Finite Group DatabasebetaFinite Group DatabasebetaOrder 2560.
7756 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 7756 conjugacy classes of subgroups — too many to draw. Only its 341 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 | #12130881 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | #12046813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11991903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11991871 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C5×#62817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#3532 | — | 2 | 12 | no | — |
| 7 | C5×#3490 | — | 2 | 6 | no | — |
| 8 | C5×#3490 | — | 2 | 3 | no | — |
| 9 | C5×#3484 | — | 2 | 6 | no | — |
| 10 | C5×#3484 | C22 | 1 | 6 | yes | — |
| 11 | C22×C5×#120 | — | 2 | 1 | no | — |
| 12 | C22×C5×#120 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×#4099 | — | 2 | 1 | no | — |
| 14 | C22×#4083 | C22 | 1 | 3 | yes | complemented |
| 15 | C2×#65533 | — | 2 | 6 | no | — |
| 16 | #10614343 | C22 | 1 | 4 | yes | complemented |
| 17 | #10602924 | C22 | 1 | 3 | yes | complemented |
| 18 | #10602923 | C22 | 1 | 6 | yes | complemented |
| 19 | #10602644 | — | 2 | 12 | no | — |
| 20 | #10602463 | C22 | 1 | 12 | yes | complemented |
| 21 | #10602447 | — | 2 | 6 | no | — |
| 22 | #10602343 | — | 2 | 3 | no | — |
| 23 | #347042 | — | 5 | 1 | no | maximal, Sylow |
| 24 | C26×C5 | D4 | 1 | 1 | yes | characteristic, complemented |
| 25 | C25×D5 | C23 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C5×H(5,𝔽2) | D4 | 1 | 6 | yes | complemented |
| 27 | C23×C5×D4 | — | 2 | 3 | no | — |
| 28 | C23×C5×D4 | C23 | 1 | 3 | yes | — |
| 29 | C23×C22⋊D5 | — | 2 | 3 | no | — |
| 30 | C5×H(3,𝔽4) | — | 2 | 4 | no | — |
| 31 | C5×#560 | — | 2 | 12 | no | — |
| 32 | C5×#551 | — | 2 | 12 | no | — |
| 33 | C5×#551 | — | 2 | 24 | no | — |
| 34 | C5×#546 | — | 2 | 24 | no | — |
| 35 | C5×#546 | — | 2 | 24 | no | — |
| 36 | C5×#546 | — | 2 | 24 | no | — |
| 37 | C5×D42 | — | 2 | 12 | no | — |
| 38 | C5×D42 | — | 2 | 24 | no | — |
| 39 | C5×#543 | — | 2 | 3 | no | — |
| 40 | C5×#538 | — | 2 | 24 | no | — |
| 41 | C5×#538 | — | 2 | 12 | no | — |
| 42 | C5×#535 | — | 2 | 12 | no | — |
| 43 | C5×#535 | — | 2 | 6 | no | — |
| 44 | C5×#534 | — | 2 | 3 | no | — |
| 45 | C5×#534 | — | 2 | 12 | no | — |
| 46 | C5×#534 | — | 2 | 6 | no | — |
| 47 | C5×#534 | D4 | 1 | 12 | yes | complemented |
| 48 | C5×#525 | — | 2 | 12 | no | — |
| 49 | C5×#525 | — | 2 | 6 | no | — |
| 50 | C2×C5×#120 | — | 2 | 6 | no | — |
| 51 | C2×C5×#120 | — | 2 | 12 | no | — |
| 52 | C2×C5×#120 | — | 2 | 4 | no | — |
| 53 | C2×C5×#120 | — | 2 | 6 | no | — |
| 54 | C2×C5×#120 | — | 2 | 6 | no | — |
| 55 | C2×C5×#120 | — | 2 | 6 | no | — |
| 56 | C2×C5×#120 | C23 | 1 | 4 | yes | — |
| 57 | C5×#518 | — | 2 | 6 | no | — |
| 58 | C5×#518 | D4 | 1 | 6 | yes | complemented |
| 59 | C22×C5×C22⋊C4 | — | 2 | 3 | no | — |
| 60 | C22×C5×C22⋊C4 | D4 | 1 | 3 | yes | complemented |
| 61 | C2×#4099 | — | 4 | 12 | no | — |
| 62 | C22×C22⋊Dic5 | — | 2 | 3 | no | — |
| 63 | C22×C22⋊Dic5 | C23 | 1 | 3 | yes | complemented |
| 64 | C2×#4083 | — | 2 | 6 | no | — |
| 65 | C2×#4083 | — | 2 | 6 | no | — |
| 66 | C2×#4083 | — | 2 | 12 | no | — |
| 67 | C2×#4083 | — | 4 | 12 | no | — |
| 68 | C22×#685 | — | 2 | 3 | no | — |
| 69 | #65536 | C23 | 1 | 4 | yes | complemented |
| 70 | #65533 | — | 4 | 24 | no | — |
| 71 | C2×#3966 | — | 2 | 12 | no | — |
| 72 | C2×#3966 | — | 2 | 6 | no | — |
| 73 | C2×#3966 | — | 2 | 6 | no | — |
| 74 | C2×#3963 | — | 2 | 3 | no | — |
| 75 | #65244 | — | 2 | 12 | no | — |
| 76 | #64746 | — | 2 | 12 | no | — |
| 77 | #62817 | D5 | 1 | 1 | yes | characteristic, complemented |
| 78 | #23900 | — | 5 | 6 | no | — |
| 79 | #15947 | — | 5 | 1 | no | — |
| 80 | #8541 | — | 5 | 1 | no | — |
| 81 | #8534 | — | 5 | 6 | no | — |
| 82 | C25×C5 | — | 2 | 1 | no | — |
| 83 | C25×C5 | — | 2 | 3 | no | — |
| 84 | C25×C5 | — | 2 | 3 | no | — |
| 85 | C25×C5 | — | 4 | 6 | no | — |
| 86 | C25×C5 | — | 8 | 3 | no | — |
| 87 | C25×C5 | C2×D4 | 1 | 3 | yes | — |
| 88 | C25×C5 | C24 | 1 | 1 | yes | characteristic |
| 89 | C24×D5 | — | 2 | 1 | no | — |
| 90 | C24×D5 | — | 2 | 6 | no | — |
| 91 | C24×D5 | — | 4 | 6 | no | — |
| 92 | C24×D5 | — | 8 | 3 | no | — |
| 93 | C5×H(5,𝔽2) | — | 4 | 12 | no | — |
| 94 | C5×H(5,𝔽2) | — | 8 | 6 | no | — |
| 95 | C2×C5×#41 | — | 2 | 6 | no | — |
| 96 | C2×C5×#41 | — | 2 | 12 | no | — |
| 97 | C22×C5×D4 | — | 2 | 6 | no | — |
| 98 | C22×C5×D4 | — | 2 | 6 | no | — |
| 99 | C22×C5×D4 | — | 2 | 12 | no | — |
| 100 | C22×C5×D4 | — | 2 | 12 | no | — |
| 101 | C22×C5×D4 | — | 2 | 12 | no | — |
| 102 | C22×C5×D4 | — | 2 | 12 | no | — |
| 103 | C22×C5×D4 | — | 4 | 6 | no | — |
| 104 | C22×C5×D4 | — | 8 | 3 | no | — |
| 105 | C22×C5×D4 | — | 8 | 6 | no | — |
| 106 | C22×C5×D4 | — | 8 | 6 | no | — |
| 107 | C22×C5×D4 | C2×D4 | 1 | 6 | yes | — |
| 108 | C22×C5×D4 | C2×D4 | 1 | 6 | yes | — |
| 109 | C22×C5×D4 | C2×D4 | 1 | 12 | yes | — |
| 110 | C23×C4×C5 | — | 2 | 3 | no | — |
| 111 | C23×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 112 | C22×C22⋊D5 | — | 2 | 12 | no | — |
| 113 | C22×C22⋊D5 | — | 4 | 12 | no | — |
| 114 | C22×C22⋊D5 | — | 4 | 6 | no | — |
| 115 | C22×C22⋊D5 | — | 4 | 3 | no | — |
| 116 | C22×C22⋊D5 | — | 4 | 3 | no | — |
| 117 | C22×C22⋊D5 | — | 4 | 4 | no | — |
| 118 | C22×C22⋊D5 | — | 8 | 6 | no | — |
| 119 | C23×Dic5 | — | 2 | 3 | no | — |
| 120 | C5×#127 | — | 2 | 12 | no | — |
| 121 | C5×#126 | — | 2 | 24 | no | — |
| 122 | C5×#124 | — | 2 | 24 | no | — |
| 123 | C5×#124 | — | 2 | 12 | no | — |
| 124 | C5×#123 | — | 2 | 12 | no | — |
| 125 | C5×#123 | — | 2 | 12 | no | — |
| 126 | C5×#123 | — | 2 | 24 | no | — |
| 127 | C5×#123 | — | 2 | 12 | no | — |
| 128 | C5×#123 | — | 2 | 12 | no | — |
| 129 | C5×C22⋊Q8 | — | 2 | 24 | no | — |
| 130 | C5×C22⋊Q8 | — | 2 | 12 | no | — |
| 131 | C5×#121 | — | 2 | 12 | no | — |
| 132 | C5×#121 | — | 2 | 24 | no | — |
| 133 | C5×#121 | — | 2 | 24 | no | — |
| 134 | C5×#121 | — | 2 | 24 | no | — |
| 135 | C5×#121 | — | 2 | 24 | no | — |
| 136 | C5×#120 | — | 2 | 4 | no | — |
| 137 | C5×#120 | — | 2 | 4 | no | — |
| 138 | C5×#120 | — | 2 | 12 | no | — |
| 139 | C5×#120 | — | 2 | 12 | no | — |
| 140 | C5×#120 | — | 2 | 12 | no | — |
| 141 | C5×#120 | — | 2 | 24 | no | — |
| 142 | C5×#120 | — | 2 | 8 | no | — |
| 143 | C5×#120 | — | 2 | 4 | no | — |
| 144 | C5×#120 | — | 2 | 12 | no | — |
| 145 | C5×#120 | — | 2 | 12 | no | — |
| 146 | C5×#120 | — | 2 | 12 | no | — |
| 147 | C5×#120 | — | 2 | 12 | no | — |
| 148 | C5×#120 | — | 2 | 4 | no | — |
| 149 | C5×#120 | — | 2 | 12 | no | — |
| 150 | C4×C5×D4 | — | 2 | 24 | no | — |
| 151 | C4×C5×D4 | — | 2 | 24 | no | — |
| 152 | C4×C5×D4 | — | 2 | 24 | no | — |
| 153 | C5×#117 | — | 2 | 12 | no | — |
| 154 | C5×#117 | — | 2 | 6 | no | — |
| 155 | C2×C5×C22⋊C4 | — | 2 | 6 | no | — |
| 156 | C2×C5×C22⋊C4 | — | 2 | 12 | no | — |
| 157 | C2×C5×C22⋊C4 | — | 2 | 12 | no | — |
| 158 | C2×C5×C22⋊C4 | — | 2 | 12 | no | — |
| 159 | C2×C5×C22⋊C4 | — | 2 | 6 | no | — |
| 160 | C2×C5×C22⋊C4 | — | 2 | 3 | no | — |
| 161 | C2×C5×C22⋊C4 | — | 2 | 3 | no | — |
| 162 | C2×C5×C22⋊C4 | — | 2 | 12 | no | — |
| 163 | C2×C5×C22⋊C4 | C2×D4 | 1 | 12 | yes | — |
| 164 | #4099 | — | 4 | 32 | no | — |
| 165 | C2×C22⋊Dic5 | — | 2 | 6 | no | — |
| 166 | C2×C22⋊Dic5 | — | 2 | 12 | no | — |
| 167 | C2×C22⋊Dic5 | — | 4 | 6 | no | — |
| 168 | C2×C22⋊Dic5 | — | 4 | 12 | no | — |
| 169 | C2×C22⋊Dic5 | — | 4 | 6 | no | — |
| 170 | #4083 | — | 2 | 24 | no | — |
| 171 | #4083 | — | 4 | 12 | no | — |
| 172 | #4083 | — | 4 | 12 | no | — |
| 173 | #4083 | — | 4 | 12 | no | — |
| 174 | #4083 | — | 4 | 24 | no | — |
| 175 | #4083 | — | 8 | 12 | no | — |
| 176 | C2×#685 | — | 4 | 6 | no | — |
| 177 | C2×#685 | — | 4 | 6 | no | — |
| 178 | C2×#685 | — | 4 | 6 | no | — |
| 179 | C2×#685 | — | 4 | 12 | no | — |
| 180 | #3966 | — | 4 | 24 | no | — |
| 181 | #3966 | — | 4 | 12 | no | — |
| 182 | #3966 | — | 8 | 6 | no | — |
| 183 | #3963 | — | 8 | 3 | no | — |
| 184 | #3532 | — | 2 | 12 | no | — |
| 185 | #3490 | — | 2 | 6 | no | — |
| 186 | #3490 | — | 2 | 3 | no | — |
| 187 | #3484 | — | 2 | 6 | no | — |
| 188 | #3484 | C2×D5 | 1 | 6 | yes | — |
| 189 | C22×#120 | — | 2 | 1 | no | — |
| 190 | C22×#120 | — | 5 | 3 | no | — |
| 191 | C22×#120 | — | 10 | 1 | no | — |
| 192 | C22×#120 | C2×D5 | 1 | 1 | yes | characteristic |
| 193 | C2×B(4,𝔽2) | — | 10 | 6 | no | — |
| 194 | #2846 | — | 5 | 4 | no | — |
| 195 | #2021 | — | 10 | 12 | no | — |
| 196 | #1898 | — | 5 | 12 | no | — |
| 197 | #1889 | — | 10 | 6 | no | — |
| 198 | #1781 | — | 5 | 6 | no | — |
| 199 | #1438 | — | 5 | 3 | no | — |
| 200 | #1438 | — | 10 | 3 | no | — |
| 201 | C24×C5 | — | 2 | 1 | no | — |
| 202 | C24×C5 | — | 2 | 3 | no | — |
| 203 | C24×C5 | — | 2 | 3 | no | — |
| 204 | C24×C5 | — | 2 | 6 | no | — |
| 205 | C24×C5 | — | 2 | 1 | no | — |
| 206 | C24×C5 | — | 2 | 6 | no | — |
| 207 | C24×C5 | — | 2 | 6 | no | — |
| 208 | C24×C5 | — | 4 | 3 | no | — |
| 209 | C24×C5 | — | 4 | 3 | no | — |
| 210 | C24×C5 | — | 4 | 3 | no | — |
| 211 | C24×C5 | — | 4 | 6 | no | — |
| 212 | C24×C5 | — | 4 | 6 | no | — |
| 213 | C24×C5 | — | 4 | 6 | no | — |
| 214 | C24×C5 | — | 4 | 6 | no | — |
| 215 | C24×C5 | — | 4 | 8 | no | — |
| 216 | C24×C5 | — | 8 | 3 | no | — |
| 217 | C24×C5 | — | 8 | 3 | no | — |
| 218 | C24×C5 | — | 8 | 12 | no | — |
| 219 | C24×C5 | — | 8 | 12 | no | — |
| 220 | C24×C5 | — | 8 | 6 | no | — |
| 221 | C24×C5 | — | 8 | 12 | no | — |
| 222 | C24×C5 | — | 8 | 12 | no | — |
| 223 | C24×C5 | — | 8 | 4 | no | — |
| 224 | C24×C5 | #120 | 1 | 3 | yes | — |
| 225 | C24×C5 | #120 | 1 | 3 | yes | — |
| 226 | C24×C5 | #120 | 1 | 4 | yes | complemented |
| 227 | C24×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 228 | C24×C5 | C22×D4 | 1 | 6 | yes | — |
| 229 | C23×D5 | — | 2 | 6 | no | — |
| 230 | C23×D5 | — | 2 | 12 | no | — |
| 231 | C23×D5 | — | 4 | 3 | no | — |
| 232 | C23×D5 | — | 4 | 6 | no | — |
| 233 | C23×D5 | — | 4 | 3 | no | — |
| 234 | C23×D5 | — | 4 | 4 | no | — |
| 235 | C23×D5 | — | 4 | 6 | no | — |
| 236 | C23×D5 | — | 4 | 12 | no | — |
| 237 | C23×D5 | — | 8 | 4 | no | — |
| 238 | C23×D5 | — | 8 | 24 | no | — |
| 239 | C23×D5 | — | 8 | 12 | no | — |
| 240 | C23×D5 | — | 8 | 12 | no | — |
| 241 | C23×D5 | — | 8 | 4 | no | — |
| 242 | C5×#41 | — | 8 | 6 | no | — |
| 243 | C5×#41 | — | 8 | 6 | no | — |
| 244 | C5×#41 | — | 8 | 24 | no | — |
| 245 | C2×C5×Q8 | — | 2 | 6 | no | — |
| 246 | C2×C5×D4 | — | 2 | 12 | no | — |
| 247 | C2×C5×D4 | — | 2 | 12 | no | — |
| 248 | C2×C5×D4 | — | 2 | 12 | no | — |
| 249 | C2×C5×D4 | — | 2 | 12 | no | — |
| 250 | C2×C5×D4 | — | 2 | 24 | no | — |
| 251 | C2×C5×D4 | — | 2 | 6 | no | — |
| 252 | C2×C5×D4 | — | 2 | 12 | no | — |
| 253 | C2×C5×D4 | — | 2 | 12 | no | — |
| 254 | C2×C5×D4 | — | 4 | 6 | no | — |
| 255 | C2×C5×D4 | — | 4 | 6 | no | — |
| 256 | C2×C5×D4 | — | 4 | 6 | no | — |
| 257 | C2×C5×D4 | — | 4 | 12 | no | — |
| 258 | C2×C5×D4 | — | 4 | 12 | no | — |
| 259 | C2×C5×D4 | — | 4 | 12 | no | — |
| 260 | C2×C5×D4 | — | 4 | 12 | no | — |
| 261 | C2×C5×D4 | — | 8 | 12 | no | — |
| 262 | C2×C5×D4 | — | 8 | 24 | no | — |
| 263 | C2×C5×D4 | — | 8 | 24 | no | — |
| 264 | C2×C5×D4 | — | 8 | 24 | no | — |
| 265 | C2×C5×D4 | — | 8 | 12 | no | — |
| 266 | C2×C5×D4 | — | 8 | 12 | no | — |
| 267 | C22×C4×C5 | — | 2 | 6 | no | — |
| 268 | C22×C4×C5 | — | 2 | 12 | no | — |
| 269 | C22×C4×C5 | — | 2 | 12 | no | — |
| 270 | C22×C4×C5 | — | 2 | 6 | no | — |
| 271 | C22×C4×C5 | — | 4 | 3 | no | — |
| 272 | C22×C4×C5 | — | 4 | 3 | no | — |
| 273 | C22×C4×C5 | — | 8 | 6 | no | — |
| 274 | C22×C4×C5 | #120 | 1 | 6 | yes | — |
| 275 | C22×C4×C5 | #120 | 1 | 12 | yes | complemented |
| 276 | C2×C22⋊D5 | — | 4 | 24 | no | — |
| 277 | C2×C22⋊D5 | — | 4 | 12 | no | — |
| 278 | C2×C22⋊D5 | — | 4 | 12 | no | — |
| 279 | C2×C22⋊D5 | — | 8 | 12 | no | — |
| 280 | C2×C22⋊D5 | — | 8 | 12 | no | — |
| 281 | C2×C22⋊D5 | — | 8 | 12 | no | — |
| 282 | C2×C22⋊D5 | — | 8 | 24 | no | — |
| 283 | C2×C22⋊D5 | — | 8 | 24 | no | — |
| 284 | C22×Dic5 | — | 2 | 6 | no | — |
| 285 | C22×Dic5 | — | 4 | 6 | no | — |
| 286 | C22×Dic5 | — | 4 | 3 | no | — |
| 287 | C22×Dic5 | — | 4 | 6 | no | — |
| 288 | C22×Dic5 | — | 4 | 3 | no | — |
| 289 | C22×Dic5 | — | 4 | 4 | no | — |
| 290 | C5×C4⋊C4 | — | 2 | 24 | no | — |
| 291 | C5×C4⋊C4 | — | 2 | 12 | no | — |
| 292 | C5×C22⋊C4 | — | 2 | 12 | no | — |
| 293 | C5×C22⋊C4 | — | 2 | 12 | no | — |
| 294 | C5×C22⋊C4 | — | 2 | 12 | no | — |
| 295 | C5×C22⋊C4 | — | 2 | 24 | no | — |
| 296 | C5×C22⋊C4 | — | 2 | 24 | no | — |
| 297 | C5×C22⋊C4 | — | 2 | 12 | no | — |
| 298 | C5×C22⋊C4 | — | 2 | 12 | no | — |
| 299 | C42×C5 | — | 2 | 12 | no | — |
| 300 | C22⋊Dic5 | — | 2 | 12 | no | — |
| 301 | C22⋊Dic5 | — | 4 | 6 | no | — |
| 302 | C22⋊Dic5 | — | 4 | 24 | no | — |
| 303 | C22⋊Dic5 | — | 4 | 12 | no | — |
| 304 | C22⋊Dic5 | — | 4 | 12 | no | — |
| 305 | #685 | — | 4 | 24 | no | — |
| 306 | #685 | — | 8 | 24 | no | — |
| 307 | C26 | — | 5 | 1 | no | — |
| 308 | C26 | C22⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 309 | C2×H(5,𝔽2) | C22⋊D5 | 1 | 6 | yes | complemented |
| 310 | C23×D4 | — | 2 | 3 | no | — |
| 311 | C23×D4 | — | 10 | 3 | no | — |
| 312 | C23×D4 | C22×D5 | 1 | 3 | yes | — |
| 313 | H(3,𝔽4) | — | 2 | 4 | no | — |
| 314 | #560 | — | 2 | 12 | no | — |
| 315 | #551 | — | 2 | 12 | no | — |
| 316 | #551 | — | 2 | 24 | no | — |
| 317 | #546 | — | 2 | 24 | no | — |
| 318 | #546 | — | 2 | 24 | no | — |
| 319 | #546 | — | 2 | 24 | no | — |
| 320 | D42 | — | 2 | 12 | no | — |
| 321 | D42 | — | 2 | 24 | no | — |
| 322 | #543 | — | 2 | 3 | no | — |
| 323 | #538 | — | 2 | 24 | no | — |
| 324 | #538 | — | 2 | 12 | no | — |
| 325 | #535 | — | 2 | 12 | no | — |
| 326 | #535 | — | 2 | 6 | no | — |
| 327 | #534 | — | 2 | 3 | no | — |
| 328 | #534 | — | 2 | 12 | no | — |
| 329 | #534 | — | 2 | 6 | no | — |
| 330 | #534 | C22⋊D5 | 1 | 12 | yes | complemented |
| 331 | #525 | — | 2 | 12 | no | — |
| 332 | #525 | — | 2 | 6 | no | — |
| 333 | C2×#120 | — | 2 | 6 | no | — |
| 334 | C2×#120 | — | 2 | 12 | no | — |
| 335 | C2×#120 | — | 2 | 4 | no | — |
| 336 | C2×#120 | — | 2 | 6 | no | — |
| 337 | C2×#120 | — | 2 | 6 | no | — |
| 338 | C2×#120 | — | 2 | 6 | no | — |
| 339 | C2×#120 | — | 10 | 6 | no | — |
| 340 | C2×#120 | — | 10 | 6 | no | — |
| 341 | C2×#120 | — | 10 | 12 | no | — |
| 342 | C2×#120 | — | 20 | 12 | no | — |
| 343 | C2×#120 | — | 20 | 12 | no | — |
| 344 | C2×#120 | C22×D5 | 1 | 4 | yes | — |
| 345 | #518 | — | 2 | 6 | no | — |
| 346 | #518 | C22⋊D5 | 1 | 6 | yes | complemented |
| 347 | C22×C22⋊C4 | — | 2 | 3 | no | — |
| 348 | C22×C22⋊C4 | — | 5 | 3 | no | — |
| 349 | C22×C22⋊C4 | — | 10 | 3 | no | — |
| 350 | C22×C22⋊C4 | — | 10 | 3 | no | — |
| 351 | C22×C22⋊C4 | C22⋊D5 | 1 | 3 | yes | complemented |
| 352 | B(4,𝔽2) | — | 20 | 24 | no | — |
| 353 | C2×#99 | — | 10 | 6 | no | — |
| 354 | C2×#99 | — | 10 | 12 | no | — |
| 355 | C2×#99 | — | 10 | 6 | no | — |
| 356 | #379 | — | 5 | 4 | no | — |
| 357 | #379 | — | 10 | 12 | no | — |
| 358 | C2×#95 | — | 10 | 3 | no | — |
| 359 | #342 | — | 10 | 12 | no | — |
| 360 | C23×C5 | — | 2 | 3 | no | — |
| 361 | C23×C5 | — | 2 | 3 | no | — |
| 362 | C23×C5 | — | 2 | 3 | no | — |
| 363 | C23×C5 | — | 2 | 6 | no | — |
| 364 | C23×C5 | — | 2 | 6 | no | — |
| 365 | C23×C5 | — | 2 | 3 | no | — |
| 366 | C23×C5 | — | 2 | 3 | no | — |
| 367 | C23×C5 | — | 2 | 4 | no | — |
| 368 | C23×C5 | — | 2 | 3 | no | — |
| 369 | C23×C5 | — | 2 | 3 | no | — |
| 370 | C23×C5 | — | 4 | 12 | no | — |
| 371 | C23×C5 | — | 4 | 12 | no | — |
| 372 | C23×C5 | — | 4 | 6 | no | — |
| 373 | C23×C5 | — | 4 | 6 | no | — |
| 374 | C23×C5 | — | 4 | 6 | no | — |
| 375 | C23×C5 | — | 4 | 6 | no | — |
| 376 | C23×C5 | — | 4 | 6 | no | — |
| 377 | C23×C5 | — | 4 | 12 | no | — |
| 378 | C23×C5 | — | 4 | 12 | no | — |
| 379 | C23×C5 | — | 4 | 6 | no | — |
| 380 | C23×C5 | — | 4 | 12 | no | — |
| 381 | C23×C5 | — | 4 | 12 | no | — |
| 382 | C23×C5 | — | 4 | 6 | no | — |
| 383 | C23×C5 | — | 4 | 6 | no | — |
| 384 | C23×C5 | — | 8 | 6 | no | — |
| 385 | C23×C5 | — | 8 | 1 | no | — |
| 386 | C23×C5 | — | 8 | 3 | no | — |
| 387 | C23×C5 | — | 8 | 3 | no | — |
| 388 | C23×C5 | — | 8 | 1 | no | — |
| 389 | C23×C5 | — | 8 | 6 | no | — |
| 390 | C23×C5 | — | 8 | 3 | no | — |
| 391 | C23×C5 | — | 8 | 3 | no | — |
| 392 | C23×C5 | — | 8 | 3 | no | — |
| 393 | C23×C5 | — | 8 | 6 | no | — |
| 394 | C23×C5 | — | 8 | 3 | no | — |
| 395 | C23×C5 | — | 8 | 12 | no | — |
| 396 | C23×C5 | — | 8 | 24 | no | — |
| 397 | C23×C5 | — | 8 | 24 | no | — |
| 398 | C23×C5 | — | 8 | 24 | no | — |
| 399 | C23×C5 | — | 8 | 24 | no | — |
| 400 | C23×C5 | — | 16 | 8 | no | — |
| 401 | C23×C5 | B(4,𝔽2) | 1 | 6 | yes | complemented |
| 402 | C23×C5 | C2×#120 | 1 | 4 | yes | — |
| 403 | C23×C5 | C2×#120 | 1 | 3 | yes | — |
| 404 | C22×D5 | — | 2 | 4 | no | — |
| 405 | C22×D5 | — | 4 | 24 | no | — |
| 406 | C22×D5 | — | 4 | 6 | no | — |
| 407 | C22×D5 | — | 4 | 12 | no | — |
| 408 | C22×D5 | — | 4 | 12 | no | — |
| 409 | C22×D5 | — | 4 | 6 | no | — |
| 410 | C22×D5 | — | 8 | 24 | no | — |
| 411 | C22×D5 | — | 8 | 24 | no | — |
| 412 | C22×D5 | — | 8 | 48 | no | — |
| 413 | C22×D5 | — | 8 | 1 | no | — |
| 414 | C22×D5 | — | 8 | 3 | no | — |
| 415 | C22×D5 | — | 8 | 2 | no | — |
| 416 | C22×D5 | — | 8 | 6 | no | — |
| 417 | C22×D5 | — | 8 | 12 | no | — |
| 418 | C22×D5 | — | 8 | 1 | no | — |
| 419 | C22×D5 | — | 8 | 3 | no | — |
| 420 | C5×Q8 | — | 8 | 6 | no | — |
| 421 | C5×D4 | — | 4 | 24 | no | — |
| 422 | C5×D4 | — | 4 | 24 | no | — |
| 423 | C5×D4 | — | 4 | 12 | no | — |
| 424 | C5×D4 | — | 4 | 12 | no | — |
| 425 | C5×D4 | — | 8 | 12 | no | — |
| 426 | C5×D4 | — | 8 | 12 | no | — |
| 427 | C5×D4 | — | 8 | 24 | no | — |
| 428 | C5×D4 | — | 8 | 6 | no | — |
| 429 | C2×C4×C5 | — | 2 | 6 | no | — |
| 430 | C2×C4×C5 | — | 2 | 12 | no | — |
| 431 | C2×C4×C5 | — | 2 | 6 | no | — |
| 432 | C2×C4×C5 | — | 2 | 6 | no | — |
| 433 | C2×C4×C5 | — | 4 | 12 | no | — |
| 434 | C2×C4×C5 | — | 4 | 12 | no | — |
| 435 | C2×C4×C5 | — | 8 | 6 | no | — |
| 436 | C2×C4×C5 | — | 8 | 12 | no | — |
| 437 | C2×C4×C5 | — | 8 | 12 | no | — |
| 438 | C22⋊D5 | — | 8 | 24 | no | — |
| 439 | C22⋊D5 | — | 8 | 24 | no | — |
| 440 | C22⋊D5 | — | 16 | 16 | no | — |
| 441 | C2×Dic5 | — | 4 | 6 | no | — |
| 442 | C2×Dic5 | — | 4 | 6 | no | — |
| 443 | C2×Dic5 | — | 4 | 6 | no | — |
| 444 | C2×Dic5 | — | 8 | 6 | no | — |
| 445 | C2×Dic5 | — | 8 | 6 | no | — |
| 446 | C2×Dic5 | — | 8 | 12 | no | — |
| 447 | C25 | — | 2 | 1 | no | — |
| 448 | C25 | — | 2 | 3 | no | — |
| 449 | C25 | — | 2 | 3 | no | — |
| 450 | C25 | — | 4 | 6 | no | — |
| 451 | C25 | — | 8 | 3 | no | — |
| 452 | C25 | — | 10 | 1 | no | — |
| 453 | C25 | — | 10 | 6 | no | — |
| 454 | C25 | — | 20 | 6 | no | — |
| 455 | C25 | — | 40 | 3 | no | — |
| 456 | C25 | C2×C22⋊D5 | 1 | 3 | yes | — |
| 457 | C25 | C23×D5 | 1 | 1 | yes | characteristic |
| 458 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 459 | H(5,𝔽2) | — | 8 | 6 | no | — |
| 460 | C2×#41 | — | 2 | 6 | no | — |
| 461 | C2×#41 | — | 2 | 12 | no | — |
| 462 | C22×D4 | — | 2 | 6 | no | — |
| 463 | C22×D4 | — | 2 | 6 | no | — |
| 464 | C22×D4 | — | 2 | 12 | no | — |
| 465 | C22×D4 | — | 2 | 12 | no | — |
| 466 | C22×D4 | — | 2 | 12 | no | — |
| 467 | C22×D4 | — | 2 | 12 | no | — |
| 468 | C22×D4 | — | 4 | 6 | no | — |
| 469 | C22×D4 | — | 8 | 3 | no | — |
| 470 | C22×D4 | — | 8 | 6 | no | — |
| 471 | C22×D4 | — | 8 | 6 | no | — |
| 472 | C22×D4 | — | 10 | 12 | no | — |
| 473 | C22×D4 | — | 20 | 6 | no | — |
| 474 | C22×D4 | — | 20 | 12 | no | — |
| 475 | C22×D4 | — | 20 | 3 | no | — |
| 476 | C22×D4 | — | 20 | 3 | no | — |
| 477 | C22×D4 | — | 20 | 4 | no | — |
| 478 | C22×D4 | — | 40 | 6 | no | — |
| 479 | C22×D4 | C2×C22⋊D5 | 1 | 6 | yes | — |
| 480 | C22×D4 | C2×C22⋊D5 | 1 | 6 | yes | — |
| 481 | C22×D4 | C2×C22⋊D5 | 1 | 12 | yes | — |
| 482 | C23×C4 | — | 2 | 3 | no | — |
| 483 | C23×C4 | — | 10 | 3 | no | — |
| 484 | C23×C4 | C2×C22⋊D5 | 1 | 3 | yes | — |
| 485 | #127 | — | 2 | 12 | no | — |
| 486 | #126 | — | 2 | 24 | no | — |
| 487 | #124 | — | 2 | 24 | no | — |
| 488 | #124 | — | 2 | 12 | no | — |
| 489 | #123 | — | 2 | 12 | no | — |
| 490 | #123 | — | 2 | 12 | no | — |
| 491 | #123 | — | 2 | 24 | no | — |
| 492 | #123 | — | 2 | 12 | no | — |
| 493 | #123 | — | 2 | 12 | no | — |
| 494 | C22⋊Q8 | — | 2 | 24 | no | — |
| 495 | C22⋊Q8 | — | 2 | 12 | no | — |
| 496 | #121 | — | 2 | 12 | no | — |
| 497 | #121 | — | 2 | 24 | no | — |
| 498 | #121 | — | 2 | 24 | no | — |
| 499 | #121 | — | 2 | 24 | no | — |
| 500 | #121 | — | 2 | 24 | no | — |
| 501 | #120 | — | 2 | 4 | no | — |
| 502 | #120 | — | 2 | 4 | no | — |
| 503 | #120 | — | 2 | 12 | no | — |
| 504 | #120 | — | 2 | 12 | no | — |
| 505 | #120 | — | 2 | 12 | no | — |
| 506 | #120 | — | 2 | 24 | no | — |
| 507 | #120 | — | 2 | 8 | no | — |
| 508 | #120 | — | 2 | 4 | no | — |
| 509 | #120 | — | 2 | 12 | no | — |
| 510 | #120 | — | 2 | 12 | no | — |
| 511 | #120 | — | 2 | 12 | no | — |
| 512 | #120 | — | 2 | 12 | no | — |
| 513 | #120 | — | 2 | 4 | no | — |
| 514 | #120 | — | 2 | 12 | no | — |
| 515 | #120 | — | 10 | 24 | no | — |
| 516 | #120 | — | 20 | 12 | no | — |
| 517 | #120 | — | 20 | 12 | no | — |
| 518 | #120 | — | 20 | 12 | no | — |
| 519 | #120 | — | 20 | 32 | no | — |
| 520 | #120 | — | 20 | 24 | no | — |
| 521 | #120 | — | 40 | 12 | no | — |
| 522 | C4×D4 | — | 2 | 24 | no | — |
| 523 | C4×D4 | — | 2 | 24 | no | — |
| 524 | C4×D4 | — | 2 | 24 | no | — |
| 525 | #117 | — | 2 | 12 | no | — |
| 526 | #117 | — | 2 | 6 | no | — |
| 527 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 528 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 529 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 530 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 531 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 532 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 533 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 534 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 535 | C2×C22⋊C4 | — | 10 | 6 | no | — |
| 536 | C2×C22⋊C4 | — | 10 | 12 | no | — |
| 537 | C2×C22⋊C4 | — | 20 | 6 | no | — |
| 538 | C2×C22⋊C4 | — | 20 | 6 | no | — |
| 539 | C2×C22⋊C4 | — | 20 | 6 | no | — |
| 540 | C2×C22⋊C4 | — | 20 | 12 | no | — |
| 541 | C2×C22⋊C4 | — | 20 | 6 | no | — |
| 542 | C2×C22⋊C4 | — | 20 | 6 | no | — |
| 543 | C2×C22⋊C4 | — | 20 | 12 | no | — |
| 544 | C2×C22⋊C4 | C2×C22⋊D5 | 1 | 12 | yes | — |
| 545 | #99 | — | 20 | 24 | no | — |
| 546 | #99 | — | 20 | 12 | no | — |
| 547 | #99 | — | 40 | 6 | no | — |
| 548 | #95 | — | 40 | 3 | no | — |
| 549 | C22×C5 | — | 2 | 1 | no | — |
| 550 | C22×C5 | — | 2 | 3 | no | — |
| 551 | C22×C5 | — | 2 | 3 | no | — |
| 552 | C22×C5 | — | 2 | 1 | no | — |
| 553 | C22×C5 | — | 2 | 6 | no | — |
| 554 | C22×C5 | — | 2 | 12 | no | — |
| 555 | C22×C5 | — | 2 | 6 | no | — |
| 556 | C22×C5 | — | 4 | 6 | no | — |
| 557 | C22×C5 | — | 4 | 6 | no | — |
| 558 | C22×C5 | — | 4 | 8 | no | — |
| 559 | C22×C5 | — | 4 | 6 | no | — |
| 560 | C22×C5 | — | 4 | 12 | no | — |
| 561 | C22×C5 | — | 4 | 3 | no | — |
| 562 | C22×C5 | — | 4 | 6 | no | — |
| 563 | C22×C5 | — | 8 | 6 | no | — |
| 564 | C22×C5 | — | 8 | 6 | no | — |
| 565 | C22×C5 | — | 8 | 3 | no | — |
| 566 | C22×C5 | — | 8 | 12 | no | — |
| 567 | C22×C5 | — | 8 | 12 | no | — |
| 568 | C22×C5 | — | 8 | 3 | no | — |
| 569 | C22×C5 | — | 8 | 12 | no | — |
| 570 | C22×C5 | — | 8 | 12 | no | — |
| 571 | C22×C5 | — | 8 | 4 | no | — |
| 572 | C22×C5 | — | 16 | 4 | no | — |
| 573 | C22×C5 | — | 16 | 12 | no | — |
| 574 | C22×C5 | #2846 | 1 | 1 | yes | characteristic |
| 575 | C22×C5 | C2×B(4,𝔽2) | 1 | 3 | yes | — |
| 576 | C22×C5 | #3026 | 1 | 3 | yes | — |
| 577 | C2×D5 | — | 4 | 12 | no | — |
| 578 | C2×D5 | — | 4 | 16 | no | — |
| 579 | C2×D5 | — | 8 | 6 | no | — |
| 580 | C2×D5 | — | 8 | 12 | no | — |
| 581 | C2×D5 | — | 8 | 24 | no | — |
| 582 | C2×D5 | — | 8 | 6 | no | — |
| 583 | C4×C5 | — | 4 | 6 | no | — |
| 584 | C4×C5 | — | 4 | 12 | no | — |
| 585 | Dic5 | — | 8 | 6 | no | — |
| 586 | Dic5 | — | 16 | 4 | no | — |
| 587 | C24 | — | 2 | 1 | no | — |
| 588 | C24 | — | 2 | 3 | no | — |
| 589 | C24 | — | 2 | 3 | no | — |
| 590 | C24 | — | 2 | 6 | no | — |
| 591 | C24 | — | 2 | 1 | no | — |
| 592 | C24 | — | 2 | 6 | no | — |
| 593 | C24 | — | 2 | 6 | no | — |
| 594 | C24 | — | 4 | 3 | no | — |
| 595 | C24 | — | 4 | 3 | no | — |
| 596 | C24 | — | 4 | 3 | no | — |
| 597 | C24 | — | 4 | 6 | no | — |
| 598 | C24 | — | 4 | 6 | no | — |
| 599 | C24 | — | 4 | 6 | no | — |
| 600 | C24 | — | 4 | 6 | no | — |
| 601 | C24 | — | 4 | 8 | no | — |
| 602 | C24 | — | 8 | 3 | no | — |
| 603 | C24 | — | 8 | 3 | no | — |
| 604 | C24 | — | 8 | 12 | no | — |
| 605 | C24 | — | 8 | 12 | no | — |
| 606 | C24 | — | 8 | 6 | no | — |
| 607 | C24 | — | 8 | 12 | no | — |
| 608 | C24 | — | 8 | 12 | no | — |
| 609 | C24 | — | 8 | 4 | no | — |
| 610 | C24 | — | 10 | 6 | no | — |
| 611 | C24 | — | 10 | 12 | no | — |
| 612 | C24 | — | 20 | 3 | no | — |
| 613 | C24 | — | 20 | 6 | no | — |
| 614 | C24 | — | 20 | 6 | no | — |
| 615 | C24 | — | 20 | 12 | no | — |
| 616 | C24 | — | 20 | 4 | no | — |
| 617 | C24 | — | 20 | 3 | no | — |
| 618 | C24 | — | 40 | 24 | no | — |
| 619 | C24 | — | 40 | 4 | no | — |
| 620 | C24 | — | 40 | 12 | no | — |
| 621 | C24 | — | 40 | 12 | no | — |
| 622 | C24 | — | 40 | 4 | no | — |
| 623 | C24 | #4099 | 1 | 3 | yes | — |
| 624 | C24 | #4099 | 1 | 3 | yes | — |
| 625 | C24 | #4099 | 1 | 4 | yes | complemented |
| 626 | C24 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 627 | C24 | C22×C22⋊D5 | 1 | 6 | yes | — |
| 628 | #41 | — | 8 | 6 | no | — |
| 629 | #41 | — | 8 | 6 | no | — |
| 630 | #41 | — | 8 | 24 | no | — |
| 631 | C2×Q8 | — | 2 | 6 | no | — |
| 632 | C2×D4 | — | 2 | 12 | no | — |
| 633 | C2×D4 | — | 2 | 12 | no | — |
| 634 | C2×D4 | — | 2 | 12 | no | — |
| 635 | C2×D4 | — | 2 | 12 | no | — |
| 636 | C2×D4 | — | 2 | 24 | no | — |
| 637 | C2×D4 | — | 2 | 6 | no | — |
| 638 | C2×D4 | — | 2 | 12 | no | — |
| 639 | C2×D4 | — | 2 | 12 | no | — |
| 640 | C2×D4 | — | 4 | 6 | no | — |
| 641 | C2×D4 | — | 4 | 6 | no | — |
| 642 | C2×D4 | — | 4 | 6 | no | — |
| 643 | C2×D4 | — | 4 | 12 | no | — |
| 644 | C2×D4 | — | 4 | 12 | no | — |
| 645 | C2×D4 | — | 4 | 12 | no | — |
| 646 | C2×D4 | — | 4 | 12 | no | — |
| 647 | C2×D4 | — | 8 | 12 | no | — |
| 648 | C2×D4 | — | 8 | 24 | no | — |
| 649 | C2×D4 | — | 8 | 24 | no | — |
| 650 | C2×D4 | — | 8 | 24 | no | — |
| 651 | C2×D4 | — | 8 | 12 | no | — |
| 652 | C2×D4 | — | 8 | 12 | no | — |
| 653 | C2×D4 | — | 20 | 12 | no | — |
| 654 | C2×D4 | — | 20 | 24 | no | — |
| 655 | C2×D4 | — | 20 | 12 | no | — |
| 656 | C2×D4 | — | 40 | 12 | no | — |
| 657 | C2×D4 | — | 40 | 12 | no | — |
| 658 | C2×D4 | — | 40 | 12 | no | — |
| 659 | C2×D4 | — | 40 | 24 | no | — |
| 660 | C2×D4 | — | 40 | 24 | no | — |
| 661 | C22×C4 | — | 2 | 6 | no | — |
| 662 | C22×C4 | — | 2 | 12 | no | — |
| 663 | C22×C4 | — | 2 | 12 | no | — |
| 664 | C22×C4 | — | 2 | 6 | no | — |
| 665 | C22×C4 | — | 4 | 3 | no | — |
| 666 | C22×C4 | — | 4 | 3 | no | — |
| 667 | C22×C4 | — | 8 | 6 | no | — |
| 668 | C22×C4 | — | 10 | 6 | no | — |
| 669 | C22×C4 | — | 20 | 6 | no | — |
| 670 | C22×C4 | — | 20 | 6 | no | — |
| 671 | C22×C4 | — | 20 | 3 | no | — |
| 672 | C22×C4 | — | 20 | 3 | no | — |
| 673 | C22×C4 | — | 20 | 4 | no | — |
| 674 | C22×C4 | #4099 | 1 | 6 | yes | — |
| 675 | C22×C4 | #4099 | 1 | 12 | yes | complemented |
| 676 | C4⋊C4 | — | 2 | 24 | no | — |
| 677 | C4⋊C4 | — | 2 | 12 | no | — |
| 678 | C22⋊C4 | — | 2 | 12 | no | — |
| 679 | C22⋊C4 | — | 2 | 12 | no | — |
| 680 | C22⋊C4 | — | 2 | 12 | no | — |
| 681 | C22⋊C4 | — | 2 | 24 | no | — |
| 682 | C22⋊C4 | — | 2 | 24 | no | — |
| 683 | C22⋊C4 | — | 2 | 12 | no | — |
| 684 | C22⋊C4 | — | 2 | 12 | no | — |
| 685 | C22⋊C4 | — | 10 | 12 | no | — |
| 686 | C22⋊C4 | — | 20 | 24 | no | — |
| 687 | C22⋊C4 | — | 20 | 6 | no | — |
| 688 | C22⋊C4 | — | 20 | 24 | no | — |
| 689 | C22⋊C4 | — | 20 | 12 | no | — |
| 690 | C22⋊C4 | — | 20 | 12 | no | — |
| 691 | C22⋊C4 | — | 40 | 24 | no | — |
| 692 | C42 | — | 2 | 12 | no | — |
| 693 | C2×C5 | — | 2 | 3 | no | — |
| 694 | C2×C5 | — | 2 | 3 | no | — |
| 695 | C2×C5 | — | 4 | 4 | no | — |
| 696 | C2×C5 | — | 4 | 6 | no | — |
| 697 | C2×C5 | — | 8 | 3 | no | — |
| 698 | C2×C5 | — | 8 | 4 | no | — |
| 699 | C2×C5 | #32898 | 1 | 3 | yes | — |
| 700 | D5 | — | 8 | 4 | no | — |
| 701 | C23 | — | 2 | 3 | no | — |
| 702 | C23 | — | 2 | 3 | no | — |
| 703 | C23 | — | 2 | 3 | no | — |
| 704 | C23 | — | 2 | 6 | no | — |
| 705 | C23 | — | 2 | 6 | no | — |
| 706 | C23 | — | 2 | 3 | no | — |
| 707 | C23 | — | 2 | 3 | no | — |
| 708 | C23 | — | 2 | 3 | no | — |
| 709 | C23 | — | 2 | 4 | no | — |
| 710 | C23 | — | 2 | 3 | no | — |
| 711 | C23 | — | 4 | 12 | no | — |
| 712 | C23 | — | 4 | 12 | no | — |
| 713 | C23 | — | 4 | 6 | no | — |
| 714 | C23 | — | 4 | 6 | no | — |
| 715 | C23 | — | 4 | 6 | no | — |
| 716 | C23 | — | 4 | 6 | no | — |
| 717 | C23 | — | 4 | 12 | no | — |
| 718 | C23 | — | 4 | 6 | no | — |
| 719 | C23 | — | 4 | 6 | no | — |
| 720 | C23 | — | 4 | 12 | no | — |
| 721 | C23 | — | 4 | 12 | no | — |
| 722 | C23 | — | 4 | 12 | no | — |
| 723 | C23 | — | 4 | 6 | no | — |
| 724 | C23 | — | 4 | 6 | no | — |
| 725 | C23 | — | 8 | 6 | no | — |
| 726 | C23 | — | 8 | 6 | no | — |
| 727 | C23 | — | 8 | 3 | no | — |
| 728 | C23 | — | 8 | 3 | no | — |
| 729 | C23 | — | 8 | 1 | no | — |
| 730 | C23 | — | 8 | 3 | no | — |
| 731 | C23 | — | 8 | 3 | no | — |
| 732 | C23 | — | 8 | 1 | no | — |
| 733 | C23 | — | 8 | 3 | no | — |
| 734 | C23 | — | 8 | 6 | no | — |
| 735 | C23 | — | 8 | 3 | no | — |
| 736 | C23 | — | 8 | 12 | no | — |
| 737 | C23 | — | 8 | 24 | no | — |
| 738 | C23 | — | 8 | 24 | no | — |
| 739 | C23 | — | 8 | 24 | no | — |
| 740 | C23 | — | 8 | 24 | no | — |
| 741 | C23 | — | 10 | 4 | no | — |
| 742 | C23 | — | 16 | 8 | no | — |
| 743 | C23 | — | 20 | 24 | no | — |
| 744 | C23 | — | 20 | 6 | no | — |
| 745 | C23 | — | 20 | 12 | no | — |
| 746 | C23 | — | 20 | 12 | no | — |
| 747 | C23 | — | 20 | 6 | no | — |
| 748 | C23 | — | 40 | 1 | no | — |
| 749 | C23 | — | 40 | 3 | no | — |
| 750 | C23 | — | 40 | 2 | no | — |
| 751 | C23 | — | 40 | 6 | no | — |
| 752 | C23 | — | 40 | 12 | no | — |
| 753 | C23 | — | 40 | 24 | no | — |
| 754 | C23 | — | 40 | 24 | no | — |
| 755 | C23 | — | 40 | 48 | no | — |
| 756 | C23 | — | 40 | 3 | no | — |
| 757 | C23 | — | 40 | 1 | no | — |
| 758 | C23 | #65533 | 1 | 6 | yes | complemented |
| 759 | C23 | C2×#4099 | 1 | 4 | yes | — |
| 760 | C23 | C2×#4099 | 1 | 3 | yes | — |
| 761 | Q8 | — | 8 | 6 | no | — |
| 762 | D4 | — | 4 | 24 | no | — |
| 763 | D4 | — | 4 | 24 | no | — |
| 764 | D4 | — | 4 | 12 | no | — |
| 765 | D4 | — | 4 | 12 | no | — |
| 766 | D4 | — | 8 | 12 | no | — |
| 767 | D4 | — | 8 | 12 | no | — |
| 768 | D4 | — | 8 | 24 | no | — |
| 769 | D4 | — | 8 | 6 | no | — |
| 770 | D4 | — | 40 | 24 | no | — |
| 771 | D4 | — | 40 | 24 | no | — |
| 772 | D4 | — | 80 | 16 | no | — |
| 773 | C2×C4 | — | 2 | 6 | no | — |
| 774 | C2×C4 | — | 2 | 6 | no | — |
| 775 | C2×C4 | — | 2 | 6 | no | — |
| 776 | C2×C4 | — | 2 | 12 | no | — |
| 777 | C2×C4 | — | 4 | 12 | no | — |
| 778 | C2×C4 | — | 4 | 12 | no | — |
| 779 | C2×C4 | — | 8 | 6 | no | — |
| 780 | C2×C4 | — | 8 | 12 | no | — |
| 781 | C2×C4 | — | 8 | 12 | no | — |
| 782 | C2×C4 | — | 20 | 6 | no | — |
| 783 | C2×C4 | — | 20 | 6 | no | — |
| 784 | C2×C4 | — | 20 | 6 | no | — |
| 785 | C2×C4 | — | 40 | 6 | no | — |
| 786 | C2×C4 | — | 40 | 6 | no | — |
| 787 | C2×C4 | — | 40 | 12 | no | — |
| 788 | C5 | #347042 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 789 | C22 | — | 2 | 1 | no | — |
| 790 | C22 | — | 2 | 3 | no | — |
| 791 | C22 | — | 2 | 3 | no | — |
| 792 | C22 | — | 2 | 1 | no | — |
| 793 | C22 | — | 2 | 6 | no | — |
| 794 | C22 | — | 2 | 6 | no | — |
| 795 | C22 | — | 2 | 12 | no | — |
| 796 | C22 | — | 4 | 6 | no | — |
| 797 | C22 | — | 4 | 6 | no | — |
| 798 | C22 | — | 4 | 8 | no | — |
| 799 | C22 | — | 4 | 6 | no | — |
| 800 | C22 | — | 4 | 12 | no | — |
| 801 | C22 | — | 4 | 3 | no | — |
| 802 | C22 | — | 4 | 6 | no | — |
| 803 | C22 | — | 8 | 3 | no | — |
| 804 | C22 | — | 8 | 6 | no | — |
| 805 | C22 | — | 8 | 6 | no | — |
| 806 | C22 | — | 8 | 12 | no | — |
| 807 | C22 | — | 8 | 12 | no | — |
| 808 | C22 | — | 8 | 3 | no | — |
| 809 | C22 | — | 8 | 12 | no | — |
| 810 | C22 | — | 8 | 12 | no | — |
| 811 | C22 | — | 8 | 4 | no | — |
| 812 | C22 | — | 16 | 4 | no | — |
| 813 | C22 | — | 16 | 12 | no | — |
| 814 | C22 | — | 20 | 12 | no | — |
| 815 | C22 | — | 20 | 16 | no | — |
| 816 | C22 | — | 40 | 6 | no | — |
| 817 | C22 | — | 40 | 12 | no | — |
| 818 | C22 | — | 40 | 24 | no | — |
| 819 | C22 | — | 40 | 6 | no | — |
| 820 | C22 | C2×#65533 | 1 | 3 | yes | — |
| 821 | C22 | #10615841 | 1 | 3 | yes | — |
| 822 | C22 | #10615859 | 1 | 1 | yes | characteristic |
| 823 | C4 | — | 4 | 6 | no | — |
| 824 | C4 | — | 4 | 12 | no | — |
| 825 | C4 | — | 40 | 6 | no | — |
| 826 | C4 | — | 80 | 4 | no | — |
| 827 | C2 | — | 2 | 3 | no | — |
| 828 | C2 | — | 2 | 3 | no | — |
| 829 | C2 | — | 4 | 4 | no | — |
| 830 | C2 | — | 4 | 6 | no | — |
| 831 | C2 | — | 8 | 3 | no | — |
| 832 | C2 | — | 8 | 4 | no | — |
| 833 | C2 | — | 40 | 4 | no | — |
| 834 | C2 | #12248071 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10615859 |
| commutator, cosocle | C25×C5 | C24 |
| Frattini | C25 | C23×D5 |
| Fitting | C5×#62817 | C2 |
| socle | C22×C5 | #2846 |
| hypercenter | #62817 | D5 |
| hypocenter | C5 | #347042 |
| LCS | G ▷ C25×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ #62817 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #12130881 | C2 | semidirect |
| 2. #12046813 | C2 | semidirect |
| 3. #11991903 | C2 | semidirect |
| 4. #11991871 | C2 | semidirect |
| 5. C5×#62817 | C2 | semidirect |
| 14. C22×#4083 | C22 | semidirect |
| 16. #10614343 | C22 | semidirect |
| 17. #10602924 | C22 | semidirect |
| 18. #10602923 | C22 | semidirect |
| 20. #10602463 | C22 | semidirect |
| 24. C26×C5 | D4 | semidirect |
| 25. C25×D5 | C23 | semidirect |
| 26. C2×C5×H(5,𝔽2) | D4 | semidirect |
| 47. C5×#534 | D4 | semidirect |
| 58. C5×#518 | D4 | semidirect |
| 60. C22×C5×C22⋊C4 | D4 | semidirect |
| 63. C22×C22⋊Dic5 | C23 | semidirect |
| 69. #65536 | C23 | semidirect |
| 77. #62817 | D5 | semidirect |
| 226. C24×C5 | #120 | semidirect |
| 275. C22×C4×C5 | #120 | semidirect |
| 308. C26 | C22⋊D5 | semidirect |
| 309. C2×H(5,𝔽2) | C22⋊D5 | semidirect |
| 330. #534 | C22⋊D5 | semidirect |
| 346. #518 | C22⋊D5 | semidirect |
| 351. C22×C22⋊C4 | C22⋊D5 | semidirect |
| 401. C23×C5 | B(4,𝔽2) | semidirect |
| 625. C24 | #4099 | semidirect |
| 675. C22×C4 | #4099 | semidirect |
| 758. C23 | #65533 | semidirect |
| 788. C5 | #347042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #12130881 | 2 |
| #12046813 | 2 |
| #11991903 | 2 |
| #11991871 | 2 |
| C5×#62817 | 2 |
| #347042 | 5 |