← C2×#20289525 #28297988
Subgroups — C2×#20289525 #28297988
Order 13568.
60570 conjugacy classes of subgroups.
The subgroup lattice has 264 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20289525 | C2 | 1 | 64 | yes | maximal, direct product factor |
| 2 | C2×#16811459 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | C2×#16811458 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | C22×#13133262 | C2 | 1 | 18 | yes | maximal, complemented |
| 5 | C2×H(5,𝔽2)×D53 | C2 | 1 | 16 | yes | maximal, complemented |
| 6 | C22×H(5,𝔽2)×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #16811459 | C22 | 1 | 384 | yes | complemented |
| 8 | #16811458 | C22 | 1 | 512 | yes | complemented |
| 9 | C2×#13133265 | C22 | 1 | 8 | yes | complemented |
| 10 | C2×#13133264 | C22 | 1 | 48 | yes | complemented |
| 11 | C2×#13133263 | C22 | 1 | 48 | yes | complemented |
| 12 | C2×#13133262 | C22 | 1 | 144 | yes | complemented |
| 13 | C2×#13133262 | C22 | 1 | 72 | yes | complemented |
| 14 | C2×#13133262 | C22 | 1 | 576 | yes | complemented |
| 15 | H(5,𝔽2)×D53 | C22 | 1 | 512 | yes | complemented |
| 16 | C22×#11719945 | C22 | 1 | 36 | yes | complemented |
| 17 | C22×#11719947 | C22 | 1 | 72 | yes | complemented |
| 18 | C2×#41×D53 | C22 | 1 | 96 | yes | complemented |
| 19 | C23×C22⋊D53 | C22 | 1 | 24 | yes | complemented |
| 20 | C22×D4×D53 | C22 | 1 | 72 | yes | complemented |
| 21 | C2×H(5,𝔽2)×C53 | C22 | 1 | 16 | yes | complemented |
| 22 | C2×H(5,𝔽2)×C53 | C22 | 1 | 32 | yes | complemented |
| 23 | C22×#41×C53 | C22 | 1 | 6 | yes | complemented |
| 24 | C23×D4×C53 | C22 | 1 | 9 | yes | complemented |
| 25 | C24×D53 | C23 | 1 | 24 | yes | complemented |
| 26 | #13133265 | C23 | 1 | 128 | yes | complemented |
| 27 | #13133264 | C23 | 1 | 768 | yes | complemented |
| 28 | #13133263 | C23 | 1 | 768 | yes | complemented |
| 29 | #13133262 | C23 | 1 | 2304 | yes | complemented |
| 30 | #13133262 | C23 | 1 | 1152 | yes | complemented |
| 31 | C2×#11719949 | C23 | 1 | 32 | yes | complemented |
| 32 | C2×#11719945 | C23 | 1 | 144 | yes | complemented |
| 33 | C2×#11719945 | C23 | 1 | 48 | yes | complemented |
| 34 | C2×#11719945 | C23 | 1 | 576 | yes | complemented |
| 35 | C2×#11719947 | C23 | 1 | 288 | yes | complemented |
| 36 | C2×#11719947 | C23 | 1 | 1152 | yes | complemented |
| 37 | #41×D53 | C23 | 1 | 1536 | yes | complemented |
| 38 | C22×Dic106 | C23 | 1 | 36 | yes | complemented |
| 39 | C2×Q8×D53 | C23 | 1 | 32 | yes | complemented |
| 40 | C22×D212 | C23 | 1 | 36 | yes | complemented |
| 41 | C22×C22⋊D53 | C23 | 1 | 144 | yes | complemented |
| 42 | C22×C22⋊D53 | C23 | 1 | 72 | yes | complemented |
| 43 | C22×C22⋊D53 | C23 | 1 | 384 | yes | complemented |
| 44 | C2×D4×D53 | C23 | 1 | 288 | yes | complemented |
| 45 | C2×D4×D53 | C23 | 1 | 1152 | yes | complemented |
| 46 | C23×Dic53 | C23 | 1 | 24 | yes | complemented |
| 47 | C22×C4×D53 | C23 | 1 | 72 | yes | complemented |
| 48 | C25×C53 | C23 | 1 | 6 | yes | complemented |
| 49 | H(5,𝔽2)×C53 | C23 | 1 | 256 | yes | complemented |
| 50 | C2×#41×C53 | C23 | 1 | 48 | yes | complemented |
| 51 | C2×#41×C53 | C23 | 1 | 96 | yes | complemented |
| 52 | C22×Q8×C53 | C23 | 1 | 2 | yes | complemented |
| 53 | C22×D4×C53 | C23 | 1 | 18 | yes | complemented |
| 54 | C22×D4×C53 | C23 | 1 | 72 | yes | complemented |
| 55 | C22×D4×C53 | C23 | 1 | 144 | yes | complemented |
| 56 | C23×C4×C53 | C23 | 1 | 9 | yes | complemented |
| 57 | C24×C53 | — | 8 | 12 | no | — |
| 58 | C24×C53 | C24 | 1 | 9 | yes | — |
| 59 | C24×C53 | C24 | 1 | 24 | yes | — |
| 60 | C24×C53 | C24 | 1 | 48 | yes | complemented |
| 61 | C23×D53 | — | 8 | 48 | no | — |
| 62 | C23×D53 | C24 | 1 | 72 | yes | — |
| 63 | C23×D53 | C24 | 1 | 192 | yes | complemented |
| 64 | #41×C53 | C24 | 1 | 384 | yes | complemented |
| 65 | C2×Q8×C53 | C24 | 1 | 8 | yes | — |
| 66 | C2×Q8×C53 | C24 | 1 | 16 | yes | complemented |
| 67 | C2×D4×C53 | C24 | 1 | 72 | yes | — |
| 68 | C2×D4×C53 | C24 | 1 | 144 | yes | complemented |
| 69 | C2×D4×C53 | C24 | 1 | 576 | yes | complemented |
| 70 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 71 | C22×C4×C53 | C24 | 1 | 36 | yes | — |
| 72 | C22×C4×C53 | C24 | 1 | 72 | yes | complemented |
| 73 | C2×C22⋊D53 | C24 | 1 | 144 | yes | — |
| 74 | C2×C22⋊D53 | C24 | 1 | 16 | yes | — |
| 75 | C2×C22⋊D53 | C24 | 1 | 1152 | yes | complemented |
| 76 | C2×C22⋊D53 | C24 | 1 | 576 | yes | complemented |
| 77 | C22×Dic53 | C24 | 1 | 72 | yes | — |
| 78 | C22×Dic53 | C24 | 1 | 192 | yes | complemented |
| 79 | #11719949 | C24 | 1 | 256 | yes | complemented |
| 80 | Q8×D53 | C24 | 1 | 256 | yes | complemented |
| 81 | #11719947 | C24 | 1 | 2304 | yes | complemented |
| 82 | D4×D53 | C24 | 1 | 2304 | yes | complemented |
| 83 | #11719945 | C24 | 1 | 1152 | yes | complemented |
| 84 | #11719945 | C24 | 1 | 384 | yes | complemented |
| 85 | C2×D212 | C24 | 1 | 48 | yes | — |
| 86 | C2×D212 | C24 | 1 | 288 | yes | complemented |
| 87 | C2×C4×D53 | C24 | 1 | 96 | yes | — |
| 88 | C2×C4×D53 | C24 | 1 | 576 | yes | complemented |
| 89 | C2×Dic106 | C24 | 1 | 48 | yes | — |
| 90 | C2×Dic106 | C24 | 1 | 288 | yes | complemented |
| 91 | C23×C53 | — | 4 | 48 | no | — |
| 92 | C23×C53 | — | 4 | 18 | no | — |
| 93 | C23×C53 | — | 8 | 48 | no | — |
| 94 | C23×C53 | C25 | 1 | 18 | yes | — |
| 95 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 96 | C23×C53 | C25 | 1 | 96 | yes | — |
| 97 | C23×C53 | C25 | 1 | 36 | yes | — |
| 98 | C22×D53 | — | 4 | 144 | no | — |
| 99 | C22×D53 | — | 8 | 192 | no | — |
| 100 | C22×D53 | C25 | 1 | 16 | yes | — |
| 101 | C22×D53 | C25 | 1 | 288 | yes | — |
| 102 | Q8×C53 | C25 | 1 | 32 | yes | — |
| 103 | D4×C53 | C25 | 1 | 288 | yes | — |
| 104 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 105 | C2×C4×C53 | C25 | 1 | 144 | yes | — |
| 106 | C2×C4×C53 | C25 | 1 | 24 | yes | — |
| 107 | C22⋊D53 | C25 | 1 | 64 | yes | — |
| 108 | C22⋊D53 | C25 | 1 | 576 | yes | — |
| 109 | C2×Dic53 | C25 | 1 | 16 | yes | — |
| 110 | C2×Dic53 | C25 | 1 | 288 | yes | — |
| 111 | D212 | C25 | 1 | 192 | yes | — |
| 112 | C4×D53 | C25 | 1 | 384 | yes | — |
| 113 | Dic106 | C25 | 1 | 192 | yes | — |
| 114 | C2×H(7,𝔽2) | — | 53 | 1 | no | maximal, Sylow |
| 115 | C22×C53 | — | 2 | 36 | no | — |
| 116 | C22×C53 | — | 2 | 2 | no | — |
| 117 | C22×C53 | — | 4 | 96 | no | — |
| 118 | C22×C53 | — | 4 | 36 | no | — |
| 119 | C22×C53 | C26 | 1 | 36 | yes | — |
| 120 | C22×C53 | C26 | 1 | 2 | yes | — |
| 121 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 122 | C2×D53 | — | 2 | 32 | no | — |
| 123 | C2×D53 | — | 4 | 288 | no | — |
| 124 | C2×D53 | C26 | 1 | 32 | yes | — |
| 125 | C4×C53 | C26 | 1 | 24 | yes | — |
| 126 | Dic53 | C26 | 1 | 32 | yes | — |
| 127 | H(7,𝔽2) | — | 53 | 64 | no | — |
| 128 | C2×#585 | — | 53 | 16 | no | — |
| 129 | C2×#585 | — | 53 | 12 | no | — |
| 130 | C22×H(5,𝔽2) | — | 53 | 16 | no | — |
| 131 | C22×H(5,𝔽2) | — | 53 | 18 | no | — |
| 132 | C22×H(5,𝔽2) | D53 | 1 | 1 | yes | characteristic, complemented |
| 133 | C2×C53 | — | 2 | 36 | no | — |
| 134 | C2×C53 | — | 2 | 2 | no | — |
| 135 | C2×C53 | H(7,𝔽2) | 1 | 2 | yes | complemented |
| 136 | C2×C53 | C27 | 1 | 1 | yes | characteristic |
| 137 | D53 | — | 2 | 32 | no | — |
| 138 | #585 | — | 53 | 512 | no | — |
| 139 | #585 | — | 53 | 384 | no | — |
| 140 | C2×2−1+4 | — | 53 | 48 | no | — |
| 141 | C2×2−1+4 | — | 53 | 8 | no | — |
| 142 | C2×H(5,𝔽2) | — | 53 | 512 | no | — |
| 143 | C2×H(5,𝔽2) | — | 53 | 48 | no | — |
| 144 | C2×H(5,𝔽2) | — | 53 | 144 | no | — |
| 145 | C2×H(5,𝔽2) | — | 53 | 72 | no | — |
| 146 | C2×H(5,𝔽2) | — | 53 | 576 | no | — |
| 147 | C2×H(5,𝔽2) | C2×D53 | 1 | 16 | yes | complemented |
| 148 | C2×H(5,𝔽2) | C2×D53 | 1 | 32 | yes | complemented |
| 149 | C22×#41 | — | 53 | 96 | no | — |
| 150 | C22×#41 | — | 53 | 72 | no | — |
| 151 | C22×#41 | — | 53 | 36 | no | — |
| 152 | C22×#41 | C2×D53 | 1 | 6 | yes | complemented |
| 153 | C23×D4 | — | 53 | 24 | no | — |
| 154 | C23×D4 | — | 53 | 72 | no | — |
| 155 | C23×D4 | C2×D53 | 1 | 9 | yes | complemented |
| 156 | C53 | C2×H(7,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 157 | C25 | — | 53 | 24 | no | — |
| 158 | C25 | C22×D53 | 1 | 6 | yes | complemented |
| 159 | 2−1+4 | — | 53 | 768 | no | — |
| 160 | 2−1+4 | — | 53 | 128 | no | — |
| 161 | H(5,𝔽2) | — | 53 | 768 | no | — |
| 162 | H(5,𝔽2) | — | 53 | 2304 | no | — |
| 163 | H(5,𝔽2) | — | 53 | 1152 | no | — |
| 164 | H(5,𝔽2) | C22×D53 | 1 | 256 | yes | complemented |
| 165 | C2×#41 | — | 53 | 1536 | no | — |
| 166 | C2×#41 | — | 53 | 32 | no | — |
| 167 | C2×#41 | — | 53 | 288 | no | — |
| 168 | C2×#41 | — | 53 | 1152 | no | — |
| 169 | C2×#41 | — | 53 | 144 | no | — |
| 170 | C2×#41 | — | 53 | 48 | no | — |
| 171 | C2×#41 | — | 53 | 576 | no | — |
| 172 | C2×#41 | C22×D53 | 1 | 48 | yes | complemented |
| 173 | C2×#41 | C22×D53 | 1 | 96 | yes | complemented |
| 174 | C22×Q8 | — | 53 | 32 | no | — |
| 175 | C22×Q8 | — | 53 | 36 | no | — |
| 176 | C22×Q8 | C22×D53 | 1 | 2 | yes | complemented |
| 177 | C22×D4 | — | 53 | 144 | no | — |
| 178 | C22×D4 | — | 53 | 72 | no | — |
| 179 | C22×D4 | — | 53 | 384 | no | — |
| 180 | C22×D4 | — | 53 | 288 | no | — |
| 181 | C22×D4 | — | 53 | 1152 | no | — |
| 182 | C22×D4 | — | 53 | 36 | no | — |
| 183 | C22×D4 | C22×D53 | 1 | 72 | yes | complemented |
| 184 | C22×D4 | C22×D53 | 1 | 18 | yes | complemented |
| 185 | C22×D4 | C22×D53 | 1 | 144 | yes | complemented |
| 186 | C23×C4 | — | 53 | 24 | no | — |
| 187 | C23×C4 | — | 53 | 72 | no | — |
| 188 | C23×C4 | C22×D53 | 1 | 9 | yes | complemented |
| 189 | C24 | — | 8 | 12 | no | — |
| 190 | C24 | — | 53 | 192 | no | — |
| 191 | C24 | — | 53 | 72 | no | — |
| 192 | C24 | — | 424 | 48 | no | — |
| 193 | C24 | C23×D53 | 1 | 24 | yes | — |
| 194 | C24 | C23×D53 | 1 | 9 | yes | — |
| 195 | C24 | C23×D53 | 1 | 48 | yes | complemented |
| 196 | #41 | — | 53 | 256 | no | — |
| 197 | #41 | — | 53 | 2304 | no | — |
| 198 | #41 | — | 53 | 1152 | no | — |
| 199 | #41 | — | 53 | 384 | no | — |
| 200 | #41 | C23×D53 | 1 | 384 | yes | complemented |
| 201 | C2×Q8 | — | 53 | 256 | no | — |
| 202 | C2×Q8 | — | 53 | 48 | no | — |
| 203 | C2×Q8 | — | 53 | 288 | no | — |
| 204 | C2×Q8 | C23×D53 | 1 | 8 | yes | — |
| 205 | C2×Q8 | C23×D53 | 1 | 16 | yes | complemented |
| 206 | C2×D4 | — | 53 | 144 | no | — |
| 207 | C2×D4 | — | 53 | 16 | no | — |
| 208 | C2×D4 | — | 53 | 1152 | no | — |
| 209 | C2×D4 | — | 53 | 576 | no | — |
| 210 | C2×D4 | — | 53 | 2304 | no | — |
| 211 | C2×D4 | — | 53 | 48 | no | — |
| 212 | C2×D4 | — | 53 | 288 | no | — |
| 213 | C2×D4 | C23×D53 | 1 | 72 | yes | — |
| 214 | C2×D4 | C23×D53 | 1 | 576 | yes | complemented |
| 215 | C2×D4 | C23×D53 | 1 | 144 | yes | complemented |
| 216 | C22×C4 | — | 53 | 72 | no | — |
| 217 | C22×C4 | — | 53 | 192 | no | — |
| 218 | C22×C4 | — | 53 | 96 | no | — |
| 219 | C22×C4 | — | 53 | 576 | no | — |
| 220 | C22×C4 | C23×D53 | 1 | 36 | yes | — |
| 221 | C22×C4 | C23×D53 | 1 | 6 | yes | — |
| 222 | C22×C4 | C23×D53 | 1 | 72 | yes | complemented |
| 223 | C23 | — | 4 | 18 | no | — |
| 224 | C23 | — | 4 | 48 | no | — |
| 225 | C23 | — | 8 | 48 | no | — |
| 226 | C23 | — | 53 | 16 | no | — |
| 227 | C23 | — | 53 | 288 | no | — |
| 228 | C23 | — | 424 | 192 | no | — |
| 229 | C23 | — | 212 | 144 | no | — |
| 230 | C23 | C24×D53 | 1 | 18 | yes | — |
| 231 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 232 | C23 | C24×D53 | 1 | 96 | yes | — |
| 233 | C23 | C24×D53 | 1 | 36 | yes | — |
| 234 | Q8 | — | 53 | 192 | no | — |
| 235 | Q8 | C24×D53 | 1 | 32 | yes | — |
| 236 | D4 | — | 53 | 576 | no | — |
| 237 | D4 | — | 53 | 64 | no | — |
| 238 | D4 | — | 53 | 192 | no | — |
| 239 | D4 | C24×D53 | 1 | 288 | yes | — |
| 240 | C2×C4 | — | 53 | 288 | no | — |
| 241 | C2×C4 | — | 53 | 16 | no | — |
| 242 | C2×C4 | — | 53 | 384 | no | — |
| 243 | C2×C4 | C24×D53 | 1 | 144 | yes | — |
| 244 | C2×C4 | C24×D53 | 1 | 24 | yes | — |
| 245 | C2×C4 | C24×D53 | 1 | 12 | yes | — |
| 246 | C22 | — | 2 | 2 | no | — |
| 247 | C22 | — | 2 | 36 | no | — |
| 248 | C22 | — | 4 | 36 | no | — |
| 249 | C22 | — | 4 | 96 | no | — |
| 250 | C22 | — | 53 | 32 | no | — |
| 251 | C22 | — | 106 | 32 | no | — |
| 252 | C22 | — | 212 | 288 | no | — |
| 253 | C22 | C25×D53 | 1 | 36 | yes | — |
| 254 | C22 | C25×D53 | 1 | 2 | yes | — |
| 255 | C22 | C25×D53 | 1 | 1 | yes | characteristic |
| 256 | C4 | — | 53 | 32 | no | — |
| 257 | C4 | C25×D53 | 1 | 24 | yes | — |
| 258 | C2 | — | 2 | 2 | no | — |
| 259 | C2 | — | 2 | 36 | no | — |
| 260 | C2 | — | 106 | 32 | no | — |
| 261 | C2 | #20289525 | 1 | 2 | yes | direct product factor |
| 262 | C2 | C26×D53 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. #20289525 | C2 | direct (N × H) |
| 2. C2×#16811459 | C2 | semidirect |
| 3. C2×#16811458 | C2 | semidirect |
| 4. C22×#13133262 | C2 | semidirect |
| 5. C2×H(5,𝔽2)×D53 | C2 | semidirect |
| 6. C22×H(5,𝔽2)×C53 | C2 | semidirect |
| 7. #16811459 | C22 | semidirect |
| 8. #16811458 | C22 | semidirect |
| 9. C2×#13133265 | C22 | semidirect |
| 10. C2×#13133264 | C22 | semidirect |
| 11. C2×#13133263 | C22 | semidirect |
| 12. C2×#13133262 | C22 | semidirect |
| 13. C2×#13133262 | C22 | semidirect |
| 14. C2×#13133262 | C22 | semidirect |
| 15. H(5,𝔽2)×D53 | C22 | semidirect |
| 16. C22×#11719945 | C22 | semidirect |
| 17. C22×#11719947 | C22 | semidirect |
| 18. C2×#41×D53 | C22 | semidirect |
| 19. C23×C22⋊D53 | C22 | semidirect |
| 20. C22×D4×D53 | C22 | semidirect |
| 21. C2×H(5,𝔽2)×C53 | C22 | semidirect |
| 22. C2×H(5,𝔽2)×C53 | C22 | semidirect |
| 23. C22×#41×C53 | C22 | semidirect |
| 24. C23×D4×C53 | C22 | semidirect |
| 25. C24×D53 | C23 | semidirect |
| 26. #13133265 | C23 | semidirect |
| 27. #13133264 | C23 | semidirect |
| 28. #13133263 | C23 | semidirect |
| 29. #13133262 | C23 | semidirect |
| 30. #13133262 | C23 | semidirect |
| 31. C2×#11719949 | C23 | semidirect |
| 32. C2×#11719945 | C23 | semidirect |
| 33. C2×#11719945 | C23 | semidirect |
| 34. C2×#11719945 | C23 | semidirect |
| 35. C2×#11719947 | C23 | semidirect |
| 36. C2×#11719947 | C23 | semidirect |
| 37. #41×D53 | C23 | semidirect |
| 38. C22×Dic106 | C23 | semidirect |
| 39. C2×Q8×D53 | C23 | semidirect |
| 40. C22×D212 | C23 | semidirect |
| 41. C22×C22⋊D53 | C23 | semidirect |
| 42. C22×C22⋊D53 | C23 | semidirect |
| 43. C22×C22⋊D53 | C23 | semidirect |
| 44. C2×D4×D53 | C23 | semidirect |
| 45. C2×D4×D53 | C23 | semidirect |
| 46. C23×Dic53 | C23 | semidirect |
| 47. C22×C4×D53 | C23 | semidirect |
| 48. C25×C53 | C23 | semidirect |
| 49. H(5,𝔽2)×C53 | C23 | semidirect |
| 50. C2×#41×C53 | C23 | semidirect |
| 51. C2×#41×C53 | C23 | semidirect |
| 52. C22×Q8×C53 | C23 | semidirect |
| 53. C22×D4×C53 | C23 | semidirect |
| 54. C22×D4×C53 | C23 | semidirect |
| 55. C22×D4×C53 | C23 | semidirect |
| 56. C23×C4×C53 | C23 | semidirect |
| 60. C24×C53 | C24 | semidirect |
| 63. C23×D53 | C24 | semidirect |
| 64. #41×C53 | C24 | semidirect |
| 66. C2×Q8×C53 | C24 | semidirect |
| 68. C2×D4×C53 | C24 | semidirect |
| 69. C2×D4×C53 | C24 | semidirect |
| 72. C22×C4×C53 | C24 | semidirect |
| 75. C2×C22⋊D53 | C24 | semidirect |
| 76. C2×C22⋊D53 | C24 | semidirect |
| 78. C22×Dic53 | C24 | semidirect |
| 79. #11719949 | C24 | semidirect |
| 80. Q8×D53 | C24 | semidirect |
| 81. #11719947 | C24 | semidirect |
| 82. D4×D53 | C24 | semidirect |
| 83. #11719945 | C24 | semidirect |
| 84. #11719945 | C24 | semidirect |
| 86. C2×D212 | C24 | semidirect |
| 88. C2×C4×D53 | C24 | semidirect |
| 90. C2×Dic106 | C24 | semidirect |
| 132. C22×H(5,𝔽2) | D53 | semidirect |
| 135. C2×C53 | H(7,𝔽2) | semidirect |
| 147. C2×H(5,𝔽2) | C2×D53 | semidirect |
| 148. C2×H(5,𝔽2) | C2×D53 | semidirect |
| 152. C22×#41 | C2×D53 | semidirect |
| 155. C23×D4 | C2×D53 | semidirect |
| 156. C53 | C2×H(7,𝔽2) | semidirect |
| 158. C25 | C22×D53 | semidirect |
| 164. H(5,𝔽2) | C22×D53 | semidirect |
| 172. C2×#41 | C22×D53 | semidirect |
| 173. C2×#41 | C22×D53 | semidirect |
| 176. C22×Q8 | C22×D53 | semidirect |
| 183. C22×D4 | C22×D53 | semidirect |
| 184. C22×D4 | C22×D53 | semidirect |
| 185. C22×D4 | C22×D53 | semidirect |
| 188. C23×C4 | C22×D53 | semidirect |
| 195. C24 | C23×D53 | semidirect |
| 200. #41 | C23×D53 | semidirect |
| 205. C2×Q8 | C23×D53 | semidirect |
| 214. C2×D4 | C23×D53 | semidirect |
| 215. C2×D4 | C23×D53 | semidirect |
| 222. C22×C4 | C23×D53 | semidirect |
| 261. C2 | #20289525 | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta