 | C22×C4 | — | 10 | 1 | no | — |
| 569 | C22×C4 | — | 20 | 1 | no | — |
| 570 | Q16 | — | 40 | 1 | no | — |
| 571 | SD16 | — | 4 | 2 | no | — |
| 572 | SD16 | — | 8 | 1 | no | — |
| 573 | SD16 | — | 20 | 4 | no | — |
| 574 | SD16 | — | 40 | 1 | no | — |
| 575 | D8 | — | 20 | 2 | no | — |
| 576 | D8 | — | 40 | 1 | no | — |
| 577 | C2×C8 | — | 2 | 1 | no | — |
| 578 | C2×C8 | — | 2 | 1 | no | — |
| 579 | C2×C8 | — | 2 | 1 | no | — |
| 580 | C2×C8 | — | 10 | 1 | no | — |
| 581 | C2×C8 | — | 10 | 1 | no | — |
| 582 | C2×C8 | — | 10 | 1 | no | — |
| 583 | C2×C8 | — | 20 | 2 | no | — |
| 584 | C4⋊C4 | — | 2 | 2 | no | — |
| 585 | C4⋊C4 | — | 2 | 2 | no | — |
| 586 | C4⋊C4 | — | 2 | 2 | no | — |
| 587 | C4⋊C4 | — | 2 | 1 | no | — |
| 588 | C4⋊C4 | — | 2 | 1 | no | — |
| 589 | C4⋊C4 | — | 2 | 1 | no | — |
| 590 | C4⋊C4 | — | 5 | 1 | no | — |
| 591 | C4⋊C4 | — | 5 | 1 | no | — |
| 592 | C4⋊C4 | — | 10 | 1 | no | — |
| 593 | C4⋊C4 | — | 10 | 1 | no | — |
| 594 | C4⋊C4 | — | 10 | 2 | no | — |
| 595 | C4⋊C4 | — | 10 | 2 | no | — |
| 596 | C4⋊C4 | — | 10 | 1 | no | — |
| 597 | C4⋊C4 | — | 10 | 1 | no | — |
| 598 | C4⋊C4 | — | 10 | 2 | no | — |
| 599 | C4⋊C4 | — | 10 | 2 | no | — |
| 600 | C4⋊C4 | — | 10 | 2 | no | — |
| 601 | C4⋊C4 | — | 10 | 2 | no | — |
| 602 | C4⋊C4 | — | 10 | 2 | no | — |
| 603 | C4⋊C4 | — | 10 | 1 | no | — |
| 604 | C4⋊C4 | — | 10 | 1 | no | — |
| 605 | C4⋊C4 | — | 10 | 1 | no | — |
| 606 | C4⋊C4 | — | 10 | 1 | no | — |
| 607 | C4⋊C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 608 | C4⋊C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 609 | C4⋊C4 | D4×D5 | 1 | 2 | yes | — |
| 610 | C22⋊C4 | — | 10 | 1 | no | — |
| 611 | C22⋊C4 | — | 10 | 1 | no | — |
| 612 | C22⋊C4 | — | 10 | 1 | no | — |
| 613 | C22⋊C4 | — | 10 | 1 | no | — |
| 614 | C22⋊C4 | — | 10 | 1 | no | — |
| 615 | C22⋊C4 | — | 10 | 2 | no | — |
| 616 | C22⋊C4 | — | 10 | 1 | no | — |
| 617 | C22⋊C4 | — | 10 | 2 | no | — |
| 618 | C22⋊C4 | — | 10 | 2 | no | — |
| 619 | C22⋊C4 | — | 10 | 2 | no | — |
| 620 | C22⋊C4 | — | 10 | 1 | no | — |
| 621 | C22⋊C4 | — | 10 | 1 | no | — |
| 622 | C22⋊C4 | — | 20 | 1 | no | — |
| 623 | C22⋊C4 | — | 20 | 1 | no | — |
| 624 | C42 | — | 2 | 2 | no | — |
| 625 | C42 | — | 2 | 1 | no | — |
| 626 | C42 | — | 2 | 1 | no | — |
| 627 | C42 | — | 5 | 1 | no | — |
| 628 | C42 | — | 5 | 1 | no | — |
| 629 | C42 | — | 5 | 1 | no | — |
| 630 | C42 | — | 10 | 1 | no | — |
| 631 | C42 | — | 10 | 1 | no | — |
| 632 | C42 | — | 10 | 2 | no | — |
| 633 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 634 | C2×C5 | — | 16 | 1 | no | — |
| 635 | C2×C5 | #3002 | 1 | 1 | yes | characteristic |
| 636 | C2×C5 | #3010 | 1 | 1 | yes | characteristic |
| 637 | C2×C5 | #3018 | 1 | 1 | yes | characteristic |
| 638 | D5 | — | 4 | 1 | no | — |
| 639 | D5 | — | 4 | 2 | no | — |
| 640 | D5 | — | 8 | 1 | no | — |
| 641 | C23 | — | 4 | 1 | no | — |
| 642 | C23 | — | 5 | 1 | no | — |
| 643 | C23 | — | 10 | 1 | no | — |
| 644 | C23 | — | 10 | 1 | no | — |
| 645 | Q8 | — | 2 | 1 | no | — |
| 646 | Q8 | — | 2 | 1 | no | — |
| 647 | Q8 | — | 2 | 1 | no | — |
| 648 | Q8 | — | 2 | 1 | no | — |
| 649 | Q8 | — | 4 | 1 | no | — |
| 650 | Q8 | — | 4 | 1 | no | — |
| 651 | Q8 | — | 20 | 2 | no | — |
| 652 | Q8 | — | 20 | 1 | no | — |
| 653 | Q8 | — | 20 | 1 | no | — |
| 654 | D4 | — | 4 | 2 | no | — |
| 655 | D4 | — | 4 | 1 | no | — |
| 656 | D4 | — | 4 | 1 | no | — |
| 657 | D4 | — | 4 | 1 | no | — |
| 658 | D4 | — | 4 | 1 | no | — |
| 659 | D4 | — | 5 | 2 | no | — |
| 660 | D4 | — | 10 | 1 | no | — |
| 661 | D4 | — | 10 | 1 | no | — |
| 662 | D4 | — | 10 | 1 | no | — |
| 663 | D4 | — | 20 | 2 | no | — |
| 664 | D4 | — | 20 | 4 | no | — |
| 665 | D4 | — | 40 | 1 | no | — |
| 666 | D4 | — | 40 | 2 | no | — |
| 667 | C2×C4 | — | 2 | 1 | no | — |
| 668 | C2×C4 | — | 2 | 1 | no | — |
| 669 | C2×C4 | — | 2 | 1 | no | — |
| 670 | C2×C4 | — | 2 | 2 | no | — |
| 671 | C2×C4 | — | 2 | 1 | no | — |
| 672 | C2×C4 | — | 5 | 1 | no | — |
| 673 | C2×C4 | — | 5 | 1 | no | — |
| 674 | C2×C4 | — | 5 | 1 | no | — |
| 675 | C2×C4 | — | 10 | 1 | no | — |
| 676 | C2×C4 | — | 10 | 1 | no | — |
| 677 | C2×C4 | — | 10 | 1 | no | — |
| 678 | C2×C4 | — | 10 | 1 | no | — |
| 679 | C2×C4 | — | 10 | 1 | no | — |
| 680 | C2×C4 | — | 10 | 2 | no | — |
| 681 | C2×C4 | — | 10 | 1 | no | — |
| 682 | C2×C4 | — | 20 | 1 | no | — |
| 683 | C2×C4 | — | 20 | 2 | no | — |
| 684 | C2×C4 | — | 20 | 4 | no | — |
| 685 | C2×C4 | — | 20 | 1 | no | — |
| 686 | C2×C4 | — | 20 | 1 | no | — |
| 687 | C2×C4 | — | 20 | 1 | no | — |
| 688 | C2×C4 | — | 20 | 1 | no | — |
| 689 | C2×C4 | — | 20 | 1 | no | — |
| 690 | C2×C4 | — | 40 | 1 | no | — |
| 691 | C2×C4 | — | 40 | 2 | no | — |
| 692 | C2×C4 | — | 40 | 2 | no | — |
| 693 | C2×C4 | — | 40 | 2 | no | — |
| 694 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 695 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 696 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 697 | C8 | — | 4 | 1 | no | — |
| 698 | C8 | — | 4 | 1 | no | — |
| 699 | C8 | — | 4 | 1 | no | — |
| 700 | C8 | — | 10 | 2 | no | — |
| 701 | C8 | — | 20 | 1 | no | — |
| 702 | C8 | — | 20 | 1 | no | — |
| 703 | C5 | #18660 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 704 | C22 | — | 8 | 1 | no | — |
| 705 | C22 | — | 8 | 1 | no | — |
| 706 | C22 | — | 8 | 1 | no | — |
| 707 | C22 | — | 10 | 1 | no | — |
| 708 | C22 | — | 10 | 1 | no | — |
| 709 | C22 | — | 10 | 1 | no | — |
| 710 | C22 | — | 10 | 2 | no | — |
| 711 | C22 | — | 20 | 1 | no | — |
| 712 | C22 | — | 20 | 1 | no | — |
| 713 | C22 | — | 20 | 1 | no | — |
| 714 | C22 | — | 20 | 1 | no | — |
| 715 | C22 | — | 20 | 1 | no | — |
| 716 | C22 | D5×#120 | 1 | 1 | yes | characteristic |
| 717 | C4 | — | 2 | 1 | no | — |
| 718 | C4 | — | 4 | 1 | no | — |
| 719 | C4 | — | 4 | 1 | no | — |
| 720 | C4 | — | 4 | 1 | no | — |
| 721 | C4 | — | 4 | 1 | no | — |
| 722 | C4 | — | 4 | 2 | no | — |
| 723 | C4 | — | 10 | 1 | no | — |
| 724 | C4 | — | 10 | 1 | no | — |
| 725 | C4 | — | 10 | 1 | no | — |
| 726 | C4 | — | 20 | 2 | no | — |
| 727 | C4 | — | 20 | 1 | no | — |
| 728 | C4 | — | 20 | 1 | no | — |
| 729 | C4 | — | 40 | 1 | no | — |
| 730 | C4 | #66096 | 1 | 1 | yes | characteristic |
| 731 | C4 | D5×#135 | 1 | 1 | yes | characteristic |
| 732 | C4 | #66107 | 1 | 1 | yes | characteristic |
| 733 | C4 | #66112 | 1 | 1 | yes | characteristic |
| 734 | C2 | — | 16 | 1 | no | — |
| 735 | C2 | — | 20 | 1 | no | — |
| 736 | C2 | — | 20 | 2 | no | — |
| 737 | C2 | — | 40 | 1 | no | — |
| 738 | C2 | #10611772 | 1 | 1 | yes | characteristic |
| 739 | C2 | #10611813 | 1 | 1 | yes | characteristic |
| 740 | C2 | #10612015 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D5×#120 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#1626 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #1626 | D5 |
| hypocenter | C5 | #18660 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1626 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10618922 | C2 | semidirect |
| 2. #10613287 | C2 | semidirect |
| 3. #10612119 | C2 | semidirect |
| 4. #10612094 | C2 | semidirect |
| 5. C5×#1626 | C2 | semidirect |
| 6. #10602731 | C2 | semidirect |
| 7. #10601989 | C2 | semidirect |
| 8. #10601821 | C2 | semidirect |
| 9. #10601821 | C2 | semidirect |
| 10. #10599232 | C2 | semidirect |
| 11. #10599220 | C2 | semidirect |
| 12. #10599063 | C2 | semidirect |
| 13. #10599042 | C2 | semidirect |
| 14. #10599034 | C2 | semidirect |
| 15. #10599022 | C2 | semidirect |
| 185. #1626 | D5 | semidirect |
| 703. C5 | #18660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618922 | 2 |
| #10613287 | 2 |
| #10612119 | 2 |
| #10612094 | 2 |
| C5×#1626 | 2 |
| #10602731 | 2 |
| #10601989 | 2 |
| #10601821 | 2 |
| #10599232 | 2 |
| #10599220 | 2 |
| #10599063 | 2 |
| #10599042 | 2 |
| #10599034 | 2 |
| #10599022 | 2 |
| #18660 | 5 |