Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1156 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #21437720 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21433572 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21423177 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #21423172 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #21423158 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #21422831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #21422536 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C59×#3151 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#14273753 | — | 2 | 2 | no | — |
| 10 | #16838132 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #16838118 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #16838116 | — | 2 | 2 | no | — |
| 13 | #16838114 | — | 2 | 2 | no | — |
| 14 | #16838072 | C22 | 1 | 2 | yes | complemented |
| 15 | #16838070 | — | 2 | 2 | no | — |
| 16 | #16837949 | — | 2 | 2 | no | — |
| 17 | #16837948 | — | 2 | 2 | no | — |
| 18 | C4×#11745685 | C22 | 1 | 2 | yes | — |
| 19 | C4×#11745687 | — | 2 | 2 | no | — |
| 20 | #16837599 | — | 2 | 2 | no | — |
| 21 | #16837599 | C22 | 1 | 4 | yes | — |
| 22 | #16837594 | — | 2 | 2 | no | — |
| 23 | #16837594 | C22 | 1 | 4 | yes | — |
| 24 | #16837426 | C22 | 1 | 2 | yes | — |
| 25 | #16837407 | — | 2 | 2 | no | — |
| 26 | #16837151 | C22 | 1 | 2 | yes | complemented |
| 27 | #16837146 | C22 | 1 | 2 | yes | complemented |
| 28 | #16837134 | C22 | 1 | 4 | yes | complemented |
| 29 | #16837131 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×AGL(1,ℤ/8)×C59 | — | 2 | 2 | no | — |
| 31 | C59×#532 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#127×C59 | C22 | 1 | 1 | yes | characteristic |
| 33 | C59×#496 | — | 2 | 2 | no | — |
| 34 | C59×#493 | C22 | 1 | 2 | yes | — |
| 35 | C59×#492 | C22 | 1 | 2 | yes | — |
| 36 | C4×M16×C59 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#11745685 | — | 2 | 2 | no | — |
| 38 | C2×#11745685 | D4 | 1 | 2 | yes | — |
| 39 | C2×#11745687 | — | 2 | 2 | no | — |
| 40 | #14273753 | — | 4 | 8 | no | — |
| 41 | C2×#11745670 | — | 2 | 4 | no | — |
| 42 | C2×#11745669 | — | 2 | 4 | no | — |
| 43 | C2×#11745664 | — | 2 | 2 | no | — |
| 44 | #14273726 | — | 2 | 2 | no | — |
| 45 | #14273725 | — | 2 | 2 | no | — |
| 46 | #14273723 | — | 2 | 2 | no | — |
| 47 | #14273723 | — | 2 | 2 | no | — |
| 48 | #14273716 | — | 2 | 2 | no | — |
| 49 | #14273714 | — | 2 | 2 | no | — |
| 50 | #14273713 | — | 2 | 4 | no | — |
| 51 | #14273702 | — | 2 | 2 | no | — |
| 52 | #14273700 | — | 2 | 4 | no | — |
| 53 | #14273699 | — | 2 | 4 | no | — |
| 54 | #14273699 | — | 2 | 4 | no | — |
| 55 | #14273698 | — | 2 | 2 | no | — |
| 56 | C4×Dic118 | D4 | 1 | 2 | yes | — |
| 57 | C4×Dic118 | C23 | 1 | 2 | yes | — |
| 58 | #14273692 | — | 2 | 2 | no | — |
| 59 | C4×D236 | D4 | 1 | 2 | yes | — |
| 60 | C4×D236 | C23 | 1 | 2 | yes | — |
| 61 | D4×Dic59 | — | 2 | 2 | no | — |
| 62 | C4×C22⋊D59 | — | 2 | 4 | no | — |
| 63 | C4×C22⋊D59 | — | 2 | 2 | no | — |
| 64 | C4×C22⋊D59 | — | 2 | 2 | no | — |
| 65 | (C22⋊D59)⋊C4 | — | 2 | 4 | no | — |
| 66 | #14273686 | D4 | 1 | 2 | yes | — |
| 67 | #14273685 | — | 2 | 2 | no | — |
| 68 | #14273684 | — | 2 | 2 | no | — |
| 69 | #14273683 | — | 2 | 4 | no | — |
| 70 | C2×C4×Dic59 | — | 2 | 2 | no | — |
| 71 | C42×D59 | — | 2 | 2 | no | — |
| 72 | C4⋊(C59⋊C8) | — | 2 | 2 | no | — |
| 73 | C4⋊(C59⋊C8) | C23 | 1 | 4 | yes | — |
| 74 | #14273648 | — | 2 | 4 | no | — |
| 75 | #14273648 | — | 2 | 4 | no | — |
| 76 | C2×#41×C59 | D4 | 1 | 2 | yes | — |
| 77 | C22×D4×C59 | — | 2 | 2 | no | — |
| 78 | C22×D4×C59 | — | 2 | 1 | no | — |
| 79 | AGL(1,ℤ/8)×C59 | — | 4 | 8 | no | — |
| 80 | C2×SD16×C59 | — | 2 | 4 | no | — |
| 81 | C2×D8×C59 | — | 2 | 4 | no | — |
| 82 | C2×M16×C59 | — | 2 | 1 | no | — |
| 83 | C4⋊Q8×C59 | C23 | 1 | 1 | yes | characteristic |
| 84 | #127×C59 | — | 2 | 1 | no | — |
| 85 | #127×C59 | — | 2 | 2 | no | — |
| 86 | #127×C59 | C23 | 1 | 2 | yes | — |
| 87 | #127×C59 | C23 | 1 | 1 | yes | characteristic |
| 88 | #124×C59 | D4 | 1 | 2 | yes | — |
| 89 | #121×C59 | — | 2 | 2 | no | — |
| 90 | C4×D4×C59 | — | 2 | 2 | no | — |
| 91 | C2×C42×C59 | C23 | 1 | 1 | yes | characteristic |
| 92 | #97×C59 | — | 2 | 1 | no | — |
| 93 | C4×C8×C59 | C23 | 1 | 2 | yes | — |
| 94 | C24×C59 | — | 4 | 1 | no | — |
| 95 | #41×C59 | — | 4 | 4 | no | — |
| 96 | C2×Q8×C59 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×D4×C59 | — | 2 | 2 | no | — |
| 98 | C2×D4×C59 | — | 2 | 2 | no | — |
| 99 | C2×D4×C59 | — | 2 | 2 | no | — |
| 100 | C2×D4×C59 | — | 2 | 4 | no | — |
| 101 | C2×D4×C59 | — | 4 | 4 | no | — |
| 102 | C2×D4×C59 | — | 4 | 4 | no | — |
| 103 | C2×D4×C59 | — | 4 | 4 | no | — |
| 104 | C2×D4×C59 | — | 4 | 2 | no | — |
| 105 | C2×D4×C59 | — | 4 | 1 | no | — |
| 106 | C2×D4×C59 | C2×D4 | 1 | 2 | yes | — |
| 107 | C22×C4×C59 | — | 2 | 2 | no | — |
| 108 | C22×C4×C59 | C2×D4 | 1 | 2 | yes | — |
| 109 | C22×C4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C22⋊D59 | — | 2 | 4 | no | — |
| 111 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 112 | C2×C22⋊D59 | — | 2 | 4 | no | — |
| 113 | C22×Dic59 | — | 2 | 4 | no | — |
| 114 | #11745687 | — | 4 | 4 | no | — |
| 115 | #11745687 | — | 4 | 4 | no | — |
| 116 | #11745685 | — | 2 | 4 | no | — |
| 117 | #11745685 | — | 4 | 2 | no | — |
| 118 | #11745685 | — | 8 | 4 | no | — |
| 119 | C2×D236 | — | 2 | 2 | no | — |
| 120 | C2×D236 | C2×D4 | 1 | 2 | yes | — |
| 121 | C2×C4×D59 | — | 2 | 2 | no | — |
| 122 | C2×C4×D59 | — | 2 | 2 | no | — |
| 123 | C2×C4×D59 | — | 2 | 2 | no | — |
| 124 | C2×Dic118 | — | 2 | 2 | no | — |
| 125 | C2×Dic118 | C2×D4 | 1 | 2 | yes | — |
| 126 | SD16×C59 | — | 4 | 8 | no | — |
| 127 | D8×C59 | — | 4 | 8 | no | — |
| 128 | M16×C59 | — | 2 | 4 | no | — |
| 129 | C2×C8×C59 | — | 2 | 2 | no | — |
| 130 | C4⋊C4×C59 | — | 2 | 2 | no | — |
| 131 | C22⋊C4×C59 | — | 2 | 4 | no | — |
| 132 | C42×C59 | C2×D4 | 1 | 2 | yes | — |
| 133 | C42×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C42×C59 | C24 | 1 | 1 | yes | characteristic |
| 135 | C22⋊Dic59 | — | 2 | 4 | no | — |
| 136 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 137 | #11745670 | — | 4 | 8 | no | — |
| 138 | #11745669 | — | 4 | 8 | no | — |
| 139 | (C2×D59)⋊C4 | — | 2 | 4 | no | — |
| 140 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 141 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 142 | C4⋊Dic59 | C2×D4 | 1 | 2 | yes | — |
| 143 | C4⋊Dic59 | C2×D4 | 1 | 2 | yes | — |
| 144 | Dic59⋊C4 | — | 2 | 4 | no | — |
| 145 | Dic59⋊C4 | — | 2 | 2 | no | — |
| 146 | Dic59⋊C4 | — | 2 | 2 | no | — |
| 147 | C4×Dic59 | — | 2 | 2 | no | — |
| 148 | C4×Dic59 | — | 2 | 2 | no | — |
| 149 | C4×Dic59 | — | 2 | 2 | no | — |
| 150 | C4×Dic59 | — | 2 | 2 | no | — |
| 151 | C4×Dic59 | — | 2 | 2 | no | — |
| 152 | #11745664 | — | 4 | 4 | no | — |
| 153 | C2×C59⋊C8 | — | 2 | 4 | no | — |
| 154 | C23×C59 | — | 2 | 2 | no | — |
| 155 | C23×C59 | — | 4 | 2 | no | — |
| 156 | C23×C59 | — | 8 | 4 | no | — |
| 157 | C23×C59 | — | 8 | 2 | no | — |
| 158 | C23×C59 | #120 | 1 | 1 | yes | characteristic |
| 159 | C22×D59 | — | 2 | 2 | no | — |
| 160 | Q8×C59 | — | 4 | 2 | no | — |
| 161 | D4×C59 | — | 4 | 2 | no | — |
| 162 | D4×C59 | — | 4 | 4 | no | — |
| 163 | D4×C59 | — | 4 | 2 | no | — |
| 164 | D4×C59 | — | 4 | 4 | no | — |
| 165 | D4×C59 | — | 4 | 2 | no | — |
| 166 | D4×C59 | — | 4 | 4 | no | — |
| 167 | D4×C59 | — | 8 | 4 | no | — |
| 168 | D4×C59 | — | 8 | 2 | no | — |
| 169 | D4×C59 | — | 8 | 2 | no | — |
| 170 | C2×C4×C59 | — | 2 | 2 | no | — |
| 171 | C2×C4×C59 | — | 2 | 2 | no | — |
| 172 | C2×C4×C59 | — | 2 | 2 | no | — |
| 173 | C2×C4×C59 | — | 2 | 2 | no | — |
| 174 | C2×C4×C59 | — | 4 | 4 | no | — |
| 175 | C2×C4×C59 | #120 | 1 | 2 | yes | — |
| 176 | C2×C4×C59 | #120 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C59 | C22×D4 | 1 | 2 | yes | — |
| 178 | C2×C4×C59 | C22×D4 | 1 | 1 | yes | characteristic |
| 179 | C22⋊D59 | — | 4 | 4 | no | — |
| 180 | C22⋊D59 | — | 4 | 8 | no | — |
| 181 | C22⋊D59 | — | 8 | 4 | no | — |
| 182 | C2×Dic59 | — | 2 | 2 | no | — |
| 183 | C2×Dic59 | — | 2 | 2 | no | — |
| 184 | C2×Dic59 | — | 2 | 2 | no | — |
| 185 | C2×Dic59 | — | 4 | 8 | no | — |
| 186 | D236 | — | 2 | 2 | no | — |
| 187 | D236 | — | 2 | 2 | no | — |
| 188 | D236 | — | 8 | 2 | no | — |
| 189 | C4×D59 | — | 4 | 4 | no | — |
| 190 | C4×D59 | — | 4 | 2 | no | — |
| 191 | C4×D59 | — | 4 | 2 | no | — |
| 192 | C4×D59 | — | 4 | 4 | no | — |
| 193 | Dic118 | — | 2 | 2 | no | — |
| 194 | Dic118 | — | 8 | 2 | no | — |
| 195 | Dic118 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 196 | C8×C59 | — | 2 | 4 | no | — |
| 197 | C59⋊C8 | — | 4 | 4 | no | — |
| 198 | #18548 | — | 59 | 1 | no | maximal, Sylow |
| 199 | C22×C59 | — | 2 | 2 | no | — |
| 200 | C22×C59 | — | 2 | 1 | no | — |
| 201 | C22×C59 | — | 4 | 4 | no | — |
| 202 | C22×C59 | — | 4 | 2 | no | — |
| 203 | C22×C59 | — | 8 | 4 | no | — |
| 204 | C22×C59 | — | 8 | 2 | no | — |
| 205 | C22×C59 | — | 16 | 4 | no | — |
| 206 | C22×C59 | C2×#120 | 1 | 1 | yes | characteristic |
| 207 | C2×D59 | — | 4 | 2 | no | — |
| 208 | C2×D59 | — | 4 | 2 | no | — |
| 209 | C2×D59 | — | 4 | 2 | no | — |
| 210 | C4×C59 | — | 2 | 2 | no | — |
| 211 | C4×C59 | — | 2 | 1 | no | — |
| 212 | C4×C59 | — | 4 | 2 | no | — |
| 213 | C4×C59 | #453 | 1 | 2 | yes | — |
| 214 | C4×C59 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 215 | C4×C59 | #575 | 1 | 2 | yes | — |
| 216 | Dic59 | — | 2 | 4 | no | — |
| 217 | Dic59 | — | 4 | 2 | no | — |
| 218 | Dic59 | — | 4 | 2 | no | — |
| 219 | #3483 | — | 59 | 1 | no | — |
| 220 | #3151 | D59 | 1 | 1 | yes | characteristic, complemented |
| 221 | #3038 | — | 59 | 2 | no | — |
| 222 | #1624 | — | 59 | 2 | no | — |
| 223 | #1623 | — | 59 | 2 | no | — |
| 224 | #1621 | — | 59 | 4 | no | — |
| 225 | #1560 | — | 59 | 1 | no | — |
| 226 | #1489 | — | 59 | 2 | no | — |
| 227 | C2×C59 | — | 4 | 1 | no | — |
| 228 | C2×C59 | — | 8 | 2 | no | — |
| 229 | C2×C59 | — | 16 | 2 | no | — |
| 230 | C2×C59 | #3006 | 1 | 2 | yes | — |
| 231 | C2×C59 | C2×#453 | 1 | 1 | yes | characteristic |
| 232 | D59 | — | 8 | 2 | no | — |
| 233 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 234 | C2×AGL(1,ℤ/8) | — | 118 | 2 | no | — |
| 235 | Q82 | — | 59 | 1 | no | — |
| 236 | #555 | — | 59 | 1 | no | — |
| 237 | #555 | — | 118 | 2 | no | — |
| 238 | #555 | — | 118 | 2 | no | — |
| 239 | #550 | — | 59 | 2 | no | — |
| 240 | #550 | — | 118 | 2 | no | — |
| 241 | #532 | — | 118 | 2 | no | — |
| 242 | #532 | — | 118 | 2 | no | — |
| 243 | #532 | C2×D59 | 1 | 1 | yes | characteristic |
| 244 | C2×#127 | C2×D59 | 1 | 1 | yes | characteristic |
| 245 | C4×#41 | — | 59 | 2 | no | — |
| 246 | C4×#41 | — | 118 | 2 | no | — |
| 247 | #496 | — | 2 | 2 | no | — |
| 248 | #493 | C2×D59 | 1 | 2 | yes | — |
| 249 | #492 | C2×D59 | 1 | 2 | yes | — |
| 250 | #460 | — | 59 | 4 | no | — |
| 251 | #460 | — | 118 | 2 | no | — |
| 252 | #459 | — | 59 | 4 | no | — |
| 253 | #459 | — | 118 | 2 | no | — |
| 254 | #423 | — | 59 | 2 | no | — |
| 255 | #418 | — | 118 | 2 | no | — |
| 256 | C4×M16 | C2×D59 | 1 | 1 | yes | characteristic |
| 257 | #333 | — | 59 | 2 | no | — |
| 258 | #331 | — | 59 | 2 | no | — |
| 259 | Q8⋊C8 | — | 59 | 4 | no | — |
| 260 | D4⋊C8 | — | 59 | 4 | no | — |
| 261 | C59 | #18548 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 262 | C2×#41 | — | 59 | 2 | no | — |
| 263 | C2×#41 | — | 118 | 2 | no | — |
| 264 | C2×#41 | — | 118 | 2 | no | — |
| 265 | C2×#41 | C22⋊D59 | 1 | 2 | yes | — |
| 266 | C22×D4 | — | 2 | 2 | no | — |
| 267 | C22×D4 | — | 2 | 1 | no | — |
| 268 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 269 | AGL(1,ℤ/8) | — | 236 | 8 | no | — |
| 270 | C2×SD16 | — | 2 | 4 | no | — |
| 271 | C2×SD16 | — | 118 | 4 | no | — |
| 272 | C2×D8 | — | 2 | 4 | no | — |
| 273 | C2×D8 | — | 118 | 4 | no | — |
| 274 | C2×M16 | — | 2 | 1 | no | — |
| 275 | C2×M16 | — | 118 | 2 | no | — |
| 276 | C4⋊Q8 | — | 118 | 2 | no | — |
| 277 | C4⋊Q8 | — | 118 | 2 | no | — |
| 278 | C4⋊Q8 | C22×D59 | 1 | 1 | yes | characteristic |
| 279 | #127 | — | 2 | 2 | no | — |
| 280 | #127 | — | 2 | 1 | no | — |
| 281 | #127 | — | 118 | 2 | no | — |
| 282 | #127 | — | 118 | 2 | no | — |
| 283 | #127 | C22×D59 | 1 | 2 | yes | — |
| 284 | #127 | C22×D59 | 1 | 1 | yes | characteristic |
| 285 | #124 | — | 118 | 4 | no | — |
| 286 | #124 | — | 118 | 2 | no | — |
| 287 | #124 | — | 118 | 2 | no | — |
| 288 | #124 | C22⋊D59 | 1 | 2 | yes | — |
| 289 | #121 | — | 2 | 2 | no | — |
| 290 | #121 | — | 118 | 4 | no | — |
| 291 | #121 | — | 118 | 2 | no | — |
| 292 | #121 | — | 118 | 2 | no | — |
| 293 | #121 | — | 118 | 4 | no | — |
| 294 | #121 | — | 118 | 4 | no | — |
| 295 | C4×Q8 | — | 59 | 2 | no | — |
| 296 | C4×Q8 | — | 59 | 2 | no | — |
| 297 | C4×Q8 | — | 118 | 2 | no | — |
| 298 | C4×D4 | — | 2 | 2 | no | — |
| 299 | C4×D4 | — | 59 | 2 | no | — |
| 300 | C4×D4 | — | 59 | 2 | no | — |
| 301 | C4×D4 | — | 118 | 4 | no | — |
| 302 | C4×D4 | — | 118 | 2 | no | — |
| 303 | C4×D4 | — | 118 | 4 | no | — |
| 304 | C4×D4 | — | 118 | 2 | no | — |
| 305 | C4×D4 | — | 118 | 2 | no | — |
| 306 | #117 | — | 59 | 2 | no | — |
| 307 | #117 | — | 118 | 4 | no | — |
| 308 | #117 | — | 118 | 2 | no | — |
| 309 | #117 | — | 118 | 2 | no | — |
| 310 | C2×C42 | — | 118 | 2 | no | — |
| 311 | C2×C42 | — | 118 | 2 | no | — |
| 312 | C2×C42 | C22×D59 | 1 | 1 | yes | characteristic |
| 313 | C4⋊C8 | — | 59 | 4 | no | — |
| 314 | C4⋊C8 | — | 118 | 2 | no | — |
| 315 | #102 | — | 118 | 4 | no | — |
| 316 | #102 | — | 118 | 4 | no | — |
| 317 | #97 | — | 2 | 1 | no | — |
| 318 | C4×C8 | C22×D59 | 1 | 2 | yes | — |
| 319 | C24 | — | 4 | 1 | no | — |
| 320 | #41 | — | 4 | 4 | no | — |
| 321 | #41 | — | 118 | 4 | no | — |
| 322 | #41 | — | 472 | 4 | no | — |
| 323 | #41 | — | 236 | 2 | no | — |
| 324 | #41 | — | 236 | 4 | no | — |
| 325 | #41 | — | 236 | 4 | no | — |
| 326 | C2×Q8 | — | 59 | 2 | no | — |
| 327 | C2×Q8 | — | 118 | 2 | no | — |
| 328 | C2×Q8 | C2×C22⋊D59 | 1 | 2 | yes | — |
| 329 | C2×D4 | — | 2 | 2 | no | — |
| 330 | C2×D4 | — | 2 | 2 | no | — |
| 331 | C2×D4 | — | 2 | 4 | no | — |
| 332 | C2×D4 | — | 2 | 2 | no | — |
| 333 | C2×D4 | — | 4 | 4 | no | — |
| 334 | C2×D4 | — | 4 | 4 | no | — |
| 335 | C2×D4 | — | 4 | 4 | no | — |
| 336 | C2×D4 | — | 4 | 2 | no | — |
| 337 | C2×D4 | — | 4 | 1 | no | — |
| 338 | C2×D4 | — | 59 | 2 | no | — |
| 339 | C2×D4 | — | 118 | 2 | no | — |
| 340 | C2×D4 | — | 118 | 4 | no | — |
| 341 | C2×D4 | — | 118 | 4 | no | — |
| 342 | C2×D4 | — | 118 | 2 | no | — |
| 343 | C2×D4 | C2×C22⋊D59 | 1 | 2 | yes | — |
| 344 | C22×C4 | — | 2 | 2 | no | — |
| 345 | C22×C4 | — | 118 | 4 | no | — |
| 346 | C22×C4 | — | 118 | 2 | no | — |
| 347 | C22×C4 | — | 118 | 2 | no | — |
| 348 | C22×C4 | — | 118 | 2 | no | — |
| 349 | C22×C4 | D4×D59 | 1 | 2 | yes | — |
| 350 | C22×C4 | C2×C22⋊D59 | 1 | 1 | yes | characteristic |
| 351 | SD16 | — | 4 | 8 | no | — |
| 352 | SD16 | — | 236 | 8 | no | — |
| 353 | D8 | — | 4 | 8 | no | — |
| 354 | D8 | — | 236 | 8 | no | — |
| 355 | M16 | — | 2 | 4 | no | — |
| 356 | M16 | — | 236 | 4 | no | — |
| 357 | C2×C8 | — | 2 | 2 | no | — |
| 358 | C2×C8 | — | 118 | 4 | no | — |
| 359 | C4⋊C4 | — | 2 | 2 | no | — |
| 360 | C4⋊C4 | — | 59 | 2 | no | — |
| 361 | C4⋊C4 | — | 59 | 2 | no | — |
| 362 | C4⋊C4 | — | 118 | 4 | no | — |
| 363 | C4⋊C4 | — | 118 | 2 | no | — |
| 364 | C4⋊C4 | — | 118 | 2 | no | — |
| 365 | C22⋊C4 | — | 2 | 4 | no | — |
| 366 | C22⋊C4 | — | 118 | 4 | no | — |
| 367 | C22⋊C4 | — | 118 | 4 | no | — |
| 368 | C22⋊C4 | — | 118 | 2 | no | — |
| 369 | C22⋊C4 | — | 118 | 2 | no | — |
| 370 | C22⋊C4 | — | 118 | 2 | no | — |
| 371 | C42 | — | 118 | 2 | no | — |
| 372 | C42 | — | 118 | 2 | no | — |
| 373 | C42 | — | 118 | 2 | no | — |
| 374 | C42 | — | 118 | 2 | no | — |
| 375 | C42 | — | 118 | 2 | no | — |
| 376 | C42 | D4×D59 | 1 | 2 | yes | — |
| 377 | C42 | C2×C22⋊D59 | 1 | 1 | yes | characteristic |
| 378 | C42 | C23×D59 | 1 | 1 | yes | characteristic |
| 379 | C23 | — | 2 | 2 | no | — |
| 380 | C23 | — | 4 | 2 | no | — |
| 381 | C23 | — | 8 | 4 | no | — |
| 382 | C23 | — | 8 | 2 | no | — |
| 383 | C23 | — | 118 | 2 | no | — |
| 384 | C23 | #14273695 | 1 | 1 | yes | characteristic |
| 385 | Q8 | — | 4 | 2 | no | — |
| 386 | Q8 | — | 59 | 4 | no | — |
| 387 | Q8 | — | 118 | 2 | no | — |
| 388 | Q8 | — | 472 | 2 | no | — |
| 389 | D4 | — | 4 | 2 | no | — |
| 390 | D4 | — | 4 | 4 | no | — |
| 391 | D4 | — | 4 | 2 | no | — |
| 392 | D4 | — | 4 | 4 | no | — |
| 393 | D4 | — | 4 | 2 | no | — |
| 394 | D4 | — | 4 | 4 | no | — |
| 395 | D4 | — | 8 | 4 | no | — |
| 396 | D4 | — | 8 | 2 | no | — |
| 397 | D4 | — | 8 | 2 | no | — |
| 398 | D4 | — | 118 | 2 | no | — |
| 399 | D4 | — | 118 | 2 | no | — |
| 400 | D4 | — | 472 | 2 | no | — |
| 401 | D4 | — | 472 | 4 | no | — |
| 402 | D4 | — | 236 | 4 | no | — |
| 403 | D4 | — | 236 | 8 | no | — |
| 404 | C2×C4 | — | 2 | 2 | no | — |
| 405 | C2×C4 | — | 2 | 2 | no | — |
| 406 | C2×C4 | — | 2 | 2 | no | — |
| 407 | C2×C4 | — | 2 | 2 | no | — |
| 408 | C2×C4 | — | 4 | 4 | no | — |
| 409 | C2×C4 | — | 118 | 2 | no | — |
| 410 | C2×C4 | — | 118 | 2 | no | — |
| 411 | C2×C4 | — | 118 | 2 | no | — |
| 412 | C2×C4 | — | 236 | 4 | no | — |
| 413 | C2×C4 | — | 236 | 8 | no | — |
| 414 | C2×C4 | — | 236 | 2 | no | — |
| 415 | C2×C4 | — | 236 | 2 | no | — |
| 416 | C2×C4 | — | 236 | 4 | no | — |
| 417 | C2×C4 | #14273695 | 1 | 2 | yes | — |
| 418 | C2×C4 | #14273695 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | C2×D4×D59 | 1 | 2 | yes | — |
| 420 | C2×C4 | C22×C22⋊D59 | 1 | 1 | yes | characteristic |
| 421 | C8 | — | 2 | 4 | no | — |
| 422 | C8 | — | 236 | 4 | no | — |
| 423 | C22 | — | 2 | 2 | no | — |
| 424 | C22 | — | 2 | 1 | no | — |
| 425 | C22 | — | 4 | 4 | no | — |
| 426 | C22 | — | 4 | 2 | no | — |
| 427 | C22 | — | 8 | 4 | no | — |
| 428 | C22 | — | 8 | 2 | no | — |
| 429 | C22 | — | 16 | 4 | no | — |
| 430 | C22 | — | 236 | 2 | no | — |
| 431 | C22 | — | 236 | 2 | no | — |
| 432 | C22 | — | 236 | 2 | no | — |
| 433 | C22 | C2×#14273695 | 1 | 1 | yes | characteristic |
| 434 | C4 | — | 2 | 2 | no | — |
| 435 | C4 | — | 2 | 1 | no | — |
| 436 | C4 | — | 4 | 2 | no | — |
| 437 | C4 | — | 118 | 4 | no | — |
| 438 | C4 | — | 236 | 2 | no | — |
| 439 | C4 | — | 236 | 2 | no | — |
| 440 | C4 | #16837569 | 1 | 2 | yes | — |
| 441 | C4 | AGL(1,ℤ/8)×D59 | 1 | 2 | yes | — |
| 442 | C4 | #16838198 | 1 | 2 | yes | — |
| 443 | C2 | — | 4 | 1 | no | — |
| 444 | C2 | — | 8 | 2 | no | — |
| 445 | C2 | — | 16 | 2 | no | — |
| 446 | C2 | — | 472 | 2 | no | — |
| 447 | C2 | #21433344 | 1 | 2 | yes | — |
| 448 | C2 | C2×#16837569 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21437720 | C2 | semidirect |
| 2. #21433572 | C2 | semidirect |
| 3. #21423177 | C2 | semidirect |
| 4. #21423172 | C2 | semidirect |
| 5. #21423158 | C2 | semidirect |
| 6. #21422831 | C2 | semidirect |
| 7. #21422536 | C2 | semidirect |
| 8. C59×#3151 | C2 | semidirect |
| 10. #16838132 | C22 | semidirect |
| 11. #16838118 | C22 | semidirect |
| 14. #16838072 | C22 | semidirect |
| 26. #16837151 | C22 | semidirect |
| 27. #16837146 | C22 | semidirect |
| 28. #16837134 | C22 | semidirect |
| 29. #16837131 | C22 | semidirect |
| 195. Dic118 | AGL(1,ℤ/8) | semidirect |
| 220. #3151 | D59 | semidirect |
| 261. C59 | #18548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437720 | 2 |
| #21433572 | 2 |
| #21423177 | 2 |
| #21423172 | 2 |
| #21423158 | 2 |
| #21422831 | 2 |
| #21422536 | 2 |
| C59×#3151 | 2 |
| #18548 | 59 |