Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1284 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 155 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 | C2×#16811365 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16810796 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20276731 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 4 | C2×#16810420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#16810419 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×C53×#454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#13133242 | — | 2 | 2 | no | — |
| 8 | #16811365 | — | 2 | 4 | no | — |
| 9 | #16811365 | — | 2 | 2 | no | — |
| 10 | #16811365 | C22 | 1 | 4 | yes | complemented |
| 11 | C2×#13133206 | C22 | 1 | 2 | yes | — |
| 12 | C2×#13133205 | — | 2 | 1 | no | — |
| 13 | C2×#13133203 | — | 2 | 2 | no | — |
| 14 | C2×#13133187 | — | 2 | 2 | no | — |
| 15 | C2×#13133185 | — | 2 | 1 | no | — |
| 16 | #16810796 | — | 2 | 4 | no | — |
| 17 | #16810796 | C22 | 1 | 8 | yes | complemented |
| 18 | C2×#13133144 | — | 2 | 2 | no | — |
| 19 | C2×#13133136 | C22 | 1 | 2 | yes | complemented |
| 20 | #16810420 | C22 | 1 | 4 | yes | complemented |
| 21 | #16810419 | C22 | 1 | 8 | yes | complemented |
| 22 | C2×2−1+4×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 24 | C2×#124×C53 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#454 | — | 2 | 2 | no | — |
| 26 | C53×#454 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#104×C53 | — | 2 | 1 | no | — |
| 28 | C2×#101×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C24×D53 | — | 2 | 1 | no | — |
| 30 | C22×Dic106 | — | 2 | 1 | no | — |
| 31 | C22×D212 | — | 2 | 1 | no | — |
| 32 | C22×D212 | D4 | 1 | 2 | yes | — |
| 33 | C22×C22⋊D53 | — | 2 | 2 | no | — |
| 34 | #13133242 | — | 2 | 8 | no | — |
| 35 | #13133242 | — | 4 | 4 | no | — |
| 36 | C2×#11719924 | — | 4 | 2 | no | — |
| 37 | C2×#11719922 | — | 4 | 2 | no | — |
| 38 | C2×#11719917 | — | 2 | 2 | no | — |
| 39 | #13133206 | — | 2 | 2 | no | — |
| 40 | #13133206 | — | 2 | 2 | no | — |
| 41 | #13133206 | D4 | 1 | 4 | yes | — |
| 42 | #13133206 | C23 | 1 | 4 | yes | — |
| 43 | #13133205 | — | 2 | 4 | no | — |
| 44 | #13133205 | — | 2 | 4 | no | — |
| 45 | #13133203 | — | 2 | 8 | no | — |
| 46 | #13133203 | — | 2 | 8 | no | — |
| 47 | #13133187 | — | 2 | 8 | no | — |
| 48 | #13133187 | — | 2 | 8 | no | — |
| 49 | #13133185 | — | 2 | 4 | no | — |
| 50 | #13133185 | — | 2 | 4 | no | — |
| 51 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 52 | C2×#11719921 | — | 2 | 2 | no | — |
| 53 | C2×#11719921 | — | 2 | 2 | no | — |
| 54 | C2×#11719921 | — | 2 | 2 | no | — |
| 55 | C2×C4×Dic53 | D4 | 1 | 2 | yes | — |
| 56 | #13133144 | — | 2 | 8 | no | — |
| 57 | #13133136 | — | 2 | 2 | no | — |
| 58 | #13133136 | C23 | 1 | 4 | yes | complemented |
| 59 | 2−1+4×C53 | — | 2 | 2 | no | — |
| 60 | 2−1+4×C53 | — | 2 | 1 | no | — |
| 61 | 2−1+4×C53 | — | 4 | 2 | no | — |
| 62 | 2−1+4×C53 | C23 | 1 | 2 | yes | complemented |
| 63 | C2×#41×C53 | — | 2 | 1 | no | — |
| 64 | C2×#41×C53 | — | 2 | 2 | no | — |
| 65 | C2×#41×C53 | — | 4 | 1 | no | — |
| 66 | C22×Q8×C53 | — | 4 | 1 | no | — |
| 67 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 69 | AGL(1,ℤ/8)×C53 | — | 2 | 4 | no | — |
| 70 | AGL(1,ℤ/8)×C53 | — | 4 | 2 | no | — |
| 71 | C2×SD16×C53 | — | 4 | 1 | no | — |
| 72 | C2×D8×C53 | — | 4 | 1 | no | — |
| 73 | C2×M16×C53 | — | 2 | 1 | no | — |
| 74 | #124×C53 | — | 2 | 2 | no | — |
| 75 | #124×C53 | D4 | 1 | 2 | yes | — |
| 76 | #124×C53 | C23 | 1 | 2 | yes | — |
| 77 | C2×C22⋊C4×C53 | — | 2 | 2 | no | — |
| 78 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 79 | #104×C53 | — | 2 | 4 | no | — |
| 80 | #101×C53 | — | 2 | 1 | no | — |
| 81 | #101×C53 | C23 | 1 | 2 | yes | complemented |
| 82 | C24×C53 | — | 2 | 1 | no | — |
| 83 | C23×D53 | — | 2 | 2 | no | — |
| 84 | C23×D53 | — | 2 | 4 | no | — |
| 85 | C23×D53 | — | 8 | 4 | no | — |
| 86 | C23×D53 | — | 8 | 1 | no | — |
| 87 | C23×D53 | — | 8 | 1 | no | — |
| 88 | #41×C53 | — | 2 | 2 | no | — |
| 89 | #41×C53 | — | 2 | 4 | no | — |
| 90 | #41×C53 | — | 2 | 2 | no | — |
| 91 | #41×C53 | — | 2 | 4 | no | — |
| 92 | #41×C53 | — | 4 | 2 | no | — |
| 93 | #41×C53 | — | 4 | 1 | no | — |
| 94 | #41×C53 | — | 4 | 2 | no | — |
| 95 | #41×C53 | — | 4 | 4 | no | — |
| 96 | #41×C53 | — | 4 | 2 | no | — |
| 97 | #41×C53 | — | 4 | 2 | no | — |
| 98 | #41×C53 | — | 4 | 1 | no | — |
| 99 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 100 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 101 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 102 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 103 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 104 | C2×Q8×C53 | — | 4 | 4 | no | — |
| 105 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 106 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 107 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 109 | C2×D4×C53 | — | 2 | 1 | no | — |
| 110 | C2×D4×C53 | — | 2 | 2 | no | — |
| 111 | C2×D4×C53 | — | 2 | 1 | no | — |
| 112 | C2×D4×C53 | — | 4 | 1 | no | — |
| 113 | C2×D4×C53 | — | 4 | 1 | no | — |
| 114 | C2×D4×C53 | — | 4 | 1 | no | — |
| 115 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 116 | C22×C4×C53 | — | 2 | 1 | no | — |
| 117 | C22×C4×C53 | — | 4 | 2 | no | — |
| 118 | C22×C4×C53 | — | 4 | 1 | no | — |
| 119 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 120 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C22⋊D53 | — | 2 | 8 | no | — |
| 122 | C2×C22⋊D53 | — | 8 | 4 | no | — |
| 123 | C22×Dic53 | — | 2 | 2 | no | — |
| 124 | C2×D212 | — | 2 | 4 | no | — |
| 125 | C2×D212 | — | 2 | 2 | no | — |
| 126 | C2×D212 | — | 4 | 2 | no | — |
| 127 | C2×D212 | — | 4 | 2 | no | — |
| 128 | C2×D212 | — | 8 | 2 | no | — |
| 129 | C2×D212 | C2×D4 | 1 | 4 | yes | — |
| 130 | C2×Dic106 | — | 2 | 4 | no | — |
| 131 | C2×Dic106 | — | 8 | 2 | no | — |
| 132 | SD16×C53 | — | 4 | 4 | no | — |
| 133 | D8×C53 | — | 4 | 4 | no | — |
| 134 | M16×C53 | — | 2 | 2 | no | — |
| 135 | M16×C53 | — | 4 | 1 | no | — |
| 136 | C2×C8×C53 | — | 4 | 1 | no | — |
| 137 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 138 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 139 | C42×C53 | — | 2 | 1 | no | — |
| 140 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 141 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 142 | #11719924 | — | 4 | 8 | no | — |
| 143 | #11719922 | — | 4 | 8 | no | — |
| 144 | #11719921 | — | 2 | 8 | no | — |
| 145 | #11719921 | — | 2 | 4 | no | — |
| 146 | #11719921 | — | 2 | 4 | no | — |
| 147 | #11719921 | — | 2 | 4 | no | — |
| 148 | #11719921 | — | 2 | 4 | no | — |
| 149 | C4×Dic53 | — | 2 | 2 | no | — |
| 150 | C4×Dic53 | C2×D4 | 1 | 4 | yes | — |
| 151 | #11719917 | — | 2 | 4 | no | — |
| 152 | #11719917 | — | 4 | 2 | no | — |
| 153 | C2×#88322 | — | 4 | 2 | no | — |
| 154 | C23×C53 | — | 2 | 2 | no | — |
| 155 | C23×C53 | — | 4 | 4 | no | — |
| 156 | C23×C53 | — | 4 | 1 | no | — |
| 157 | C23×C53 | — | 4 | 1 | no | — |
| 158 | C23×C53 | — | 4 | 1 | no | — |
| 159 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 160 | C22×D53 | — | 2 | 4 | no | — |
| 161 | C22×D53 | — | 4 | 4 | no | — |
| 162 | C22×D53 | — | 4 | 4 | no | — |
| 163 | C22×D53 | — | 4 | 2 | no | — |
| 164 | C22×D53 | — | 4 | 2 | no | — |
| 165 | C22×D53 | — | 8 | 8 | no | — |
| 166 | C22×D53 | — | 8 | 4 | no | — |
| 167 | C22×D53 | — | 8 | 8 | no | — |
| 168 | C22×D53 | — | 8 | 8 | no | — |
| 169 | Q8×C53 | — | 2 | 4 | no | — |
| 170 | Q8×C53 | — | 2 | 2 | no | — |
| 171 | Q8×C53 | — | 4 | 2 | no | — |
| 172 | Q8×C53 | — | 4 | 1 | no | — |
| 173 | Q8×C53 | — | 4 | 1 | no | — |
| 174 | Q8×C53 | — | 4 | 2 | no | — |
| 175 | Q8×C53 | — | 4 | 1 | no | — |
| 176 | D4×C53 | — | 2 | 4 | no | — |
| 177 | D4×C53 | — | 2 | 2 | no | — |
| 178 | D4×C53 | — | 4 | 2 | no | — |
| 179 | D4×C53 | — | 4 | 2 | no | — |
| 180 | D4×C53 | — | 4 | 1 | no | — |
| 181 | D4×C53 | — | 4 | 2 | no | — |
| 182 | D4×C53 | — | 4 | 2 | no | — |
| 183 | D4×C53 | — | 8 | 1 | no | — |
| 184 | C2×C4×C53 | — | 2 | 2 | no | — |
| 185 | C2×C4×C53 | — | 2 | 2 | no | — |
| 186 | C2×C4×C53 | — | 2 | 1 | no | — |
| 187 | C2×C4×C53 | — | 2 | 1 | no | — |
| 188 | C2×C4×C53 | — | 2 | 2 | no | — |
| 189 | C2×C4×C53 | — | 4 | 4 | no | — |
| 190 | C2×C4×C53 | — | 4 | 2 | no | — |
| 191 | C2×C4×C53 | — | 4 | 4 | no | — |
| 192 | C2×C4×C53 | — | 4 | 2 | no | — |
| 193 | C2×C4×C53 | — | 4 | 2 | no | — |
| 194 | C2×C4×C53 | — | 4 | 1 | no | — |
| 195 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 196 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 198 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 199 | C22⋊D53 | — | 8 | 8 | no | — |
| 200 | C2×Dic53 | — | 2 | 4 | no | — |
| 201 | C2×Dic53 | — | 4 | 4 | no | — |
| 202 | D212 | — | 4 | 4 | no | — |
| 203 | D212 | — | 8 | 2 | no | — |
| 204 | D212 | — | 8 | 4 | no | — |
| 205 | Dic106 | — | 8 | 4 | no | — |
| 206 | C8×C53 | — | 4 | 2 | no | — |
| 207 | #88322 | — | 4 | 4 | no | — |
| 208 | C2×#2202 | — | 53 | 1 | no | maximal, Sylow |
| 209 | C22×C53 | — | 2 | 2 | no | — |
| 210 | C22×C53 | — | 4 | 4 | no | — |
| 211 | C22×C53 | — | 4 | 2 | no | — |
| 212 | C22×C53 | — | 4 | 2 | no | — |
| 213 | C22×C53 | — | 8 | 2 | no | — |
| 214 | C22×C53 | — | 8 | 2 | no | — |
| 215 | C22×C53 | — | 8 | 2 | no | — |
| 216 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 217 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 218 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 219 | C2×D53 | — | 4 | 4 | no | — |
| 220 | C2×D53 | — | 4 | 4 | no | — |
| 221 | C2×D53 | — | 4 | 4 | no | — |
| 222 | C2×D53 | — | 8 | 4 | no | — |
| 223 | C2×D53 | — | 8 | 16 | no | — |
| 224 | C2×D53 | — | 8 | 4 | no | — |
| 225 | C4×C53 | — | 2 | 2 | no | — |
| 226 | C4×C53 | — | 2 | 1 | no | — |
| 227 | C4×C53 | — | 2 | 2 | no | — |
| 228 | C4×C53 | — | 2 | 1 | no | — |
| 229 | C4×C53 | — | 4 | 2 | no | — |
| 230 | C4×C53 | — | 4 | 2 | no | — |
| 231 | Dic53 | — | 4 | 4 | no | — |
| 232 | C2×H(3,𝔽4) | — | 53 | 1 | no | — |
| 233 | C2×#454 | — | 53 | 2 | no | — |
| 234 | C2×#454 | D53 | 1 | 1 | yes | characteristic, complemented |
| 235 | #2202 | — | 53 | 8 | no | — |
| 236 | C2×#355 | — | 53 | 2 | no | — |
| 237 | C2×#355 | — | 53 | 1 | no | — |
| 238 | C2×C53 | — | 2 | 1 | no | — |
| 239 | C2×C53 | — | 2 | 1 | no | — |
| 240 | C2×C53 | — | 8 | 2 | no | — |
| 241 | C2×C53 | — | 8 | 2 | no | — |
| 242 | C2×C53 | #2202 | 1 | 2 | yes | complemented |
| 243 | C2×C53 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 244 | D53 | — | 8 | 4 | no | — |
| 245 | C2×2−1+4 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 246 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 247 | C2×AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 248 | H(3,𝔽4) | — | 53 | 4 | no | — |
| 249 | H(3,𝔽4) | — | 106 | 4 | no | — |
| 250 | H(3,𝔽4) | — | 106 | 2 | no | — |
| 251 | C2×#124 | — | 53 | 2 | no | — |
| 252 | C2×#124 | — | 106 | 2 | no | — |
| 253 | C2×#124 | — | 106 | 1 | no | — |
| 254 | C2×#124 | C2×D53 | 1 | 1 | yes | characteristic |
| 255 | C2×#120 | — | 106 | 2 | no | — |
| 256 | C2×#120 | — | 106 | 1 | no | — |
| 257 | #454 | — | 2 | 2 | no | — |
| 258 | #454 | — | 53 | 8 | no | — |
| 259 | #454 | — | 106 | 4 | no | — |
| 260 | #454 | C2×D53 | 1 | 4 | yes | complemented |
| 261 | C2×#104 | — | 2 | 1 | no | — |
| 262 | C2×#104 | — | 106 | 2 | no | — |
| 263 | C2×#101 | — | 53 | 2 | no | — |
| 264 | C2×#101 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 265 | #355 | — | 53 | 4 | no | — |
| 266 | #355 | — | 53 | 8 | no | — |
| 267 | C53 | C2×#2202 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 268 | C25 | — | 106 | 1 | no | — |
| 269 | 2−1+4 | — | 2 | 2 | no | — |
| 270 | 2−1+4 | — | 2 | 1 | no | — |
| 271 | 2−1+4 | — | 4 | 2 | no | — |
| 272 | 2−1+4 | C22×D53 | 1 | 2 | yes | complemented |
| 273 | C2×#41 | — | 2 | 2 | no | — |
| 274 | C2×#41 | — | 2 | 1 | no | — |
| 275 | C2×#41 | — | 4 | 1 | no | — |
| 276 | C22×Q8 | — | 4 | 1 | no | — |
| 277 | C22×Q8 | — | 106 | 1 | no | — |
| 278 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 279 | C22×D4 | — | 53 | 2 | no | — |
| 280 | C22×D4 | — | 106 | 1 | no | — |
| 281 | C22×D4 | — | 106 | 2 | no | — |
| 282 | C22×D4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 283 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 284 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 285 | AGL(1,ℤ/8) | — | 106 | 8 | no | — |
| 286 | AGL(1,ℤ/8) | — | 212 | 4 | no | — |
| 287 | C2×SD16 | — | 4 | 1 | no | — |
| 288 | C2×SD16 | — | 212 | 2 | no | — |
| 289 | C2×D8 | — | 4 | 1 | no | — |
| 290 | C2×D8 | — | 212 | 2 | no | — |
| 291 | C2×M16 | — | 2 | 1 | no | — |
| 292 | C2×M16 | — | 106 | 2 | no | — |
| 293 | #124 | — | 2 | 2 | no | — |
| 294 | #124 | — | 53 | 4 | no | — |
| 295 | #124 | — | 53 | 4 | no | — |
| 296 | #124 | — | 106 | 4 | no | — |
| 297 | #124 | — | 106 | 8 | no | — |
| 298 | #124 | — | 106 | 8 | no | — |
| 299 | #124 | — | 106 | 2 | no | — |
| 300 | #124 | — | 106 | 2 | no | — |
| 301 | #124 | — | 106 | 4 | no | — |
| 302 | #124 | C22⋊D53 | 1 | 2 | yes | — |
| 303 | #124 | C22×D53 | 1 | 2 | yes | — |
| 304 | #120 | — | 106 | 8 | no | — |
| 305 | #120 | — | 106 | 8 | no | — |
| 306 | #120 | — | 106 | 4 | no | — |
| 307 | #120 | — | 106 | 4 | no | — |
| 308 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 309 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 310 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 311 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 312 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 313 | C2×C42 | — | 53 | 2 | no | — |
| 314 | C2×C42 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 315 | #104 | — | 2 | 4 | no | — |
| 316 | #104 | — | 106 | 8 | no | — |
| 317 | #101 | — | 2 | 1 | no | — |
| 318 | #101 | — | 53 | 4 | no | — |
| 319 | #101 | — | 106 | 2 | no | — |
| 320 | #101 | C22×D53 | 1 | 2 | yes | complemented |
| 321 | C24 | — | 2 | 1 | no | — |
| 322 | C24 | — | 106 | 4 | no | — |
| 323 | C24 | — | 106 | 2 | no | — |
| 324 | C24 | — | 424 | 4 | no | — |
| 325 | C24 | — | 424 | 1 | no | — |
| 326 | C24 | — | 424 | 1 | no | — |
| 327 | #41 | — | 2 | 2 | no | — |
| 328 | #41 | — | 2 | 4 | no | — |
| 329 | #41 | — | 2 | 4 | no | — |
| 330 | #41 | — | 2 | 2 | no | — |
| 331 | #41 | — | 4 | 1 | no | — |
| 332 | #41 | — | 4 | 2 | no | — |
| 333 | #41 | — | 4 | 2 | no | — |
| 334 | #41 | — | 4 | 2 | no | — |
| 335 | #41 | — | 4 | 4 | no | — |
| 336 | #41 | — | 4 | 1 | no | — |
| 337 | #41 | — | 4 | 2 | no | — |
| 338 | C2×Q8 | — | 2 | 1 | no | — |
| 339 | C2×Q8 | — | 2 | 2 | no | — |
| 340 | C2×Q8 | — | 4 | 1 | no | — |
| 341 | C2×Q8 | — | 4 | 1 | no | — |
| 342 | C2×Q8 | — | 4 | 2 | no | — |
| 343 | C2×Q8 | — | 4 | 2 | no | — |
| 344 | C2×Q8 | — | 4 | 4 | no | — |
| 345 | C2×Q8 | — | 106 | 4 | no | — |
| 346 | C2×Q8 | — | 424 | 2 | no | — |
| 347 | C2×Q8 | D4×D53 | 1 | 2 | yes | — |
| 348 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 349 | C2×Q8 | C23×D53 | 1 | 1 | yes | characteristic |
| 350 | C2×D4 | — | 2 | 1 | no | — |
| 351 | C2×D4 | — | 2 | 2 | no | — |
| 352 | C2×D4 | — | 2 | 1 | no | — |
| 353 | C2×D4 | — | 4 | 1 | no | — |
| 354 | C2×D4 | — | 4 | 1 | no | — |
| 355 | C2×D4 | — | 4 | 1 | no | — |
| 356 | C2×D4 | — | 53 | 4 | no | — |
| 357 | C2×D4 | — | 106 | 4 | no | — |
| 358 | C2×D4 | — | 106 | 8 | no | — |
| 359 | C2×D4 | — | 106 | 2 | no | — |
| 360 | C2×D4 | — | 424 | 2 | no | — |
| 361 | C2×D4 | — | 424 | 4 | no | — |
| 362 | C2×D4 | — | 212 | 2 | no | — |
| 363 | C2×D4 | — | 212 | 2 | no | — |
| 364 | C2×D4 | C2×C22⋊D53 | 1 | 2 | yes | — |
| 365 | C22×C4 | — | 2 | 1 | no | — |
| 366 | C22×C4 | — | 4 | 1 | no | — |
| 367 | C22×C4 | — | 4 | 2 | no | — |
| 368 | C22×C4 | — | 106 | 2 | no | — |
| 369 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 370 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 371 | SD16 | — | 4 | 4 | no | — |
| 372 | SD16 | — | 212 | 8 | no | — |
| 373 | D8 | — | 4 | 4 | no | — |
| 374 | D8 | — | 212 | 8 | no | — |
| 375 | M16 | — | 2 | 2 | no | — |
| 376 | M16 | — | 4 | 1 | no | — |
| 377 | M16 | — | 106 | 4 | no | — |
| 378 | M16 | — | 212 | 2 | no | — |
| 379 | C2×C8 | — | 4 | 1 | no | — |
| 380 | C2×C8 | — | 212 | 2 | no | — |
| 381 | C22⋊C4 | — | 2 | 4 | no | — |
| 382 | C22⋊C4 | — | 2 | 4 | no | — |
| 383 | C22⋊C4 | — | 106 | 8 | no | — |
| 384 | C22⋊C4 | — | 106 | 4 | no | — |
| 385 | C22⋊C4 | — | 106 | 4 | no | — |
| 386 | C22⋊C4 | — | 106 | 4 | no | — |
| 387 | C22⋊C4 | — | 106 | 4 | no | — |
| 388 | C22⋊C4 | — | 106 | 4 | no | — |
| 389 | C42 | — | 2 | 1 | no | — |
| 390 | C42 | — | 53 | 4 | no | — |
| 391 | C42 | — | 106 | 2 | no | — |
| 392 | C42 | C2×C22⋊D53 | 1 | 2 | yes | — |
| 393 | C23 | — | 2 | 2 | no | — |
| 394 | C23 | — | 4 | 4 | no | — |
| 395 | C23 | — | 4 | 1 | no | — |
| 396 | C23 | — | 4 | 1 | no | — |
| 397 | C23 | — | 4 | 1 | no | — |
| 398 | C23 | — | 106 | 4 | no | — |
| 399 | C23 | — | 424 | 8 | no | — |
| 400 | C23 | — | 424 | 4 | no | — |
| 401 | C23 | — | 424 | 8 | no | — |
| 402 | C23 | — | 424 | 8 | no | — |
| 403 | C23 | — | 212 | 4 | no | — |
| 404 | C23 | — | 212 | 4 | no | — |
| 405 | C23 | — | 212 | 2 | no | — |
| 406 | C23 | — | 212 | 2 | no | — |
| 407 | C23 | #13133185 | 1 | 1 | yes | characteristic |
| 408 | Q8 | — | 2 | 2 | no | — |
| 409 | Q8 | — | 2 | 4 | no | — |
| 410 | Q8 | — | 4 | 2 | no | — |
| 411 | Q8 | — | 4 | 1 | no | — |
| 412 | Q8 | — | 4 | 1 | no | — |
| 413 | Q8 | — | 4 | 1 | no | — |
| 414 | Q8 | — | 4 | 2 | no | — |
| 415 | Q8 | — | 424 | 4 | no | — |
| 416 | D4 | — | 2 | 2 | no | — |
| 417 | D4 | — | 2 | 4 | no | — |
| 418 | D4 | — | 4 | 2 | no | — |
| 419 | D4 | — | 4 | 1 | no | — |
| 420 | D4 | — | 4 | 2 | no | — |
| 421 | D4 | — | 4 | 2 | no | — |
| 422 | D4 | — | 4 | 2 | no | — |
| 423 | D4 | — | 8 | 1 | no | — |
| 424 | D4 | — | 424 | 2 | no | — |
| 425 | D4 | — | 424 | 4 | no | — |
| 426 | D4 | — | 424 | 8 | no | — |
| 427 | D4 | — | 212 | 4 | no | — |
| 428 | C2×C4 | — | 2 | 1 | no | — |
| 429 | C2×C4 | — | 2 | 2 | no | — |
| 430 | C2×C4 | — | 2 | 1 | no | — |
| 431 | C2×C4 | — | 2 | 2 | no | — |
| 432 | C2×C4 | — | 2 | 2 | no | — |
| 433 | C2×C4 | — | 4 | 2 | no | — |
| 434 | C2×C4 | — | 4 | 4 | no | — |
| 435 | C2×C4 | — | 4 | 2 | no | — |
| 436 | C2×C4 | — | 4 | 4 | no | — |
| 437 | C2×C4 | — | 4 | 2 | no | — |
| 438 | C2×C4 | — | 4 | 1 | no | — |
| 439 | C2×C4 | — | 106 | 4 | no | — |
| 440 | C2×C4 | — | 212 | 4 | no | — |
| 441 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 442 | C2×C4 | #13133185 | 1 | 2 | yes | — |
| 443 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 444 | C2×C4 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 445 | C8 | — | 4 | 2 | no | — |
| 446 | C8 | — | 212 | 4 | no | — |
| 447 | C22 | — | 2 | 2 | no | — |
| 448 | C22 | — | 4 | 4 | no | — |
| 449 | C22 | — | 4 | 2 | no | — |
| 450 | C22 | — | 4 | 2 | no | — |
| 451 | C22 | — | 8 | 2 | no | — |
| 452 | C22 | — | 8 | 2 | no | — |
| 453 | C22 | — | 8 | 2 | no | — |
| 454 | C22 | — | 424 | 4 | no | — |
| 455 | C22 | — | 424 | 16 | no | — |
| 456 | C22 | — | 424 | 4 | no | — |
| 457 | C22 | — | 212 | 4 | no | — |
| 458 | C22 | — | 212 | 4 | no | — |
| 459 | C22 | — | 212 | 4 | no | — |
| 460 | C22 | #16810809 | 1 | 1 | yes | characteristic |
| 461 | C22 | #16810809 | 1 | 1 | yes | characteristic |
| 462 | C22 | C2×#13133185 | 1 | 1 | yes | characteristic |
| 463 | C4 | — | 2 | 1 | no | — |
| 464 | C4 | — | 2 | 2 | no | — |
| 465 | C4 | — | 2 | 1 | no | — |
| 466 | C4 | — | 2 | 2 | no | — |
| 467 | C4 | — | 4 | 2 | no | — |
| 468 | C4 | — | 4 | 2 | no | — |
| 469 | C4 | — | 212 | 4 | no | — |
| 470 | C2 | — | 2 | 1 | no | — |
| 471 | C2 | — | 2 | 1 | no | — |
| 472 | C2 | — | 8 | 2 | no | — |
| 473 | C2 | — | 8 | 2 | no | — |
| 474 | C2 | — | 424 | 4 | no | — |
| 475 | C2 | #20276731 | 1 | 2 | yes | direct product factor |
| 476 | C2 | C2×#16810809 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16811365 | C2 | semidirect |
| 2. C2×#16810796 | C2 | semidirect |
| 3. #20276731 | C2 | direct (N × H) |
| 4. C2×#16810420 | C2 | semidirect |
| 5. C2×#16810419 | C2 | semidirect |
| 6. C2×C53×#454 | C2 | semidirect |
| 10. #16811365 | C22 | semidirect |
| 17. #16810796 | C22 | semidirect |
| 19. C2×#13133136 | C22 | semidirect |
| 20. #16810420 | C22 | semidirect |
| 21. #16810419 | C22 | semidirect |
| 22. C2×2−1+4×C53 | C22 | semidirect |
| 26. C53×#454 | C22 | semidirect |
| 28. C2×#101×C53 | C22 | semidirect |
| 58. #13133136 | C23 | semidirect |
| 62. 2−1+4×C53 | C23 | semidirect |
| 81. #101×C53 | C23 | semidirect |
| 234. C2×#454 | D53 | semidirect |
| 242. C2×C53 | #2202 | semidirect |
| 245. C2×2−1+4 | C2×D53 | semidirect |
| 260. #454 | C2×D53 | semidirect |
| 264. C2×#101 | C2×D53 | semidirect |
| 267. C53 | C2×#2202 | semidirect |
| 272. 2−1+4 | C22×D53 | semidirect |
| 320. #101 | C22×D53 | semidirect |
| 475. C2 | #20276731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811365 | 2 |
| C2×#16810796 | 2 |
| #20276731 | 2 |
| C2×#16810420 | 2 |
| C2×#16810419 | 2 |
| C2×C53×#454 | 2 |
| C2×#2202 | 53 |