Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3540 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 3540 conjugacy classes of subgroups — too many to draw. Only its 311 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 | #21433498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21433468 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #21433382 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #21424071 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #21424060 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #21424047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C59×2−1+6 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14273752 | C22 | 1 | 3 | yes | complemented |
| 9 | C22×#11745671 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #16837966 | C22 | 1 | 3 | yes | complemented |
| 11 | #16837589 | — | 2 | 4 | no | — |
| 12 | #16837575 | — | 2 | 6 | no | — |
| 13 | #16837570 | — | 2 | 6 | no | — |
| 14 | #16837547 | — | 2 | 6 | no | — |
| 15 | #16837541 | — | 2 | 6 | no | — |
| 16 | #16837419 | C22 | 1 | 6 | yes | complemented |
| 17 | #16837411 | C22 | 1 | 3 | yes | complemented |
| 18 | #16837398 | C22 | 1 | 3 | yes | complemented |
| 19 | #16837386 | C22 | 1 | 3 | yes | complemented |
| 20 | #16837376 | C22 | 1 | 3 | yes | complemented |
| 21 | #16837369 | C22 | 1 | 3 | yes | complemented |
| 22 | C59×#585 | — | 2 | 4 | no | — |
| 23 | C59×#585 | — | 2 | 6 | no | — |
| 24 | C59×#585 | — | 2 | 6 | no | — |
| 25 | C59×#585 | C22 | 1 | 3 | yes | — |
| 26 | C59×#585 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×2−1+4×C59 | — | 2 | 6 | no | — |
| 28 | C2×2−1+4×C59 | — | 2 | 6 | no | — |
| 29 | C2×2−1+4×C59 | C22 | 1 | 3 | yes | — |
| 30 | C22×D236 | C23 | 1 | 1 | yes | characteristic |
| 31 | #14273752 | — | 2 | 12 | no | — |
| 32 | C2×#11745671 | — | 2 | 6 | no | — |
| 33 | C2×#11745671 | — | 2 | 3 | no | — |
| 34 | C2×#11745669 | — | 2 | 3 | no | — |
| 35 | C2×#11745664 | C23 | 1 | 3 | yes | — |
| 36 | C22×C59⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 37 | #14273723 | — | 2 | 3 | no | — |
| 38 | #14273716 | — | 2 | 3 | no | — |
| 39 | #14273701 | — | 2 | 6 | no | — |
| 40 | #14273695 | — | 2 | 6 | no | — |
| 41 | #14273686 | C23 | 1 | 3 | yes | — |
| 42 | #14273654 | — | 2 | 12 | no | — |
| 43 | #14273651 | — | 2 | 3 | no | — |
| 44 | #14273651 | — | 2 | 6 | no | — |
| 45 | #14273648 | — | 2 | 3 | no | — |
| 46 | #14273646 | — | 2 | 3 | no | — |
| 47 | #14273644 | — | 2 | 3 | no | — |
| 48 | #14273642 | — | 2 | 6 | no | — |
| 49 | C22⋊(C59⋊C8) | — | 2 | 6 | no | — |
| 50 | 2−1+4×C59 | — | 2 | 12 | no | — |
| 51 | 2−1+4×C59 | — | 2 | 24 | no | — |
| 52 | 2−1+4×C59 | — | 2 | 24 | no | — |
| 53 | 2−1+4×C59 | — | 2 | 12 | no | — |
| 54 | 2−1+4×C59 | — | 2 | 12 | no | — |
| 55 | 2−1+4×C59 | — | 2 | 3 | no | — |
| 56 | 2−1+4×C59 | — | 2 | 6 | no | — |
| 57 | 2−1+4×C59 | — | 2 | 12 | no | — |
| 58 | 2−1+4×C59 | D4 | 1 | 6 | yes | complemented |
| 59 | H(5,𝔽2)×C59 | — | 2 | 4 | no | — |
| 60 | H(5,𝔽2)×C59 | — | 2 | 12 | no | — |
| 61 | H(5,𝔽2)×C59 | — | 2 | 24 | no | — |
| 62 | H(5,𝔽2)×C59 | — | 2 | 6 | no | — |
| 63 | H(5,𝔽2)×C59 | — | 2 | 3 | no | — |
| 64 | H(5,𝔽2)×C59 | — | 2 | 6 | no | — |
| 65 | H(5,𝔽2)×C59 | D4 | 1 | 4 | yes | — |
| 66 | H(5,𝔽2)×C59 | D4 | 1 | 6 | yes | complemented |
| 67 | C2×#41×C59 | — | 2 | 12 | no | — |
| 68 | C2×#41×C59 | — | 2 | 12 | no | — |
| 69 | C2×#41×C59 | — | 2 | 24 | no | — |
| 70 | C2×#41×C59 | — | 2 | 24 | no | — |
| 71 | C2×#41×C59 | — | 2 | 24 | no | — |
| 72 | C2×#41×C59 | — | 2 | 12 | no | — |
| 73 | C2×#41×C59 | — | 2 | 3 | no | — |
| 74 | C2×#41×C59 | — | 2 | 6 | no | — |
| 75 | C2×#41×C59 | — | 2 | 6 | no | — |
| 76 | C2×#41×C59 | — | 2 | 6 | no | — |
| 77 | C2×#41×C59 | D4 | 1 | 6 | yes | complemented |
| 78 | C2×#41×C59 | C23 | 1 | 3 | yes | — |
| 79 | C2×#41×C59 | C23 | 1 | 3 | yes | — |
| 80 | C22×Q8×C59 | — | 2 | 12 | no | — |
| 81 | C22×Q8×C59 | — | 2 | 4 | no | — |
| 82 | C22×Q8×C59 | — | 2 | 3 | no | — |
| 83 | C22×Q8×C59 | D4 | 1 | 6 | yes | complemented |
| 84 | C22×Q8×C59 | C23 | 1 | 1 | yes | characteristic |
| 85 | C23×D59 | — | 2 | 1 | no | — |
| 86 | #41×C59 | — | 2 | 48 | no | — |
| 87 | #41×C59 | — | 2 | 24 | no | — |
| 88 | #41×C59 | — | 2 | 48 | no | — |
| 89 | #41×C59 | — | 2 | 8 | no | — |
| 90 | #41×C59 | — | 2 | 24 | no | — |
| 91 | #41×C59 | — | 2 | 48 | no | — |
| 92 | #41×C59 | — | 2 | 24 | no | — |
| 93 | #41×C59 | — | 2 | 12 | no | — |
| 94 | #41×C59 | — | 2 | 12 | no | — |
| 95 | #41×C59 | — | 2 | 12 | no | — |
| 96 | #41×C59 | — | 2 | 4 | no | — |
| 97 | #41×C59 | — | 2 | 12 | no | — |
| 98 | #41×C59 | — | 2 | 12 | no | — |
| 99 | #41×C59 | — | 2 | 12 | no | — |
| 100 | #41×C59 | — | 2 | 12 | no | — |
| 101 | #41×C59 | — | 2 | 12 | no | — |
| 102 | #41×C59 | — | 2 | 12 | no | — |
| 103 | #41×C59 | — | 2 | 6 | no | — |
| 104 | #41×C59 | — | 2 | 6 | no | — |
| 105 | #41×C59 | — | 2 | 6 | no | — |
| 106 | #41×C59 | C2×D4 | 1 | 12 | yes | — |
| 107 | C2×Q8×C59 | — | 2 | 24 | no | — |
| 108 | C2×Q8×C59 | — | 2 | 24 | no | — |
| 109 | C2×Q8×C59 | — | 2 | 24 | no | — |
| 110 | C2×Q8×C59 | — | 2 | 6 | no | — |
| 111 | C2×Q8×C59 | — | 2 | 6 | no | — |
| 112 | C2×Q8×C59 | — | 2 | 12 | no | — |
| 113 | C2×Q8×C59 | — | 2 | 12 | no | — |
| 114 | C2×Q8×C59 | — | 2 | 12 | no | — |
| 115 | C2×Q8×C59 | — | 2 | 6 | no | — |
| 116 | C2×Q8×C59 | — | 2 | 3 | no | — |
| 117 | C2×Q8×C59 | C2×D4 | 1 | 3 | yes | — |
| 118 | C2×Q8×C59 | C2×D4 | 1 | 6 | yes | — |
| 119 | C2×Q8×C59 | C2×D4 | 1 | 3 | yes | — |
| 120 | C2×D4×C59 | — | 2 | 24 | no | — |
| 121 | C2×D4×C59 | — | 2 | 24 | no | — |
| 122 | C2×D4×C59 | — | 2 | 24 | no | — |
| 123 | C2×D4×C59 | — | 2 | 6 | no | — |
| 124 | C2×D4×C59 | — | 2 | 6 | no | — |
| 125 | C2×D4×C59 | — | 2 | 12 | no | — |
| 126 | C2×D4×C59 | — | 2 | 12 | no | — |
| 127 | C2×D4×C59 | — | 2 | 6 | no | — |
| 128 | C2×D4×C59 | — | 2 | 3 | no | — |
| 129 | C2×D4×C59 | — | 2 | 12 | no | — |
| 130 | C2×D4×C59 | C2×D4 | 1 | 6 | yes | — |
| 131 | C2×D4×C59 | C2×D4 | 1 | 3 | yes | — |
| 132 | C2×D4×C59 | C2×D4 | 1 | 3 | yes | — |
| 133 | C22×C4×C59 | — | 2 | 8 | no | — |
| 134 | C22×C4×C59 | — | 2 | 24 | no | — |
| 135 | C22×C4×C59 | — | 2 | 12 | no | — |
| 136 | C22×C4×C59 | — | 2 | 4 | no | — |
| 137 | C22×C4×C59 | — | 2 | 6 | no | — |
| 138 | C22×C4×C59 | — | 2 | 1 | no | — |
| 139 | C22×C4×C59 | — | 2 | 6 | no | — |
| 140 | C22×C4×C59 | — | 2 | 3 | no | — |
| 141 | C22×C4×C59 | C2×D4 | 1 | 6 | yes | — |
| 142 | C22×C4×C59 | C24 | 1 | 1 | yes | characteristic |
| 143 | C2×C22⋊D59 | — | 4 | 6 | no | — |
| 144 | C2×D236 | — | 2 | 3 | no | — |
| 145 | C2×D236 | — | 2 | 3 | no | — |
| 146 | C22⋊Dic59 | — | 2 | 3 | no | — |
| 147 | #11745671 | — | 4 | 4 | no | — |
| 148 | #11745671 | — | 4 | 6 | no | — |
| 149 | #11745669 | — | 4 | 6 | no | — |
| 150 | (C2×D59)⋊C4 | — | 4 | 6 | no | — |
| 151 | C4⋊Dic59 | — | 2 | 3 | no | — |
| 152 | C4×Dic59 | — | 2 | 3 | no | — |
| 153 | #11745664 | — | 2 | 6 | no | — |
| 154 | C2×C59⋊C8 | — | 2 | 3 | no | — |
| 155 | C2×C59⋊C8 | — | 2 | 3 | no | — |
| 156 | C23×C59 | — | 2 | 4 | no | — |
| 157 | C23×C59 | — | 2 | 12 | no | — |
| 158 | C23×C59 | — | 2 | 3 | no | — |
| 159 | C23×C59 | #120 | 1 | 6 | yes | — |
| 160 | C23×C59 | C22×D4 | 1 | 1 | yes | characteristic |
| 161 | C22×D59 | — | 4 | 3 | no | — |
| 162 | C22×D59 | — | 16 | 1 | no | — |
| 163 | Q8×C59 | — | 2 | 12 | no | — |
| 164 | Q8×C59 | — | 2 | 24 | no | — |
| 165 | Q8×C59 | — | 2 | 4 | no | — |
| 166 | Q8×C59 | — | 2 | 3 | no | — |
| 167 | Q8×C59 | — | 2 | 6 | no | — |
| 168 | Q8×C59 | — | 2 | 6 | no | — |
| 169 | Q8×C59 | #120 | 1 | 6 | yes | — |
| 170 | Q8×C59 | #120 | 1 | 4 | yes | — |
| 171 | D4×C59 | — | 2 | 24 | no | — |
| 172 | D4×C59 | — | 2 | 24 | no | — |
| 173 | D4×C59 | — | 2 | 12 | no | — |
| 174 | D4×C59 | — | 2 | 12 | no | — |
| 175 | D4×C59 | — | 2 | 12 | no | — |
| 176 | D4×C59 | — | 2 | 12 | no | — |
| 177 | D4×C59 | — | 2 | 3 | no | — |
| 178 | D4×C59 | — | 2 | 6 | no | — |
| 179 | D4×C59 | #120 | 1 | 6 | yes | — |
| 180 | C2×C4×C59 | — | 2 | 12 | no | — |
| 181 | C2×C4×C59 | — | 2 | 24 | no | — |
| 182 | C2×C4×C59 | — | 2 | 24 | no | — |
| 183 | C2×C4×C59 | — | 2 | 24 | no | — |
| 184 | C2×C4×C59 | — | 2 | 12 | no | — |
| 185 | C2×C4×C59 | — | 2 | 3 | no | — |
| 186 | C2×C4×C59 | — | 2 | 6 | no | — |
| 187 | C2×C4×C59 | — | 2 | 12 | no | — |
| 188 | C2×C4×C59 | — | 2 | 6 | no | — |
| 189 | C2×C4×C59 | — | 2 | 6 | no | — |
| 190 | C2×C4×C59 | #120 | 1 | 6 | yes | — |
| 191 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 192 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 193 | C22⋊D59 | — | 16 | 6 | no | — |
| 194 | C2×Dic59 | — | 4 | 3 | no | — |
| 195 | D236 | — | 4 | 3 | no | — |
| 196 | D236 | — | 4 | 1 | no | — |
| 197 | C59⋊C8 | — | 4 | 1 | no | — |
| 198 | C59⋊C8 | — | 4 | 3 | no | — |
| 199 | #32895 | — | 59 | 1 | no | maximal, Sylow |
| 200 | C22×C59 | — | 2 | 6 | no | — |
| 201 | C22×C59 | — | 2 | 6 | no | — |
| 202 | C22×C59 | — | 4 | 1 | no | — |
| 203 | C22×C59 | — | 4 | 6 | no | — |
| 204 | C22×C59 | — | 8 | 3 | no | — |
| 205 | C22×C59 | — | 8 | 4 | no | — |
| 206 | C22×C59 | — | 8 | 12 | no | — |
| 207 | C22×C59 | C2×#120 | 1 | 3 | yes | — |
| 208 | C2×D59 | — | 8 | 6 | no | — |
| 209 | C2×D59 | — | 8 | 1 | no | — |
| 210 | C4×C59 | — | 2 | 4 | no | — |
| 211 | C4×C59 | — | 2 | 6 | no | — |
| 212 | C4×C59 | — | 2 | 6 | no | — |
| 213 | C4×C59 | C2×#120 | 1 | 1 | yes | characteristic |
| 214 | C4×C59 | C2×#120 | 1 | 3 | yes | — |
| 215 | Dic59 | — | 8 | 3 | no | — |
| 216 | 2−1+6 | D59 | 1 | 1 | yes | characteristic, complemented |
| 217 | #3027 | — | 59 | 1 | no | — |
| 218 | #3021 | — | 59 | 3 | no | — |
| 219 | #3010 | — | 59 | 3 | no | — |
| 220 | #1796 | — | 59 | 3 | no | — |
| 221 | #1794 | — | 59 | 3 | no | — |
| 222 | #1791 | — | 59 | 1 | no | — |
| 223 | C2×C59 | — | 2 | 3 | no | — |
| 224 | C2×C59 | — | 4 | 6 | no | — |
| 225 | C2×C59 | — | 4 | 6 | no | — |
| 226 | C2×C59 | #2846 | 1 | 1 | yes | characteristic |
| 227 | D59 | — | 16 | 1 | no | — |
| 228 | #585 | — | 2 | 4 | no | — |
| 229 | #585 | — | 2 | 6 | no | — |
| 230 | #585 | — | 2 | 6 | no | — |
| 231 | #585 | C2×D59 | 1 | 3 | yes | — |
| 232 | #585 | C2×D59 | 1 | 1 | yes | characteristic |
| 233 | C2×2−1+4 | — | 2 | 6 | no | — |
| 234 | C2×2−1+4 | — | 2 | 6 | no | — |
| 235 | C2×2−1+4 | C2×D59 | 1 | 3 | yes | — |
| 236 | C2×AGL(1,ℤ/8) | — | 59 | 3 | no | — |
| 237 | C22×SD16 | — | 59 | 1 | no | — |
| 238 | #535 | — | 59 | 3 | no | — |
| 239 | B(4,𝔽2) | — | 118 | 4 | no | — |
| 240 | #454 | — | 118 | 6 | no | — |
| 241 | #453 | — | 118 | 6 | no | — |
| 242 | #449 | — | 118 | 6 | no | — |
| 243 | #448 | — | 118 | 6 | no | — |
| 244 | #421 | — | 59 | 6 | no | — |
| 245 | #419 | — | 59 | 3 | no | — |
| 246 | #416 | — | 59 | 3 | no | — |
| 247 | #413 | — | 59 | 3 | no | — |
| 248 | #410 | — | 59 | 3 | no | — |
| 249 | #408 | — | 59 | 3 | no | — |
| 250 | C59 | #32895 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 251 | 2−1+4 | — | 2 | 12 | no | — |
| 252 | 2−1+4 | — | 2 | 24 | no | — |
| 253 | 2−1+4 | — | 2 | 24 | no | — |
| 254 | 2−1+4 | — | 2 | 12 | no | — |
| 255 | 2−1+4 | — | 2 | 12 | no | — |
| 256 | 2−1+4 | — | 2 | 3 | no | — |
| 257 | 2−1+4 | — | 2 | 6 | no | — |
| 258 | 2−1+4 | — | 2 | 12 | no | — |
| 259 | 2−1+4 | C22⋊D59 | 1 | 6 | yes | complemented |
| 260 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 261 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 262 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 263 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 264 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 265 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 266 | H(5,𝔽2) | C22⋊D59 | 1 | 4 | yes | — |
| 267 | H(5,𝔽2) | C22⋊D59 | 1 | 6 | yes | complemented |
| 268 | C2×#41 | — | 2 | 12 | no | — |
| 269 | C2×#41 | — | 2 | 12 | no | — |
| 270 | C2×#41 | — | 2 | 24 | no | — |
| 271 | C2×#41 | — | 2 | 24 | no | — |
| 272 | C2×#41 | — | 2 | 24 | no | — |
| 273 | C2×#41 | — | 2 | 12 | no | — |
| 274 | C2×#41 | — | 2 | 3 | no | — |
| 275 | C2×#41 | — | 2 | 6 | no | — |
| 276 | C2×#41 | — | 2 | 6 | no | — |
| 277 | C2×#41 | — | 2 | 6 | no | — |
| 278 | C2×#41 | C22⋊D59 | 1 | 6 | yes | complemented |
| 279 | C2×#41 | C22×D59 | 1 | 3 | yes | — |
| 280 | C2×#41 | C22×D59 | 1 | 3 | yes | — |
| 281 | C22×Q8 | — | 2 | 12 | no | — |
| 282 | C22×Q8 | — | 2 | 4 | no | — |
| 283 | C22×Q8 | — | 2 | 3 | no | — |
| 284 | C22×Q8 | C22⋊D59 | 1 | 6 | yes | complemented |
| 285 | C22×Q8 | C22×D59 | 1 | 1 | yes | characteristic |
| 286 | C22×D4 | — | 59 | 1 | no | — |
| 287 | AGL(1,ℤ/8) | — | 118 | 12 | no | — |
| 288 | C2×SD16 | — | 118 | 6 | no | — |
| 289 | C2×SD16 | — | 118 | 3 | no | — |
| 290 | C2×D8 | — | 118 | 3 | no | — |
| 291 | C2×M16 | — | 59 | 3 | no | — |
| 292 | C22×C8 | — | 59 | 1 | no | — |
| 293 | #127 | — | 118 | 3 | no | — |
| 294 | #124 | — | 118 | 3 | no | — |
| 295 | #121 | — | 118 | 6 | no | — |
| 296 | #120 | — | 118 | 6 | no | — |
| 297 | #117 | — | 59 | 3 | no | — |
| 298 | #104 | — | 118 | 12 | no | — |
| 299 | #103 | — | 118 | 3 | no | — |
| 300 | #103 | — | 118 | 6 | no | — |
| 301 | #102 | — | 118 | 3 | no | — |
| 302 | #101 | — | 118 | 3 | no | — |
| 303 | #100 | — | 118 | 3 | no | — |
| 304 | #99 | — | 118 | 6 | no | — |
| 305 | C22⋊C8 | — | 118 | 6 | no | — |
| 306 | C24 | — | 118 | 1 | no | — |
| 307 | #41 | — | 2 | 48 | no | — |
| 308 | #41 | — | 2 | 24 | no | — |
| 309 | #41 | — | 2 | 48 | no | — |
| 310 | #41 | — | 2 | 8 | no | — |
| 311 | #41 | — | 2 | 24 | no | — |
| 312 | #41 | — | 2 | 48 | no | — |
| 313 | #41 | — | 2 | 24 | no | — |
| 314 | #41 | — | 2 | 12 | no | — |
| 315 | #41 | — | 2 | 12 | no | — |
| 316 | #41 | — | 2 | 12 | no | — |
| 317 | #41 | — | 2 | 4 | no | — |
| 318 | #41 | — | 2 | 12 | no | — |
| 319 | #41 | — | 2 | 12 | no | — |
| 320 | #41 | — | 2 | 12 | no | — |
| 321 | #41 | — | 2 | 12 | no | — |
| 322 | #41 | — | 2 | 12 | no | — |
| 323 | #41 | — | 2 | 12 | no | — |
| 324 | #41 | — | 2 | 6 | no | — |
| 325 | #41 | — | 2 | 6 | no | — |
| 326 | #41 | — | 2 | 6 | no | — |
| 327 | #41 | C2×C22⋊D59 | 1 | 12 | yes | — |
| 328 | C2×Q8 | — | 2 | 24 | no | — |
| 329 | C2×Q8 | — | 2 | 24 | no | — |
| 330 | C2×Q8 | — | 2 | 24 | no | — |
| 331 | C2×Q8 | — | 2 | 6 | no | — |
| 332 | C2×Q8 | — | 2 | 6 | no | — |
| 333 | C2×Q8 | — | 2 | 12 | no | — |
| 334 | C2×Q8 | — | 2 | 12 | no | — |
| 335 | C2×Q8 | — | 2 | 12 | no | — |
| 336 | C2×Q8 | — | 2 | 6 | no | — |
| 337 | C2×Q8 | — | 2 | 3 | no | — |
| 338 | C2×Q8 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 339 | C2×Q8 | C2×C22⋊D59 | 1 | 6 | yes | — |
| 340 | C2×Q8 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 341 | C2×D4 | — | 2 | 24 | no | — |
| 342 | C2×D4 | — | 2 | 24 | no | — |
| 343 | C2×D4 | — | 2 | 24 | no | — |
| 344 | C2×D4 | — | 2 | 6 | no | — |
| 345 | C2×D4 | — | 2 | 6 | no | — |
| 346 | C2×D4 | — | 2 | 12 | no | — |
| 347 | C2×D4 | — | 2 | 12 | no | — |
| 348 | C2×D4 | — | 2 | 6 | no | — |
| 349 | C2×D4 | — | 2 | 3 | no | — |
| 350 | C2×D4 | — | 2 | 12 | no | — |
| 351 | C2×D4 | — | 118 | 3 | no | — |
| 352 | C2×D4 | — | 118 | 3 | no | — |
| 353 | C2×D4 | — | 236 | 6 | no | — |
| 354 | C2×D4 | C2×C22⋊D59 | 1 | 6 | yes | — |
| 355 | C2×D4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 356 | C2×D4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 357 | C22×C4 | — | 2 | 8 | no | — |
| 358 | C22×C4 | — | 2 | 24 | no | — |
| 359 | C22×C4 | — | 2 | 12 | no | — |
| 360 | C22×C4 | — | 2 | 4 | no | — |
| 361 | C22×C4 | — | 2 | 6 | no | — |
| 362 | C22×C4 | — | 2 | 1 | no | — |
| 363 | C22×C4 | — | 2 | 6 | no | — |
| 364 | C22×C4 | — | 2 | 3 | no | — |
| 365 | C22×C4 | C2×C22⋊D59 | 1 | 6 | yes | — |
| 366 | C22×C4 | C23×D59 | 1 | 1 | yes | characteristic |
| 367 | SD16 | — | 236 | 4 | no | — |
| 368 | SD16 | — | 236 | 6 | no | — |
| 369 | D8 | — | 236 | 6 | no | — |
| 370 | M16 | — | 118 | 6 | no | — |
| 371 | C2×C8 | — | 118 | 3 | no | — |
| 372 | C2×C8 | — | 118 | 3 | no | — |
| 373 | C4⋊C4 | — | 118 | 3 | no | — |
| 374 | C22⋊C4 | — | 118 | 3 | no | — |
| 375 | C22⋊C4 | — | 236 | 6 | no | — |
| 376 | C42 | — | 118 | 3 | no | — |
| 377 | C23 | — | 2 | 4 | no | — |
| 378 | C23 | — | 2 | 12 | no | — |
| 379 | C23 | — | 2 | 3 | no | — |
| 380 | C23 | — | 944 | 1 | no | — |
| 381 | C23 | — | 236 | 3 | no | — |
| 382 | C23 | #14273696 | 1 | 6 | yes | — |
| 383 | C23 | C22×C22⋊D59 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 2 | 12 | no | — |
| 385 | Q8 | — | 2 | 24 | no | — |
| 386 | Q8 | — | 2 | 4 | no | — |
| 387 | Q8 | — | 2 | 3 | no | — |
| 388 | Q8 | — | 2 | 6 | no | — |
| 389 | Q8 | — | 2 | 6 | no | — |
| 390 | Q8 | #14273696 | 1 | 6 | yes | — |
| 391 | Q8 | #14273696 | 1 | 4 | yes | — |
| 392 | D4 | — | 2 | 24 | no | — |
| 393 | D4 | — | 2 | 24 | no | — |
| 394 | D4 | — | 2 | 12 | no | — |
| 395 | D4 | — | 2 | 12 | no | — |
| 396 | D4 | — | 2 | 12 | no | — |
| 397 | D4 | — | 2 | 12 | no | — |
| 398 | D4 | — | 2 | 3 | no | — |
| 399 | D4 | — | 2 | 6 | no | — |
| 400 | D4 | — | 944 | 6 | no | — |
| 401 | D4 | — | 236 | 3 | no | — |
| 402 | D4 | — | 236 | 1 | no | — |
| 403 | D4 | #14273696 | 1 | 6 | yes | — |
| 404 | C2×C4 | — | 2 | 12 | no | — |
| 405 | C2×C4 | — | 2 | 24 | no | — |
| 406 | C2×C4 | — | 2 | 24 | no | — |
| 407 | C2×C4 | — | 2 | 24 | no | — |
| 408 | C2×C4 | — | 2 | 12 | no | — |
| 409 | C2×C4 | — | 2 | 3 | no | — |
| 410 | C2×C4 | — | 2 | 6 | no | — |
| 411 | C2×C4 | — | 2 | 12 | no | — |
| 412 | C2×C4 | — | 2 | 6 | no | — |
| 413 | C2×C4 | — | 2 | 6 | no | — |
| 414 | C2×C4 | — | 236 | 3 | no | — |
| 415 | C2×C4 | #14273696 | 1 | 6 | yes | — |
| 416 | C2×C4 | C22×C22⋊D59 | 1 | 3 | yes | — |
| 417 | C2×C4 | C22×C22⋊D59 | 1 | 3 | yes | — |
| 418 | C8 | — | 236 | 1 | no | — |
| 419 | C8 | — | 236 | 3 | no | — |
| 420 | C22 | — | 2 | 6 | no | — |
| 421 | C22 | — | 2 | 6 | no | — |
| 422 | C22 | — | 4 | 1 | no | — |
| 423 | C22 | — | 4 | 6 | no | — |
| 424 | C22 | — | 8 | 3 | no | — |
| 425 | C22 | — | 8 | 4 | no | — |
| 426 | C22 | — | 8 | 12 | no | — |
| 427 | C22 | — | 472 | 6 | no | — |
| 428 | C22 | — | 472 | 1 | no | — |
| 429 | C22 | C2×#14273696 | 1 | 3 | yes | — |
| 430 | C4 | — | 2 | 4 | no | — |
| 431 | C4 | — | 2 | 6 | no | — |
| 432 | C4 | — | 2 | 6 | no | — |
| 433 | C4 | — | 472 | 3 | no | — |
| 434 | C4 | C2×#14273696 | 1 | 1 | yes | characteristic |
| 435 | C4 | C2×#14273696 | 1 | 3 | yes | — |
| 436 | C2 | — | 2 | 3 | no | — |
| 437 | C2 | — | 4 | 6 | no | — |
| 438 | C2 | — | 4 | 6 | no | — |
| 439 | C2 | — | 944 | 1 | no | — |
| 440 | C2 | #21432373 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21433498 | C2 | semidirect |
| 2. #21433468 | C2 | semidirect |
| 3. #21433382 | C2 | semidirect |
| 4. #21424071 | C2 | semidirect |
| 5. #21424060 | C2 | semidirect |
| 6. #21424047 | C2 | semidirect |
| 7. C59×2−1+6 | C2 | semidirect |
| 8. C2×#14273752 | C22 | semidirect |
| 9. C22×#11745671 | C22 | semidirect |
| 10. #16837966 | C22 | semidirect |
| 16. #16837419 | C22 | semidirect |
| 17. #16837411 | C22 | semidirect |
| 18. #16837398 | C22 | semidirect |
| 19. #16837386 | C22 | semidirect |
| 20. #16837376 | C22 | semidirect |
| 21. #16837369 | C22 | semidirect |
| 58. 2−1+4×C59 | D4 | semidirect |
| 66. H(5,𝔽2)×C59 | D4 | semidirect |
| 77. C2×#41×C59 | D4 | semidirect |
| 83. C22×Q8×C59 | D4 | semidirect |
| 216. 2−1+6 | D59 | semidirect |
| 250. C59 | #32895 | semidirect |
| 259. 2−1+4 | C22⋊D59 | semidirect |
| 267. H(5,𝔽2) | C22⋊D59 | semidirect |
| 278. C2×#41 | C22⋊D59 | semidirect |
| 284. C22×Q8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433498 | 2 |
| #21433468 | 2 |
| #21433382 | 2 |
| #21424071 | 2 |
| #21424060 | 2 |
| #21424047 | 2 |
| C59×2−1+6 | 2 |
| #32895 | 59 |