Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
976 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #21437888 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #21425779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #21425759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21425746 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #21424072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21424069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C59×#2122 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14273774 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14273772 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #16838058 | — | 2 | 1 | no | — |
| 11 | #16838058 | — | 2 | 1 | no | — |
| 12 | #16838049 | — | 2 | 1 | no | — |
| 13 | #16838049 | — | 2 | 1 | no | — |
| 14 | #16838039 | — | 2 | 2 | no | — |
| 15 | #16838039 | — | 2 | 2 | no | — |
| 16 | #16837978 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16837972 | — | 2 | 1 | no | — |
| 18 | #16837965 | — | 2 | 1 | no | — |
| 19 | #16837950 | — | 2 | 1 | no | — |
| 20 | #16837948 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#14273714 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #124×D59 | — | 2 | 1 | no | — |
| 23 | #16837870 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #16837420 | — | 2 | 1 | no | — |
| 25 | #16837418 | — | 2 | 1 | no | — |
| 26 | #16837412 | — | 2 | 1 | no | — |
| 27 | #16837410 | — | 2 | 1 | no | — |
| 28 | #16837386 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16837376 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #16837200 | — | 2 | 1 | no | — |
| 31 | #16837198 | — | 2 | 1 | no | — |
| 32 | #16837196 | — | 2 | 1 | no | — |
| 33 | #16837194 | — | 2 | 1 | no | — |
| 34 | #16837189 | — | 2 | 2 | no | — |
| 35 | C59×#535 | C22 | 1 | 1 | yes | characteristic |
| 36 | C59×#413 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C59×#410 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C59×AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 39 | #14273774 | — | 4 | 2 | no | — |
| 40 | #14273774 | — | 4 | 2 | no | — |
| 41 | #14273772 | — | 4 | 2 | no | — |
| 42 | #14273772 | — | 4 | 2 | no | — |
| 43 | C2×#11745685 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×#11745685 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×#11745685 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×#11745685 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×#11745687 | — | 2 | 1 | no | — |
| 48 | C2×#11745687 | — | 2 | 1 | no | — |
| 49 | C2×#11745687 | — | 2 | 1 | no | — |
| 50 | C2×#11745687 | — | 2 | 1 | no | — |
| 51 | C2×#11745687 | — | 2 | 1 | no | — |
| 52 | C22×Dic118 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C22×Dic118 | D4 | 1 | 1 | yes | characteristic |
| 54 | C22×Dic118 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×Q8×D59 | — | 2 | 1 | no | — |
| 56 | C22×C22⋊D59 | — | 2 | 2 | no | — |
| 57 | C2×D4×D59 | — | 2 | 1 | no | — |
| 58 | C2×D4×D59 | — | 2 | 1 | no | — |
| 59 | C2×#11745664 | — | 2 | 1 | no | — |
| 60 | #14273727 | — | 2 | 1 | no | — |
| 61 | #14273725 | D4 | 1 | 1 | yes | characteristic |
| 62 | #14273723 | D4 | 1 | 1 | yes | characteristic |
| 63 | #14273716 | D4 | 1 | 1 | yes | characteristic |
| 64 | #14273715 | — | 2 | 1 | no | — |
| 65 | #14273714 | — | 2 | 1 | no | — |
| 66 | #14273714 | — | 2 | 1 | no | — |
| 67 | #14273714 | — | 2 | 1 | no | — |
| 68 | #14273714 | — | 2 | 1 | no | — |
| 69 | #14273714 | D4 | 1 | 1 | yes | characteristic |
| 70 | #14273713 | — | 2 | 2 | no | — |
| 71 | #14273713 | — | 2 | 2 | no | — |
| 72 | #14273711 | — | 2 | 2 | no | — |
| 73 | #14273709 | — | 2 | 2 | no | — |
| 74 | #14273709 | — | 2 | 2 | no | — |
| 75 | #14273707 | — | 2 | 1 | no | — |
| 76 | #14273707 | — | 2 | 1 | no | — |
| 77 | #14273704 | — | 2 | 2 | no | — |
| 78 | #14273704 | — | 2 | 2 | no | — |
| 79 | #14273699 | — | 2 | 2 | no | — |
| 80 | #14273699 | — | 2 | 2 | no | — |
| 81 | #14273699 | — | 2 | 1 | no | — |
| 82 | #14273699 | — | 2 | 1 | no | — |
| 83 | #14273698 | — | 2 | 2 | no | — |
| 84 | #14273698 | — | 2 | 2 | no | — |
| 85 | #14273695 | — | 2 | 2 | no | — |
| 86 | #14273695 | — | 2 | 2 | no | — |
| 87 | #14273692 | — | 2 | 1 | no | — |
| 88 | D4×Dic59 | — | 2 | 2 | no | — |
| 89 | D4×Dic59 | — | 2 | 2 | no | — |
| 90 | #14273689 | — | 2 | 1 | no | — |
| 91 | C4×C22⋊D59 | — | 2 | 1 | no | — |
| 92 | C4×C22⋊D59 | — | 2 | 1 | no | — |
| 93 | (C22⋊D59)⋊C4 | — | 2 | 2 | no | — |
| 94 | #14273686 | — | 2 | 1 | no | — |
| 95 | #14273684 | — | 2 | 1 | no | — |
| 96 | C2×C22⋊Dic59 | — | 2 | 2 | no | — |
| 97 | C22⋊C4×D59 | — | 2 | 2 | no | — |
| 98 | C22⋊C4×D59 | — | 2 | 2 | no | — |
| 99 | C2×C4×Dic59 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | C42×D59 | — | 2 | 1 | no | — |
| 101 | #14273655 | — | 4 | 2 | no | — |
| 102 | #14273653 | — | 4 | 2 | no | — |
| 103 | #14273652 | — | 4 | 2 | no | — |
| 104 | #14273650 | — | 4 | 2 | no | — |
| 105 | #14273646 | — | 2 | 1 | no | — |
| 106 | #14273644 | — | 2 | 1 | no | — |
| 107 | #14273642 | — | 2 | 1 | no | — |
| 108 | #14273642 | — | 2 | 1 | no | — |
| 109 | C2×#41×C59 | C23 | 1 | 1 | yes | characteristic |
| 110 | C22×D4×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×M16×C59 | — | 2 | 1 | no | — |
| 112 | #127×C59 | — | 2 | 1 | no | — |
| 113 | #124×C59 | — | 2 | 1 | no | — |
| 114 | #121×C59 | — | 2 | 1 | no | — |
| 115 | #121×C59 | — | 2 | 1 | no | — |
| 116 | #120×C59 | D4 | 1 | 2 | yes | — |
| 117 | #120×C59 | D4 | 1 | 2 | yes | — |
| 118 | #117×C59 | — | 2 | 1 | no | — |
| 119 | #117×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | #101×C59 | — | 2 | 1 | no | — |
| 121 | #100×C59 | — | 2 | 1 | no | — |
| 122 | #99×C59 | — | 2 | 1 | no | — |
| 123 | #99×C59 | — | 2 | 1 | no | — |
| 124 | C24×C59 | C22⋊C4 | 1 | 2 | yes | — |
| 125 | C23×D59 | — | 2 | 2 | no | — |
| 126 | #41×C59 | — | 4 | 1 | no | — |
| 127 | #41×C59 | — | 4 | 1 | no | — |
| 128 | C2×Q8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×D4×C59 | — | 2 | 2 | no | — |
| 130 | C2×D4×C59 | — | 2 | 2 | no | — |
| 131 | C2×D4×C59 | — | 2 | 1 | no | — |
| 132 | C2×D4×C59 | — | 2 | 1 | no | — |
| 133 | C2×D4×C59 | — | 4 | 1 | no | — |
| 134 | C2×D4×C59 | — | 4 | 1 | no | — |
| 135 | C2×D4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×D4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×D4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C59 | C22×C4 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 142 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊D59 | — | 2 | 2 | no | — |
| 144 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 145 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 146 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 147 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 148 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 149 | C2×C22⋊D59 | — | 4 | 8 | no | — |
| 150 | C22×Dic59 | — | 2 | 2 | no | — |
| 151 | C22×Dic59 | — | 2 | 1 | no | — |
| 152 | C22×Dic59 | — | 2 | 1 | no | — |
| 153 | C22×Dic59 | — | 2 | 1 | no | — |
| 154 | C22×Dic59 | — | 2 | 1 | no | — |
| 155 | Q8×D59 | — | 4 | 4 | no | — |
| 156 | #11745687 | — | 4 | 2 | no | — |
| 157 | #11745687 | — | 4 | 4 | no | — |
| 158 | #11745687 | — | 4 | 4 | no | — |
| 159 | #11745687 | — | 4 | 4 | no | — |
| 160 | #11745687 | — | 4 | 4 | no | — |
| 161 | #11745687 | — | 4 | 2 | no | — |
| 162 | D4×D59 | — | 4 | 4 | no | — |
| 163 | D4×D59 | — | 4 | 2 | no | — |
| 164 | D4×D59 | — | 4 | 2 | no | — |
| 165 | #11745685 | — | 2 | 2 | no | — |
| 166 | #11745685 | — | 2 | 2 | no | — |
| 167 | #11745685 | — | 2 | 2 | no | — |
| 168 | #11745685 | — | 2 | 2 | no | — |
| 169 | #11745685 | — | 4 | 1 | no | — |
| 170 | #11745685 | — | 4 | 1 | no | — |
| 171 | #11745685 | — | 4 | 1 | no | — |
| 172 | #11745685 | — | 4 | 1 | no | — |
| 173 | C2×D236 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 174 | C2×D236 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×D59 | — | 2 | 1 | no | — |
| 176 | C2×C4×D59 | — | 2 | 1 | no | — |
| 177 | C2×C4×D59 | — | 2 | 1 | no | — |
| 178 | C2×C4×D59 | — | 2 | 1 | no | — |
| 179 | C2×C4×D59 | — | 2 | 2 | no | — |
| 180 | C2×Dic118 | — | 2 | 2 | no | — |
| 181 | C2×Dic118 | — | 2 | 2 | no | — |
| 182 | C2×Dic118 | — | 2 | 1 | no | — |
| 183 | C2×Dic118 | — | 2 | 1 | no | — |
| 184 | C2×Dic118 | — | 2 | 1 | no | — |
| 185 | C2×Dic118 | — | 4 | 1 | no | — |
| 186 | C2×Dic118 | — | 4 | 1 | no | — |
| 187 | C2×Dic118 | — | 4 | 1 | no | — |
| 188 | C2×Dic118 | — | 4 | 1 | no | — |
| 189 | C2×Dic118 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 190 | C2×Dic118 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 191 | C2×Dic118 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 192 | C2×Dic118 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 193 | M16×C59 | — | 4 | 1 | no | — |
| 194 | M16×C59 | — | 4 | 1 | no | — |
| 195 | C2×C8×C59 | — | 4 | 1 | no | — |
| 196 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 197 | C4⋊C4×C59 | — | 4 | 1 | no | — |
| 198 | C22⋊C4×C59 | — | 2 | 2 | no | — |
| 199 | C22⋊C4×C59 | — | 2 | 2 | no | — |
| 200 | C22⋊C4×C59 | — | 4 | 1 | no | — |
| 201 | C22⋊C4×C59 | C22⋊C4 | 1 | 2 | yes | — |
| 202 | C42×C59 | — | 2 | 1 | no | — |
| 203 | C42×C59 | — | 4 | 1 | no | — |
| 204 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 205 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 206 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 207 | C22⋊Dic59 | — | 2 | 2 | no | — |
| 208 | C22⋊Dic59 | — | 2 | 1 | no | — |
| 209 | C22⋊Dic59 | — | 2 | 1 | no | — |
| 210 | C22⋊Dic59 | — | 4 | 1 | no | — |
| 211 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 212 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 213 | (C2×D59)⋊C4 | — | 2 | 2 | no | — |
| 214 | (C2×D59)⋊C4 | — | 2 | 1 | no | — |
| 215 | (C2×D59)⋊C4 | — | 2 | 1 | no | — |
| 216 | C4⋊Dic59 | — | 2 | 2 | no | — |
| 217 | C4⋊Dic59 | — | 2 | 2 | no | — |
| 218 | C4⋊Dic59 | — | 4 | 1 | no | — |
| 219 | Dic59⋊C4 | — | 2 | 2 | no | — |
| 220 | Dic59⋊C4 | — | 2 | 1 | no | — |
| 221 | Dic59⋊C4 | — | 2 | 1 | no | — |
| 222 | C4×Dic59 | — | 2 | 2 | no | — |
| 223 | C4×Dic59 | — | 2 | 1 | no | — |
| 224 | C4×Dic59 | — | 4 | 1 | no | — |
| 225 | C4×Dic59 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 226 | C4×Dic59 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 227 | #11745664 | — | 4 | 1 | no | — |
| 228 | #11745664 | — | 4 | 1 | no | — |
| 229 | C2×C59⋊C8 | — | 4 | 1 | no | — |
| 230 | C23×C59 | — | 2 | 2 | no | — |
| 231 | C23×C59 | — | 4 | 2 | no | — |
| 232 | C23×C59 | — | 8 | 2 | no | — |
| 233 | C23×C59 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C23×C59 | #120 | 1 | 1 | yes | characteristic |
| 235 | C23×C59 | #120 | 1 | 1 | yes | characteristic |
| 236 | C22×D59 | — | 2 | 1 | no | — |
| 237 | C22×D59 | — | 2 | 1 | no | — |
| 238 | C22×D59 | — | 4 | 4 | no | — |
| 239 | C22×D59 | — | 8 | 2 | no | — |
| 240 | C22×D59 | — | 8 | 2 | no | — |
| 241 | Q8×C59 | — | 4 | 1 | no | — |
| 242 | D4×C59 | — | 4 | 1 | no | — |
| 243 | D4×C59 | — | 4 | 1 | no | — |
| 244 | D4×C59 | — | 4 | 1 | no | — |
| 245 | D4×C59 | — | 4 | 2 | no | — |
| 246 | D4×C59 | — | 4 | 1 | no | — |
| 247 | D4×C59 | — | 4 | 1 | no | — |
| 248 | D4×C59 | — | 8 | 2 | no | — |
| 249 | D4×C59 | — | 8 | 2 | no | — |
| 250 | C2×C4×C59 | — | 2 | 1 | no | — |
| 251 | C2×C4×C59 | — | 2 | 1 | no | — |
| 252 | C2×C4×C59 | — | 2 | 1 | no | — |
| 253 | C2×C4×C59 | — | 2 | 1 | no | — |
| 254 | C2×C4×C59 | — | 2 | 1 | no | — |
| 255 | C2×C4×C59 | — | 2 | 1 | no | — |
| 256 | C2×C4×C59 | — | 2 | 2 | no | — |
| 257 | C2×C4×C59 | — | 8 | 1 | no | — |
| 258 | C2×C4×C59 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C59 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C59 | #120 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C59 | #120 | 1 | 1 | yes | characteristic |
| 262 | C22⋊D59 | — | 2 | 4 | no | — |
| 263 | C22⋊D59 | — | 4 | 4 | no | — |
| 264 | C22⋊D59 | — | 4 | 2 | no | — |
| 265 | C22⋊D59 | — | 4 | 2 | no | — |
| 266 | C22⋊D59 | — | 4 | 4 | no | — |
| 267 | C22⋊D59 | — | 4 | 2 | no | — |
| 268 | C22⋊D59 | — | 8 | 1 | no | — |
| 269 | C22⋊D59 | — | 8 | 1 | no | — |
| 270 | C2×Dic59 | — | 2 | 1 | no | — |
| 271 | C2×Dic59 | — | 2 | 1 | no | — |
| 272 | C2×Dic59 | — | 2 | 1 | no | — |
| 273 | C2×Dic59 | — | 2 | 1 | no | — |
| 274 | C2×Dic59 | — | 2 | 1 | no | — |
| 275 | C2×Dic59 | — | 2 | 1 | no | — |
| 276 | C2×Dic59 | — | 4 | 2 | no | — |
| 277 | C2×Dic59 | — | 4 | 2 | no | — |
| 278 | C2×Dic59 | — | 4 | 4 | no | — |
| 279 | C2×Dic59 | — | 4 | 2 | no | — |
| 280 | C2×Dic59 | — | 8 | 1 | no | — |
| 281 | C2×Dic59 | — | 8 | 1 | no | — |
| 282 | D236 | — | 2 | 1 | no | — |
| 283 | D236 | — | 4 | 1 | no | — |
| 284 | D236 | #99 | 1 | 2 | yes | — |
| 285 | C4×D59 | — | 2 | 4 | no | — |
| 286 | C4×D59 | — | 4 | 2 | no | — |
| 287 | C4×D59 | — | 4 | 2 | no | — |
| 288 | C4×D59 | — | 4 | 1 | no | — |
| 289 | C4×D59 | — | 4 | 1 | no | — |
| 290 | C4×D59 | — | 8 | 2 | no | — |
| 291 | Dic118 | — | 2 | 1 | no | — |
| 292 | Dic118 | — | 2 | 1 | no | — |
| 293 | Dic118 | — | 2 | 1 | no | — |
| 294 | Dic118 | — | 2 | 1 | no | — |
| 295 | Dic118 | — | 2 | 1 | no | — |
| 296 | Dic118 | — | 4 | 2 | no | — |
| 297 | Dic118 | — | 4 | 2 | no | — |
| 298 | Dic118 | — | 4 | 2 | no | — |
| 299 | Dic118 | — | 4 | 1 | no | — |
| 300 | Dic118 | #99 | 1 | 2 | yes | — |
| 301 | C8×C59 | — | 8 | 1 | no | — |
| 302 | C59⋊C8 | — | 8 | 1 | no | — |
| 303 | #12715 | — | 59 | 1 | no | maximal, Sylow |
| 304 | C22×C59 | — | 2 | 1 | no | — |
| 305 | C22×C59 | — | 2 | 1 | no | — |
| 306 | C22×C59 | — | 2 | 1 | no | — |
| 307 | C22×C59 | — | 4 | 1 | no | — |
| 308 | C22×C59 | — | 4 | 1 | no | — |
| 309 | C22×C59 | — | 4 | 1 | no | — |
| 310 | C22×C59 | — | 4 | 2 | no | — |
| 311 | C22×C59 | — | 4 | 2 | no | — |
| 312 | C22×C59 | — | 4 | 2 | no | — |
| 313 | C22×C59 | — | 16 | 2 | no | — |
| 314 | C22×C59 | #379 | 1 | 1 | yes | characteristic |
| 315 | C2×D59 | — | 2 | 2 | no | — |
| 316 | C2×D59 | — | 4 | 2 | no | — |
| 317 | C2×D59 | — | 4 | 1 | no | — |
| 318 | C2×D59 | — | 4 | 1 | no | — |
| 319 | C2×D59 | — | 4 | 1 | no | — |
| 320 | C2×D59 | — | 16 | 4 | no | — |
| 321 | C4×C59 | — | 2 | 1 | no | — |
| 322 | C4×C59 | — | 2 | 1 | no | — |
| 323 | C4×C59 | — | 2 | 1 | no | — |
| 324 | C4×C59 | — | 4 | 2 | no | — |
| 325 | C4×C59 | — | 16 | 1 | no | — |
| 326 | C4×C59 | C2×#99 | 1 | 1 | yes | characteristic |
| 327 | C4×C59 | C2×#99 | 1 | 1 | yes | characteristic |
| 328 | Dic59 | — | 2 | 2 | no | — |
| 329 | Dic59 | — | 4 | 1 | no | — |
| 330 | Dic59 | — | 4 | 1 | no | — |
| 331 | Dic59 | — | 4 | 1 | no | — |
| 332 | Dic59 | — | 4 | 1 | no | — |
| 333 | Dic59 | — | 4 | 1 | no | — |
| 334 | Dic59 | — | 16 | 1 | no | — |
| 335 | #3500 | — | 59 | 1 | no | — |
| 336 | #2132 | — | 59 | 1 | no | — |
| 337 | #2126 | — | 59 | 1 | no | — |
| 338 | #2122 | — | 59 | 1 | no | — |
| 339 | #2122 | D59 | 1 | 1 | yes | characteristic, complemented |
| 340 | #1796 | — | 59 | 1 | no | — |
| 341 | #1796 | — | 59 | 1 | no | — |
| 342 | C2×C59 | — | 2 | 1 | no | — |
| 343 | C2×C59 | — | 4 | 1 | no | — |
| 344 | C2×C59 | — | 4 | 1 | no | — |
| 345 | C2×C59 | — | 4 | 1 | no | — |
| 346 | C2×C59 | — | 8 | 2 | no | — |
| 347 | C2×C59 | #1781 | 1 | 1 | yes | characteristic |
| 348 | D59 | — | 4 | 2 | no | — |
| 349 | D59 | — | 8 | 1 | no | — |
| 350 | C2×2−1+4 | — | 59 | 1 | no | — |
| 351 | C2×H(5,𝔽2) | — | 59 | 1 | no | — |
| 352 | #548 | — | 118 | 1 | no | — |
| 353 | #548 | — | 118 | 1 | no | — |
| 354 | #546 | — | 118 | 1 | no | — |
| 355 | #546 | — | 118 | 1 | no | — |
| 356 | #546 | — | 118 | 2 | no | — |
| 357 | #546 | — | 118 | 2 | no | — |
| 358 | #536 | — | 59 | 1 | no | — |
| 359 | #536 | — | 118 | 1 | no | — |
| 360 | #535 | — | 118 | 1 | no | — |
| 361 | #535 | C2×D59 | 1 | 1 | yes | characteristic |
| 362 | #532 | — | 59 | 1 | no | — |
| 363 | #532 | — | 118 | 1 | no | — |
| 364 | C2×#124 | — | 59 | 1 | no | — |
| 365 | C2×#124 | — | 118 | 1 | no | — |
| 366 | C4×#41 | — | 59 | 1 | no | — |
| 367 | #421 | — | 118 | 1 | no | — |
| 368 | #421 | — | 118 | 1 | no | — |
| 369 | #419 | — | 118 | 1 | no | — |
| 370 | #419 | — | 118 | 1 | no | — |
| 371 | #413 | — | 59 | 1 | no | — |
| 372 | #413 | C2×D59 | 1 | 1 | yes | characteristic, complemented |
| 373 | #410 | — | 59 | 1 | no | — |
| 374 | #410 | C2×D59 | 1 | 1 | yes | characteristic, complemented |
| 375 | #356 | — | 118 | 1 | no | — |
| 376 | #355 | — | 118 | 1 | no | — |
| 377 | #354 | — | 118 | 1 | no | — |
| 378 | #353 | — | 118 | 1 | no | — |
| 379 | AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 380 | AΣL(1,𝔽16) | — | 118 | 2 | no | — |
| 381 | C59 | #12715 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 382 | 2−1+4 | — | 236 | 2 | no | — |
| 383 | 2−1+4 | — | 236 | 2 | no | — |
| 384 | H(5,𝔽2) | — | 236 | 2 | no | — |
| 385 | H(5,𝔽2) | — | 236 | 2 | no | — |
| 386 | C2×#41 | — | 59 | 1 | no | — |
| 387 | C2×#41 | — | 59 | 1 | no | — |
| 388 | C2×#41 | — | 59 | 1 | no | — |
| 389 | C2×#41 | — | 59 | 1 | no | — |
| 390 | C2×#41 | — | 118 | 1 | no | — |
| 391 | C2×#41 | — | 118 | 1 | no | — |
| 392 | C2×#41 | — | 118 | 1 | no | — |
| 393 | C2×#41 | — | 118 | 1 | no | — |
| 394 | C2×#41 | — | 118 | 1 | no | — |
| 395 | C2×#41 | C22×D59 | 1 | 1 | yes | characteristic |
| 396 | C22×Q8 | — | 59 | 1 | no | — |
| 397 | C22×Q8 | — | 59 | 1 | no | — |
| 398 | C22×Q8 | — | 59 | 1 | no | — |
| 399 | C22×Q8 | — | 118 | 1 | no | — |
| 400 | C22×D4 | — | 118 | 1 | no | — |
| 401 | C22×D4 | — | 118 | 1 | no | — |
| 402 | C22×D4 | — | 118 | 2 | no | — |
| 403 | C22×D4 | C4×D59 | 1 | 1 | yes | characteristic |
| 404 | C2×M16 | — | 2 | 1 | no | — |
| 405 | C2×M16 | — | 118 | 1 | no | — |
| 406 | C4⋊Q8 | — | 59 | 1 | no | — |
| 407 | C4⋊Q8 | — | 118 | 1 | no | — |
| 408 | #127 | — | 2 | 1 | no | — |
| 409 | #127 | — | 59 | 1 | no | — |
| 410 | #124 | — | 2 | 1 | no | — |
| 411 | #124 | — | 59 | 1 | no | — |
| 412 | #124 | — | 59 | 1 | no | — |
| 413 | #124 | — | 118 | 1 | no | — |
| 414 | #124 | — | 118 | 1 | no | — |
| 415 | #124 | — | 118 | 1 | no | — |
| 416 | #124 | — | 118 | 2 | no | — |
| 417 | #124 | — | 118 | 2 | no | — |
| 418 | #124 | — | 118 | 1 | no | — |
| 419 | #124 | — | 118 | 1 | no | — |
| 420 | #123 | — | 118 | 2 | no | — |
| 421 | #123 | — | 118 | 2 | no | — |
| 422 | #123 | — | 118 | 2 | no | — |
| 423 | C22⋊Q8 | — | 118 | 2 | no | — |
| 424 | C22⋊Q8 | — | 118 | 2 | no | — |
| 425 | C22⋊Q8 | — | 118 | 1 | no | — |
| 426 | C22⋊Q8 | — | 118 | 1 | no | — |
| 427 | #121 | — | 2 | 1 | no | — |
| 428 | #121 | — | 2 | 1 | no | — |
| 429 | #121 | — | 118 | 2 | no | — |
| 430 | #121 | — | 118 | 2 | no | — |
| 431 | #121 | — | 118 | 2 | no | — |
| 432 | #121 | — | 118 | 2 | no | — |
| 433 | #121 | — | 118 | 1 | no | — |
| 434 | #121 | — | 118 | 1 | no | — |
| 435 | #120 | — | 118 | 2 | no | — |
| 436 | #120 | — | 118 | 2 | no | — |
| 437 | #120 | D236 | 1 | 2 | yes | — |
| 438 | #120 | C22⋊D59 | 1 | 2 | yes | — |
| 439 | C4×Q8 | — | 118 | 1 | no | — |
| 440 | C4×D4 | — | 118 | 1 | no | — |
| 441 | C4×D4 | — | 118 | 2 | no | — |
| 442 | C4×D4 | — | 118 | 2 | no | — |
| 443 | C4×D4 | — | 118 | 1 | no | — |
| 444 | C4×D4 | — | 118 | 1 | no | — |
| 445 | C4×D4 | — | 118 | 2 | no | — |
| 446 | #117 | — | 2 | 1 | no | — |
| 447 | #117 | — | 118 | 1 | no | — |
| 448 | #117 | — | 118 | 1 | no | — |
| 449 | #117 | C4×D59 | 1 | 1 | yes | characteristic |
| 450 | C2×C22⋊C4 | — | 118 | 2 | no | — |
| 451 | C2×C22⋊C4 | — | 118 | 2 | no | — |
| 452 | C2×C22⋊C4 | — | 118 | 2 | no | — |
| 453 | C2×C42 | — | 59 | 1 | no | — |
| 454 | C2×C42 | — | 118 | 1 | no | — |
| 455 | #104 | — | 236 | 2 | no | — |
| 456 | #104 | — | 236 | 2 | no | — |
| 457 | #103 | — | 236 | 2 | no | — |
| 458 | #103 | — | 236 | 2 | no | — |
| 459 | #101 | — | 2 | 1 | no | — |
| 460 | #101 | — | 118 | 1 | no | — |
| 461 | #100 | — | 2 | 1 | no | — |
| 462 | #100 | — | 118 | 1 | no | — |
| 463 | #99 | — | 2 | 1 | no | — |
| 464 | #99 | — | 2 | 1 | no | — |
| 465 | #99 | — | 118 | 1 | no | — |
| 466 | #99 | — | 118 | 1 | no | — |
| 467 | C24 | — | 118 | 2 | no | — |
| 468 | C24 | (C2×D59)⋊C4 | 1 | 2 | yes | — |
| 469 | #41 | — | 4 | 1 | no | — |
| 470 | #41 | — | 4 | 1 | no | — |
| 471 | #41 | — | 118 | 2 | no | — |
| 472 | #41 | — | 118 | 2 | no | — |
| 473 | #41 | — | 118 | 2 | no | — |
| 474 | #41 | — | 118 | 2 | no | — |
| 475 | #41 | — | 236 | 1 | no | — |
| 476 | #41 | — | 236 | 1 | no | — |
| 477 | #41 | — | 236 | 1 | no | — |
| 478 | #41 | — | 236 | 1 | no | — |
| 479 | #41 | — | 236 | 4 | no | — |
| 480 | #41 | — | 236 | 4 | no | — |
| 481 | #41 | — | 236 | 4 | no | — |
| 482 | #41 | — | 236 | 4 | no | — |
| 483 | #41 | — | 236 | 2 | no | — |
| 484 | #41 | — | 236 | 2 | no | — |
| 485 | C2×Q8 | — | 59 | 1 | no | — |
| 486 | C2×Q8 | — | 59 | 1 | no | — |
| 487 | C2×Q8 | — | 59 | 1 | no | — |
| 488 | C2×Q8 | — | 59 | 1 | no | — |
| 489 | C2×Q8 | — | 118 | 2 | no | — |
| 490 | C2×Q8 | — | 118 | 2 | no | — |
| 491 | C2×Q8 | — | 118 | 1 | no | — |
| 492 | C2×Q8 | — | 118 | 1 | no | — |
| 493 | C2×Q8 | — | 118 | 1 | no | — |
| 494 | C2×Q8 | — | 236 | 1 | no | — |
| 495 | C2×Q8 | — | 236 | 1 | no | — |
| 496 | C2×Q8 | — | 236 | 1 | no | — |
| 497 | C2×Q8 | — | 236 | 1 | no | — |
| 498 | C2×Q8 | — | 236 | 4 | no | — |
| 499 | C2×Q8 | D4×D59 | 1 | 1 | yes | characteristic |
| 500 | C2×D4 | — | 2 | 2 | no | — |
| 501 | C2×D4 | — | 2 | 2 | no | — |
| 502 | C2×D4 | — | 2 | 1 | no | — |
| 503 | C2×D4 | — | 2 | 1 | no | — |
| 504 | C2×D4 | — | 4 | 1 | no | — |
| 505 | C2×D4 | — | 4 | 1 | no | — |
| 506 | C2×D4 | — | 59 | 1 | no | — |
| 507 | C2×D4 | — | 59 | 1 | no | — |
| 508 | C2×D4 | — | 118 | 1 | no | — |
| 509 | C2×D4 | — | 118 | 1 | no | — |
| 510 | C2×D4 | — | 118 | 1 | no | — |
| 511 | C2×D4 | — | 118 | 2 | no | — |
| 512 | C2×D4 | — | 118 | 2 | no | — |
| 513 | C2×D4 | — | 118 | 1 | no | — |
| 514 | C2×D4 | — | 118 | 1 | no | — |
| 515 | C2×D4 | — | 118 | 1 | no | — |
| 516 | C2×D4 | — | 236 | 4 | no | — |
| 517 | C2×D4 | — | 236 | 2 | no | — |
| 518 | C2×D4 | — | 236 | 2 | no | — |
| 519 | C2×D4 | — | 236 | 8 | no | — |
| 520 | C2×D4 | C2×D236 | 1 | 1 | yes | characteristic |
| 521 | C2×D4 | D4×D59 | 1 | 1 | yes | characteristic |
| 522 | C2×D4 | C2×C22⋊D59 | 1 | 1 | yes | characteristic |
| 523 | C22×C4 | — | 118 | 2 | no | — |
| 524 | C22×C4 | — | 118 | 1 | no | — |
| 525 | C22×C4 | — | 118 | 1 | no | — |
| 526 | C22×C4 | — | 118 | 2 | no | — |
| 527 | C22×C4 | — | 118 | 1 | no | — |
| 528 | C22×C4 | — | 118 | 1 | no | — |
| 529 | C22×C4 | — | 118 | 1 | no | — |
| 530 | C22×C4 | — | 118 | 1 | no | — |
| 531 | C22×C4 | — | 118 | 1 | no | — |
| 532 | C22×C4 | — | 118 | 1 | no | — |
| 533 | C22×C4 | C2×C4×D59 | 1 | 1 | yes | characteristic |
| 534 | C22×C4 | D4×D59 | 1 | 1 | yes | characteristic |
| 535 | C22×C4 | D4×D59 | 1 | 1 | yes | characteristic |
| 536 | M16 | — | 4 | 1 | no | — |
| 537 | M16 | — | 4 | 1 | no | — |
| 538 | M16 | — | 236 | 1 | no | — |
| 539 | M16 | — | 236 | 1 | no | — |
| 540 | C2×C8 | — | 4 | 1 | no | — |
| 541 | C2×C8 | — | 236 | 1 | no | — |
| 542 | C4⋊C4 | — | 2 | 1 | no | — |
| 543 | C4⋊C4 | — | 4 | 1 | no | — |
| 544 | C4⋊C4 | — | 118 | 2 | no | — |
| 545 | C4⋊C4 | — | 118 | 2 | no | — |
| 546 | C4⋊C4 | — | 118 | 2 | no | — |
| 547 | C4⋊C4 | — | 118 | 1 | no | — |
| 548 | C4⋊C4 | — | 118 | 1 | no | — |
| 549 | C4⋊C4 | — | 236 | 1 | no | — |
| 550 | C22⋊C4 | — | 2 | 2 | no | — |
| 551 | C22⋊C4 | — | 2 | 2 | no | — |
| 552 | C22⋊C4 | — | 4 | 1 | no | — |
| 553 | C22⋊C4 | — | 118 | 2 | no | — |
| 554 | C22⋊C4 | — | 118 | 2 | no | — |
| 555 | C22⋊C4 | — | 118 | 2 | no | — |
| 556 | C22⋊C4 | — | 118 | 2 | no | — |
| 557 | C22⋊C4 | — | 118 | 2 | no | — |
| 558 | C22⋊C4 | — | 118 | 2 | no | — |
| 559 | C22⋊C4 | — | 118 | 2 | no | — |
| 560 | C22⋊C4 | — | 118 | 1 | no | — |
| 561 | C22⋊C4 | — | 118 | 1 | no | — |
| 562 | C22⋊C4 | — | 118 | 1 | no | — |
| 563 | C22⋊C4 | — | 118 | 1 | no | — |
| 564 | C22⋊C4 | — | 236 | 1 | no | — |
| 565 | C22⋊C4 | (C2×D59)⋊C4 | 1 | 2 | yes | — |
| 566 | C42 | — | 2 | 1 | no | — |
| 567 | C42 | — | 4 | 1 | no | — |
| 568 | C42 | — | 59 | 1 | no | — |
| 569 | C42 | — | 59 | 1 | no | — |
| 570 | C42 | — | 118 | 2 | no | — |
| 571 | C42 | — | 118 | 1 | no | — |
| 572 | C42 | — | 236 | 1 | no | — |
| 573 | C23 | — | 2 | 2 | no | — |
| 574 | C23 | — | 4 | 2 | no | — |
| 575 | C23 | — | 8 | 2 | no | — |
| 576 | C23 | — | 118 | 1 | no | — |
| 577 | C23 | — | 118 | 1 | no | — |
| 578 | C23 | — | 472 | 2 | no | — |
| 579 | C23 | — | 472 | 2 | no | — |
| 580 | C23 | — | 236 | 4 | no | — |
| 581 | C23 | C2×(C2×D59)⋊C4 | 1 | 1 | yes | characteristic |
| 582 | C23 | #14273695 | 1 | 1 | yes | characteristic |
| 583 | C23 | #14273697 | 1 | 1 | yes | characteristic |
| 584 | Q8 | — | 4 | 1 | no | — |
| 585 | Q8 | — | 59 | 2 | no | — |
| 586 | Q8 | — | 118 | 1 | no | — |
| 587 | Q8 | — | 118 | 1 | no | — |
| 588 | Q8 | — | 118 | 1 | no | — |
| 589 | Q8 | — | 118 | 1 | no | — |
| 590 | Q8 | — | 118 | 1 | no | — |
| 591 | Q8 | — | 236 | 2 | no | — |
| 592 | Q8 | — | 236 | 2 | no | — |
| 593 | Q8 | — | 236 | 1 | no | — |
| 594 | Q8 | — | 236 | 2 | no | — |
| 595 | D4 | — | 4 | 1 | no | — |
| 596 | D4 | — | 4 | 1 | no | — |
| 597 | D4 | — | 4 | 1 | no | — |
| 598 | D4 | — | 4 | 2 | no | — |
| 599 | D4 | — | 4 | 1 | no | — |
| 600 | D4 | — | 4 | 1 | no | — |
| 601 | D4 | — | 8 | 2 | no | — |
| 602 | D4 | — | 8 | 2 | no | — |
| 603 | D4 | — | 59 | 2 | no | — |
| 604 | D4 | — | 118 | 4 | no | — |
| 605 | D4 | — | 118 | 1 | no | — |
| 606 | D4 | — | 472 | 1 | no | — |
| 607 | D4 | — | 472 | 1 | no | — |
| 608 | D4 | — | 236 | 1 | no | — |
| 609 | D4 | — | 236 | 4 | no | — |
| 610 | D4 | — | 236 | 2 | no | — |
| 611 | D4 | — | 236 | 2 | no | — |
| 612 | D4 | — | 236 | 2 | no | — |
| 613 | D4 | — | 236 | 4 | no | — |
| 614 | C2×C4 | — | 2 | 1 | no | — |
| 615 | C2×C4 | — | 2 | 1 | no | — |
| 616 | C2×C4 | — | 2 | 1 | no | — |
| 617 | C2×C4 | — | 2 | 1 | no | — |
| 618 | C2×C4 | — | 2 | 1 | no | — |
| 619 | C2×C4 | — | 2 | 1 | no | — |
| 620 | C2×C4 | — | 2 | 2 | no | — |
| 621 | C2×C4 | — | 8 | 1 | no | — |
| 622 | C2×C4 | — | 118 | 4 | no | — |
| 623 | C2×C4 | — | 118 | 1 | no | — |
| 624 | C2×C4 | — | 118 | 1 | no | — |
| 625 | C2×C4 | — | 118 | 1 | no | — |
| 626 | C2×C4 | — | 118 | 1 | no | — |
| 627 | C2×C4 | — | 118 | 1 | no | — |
| 628 | C2×C4 | — | 118 | 1 | no | — |
| 629 | C2×C4 | — | 472 | 2 | no | — |
| 630 | C2×C4 | — | 472 | 1 | no | — |
| 631 | C2×C4 | — | 472 | 1 | no | — |
| 632 | C2×C4 | — | 236 | 2 | no | — |
| 633 | C2×C4 | — | 236 | 2 | no | — |
| 634 | C2×C4 | — | 236 | 2 | no | — |
| 635 | C2×C4 | — | 236 | 2 | no | — |
| 636 | C2×C4 | — | 236 | 4 | no | — |
| 637 | C2×C4 | — | 236 | 2 | no | — |
| 638 | C2×C4 | — | 236 | 1 | no | — |
| 639 | C2×C4 | — | 236 | 1 | no | — |
| 640 | C2×C4 | C22⋊C4×D59 | 1 | 1 | yes | characteristic |
| 641 | C2×C4 | C22⋊C4×D59 | 1 | 1 | yes | characteristic |
| 642 | C2×C4 | #14273695 | 1 | 1 | yes | characteristic |
| 643 | C2×C4 | #14273697 | 1 | 1 | yes | characteristic |
| 644 | C8 | — | 8 | 1 | no | — |
| 645 | C8 | — | 472 | 1 | no | — |
| 646 | C22 | — | 2 | 1 | no | — |
| 647 | C22 | — | 2 | 1 | no | — |
| 648 | C22 | — | 2 | 1 | no | — |
| 649 | C22 | — | 4 | 1 | no | — |
| 650 | C22 | — | 4 | 1 | no | — |
| 651 | C22 | — | 4 | 1 | no | — |
| 652 | C22 | — | 4 | 2 | no | — |
| 653 | C22 | — | 4 | 2 | no | — |
| 654 | C22 | — | 4 | 2 | no | — |
| 655 | C22 | — | 16 | 2 | no | — |
| 656 | C22 | — | 118 | 2 | no | — |
| 657 | C22 | — | 944 | 4 | no | — |
| 658 | C22 | — | 236 | 1 | no | — |
| 659 | C22 | — | 236 | 1 | no | — |
| 660 | C22 | — | 236 | 2 | no | — |
| 661 | C22 | — | 236 | 1 | no | — |
| 662 | C22 | #16837257 | 1 | 1 | yes | characteristic |
| 663 | C4 | — | 2 | 1 | no | — |
| 664 | C4 | — | 2 | 1 | no | — |
| 665 | C4 | — | 2 | 1 | no | — |
| 666 | C4 | — | 4 | 2 | no | — |
| 667 | C4 | — | 16 | 1 | no | — |
| 668 | C4 | — | 118 | 2 | no | — |
| 669 | C4 | — | 944 | 1 | no | — |
| 670 | C4 | — | 236 | 1 | no | — |
| 671 | C4 | — | 236 | 1 | no | — |
| 672 | C4 | — | 236 | 1 | no | — |
| 673 | C4 | — | 236 | 1 | no | — |
| 674 | C4 | — | 236 | 1 | no | — |
| 675 | C4 | #99×D59 | 1 | 1 | yes | characteristic |
| 676 | C4 | #99×D59 | 1 | 1 | yes | characteristic |
| 677 | C2 | — | 2 | 1 | no | — |
| 678 | C2 | — | 4 | 1 | no | — |
| 679 | C2 | — | 4 | 1 | no | — |
| 680 | C2 | — | 4 | 1 | no | — |
| 681 | C2 | — | 8 | 2 | no | — |
| 682 | C2 | — | 472 | 1 | no | — |
| 683 | C2 | — | 236 | 2 | no | — |
| 684 | C2 | #21424009 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21425779 | C2 | semidirect |
| 3. #21425759 | C2 | semidirect |
| 4. #21425746 | C2 | semidirect |
| 5. #21424072 | C2 | semidirect |
| 6. #21424069 | C2 | semidirect |
| 7. C59×#2122 | C2 | semidirect |
| 9. C2×#14273772 | C4 | semidirect |
| 16. #16837978 | C4 | semidirect |
| 21. C2×#14273714 | C4 | semidirect |
| 23. #16837870 | C4 | semidirect |
| 28. #16837386 | C22 | semidirect |
| 29. #16837376 | C22 | semidirect |
| 36. C59×#413 | C22 | semidirect |
| 37. C59×#410 | C22 | semidirect |
| 339. #2122 | D59 | semidirect |
| 372. #413 | C2×D59 | semidirect |
| 374. #410 | C2×D59 | semidirect |
| 381. C59 | #12715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437888 | 2 |
| #21425779 | 2 |
| #21425759 | 2 |
| #21425746 | 2 |
| #21424072 | 2 |
| #21424069 | 2 |
| C59×#2122 | 2 |
| #12715 | 59 |