Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1082 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21438498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21435475 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21434523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21423243 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #21423213 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21423212 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #21423178 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #21423148 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #21422828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #21422545 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C59×#1619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14273746 | — | 2 | 2 | no | — |
| 13 | #16838145 | — | 2 | 2 | no | — |
| 14 | #16838117 | C22 | 1 | 2 | yes | — |
| 15 | #16838116 | — | 2 | 2 | no | — |
| 16 | #16838037 | C22 | 1 | 1 | yes | characteristic |
| 17 | D4×C22⋊D59 | — | 2 | 2 | no | — |
| 18 | #16837969 | — | 2 | 2 | no | — |
| 19 | #16837968 | — | 2 | 2 | no | — |
| 20 | #16837967 | — | 2 | 2 | no | — |
| 21 | #16837950 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16837950 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #16837949 | C22 | 1 | 2 | yes | — |
| 24 | #16837785 | — | 2 | 2 | no | — |
| 25 | #16837782 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #16837774 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16837774 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16837693 | C22 | 1 | 2 | yes | complemented |
| 29 | #16837692 | C22 | 1 | 2 | yes | complemented |
| 30 | #16837690 | — | 2 | 2 | no | — |
| 31 | #16837654 | — | 2 | 2 | no | — |
| 32 | #16837652 | — | 2 | 2 | no | — |
| 33 | #16837595 | — | 2 | 2 | no | — |
| 34 | #16837594 | C22 | 1 | 2 | yes | complemented |
| 35 | #16837424 | C22 | 1 | 2 | yes | complemented |
| 36 | C4×C8×D59 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16837150 | C22 | 1 | 2 | yes | complemented |
| 38 | #16837146 | C22 | 1 | 1 | yes | characteristic |
| 39 | #16837131 | C22 | 1 | 2 | yes | complemented |
| 40 | D4⋊(C59⋊C8) | C22 | 1 | 2 | yes | complemented |
| 41 | #16837129 | C22 | 1 | 2 | yes | complemented |
| 42 | D42×C59 | C22 | 1 | 1 | yes | characteristic |
| 43 | C59×#493 | C22 | 1 | 1 | yes | characteristic |
| 44 | C59×#459 | C22 | 1 | 2 | yes | complemented |
| 45 | C59×#331 | C22 | 1 | 1 | yes | characteristic |
| 46 | C59×D4⋊C8 | C22 | 1 | 2 | yes | complemented |
| 47 | C2×#11745685 | — | 2 | 2 | no | — |
| 48 | C2×#11745687 | — | 2 | 1 | no | — |
| 49 | C2×#11745687 | D4 | 1 | 2 | yes | — |
| 50 | C22×C22⋊D59 | — | 2 | 2 | no | — |
| 51 | C2×D4×D59 | — | 2 | 2 | no | — |
| 52 | #14273746 | — | 4 | 8 | no | — |
| 53 | C2×Dic236 | — | 2 | 2 | no | — |
| 54 | C2×#11745670 | — | 2 | 2 | no | — |
| 55 | C2×#11745670 | — | 2 | 2 | no | — |
| 56 | C2×#11745669 | — | 2 | 2 | no | — |
| 57 | C2×#11745659 | — | 2 | 2 | no | — |
| 58 | C2×C8×D59 | — | 2 | 1 | no | — |
| 59 | #14273727 | C23 | 1 | 1 | yes | characteristic |
| 60 | #14273727 | C23 | 1 | 1 | yes | characteristic |
| 61 | #14273726 | D4 | 1 | 2 | yes | — |
| 62 | #14273723 | — | 2 | 4 | no | — |
| 63 | #14273723 | D4 | 1 | 2 | yes | — |
| 64 | #14273714 | — | 2 | 4 | no | — |
| 65 | #14273714 | — | 2 | 1 | no | — |
| 66 | #14273714 | D4 | 1 | 2 | yes | — |
| 67 | #14273713 | — | 2 | 4 | no | — |
| 68 | #14273713 | — | 2 | 4 | no | — |
| 69 | #14273713 | — | 2 | 2 | no | — |
| 70 | #14273702 | D4 | 1 | 2 | yes | — |
| 71 | #14273701 | — | 2 | 2 | no | — |
| 72 | #14273700 | — | 2 | 2 | no | — |
| 73 | #14273699 | — | 2 | 4 | no | — |
| 74 | #14273698 | — | 2 | 2 | no | — |
| 75 | #14273698 | — | 2 | 2 | no | — |
| 76 | #14273698 | — | 2 | 2 | no | — |
| 77 | #14273698 | — | 2 | 2 | no | — |
| 78 | #14273698 | D4 | 1 | 2 | yes | — |
| 79 | #14273697 | — | 2 | 2 | no | — |
| 80 | #14273696 | — | 2 | 4 | no | — |
| 81 | #14273696 | — | 2 | 2 | no | — |
| 82 | #14273695 | — | 2 | 4 | no | — |
| 83 | #14273695 | — | 2 | 2 | no | — |
| 84 | C4×D236 | C23 | 1 | 2 | yes | — |
| 85 | D4×Dic59 | — | 2 | 2 | no | — |
| 86 | D4×Dic59 | — | 2 | 2 | no | — |
| 87 | C4×C22⋊D59 | — | 2 | 2 | no | — |
| 88 | #14273686 | — | 2 | 2 | no | — |
| 89 | #14273685 | — | 2 | 2 | no | — |
| 90 | #14273683 | — | 2 | 2 | no | — |
| 91 | C42×D59 | C23 | 1 | 1 | yes | characteristic |
| 92 | #14273659 | — | 2 | 2 | no | — |
| 93 | #14273658 | — | 2 | 2 | no | — |
| 94 | C4⋊(C59⋊C8) | C23 | 1 | 2 | yes | — |
| 95 | Dic59⋊C8 | — | 2 | 2 | no | — |
| 96 | #14273649 | — | 2 | 2 | no | — |
| 97 | #14273648 | — | 2 | 2 | no | — |
| 98 | #14273648 | — | 2 | 2 | no | — |
| 99 | C4×C59⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 100 | C8×Dic59 | — | 2 | 1 | no | — |
| 101 | C22×D4×C59 | — | 2 | 2 | no | — |
| 102 | C2×D8×C59 | — | 2 | 2 | no | — |
| 103 | C2×D8×C59 | — | 2 | 2 | no | — |
| 104 | #127×C59 | C23 | 1 | 1 | yes | characteristic |
| 105 | #127×C59 | C23 | 1 | 1 | yes | characteristic |
| 106 | #121×C59 | — | 2 | 2 | no | — |
| 107 | #120×C59 | — | 2 | 2 | no | — |
| 108 | C4×D4×C59 | C23 | 1 | 2 | yes | — |
| 109 | C4⋊C8×C59 | C23 | 1 | 2 | yes | — |
| 110 | #102×C59 | — | 2 | 2 | no | — |
| 111 | C4×C8×C59 | C23 | 1 | 1 | yes | characteristic |
| 112 | C24×C59 | — | 2 | 2 | no | — |
| 113 | C23×D59 | — | 2 | 2 | no | — |
| 114 | C2×D4×C59 | — | 2 | 4 | no | — |
| 115 | C2×D4×C59 | — | 2 | 2 | no | — |
| 116 | C2×D4×C59 | — | 2 | 2 | no | — |
| 117 | C2×D4×C59 | — | 2 | 1 | no | — |
| 118 | C2×D4×C59 | — | 8 | 2 | no | — |
| 119 | C2×D4×C59 | — | 8 | 2 | no | — |
| 120 | C2×D4×C59 | C2×D4 | 1 | 2 | yes | — |
| 121 | C2×D4×C59 | C2×D4 | 1 | 2 | yes | — |
| 122 | C22×C4×C59 | — | 2 | 2 | no | — |
| 123 | C2×C22⋊D59 | — | 2 | 4 | no | — |
| 124 | C2×C22⋊D59 | — | 2 | 4 | no | — |
| 125 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 126 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 127 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 128 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 129 | C2×C22⋊D59 | — | 4 | 1 | no | — |
| 130 | C2×C22⋊D59 | — | 8 | 4 | no | — |
| 131 | C22×Dic59 | — | 2 | 2 | no | — |
| 132 | C22×Dic59 | — | 4 | 1 | no | — |
| 133 | #11745687 | — | 4 | 4 | no | — |
| 134 | #11745687 | — | 4 | 4 | no | — |
| 135 | D4×D59 | — | 8 | 2 | no | — |
| 136 | D4×D59 | — | 8 | 2 | no | — |
| 137 | #11745685 | — | 8 | 2 | no | — |
| 138 | #11745685 | — | 8 | 2 | no | — |
| 139 | C2×D236 | — | 2 | 2 | no | — |
| 140 | C2×D236 | C2×D4 | 1 | 2 | yes | — |
| 141 | C2×C4×D59 | — | 2 | 2 | no | — |
| 142 | C2×C4×D59 | C2×D4 | 1 | 2 | yes | — |
| 143 | C2×C4×D59 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×Dic118 | — | 2 | 1 | no | — |
| 145 | C2×Dic118 | — | 2 | 2 | no | — |
| 146 | C2×Dic118 | C2×D4 | 1 | 2 | yes | — |
| 147 | D8×C59 | — | 4 | 4 | no | — |
| 148 | D8×C59 | — | 8 | 2 | no | — |
| 149 | C2×C8×C59 | — | 2 | 1 | no | — |
| 150 | C2×C8×C59 | — | 2 | 2 | no | — |
| 151 | C4⋊C4×C59 | C2×D4 | 1 | 2 | yes | — |
| 152 | C22⋊C4×C59 | — | 2 | 2 | no | — |
| 153 | C22⋊C4×C59 | — | 2 | 2 | no | — |
| 154 | C42×C59 | C24 | 1 | 1 | yes | characteristic |
| 155 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 156 | C22⋊Dic59 | — | 2 | 4 | no | — |
| 157 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 158 | C22⋊Dic59 | — | 2 | 4 | no | — |
| 159 | C22⋊Dic59 | — | 4 | 2 | no | — |
| 160 | #11745670 | — | 4 | 4 | no | — |
| 161 | #11745670 | — | 4 | 4 | no | — |
| 162 | #11745669 | — | 8 | 2 | no | — |
| 163 | (C2×D59)⋊C4 | — | 2 | 4 | no | — |
| 164 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 165 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 166 | C4⋊Dic59 | — | 2 | 2 | no | — |
| 167 | C4⋊Dic59 | — | 2 | 2 | no | — |
| 168 | C4⋊Dic59 | C2×D4 | 1 | 2 | yes | — |
| 169 | Dic59⋊C4 | — | 2 | 2 | no | — |
| 170 | C4×Dic59 | — | 2 | 4 | no | — |
| 171 | C4×Dic59 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C4×Dic59 | C2×D4 | 1 | 2 | yes | — |
| 173 | C2×C59⋊C8 | — | 2 | 1 | no | — |
| 174 | C2×C59⋊C8 | — | 2 | 2 | no | — |
| 175 | Dic236 | — | 4 | 4 | no | — |
| 176 | #11745659 | — | 8 | 2 | no | — |
| 177 | C8×D59 | — | 2 | 4 | no | — |
| 178 | C23×C59 | — | 2 | 2 | no | — |
| 179 | C23×C59 | — | 2 | 2 | no | — |
| 180 | C23×C59 | — | 4 | 1 | no | — |
| 181 | C23×C59 | — | 8 | 2 | no | — |
| 182 | C23×C59 | — | 8 | 4 | no | — |
| 183 | C22×D59 | — | 2 | 2 | no | — |
| 184 | C22×D59 | — | 8 | 4 | no | — |
| 185 | C22×D59 | — | 8 | 2 | no | — |
| 186 | C22×D59 | #120 | 1 | 1 | yes | characteristic |
| 187 | D4×C59 | — | 2 | 2 | no | — |
| 188 | D4×C59 | — | 2 | 2 | no | — |
| 189 | D4×C59 | — | 4 | 2 | no | — |
| 190 | D4×C59 | — | 4 | 2 | no | — |
| 191 | D4×C59 | — | 4 | 2 | no | — |
| 192 | D4×C59 | — | 4 | 2 | no | — |
| 193 | D4×C59 | — | 4 | 2 | no | — |
| 194 | D4×C59 | — | 4 | 2 | no | — |
| 195 | D4×C59 | — | 8 | 4 | no | — |
| 196 | C2×C4×C59 | — | 2 | 2 | no | — |
| 197 | C2×C4×C59 | — | 4 | 2 | no | — |
| 198 | C2×C4×C59 | — | 4 | 2 | no | — |
| 199 | C2×C4×C59 | C22×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×C59 | C22×D4 | 1 | 2 | yes | — |
| 201 | C22⋊D59 | — | 4 | 4 | no | — |
| 202 | C22⋊D59 | — | 8 | 2 | no | — |
| 203 | C22⋊D59 | — | 8 | 2 | no | — |
| 204 | C22⋊D59 | — | 8 | 2 | no | — |
| 205 | C22⋊D59 | — | 8 | 4 | no | — |
| 206 | C22⋊D59 | — | 8 | 4 | no | — |
| 207 | C22⋊D59 | — | 8 | 2 | no | — |
| 208 | C2×Dic59 | — | 2 | 2 | no | — |
| 209 | C2×Dic59 | — | 2 | 2 | no | — |
| 210 | C2×Dic59 | — | 4 | 4 | no | — |
| 211 | C2×Dic59 | — | 4 | 1 | no | — |
| 212 | C2×Dic59 | — | 8 | 2 | no | — |
| 213 | C2×Dic59 | #120 | 1 | 2 | yes | — |
| 214 | C2×Dic59 | #120 | 1 | 1 | yes | characteristic |
| 215 | D236 | — | 2 | 2 | no | — |
| 216 | D236 | — | 2 | 2 | no | — |
| 217 | D236 | — | 8 | 2 | no | — |
| 218 | C4×D59 | — | 2 | 2 | no | — |
| 219 | C4×D59 | — | 2 | 2 | no | — |
| 220 | C4×D59 | — | 2 | 2 | no | — |
| 221 | C4×D59 | — | 4 | 2 | no | — |
| 222 | C4×D59 | — | 4 | 2 | no | — |
| 223 | Dic118 | — | 4 | 2 | no | — |
| 224 | Dic118 | — | 4 | 2 | no | — |
| 225 | Dic118 | — | 8 | 2 | no | — |
| 226 | C8×C59 | — | 2 | 2 | no | — |
| 227 | C8×C59 | — | 4 | 2 | no | — |
| 228 | C59⋊C8 | — | 2 | 2 | no | — |
| 229 | C59⋊C8 | — | 4 | 2 | no | — |
| 230 | #18686 | — | 59 | 1 | no | maximal, Sylow |
| 231 | C22×C59 | — | 4 | 2 | no | — |
| 232 | C22×C59 | — | 4 | 4 | no | — |
| 233 | C22×C59 | — | 4 | 2 | no | — |
| 234 | C22×C59 | — | 4 | 2 | no | — |
| 235 | C22×C59 | — | 4 | 2 | no | — |
| 236 | C22×C59 | — | 8 | 2 | no | — |
| 237 | C22×C59 | — | 8 | 1 | no | — |
| 238 | C22×C59 | — | 16 | 4 | no | — |
| 239 | C22×C59 | C2×#120 | 1 | 1 | yes | characteristic |
| 240 | C2×D59 | — | 2 | 2 | no | — |
| 241 | C2×D59 | — | 2 | 1 | no | — |
| 242 | C2×D59 | — | 4 | 2 | no | — |
| 243 | C2×D59 | — | 4 | 2 | no | — |
| 244 | C2×D59 | — | 4 | 2 | no | — |
| 245 | C2×D59 | — | 16 | 4 | no | — |
| 246 | C4×C59 | — | 2 | 1 | no | — |
| 247 | C4×C59 | — | 4 | 2 | no | — |
| 248 | C4×C59 | #576 | 1 | 2 | yes | — |
| 249 | C4×C59 | #577 | 1 | 2 | yes | — |
| 250 | Dic59 | — | 2 | 2 | no | — |
| 251 | Dic59 | — | 4 | 2 | no | — |
| 252 | Dic59 | — | 4 | 2 | no | — |
| 253 | Dic59 | — | 8 | 1 | no | — |
| 254 | Dic59 | #453 | 1 | 2 | yes | — |
| 255 | #3549 | — | 59 | 1 | no | — |
| 256 | #3253 | — | 59 | 2 | no | — |
| 257 | #3147 | — | 59 | 1 | no | — |
| 258 | #1634 | — | 59 | 2 | no | — |
| 259 | #1629 | — | 59 | 1 | no | — |
| 260 | #1629 | — | 59 | 1 | no | — |
| 261 | #1624 | — | 59 | 2 | no | — |
| 262 | #1619 | — | 59 | 1 | no | — |
| 263 | #1619 | D59 | 1 | 1 | yes | characteristic, complemented |
| 264 | #1560 | — | 59 | 1 | no | — |
| 265 | #1492 | — | 59 | 2 | no | — |
| 266 | C2×C59 | — | 8 | 2 | no | — |
| 267 | C2×C59 | — | 8 | 2 | no | — |
| 268 | C2×C59 | — | 16 | 1 | no | — |
| 269 | C2×C59 | #3012 | 1 | 2 | yes | — |
| 270 | C2×C59 | C2×#453 | 1 | 1 | yes | characteristic |
| 271 | D59 | — | 4 | 1 | no | — |
| 272 | D59 | — | 8 | 2 | no | — |
| 273 | C2×#135 | — | 118 | 2 | no | — |
| 274 | H(3,𝔽4) | — | 118 | 2 | no | — |
| 275 | #555 | — | 59 | 2 | no | — |
| 276 | #555 | — | 118 | 2 | no | — |
| 277 | D42 | — | 59 | 1 | no | — |
| 278 | D42 | — | 118 | 2 | no | — |
| 279 | D42 | C2×D59 | 1 | 1 | yes | characteristic |
| 280 | #535 | — | 118 | 2 | no | — |
| 281 | #535 | — | 118 | 2 | no | — |
| 282 | #535 | — | 118 | 2 | no | — |
| 283 | #532 | — | 59 | 2 | no | — |
| 284 | #532 | — | 59 | 1 | no | — |
| 285 | #532 | — | 59 | 1 | no | — |
| 286 | #495 | — | 118 | 2 | no | — |
| 287 | #494 | — | 59 | 1 | no | — |
| 288 | #493 | C2×D59 | 1 | 1 | yes | characteristic |
| 289 | #492 | — | 59 | 1 | no | — |
| 290 | #492 | — | 59 | 1 | no | — |
| 291 | #476 | — | 59 | 2 | no | — |
| 292 | #476 | — | 59 | 2 | no | — |
| 293 | #476 | — | 118 | 2 | no | — |
| 294 | #469 | — | 118 | 2 | no | — |
| 295 | #469 | — | 118 | 2 | no | — |
| 296 | #459 | — | 59 | 2 | no | — |
| 297 | #459 | — | 118 | 2 | no | — |
| 298 | #459 | C2×D59 | 1 | 2 | yes | complemented |
| 299 | #423 | — | 59 | 2 | no | — |
| 300 | C2×C4×C8 | — | 59 | 1 | no | — |
| 301 | #333 | — | 59 | 2 | no | — |
| 302 | #331 | — | 59 | 1 | no | — |
| 303 | #331 | C2×D59 | 1 | 1 | yes | characteristic |
| 304 | D4⋊C8 | — | 59 | 2 | no | — |
| 305 | D4⋊C8 | — | 59 | 2 | no | — |
| 306 | D4⋊C8 | — | 59 | 2 | no | — |
| 307 | D4⋊C8 | C2×D59 | 1 | 2 | yes | complemented |
| 308 | C59 | #18686 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 309 | C2×#41 | — | 59 | 2 | no | — |
| 310 | C2×#41 | — | 118 | 2 | no | — |
| 311 | C2×#41 | — | 118 | 1 | no | — |
| 312 | C22×D4 | — | 2 | 2 | no | — |
| 313 | C22×D4 | — | 118 | 2 | no | — |
| 314 | C22×D4 | — | 118 | 2 | no | — |
| 315 | #135 | — | 236 | 8 | no | — |
| 316 | C2×Q16 | — | 118 | 2 | no | — |
| 317 | C2×SD16 | — | 118 | 2 | no | — |
| 318 | C2×SD16 | — | 118 | 2 | no | — |
| 319 | C2×D8 | — | 2 | 2 | no | — |
| 320 | C2×D8 | — | 2 | 2 | no | — |
| 321 | C2×D8 | — | 118 | 2 | no | — |
| 322 | C2×M16 | — | 118 | 2 | no | — |
| 323 | C22×C8 | — | 118 | 1 | no | — |
| 324 | C4⋊Q8 | — | 59 | 2 | no | — |
| 325 | C4⋊Q8 | — | 59 | 1 | no | — |
| 326 | C4⋊Q8 | — | 59 | 1 | no | — |
| 327 | #127 | — | 59 | 2 | no | — |
| 328 | #127 | — | 118 | 4 | no | — |
| 329 | #127 | C22×D59 | 1 | 1 | yes | characteristic |
| 330 | #127 | C22×D59 | 1 | 1 | yes | characteristic |
| 331 | #124 | — | 59 | 2 | no | — |
| 332 | #124 | — | 118 | 2 | no | — |
| 333 | #124 | — | 118 | 1 | no | — |
| 334 | #124 | — | 118 | 4 | no | — |
| 335 | #124 | — | 118 | 4 | no | — |
| 336 | #124 | — | 118 | 4 | no | — |
| 337 | #121 | — | 2 | 2 | no | — |
| 338 | #121 | — | 59 | 2 | no | — |
| 339 | #121 | — | 59 | 2 | no | — |
| 340 | #121 | — | 118 | 2 | no | — |
| 341 | #121 | — | 118 | 2 | no | — |
| 342 | #121 | — | 118 | 2 | no | — |
| 343 | #121 | — | 118 | 2 | no | — |
| 344 | #121 | — | 118 | 4 | no | — |
| 345 | #121 | — | 118 | 2 | no | — |
| 346 | #121 | — | 118 | 2 | no | — |
| 347 | #120 | — | 2 | 2 | no | — |
| 348 | #120 | — | 118 | 2 | no | — |
| 349 | #120 | — | 118 | 4 | no | — |
| 350 | #120 | — | 118 | 2 | no | — |
| 351 | #120 | — | 118 | 4 | no | — |
| 352 | #120 | — | 118 | 2 | no | — |
| 353 | C4×D4 | — | 59 | 2 | no | — |
| 354 | C4×D4 | — | 118 | 2 | no | — |
| 355 | C4×D4 | — | 118 | 2 | no | — |
| 356 | C4×D4 | — | 118 | 2 | no | — |
| 357 | C4×D4 | C22×D59 | 1 | 2 | yes | — |
| 358 | #117 | — | 118 | 2 | no | — |
| 359 | #117 | — | 118 | 2 | no | — |
| 360 | #117 | — | 118 | 2 | no | — |
| 361 | C2×C42 | — | 59 | 1 | no | — |
| 362 | #106 | — | 118 | 2 | no | — |
| 363 | #106 | — | 118 | 2 | no | — |
| 364 | C4⋊C8 | — | 59 | 2 | no | — |
| 365 | C4⋊C8 | — | 118 | 2 | no | — |
| 366 | C4⋊C8 | C22×D59 | 1 | 2 | yes | — |
| 367 | #102 | — | 2 | 2 | no | — |
| 368 | #102 | — | 118 | 2 | no | — |
| 369 | #102 | — | 118 | 2 | no | — |
| 370 | #102 | — | 118 | 2 | no | — |
| 371 | C4×C8 | — | 59 | 1 | no | — |
| 372 | C4×C8 | — | 118 | 1 | no | — |
| 373 | C4×C8 | C22×D59 | 1 | 1 | yes | characteristic |
| 374 | C24 | — | 2 | 2 | no | — |
| 375 | C24 | — | 118 | 2 | no | — |
| 376 | #41 | — | 472 | 2 | no | — |
| 377 | #41 | — | 472 | 2 | no | — |
| 378 | #41 | — | 236 | 4 | no | — |
| 379 | #41 | — | 236 | 4 | no | — |
| 380 | C2×Q8 | — | 59 | 2 | no | — |
| 381 | C2×Q8 | — | 118 | 2 | no | — |
| 382 | C2×Q8 | — | 118 | 1 | no | — |
| 383 | C2×D4 | — | 2 | 4 | no | — |
| 384 | C2×D4 | — | 2 | 2 | no | — |
| 385 | C2×D4 | — | 2 | 2 | no | — |
| 386 | C2×D4 | — | 2 | 1 | no | — |
| 387 | C2×D4 | — | 8 | 2 | no | — |
| 388 | C2×D4 | — | 8 | 2 | no | — |
| 389 | C2×D4 | — | 59 | 2 | no | — |
| 390 | C2×D4 | — | 118 | 2 | no | — |
| 391 | C2×D4 | — | 118 | 2 | no | — |
| 392 | C2×D4 | — | 118 | 2 | no | — |
| 393 | C2×D4 | — | 118 | 2 | no | — |
| 394 | C2×D4 | — | 118 | 2 | no | — |
| 395 | C2×D4 | — | 118 | 4 | no | — |
| 396 | C2×D4 | — | 118 | 4 | no | — |
| 397 | C2×D4 | — | 472 | 2 | no | — |
| 398 | C2×D4 | — | 472 | 2 | no | — |
| 399 | C2×D4 | — | 472 | 4 | no | — |
| 400 | C2×D4 | — | 236 | 1 | no | — |
| 401 | C2×D4 | D4×D59 | 1 | 2 | yes | — |
| 402 | C2×D4 | D4×D59 | 1 | 2 | yes | — |
| 403 | C22×C4 | — | 2 | 2 | no | — |
| 404 | C22×C4 | — | 59 | 2 | no | — |
| 405 | C22×C4 | — | 59 | 1 | no | — |
| 406 | C22×C4 | — | 118 | 2 | no | — |
| 407 | C22×C4 | — | 118 | 2 | no | — |
| 408 | C22×C4 | — | 236 | 1 | no | — |
| 409 | Q16 | — | 236 | 4 | no | — |
| 410 | SD16 | — | 236 | 4 | no | — |
| 411 | SD16 | — | 236 | 4 | no | — |
| 412 | D8 | — | 4 | 4 | no | — |
| 413 | D8 | — | 8 | 2 | no | — |
| 414 | D8 | — | 472 | 2 | no | — |
| 415 | M16 | — | 472 | 2 | no | — |
| 416 | C2×C8 | — | 2 | 1 | no | — |
| 417 | C2×C8 | — | 2 | 2 | no | — |
| 418 | C2×C8 | — | 118 | 4 | no | — |
| 419 | C2×C8 | — | 118 | 1 | no | — |
| 420 | C2×C8 | — | 118 | 2 | no | — |
| 421 | C4⋊C4 | — | 59 | 2 | no | — |
| 422 | C4⋊C4 | — | 118 | 2 | no | — |
| 423 | C4⋊C4 | — | 118 | 2 | no | — |
| 424 | C4⋊C4 | — | 118 | 2 | no | — |
| 425 | C4⋊C4 | D4×D59 | 1 | 2 | yes | — |
| 426 | C22⋊C4 | — | 2 | 2 | no | — |
| 427 | C22⋊C4 | — | 2 | 2 | no | — |
| 428 | C22⋊C4 | — | 118 | 2 | no | — |
| 429 | C22⋊C4 | — | 118 | 4 | no | — |
| 430 | C22⋊C4 | — | 118 | 2 | no | — |
| 431 | C22⋊C4 | — | 118 | 4 | no | — |
| 432 | C22⋊C4 | — | 118 | 2 | no | — |
| 433 | C22⋊C4 | — | 118 | 4 | no | — |
| 434 | C22⋊C4 | — | 118 | 2 | no | — |
| 435 | C22⋊C4 | — | 236 | 2 | no | — |
| 436 | C42 | — | 59 | 1 | no | — |
| 437 | C42 | — | 59 | 2 | no | — |
| 438 | C42 | — | 118 | 4 | no | — |
| 439 | C42 | C23×D59 | 1 | 1 | yes | characteristic |
| 440 | C23 | — | 2 | 2 | no | — |
| 441 | C23 | — | 2 | 2 | no | — |
| 442 | C23 | — | 4 | 1 | no | — |
| 443 | C23 | — | 8 | 4 | no | — |
| 444 | C23 | — | 8 | 2 | no | — |
| 445 | C23 | — | 59 | 1 | no | — |
| 446 | C23 | — | 118 | 2 | no | — |
| 447 | C23 | — | 472 | 4 | no | — |
| 448 | C23 | — | 472 | 2 | no | — |
| 449 | Q8 | — | 472 | 2 | no | — |
| 450 | Q8 | — | 236 | 2 | no | — |
| 451 | Q8 | — | 236 | 2 | no | — |
| 452 | D4 | — | 2 | 2 | no | — |
| 453 | D4 | — | 2 | 2 | no | — |
| 454 | D4 | — | 4 | 2 | no | — |
| 455 | D4 | — | 4 | 2 | no | — |
| 456 | D4 | — | 4 | 2 | no | — |
| 457 | D4 | — | 4 | 2 | no | — |
| 458 | D4 | — | 4 | 2 | no | — |
| 459 | D4 | — | 4 | 2 | no | — |
| 460 | D4 | — | 8 | 4 | no | — |
| 461 | D4 | — | 118 | 2 | no | — |
| 462 | D4 | — | 118 | 2 | no | — |
| 463 | D4 | — | 472 | 2 | no | — |
| 464 | D4 | — | 472 | 2 | no | — |
| 465 | D4 | — | 472 | 2 | no | — |
| 466 | D4 | — | 472 | 2 | no | — |
| 467 | D4 | — | 472 | 2 | no | — |
| 468 | D4 | — | 472 | 4 | no | — |
| 469 | D4 | — | 472 | 4 | no | — |
| 470 | D4 | — | 236 | 4 | no | — |
| 471 | C2×C4 | — | 2 | 2 | no | — |
| 472 | C2×C4 | — | 4 | 2 | no | — |
| 473 | C2×C4 | — | 4 | 2 | no | — |
| 474 | C2×C4 | — | 59 | 1 | no | — |
| 475 | C2×C4 | — | 59 | 2 | no | — |
| 476 | C2×C4 | — | 118 | 2 | no | — |
| 477 | C2×C4 | — | 118 | 2 | no | — |
| 478 | C2×C4 | — | 118 | 2 | no | — |
| 479 | C2×C4 | — | 118 | 2 | no | — |
| 480 | C2×C4 | — | 118 | 2 | no | — |
| 481 | C2×C4 | — | 472 | 2 | no | — |
| 482 | C2×C4 | — | 236 | 4 | no | — |
| 483 | C2×C4 | — | 236 | 1 | no | — |
| 484 | C2×C4 | — | 236 | 2 | no | — |
| 485 | C2×C4 | — | 236 | 2 | no | — |
| 486 | C2×C4 | C2×D4×D59 | 1 | 1 | yes | characteristic |
| 487 | C2×C4 | C2×D4×D59 | 1 | 2 | yes | — |
| 488 | C8 | — | 2 | 2 | no | — |
| 489 | C8 | — | 4 | 2 | no | — |
| 490 | C8 | — | 118 | 2 | no | — |
| 491 | C8 | — | 236 | 2 | no | — |
| 492 | C22 | — | 4 | 2 | no | — |
| 493 | C22 | — | 4 | 2 | no | — |
| 494 | C22 | — | 4 | 4 | no | — |
| 495 | C22 | — | 4 | 2 | no | — |
| 496 | C22 | — | 4 | 2 | no | — |
| 497 | C22 | — | 8 | 2 | no | — |
| 498 | C22 | — | 8 | 1 | no | — |
| 499 | C22 | — | 16 | 4 | no | — |
| 500 | C22 | — | 118 | 2 | no | — |
| 501 | C22 | — | 118 | 1 | no | — |
| 502 | C22 | — | 944 | 4 | no | — |
| 503 | C22 | — | 236 | 2 | no | — |
| 504 | C22 | — | 236 | 2 | no | — |
| 505 | C22 | — | 236 | 2 | no | — |
| 506 | C22 | #120×D59 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 1 | no | — |
| 508 | C4 | — | 4 | 2 | no | — |
| 509 | C4 | — | 59 | 2 | no | — |
| 510 | C4 | — | 118 | 2 | no | — |
| 511 | C4 | — | 472 | 1 | no | — |
| 512 | C4 | — | 236 | 2 | no | — |
| 513 | C4 | — | 236 | 2 | no | — |
| 514 | C4 | #16838203 | 1 | 2 | yes | — |
| 515 | C4 | #16838212 | 1 | 2 | yes | — |
| 516 | C2 | — | 8 | 2 | no | — |
| 517 | C2 | — | 8 | 2 | no | — |
| 518 | C2 | — | 16 | 1 | no | — |
| 519 | C2 | — | 472 | 2 | no | — |
| 520 | C2 | — | 236 | 1 | no | — |
| 521 | C2 | #21433395 | 1 | 2 | yes | — |
| 522 | C2 | #453×D59 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21438498 | C2 | semidirect |
| 2. #21435475 | C2 | semidirect |
| 3. #21434523 | C2 | semidirect |
| 4. #21423243 | C2 | semidirect |
| 5. #21423213 | C2 | semidirect |
| 6. #21423212 | C2 | semidirect |
| 7. #21423178 | C2 | semidirect |
| 8. #21423148 | C2 | semidirect |
| 9. #21422828 | C2 | semidirect |
| 10. #21422545 | C2 | semidirect |
| 11. C59×#1619 | C2 | semidirect |
| 22. #16837950 | C22 | semidirect |
| 25. #16837782 | C22 | semidirect |
| 27. #16837774 | C22 | semidirect |
| 28. #16837693 | C22 | semidirect |
| 29. #16837692 | C22 | semidirect |
| 34. #16837594 | C22 | semidirect |
| 35. #16837424 | C22 | semidirect |
| 36. C4×C8×D59 | C22 | semidirect |
| 37. #16837150 | C22 | semidirect |
| 39. #16837131 | C22 | semidirect |
| 40. D4⋊(C59⋊C8) | C22 | semidirect |
| 41. #16837129 | C22 | semidirect |
| 44. C59×#459 | C22 | semidirect |
| 46. C59×D4⋊C8 | C22 | semidirect |
| 263. #1619 | D59 | semidirect |
| 298. #459 | C2×D59 | semidirect |
| 307. D4⋊C8 | C2×D59 | semidirect |
| 308. C59 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438498 | 2 |
| #21435475 | 2 |
| #21434523 | 2 |
| #21423243 | 2 |
| #21423213 | 2 |
| #21423212 | 2 |
| #21423178 | 2 |
| #21423148 | 2 |
| #21422828 | 2 |
| #21422545 | 2 |
| C59×#1619 | 2 |
| #18686 | 59 |