← C2×C22⋊C4×H(5,𝔽2) #72298635
Order 1024.
318325 conjugacy classes of subgroups.
The subgroup lattice has 720 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C24×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C22×C4×H(5,𝔽2) | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C22⋊C4×H(5,𝔽2) | C2 | 1 | 64 | yes | maximal, direct product factor |
| 4 | C2×#34258 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | C2×#34256 | C2 | 1 | 18 | yes | maximal, complemented |
| 6 | C2×#34175 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#34171 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | C2×C22⋊C4×#41 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C22×D4×C22⋊C4 | C2 | 1 | 9 | yes | maximal, complemented |
| 10 | C23×H(5,𝔽2) | — | 2 | 64 | no | — |
| 11 | C23×H(5,𝔽2) | C4 | 1 | 64 | yes | complemented |
| 12 | C23×H(5,𝔽2) | C22 | 1 | 32 | yes | — |
| 13 | C23×H(5,𝔽2) | C22 | 1 | 9 | yes | — |
| 14 | C23×H(5,𝔽2) | C22 | 1 | 6 | yes | — |
| 15 | C23×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 16 | C24×#41 | C22 | 1 | 6 | yes | — |
| 17 | C25×D4 | C22 | 1 | 9 | yes | — |
| 18 | C2×C4×H(5,𝔽2) | — | 2 | 64 | no | — |
| 19 | C2×C4×H(5,𝔽2) | C22 | 1 | 64 | yes | complemented |
| 20 | C22×#520 | C22 | 1 | 12 | yes | complemented |
| 21 | C22×#518 | C22 | 1 | 18 | yes | complemented |
| 22 | C22×C4×#41 | C22 | 1 | 12 | yes | complemented |
| 23 | C23×C4×D4 | C22 | 1 | 18 | yes | complemented |
| 24 | C24×C22⋊C4 | C22 | 1 | 6 | yes | complemented |
| 25 | #34258 | C22 | 1 | 384 | yes | complemented |
| 26 | #34256 | C22 | 1 | 576 | yes | complemented |
| 27 | #34175 | C22 | 1 | 192 | yes | complemented |
| 28 | #34171 | C22 | 1 | 288 | yes | complemented |
| 29 | C22⋊C4×#41 | C22 | 1 | 192 | yes | complemented |
| 30 | C2×#2341 | C22 | 1 | 12 | yes | complemented |
| 31 | C2×#2341 | C22 | 1 | 12 | yes | complemented |
| 32 | C2×Q8×C22⋊C4 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×Q8×C22⋊C4 | C22 | 1 | 6 | yes | complemented |
| 34 | C2×#2339 | C22 | 1 | 36 | yes | complemented |
| 35 | C2×#2339 | C22 | 1 | 36 | yes | complemented |
| 36 | C2×D4×C22⋊C4 | C22 | 1 | 18 | yes | complemented |
| 37 | C2×D4×C22⋊C4 | C22 | 1 | 36 | yes | complemented |
| 38 | C2×D4×C22⋊C4 | C22 | 1 | 18 | yes | complemented |
| 39 | C2×D4×C22⋊C4 | C22 | 1 | 288 | yes | complemented |
| 40 | C2×D4×C22⋊C4 | C22 | 1 | 72 | yes | complemented |
| 41 | C2×D4×C22⋊C4 | C22 | 1 | 72 | yes | complemented |
| 42 | C2×#2311 | C22 | 1 | 36 | yes | complemented |
| 43 | C2×#2309 | C22 | 1 | 18 | yes | complemented |
| 44 | C2×#2308 | C22 | 1 | 36 | yes | complemented |
| 45 | C2×#2297 | C22 | 1 | 36 | yes | complemented |
| 46 | C22×#390 | C22 | 1 | 18 | yes | complemented |
| 47 | C22×#386 | C22 | 1 | 36 | yes | complemented |
| 48 | C2×#2280 | C22 | 1 | 18 | yes | complemented |
| 49 | C22×#380 | C22 | 1 | 9 | yes | complemented |
| 50 | C22×#379 | C22 | 1 | 18 | yes | complemented |
| 51 | C22×C4×C22⋊C4 | C22 | 1 | 9 | yes | complemented |
| 52 | C27 | C23 | 1 | 6 | yes | — |
| 53 | C22×H(5,𝔽2) | — | 2 | 2048 | no | — |
| 54 | C22×H(5,𝔽2) | — | 2 | 1024 | no | — |
| 55 | C22×H(5,𝔽2) | — | 2 | 192 | no | — |
| 56 | C22×H(5,𝔽2) | — | 2 | 288 | no | — |
| 57 | C22×H(5,𝔽2) | C2×C4 | 1 | 32 | yes | — |
| 58 | C22×H(5,𝔽2) | C2×C4 | 1 | 288 | yes | complemented |
| 59 | C22×H(5,𝔽2) | C2×C4 | 1 | 192 | yes | complemented |
| 60 | C22×H(5,𝔽2) | C2×C4 | 1 | 1024 | yes | complemented |
| 61 | C22×H(5,𝔽2) | D4 | 1 | 64 | yes | — |
| 62 | C22×H(5,𝔽2) | C23 | 1 | 144 | yes | — |
| 63 | C22×H(5,𝔽2) | C23 | 1 | 96 | yes | — |
| 64 | C22×H(5,𝔽2) | C23 | 1 | 16 | yes | — |
| 65 | C23×#41 | — | 2 | 192 | no | — |
| 66 | C23×#41 | C2×C4 | 1 | 192 | yes | complemented |
| 67 | C23×#41 | C23 | 1 | 18 | yes | — |
| 68 | C23×#41 | C23 | 1 | 6 | yes | — |
| 69 | C23×#41 | C23 | 1 | 96 | yes | — |
| 70 | C23×#41 | C23 | 1 | 18 | yes | — |
| 71 | C23×#41 | C23 | 1 | 6 | yes | — |
| 72 | C24×Q8 | C23 | 1 | 2 | yes | — |
| 73 | C24×D4 | — | 2 | 288 | no | — |
| 74 | C24×D4 | C2×C4 | 1 | 288 | yes | complemented |
| 75 | C24×D4 | C23 | 1 | 18 | yes | — |
| 76 | C24×D4 | C23 | 1 | 36 | yes | — |
| 77 | C24×D4 | C23 | 1 | 144 | yes | — |
| 78 | C24×D4 | C23 | 1 | 18 | yes | — |
| 79 | C24×D4 | C23 | 1 | 9 | yes | — |
| 80 | C24×D4 | C23 | 1 | 9 | yes | — |
| 81 | C25×C4 | C23 | 1 | 9 | yes | — |
| 82 | C25×C4 | C23 | 1 | 12 | yes | complemented |
| 83 | C4×H(5,𝔽2) | — | 2 | 1024 | no | — |
| 84 | C2×#520 | — | 2 | 192 | no | — |
| 85 | C2×#520 | C23 | 1 | 192 | yes | complemented |
| 86 | C2×#518 | — | 2 | 288 | no | — |
| 87 | C2×#518 | C23 | 1 | 288 | yes | complemented |
| 88 | C2×C4×#41 | — | 2 | 192 | no | — |
| 89 | C2×C4×#41 | C23 | 1 | 192 | yes | complemented |
| 90 | C22×C4×Q8 | C23 | 1 | 4 | yes | complemented |
| 91 | C22×C4×Q8 | C23 | 1 | 12 | yes | complemented |
| 92 | C22×C4×D4 | — | 2 | 288 | no | — |
| 93 | C22×C4×D4 | C23 | 1 | 36 | yes | complemented |
| 94 | C22×C4×D4 | C23 | 1 | 72 | yes | complemented |
| 95 | C22×C4×D4 | C23 | 1 | 36 | yes | complemented |
| 96 | C22×C4×D4 | C23 | 1 | 288 | yes | complemented |
| 97 | C22×#117 | C23 | 1 | 36 | yes | complemented |
| 98 | C23×C4⋊C4 | C23 | 1 | 18 | yes | complemented |
| 99 | C23×C22⋊C4 | — | 4 | 48 | no | — |
| 100 | C23×C22⋊C4 | C23 | 1 | 9 | yes | — |
| 101 | C23×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 102 | C23×C22⋊C4 | C23 | 1 | 9 | yes | — |
| 103 | C23×C22⋊C4 | C23 | 1 | 36 | yes | complemented |
| 104 | C23×C22⋊C4 | C23 | 1 | 96 | yes | complemented |
| 105 | C23×C22⋊C4 | C23 | 1 | 36 | yes | complemented |
| 106 | C23×C22⋊C4 | C23 | 1 | 36 | yes | complemented |
| 107 | C23×C42 | C23 | 1 | 18 | yes | complemented |
| 108 | #2341 | C23 | 1 | 192 | yes | complemented |
| 109 | #2341 | C23 | 1 | 192 | yes | complemented |
| 110 | Q8×C22⋊C4 | C23 | 1 | 32 | yes | complemented |
| 111 | Q8×C22⋊C4 | C23 | 1 | 96 | yes | complemented |
| 112 | #2339 | C23 | 1 | 576 | yes | complemented |
| 113 | #2339 | C23 | 1 | 576 | yes | complemented |
| 114 | D4×C22⋊C4 | C23 | 1 | 288 | yes | complemented |
| 115 | D4×C22⋊C4 | C23 | 1 | 576 | yes | complemented |
| 116 | D4×C22⋊C4 | C23 | 1 | 288 | yes | complemented |
| 117 | D4×C22⋊C4 | C23 | 1 | 1152 | yes | complemented |
| 118 | D4×C22⋊C4 | C23 | 1 | 1152 | yes | complemented |
| 119 | #2311 | C23 | 1 | 576 | yes | complemented |
| 120 | #2309 | C23 | 1 | 288 | yes | complemented |
| 121 | #2308 | C23 | 1 | 576 | yes | complemented |
| 122 | #2297 | C23 | 1 | 576 | yes | complemented |
| 123 | C2×#391 | C23 | 1 | 12 | yes | complemented |
| 124 | C2×#391 | C23 | 1 | 36 | yes | complemented |
| 125 | C2×#390 | C23 | 1 | 36 | yes | complemented |
| 126 | C2×#390 | C23 | 1 | 72 | yes | complemented |
| 127 | C2×#390 | C23 | 1 | 36 | yes | complemented |
| 128 | C2×#390 | C23 | 1 | 288 | yes | complemented |
| 129 | C2×#386 | C23 | 1 | 72 | yes | complemented |
| 130 | C2×#386 | C23 | 1 | 144 | yes | complemented |
| 131 | C2×#386 | C23 | 1 | 72 | yes | complemented |
| 132 | C2×#386 | C23 | 1 | 576 | yes | complemented |
| 133 | #2280 | C23 | 1 | 288 | yes | complemented |
| 134 | C2×#381 | C23 | 1 | 36 | yes | complemented |
| 135 | C2×#380 | C23 | 1 | 18 | yes | — |
| 136 | C2×#380 | C23 | 1 | 6 | yes | — |
| 137 | C2×#380 | C23 | 1 | 36 | yes | complemented |
| 138 | C2×#380 | C23 | 1 | 36 | yes | complemented |
| 139 | C2×#380 | C23 | 1 | 144 | yes | complemented |
| 140 | C2×#379 | C23 | 1 | 36 | yes | — |
| 141 | C2×#379 | C23 | 1 | 72 | yes | complemented |
| 142 | C2×#379 | C23 | 1 | 288 | yes | complemented |
| 143 | C2×C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 144 | C2×C4×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 145 | C2×C4×C22⋊C4 | C23 | 1 | 36 | yes | complemented |
| 146 | C2×C4×C22⋊C4 | C23 | 1 | 36 | yes | complemented |
| 147 | C2×C4×C22⋊C4 | C23 | 1 | 144 | yes | complemented |
| 148 | C22×#95 | C23 | 1 | 18 | yes | complemented |
| 149 | C22×#95 | C23 | 1 | 18 | yes | complemented |
| 150 | C26 | — | 2 | 96 | no | — |
| 151 | C26 | — | 4 | 24 | no | — |
| 152 | C26 | — | 4 | 24 | no | — |
| 153 | C26 | — | 8 | 24 | no | — |
| 154 | C26 | C22×C4 | 1 | 96 | yes | complemented |
| 155 | C26 | C24 | 1 | 9 | yes | — |
| 156 | C26 | C24 | 1 | 18 | yes | — |
| 157 | C26 | C24 | 1 | 48 | yes | — |
| 158 | C26 | C24 | 1 | 6 | yes | — |
| 159 | C2×H(5,𝔽2) | — | 2 | 16384 | no | — |
| 160 | C2×H(5,𝔽2) | — | 2 | 3072 | no | — |
| 161 | C2×H(5,𝔽2) | — | 2 | 1536 | no | — |
| 162 | C2×H(5,𝔽2) | — | 2 | 4608 | no | — |
| 163 | C2×H(5,𝔽2) | — | 2 | 2304 | no | — |
| 164 | C2×H(5,𝔽2) | C22⋊C4 | 1 | 1024 | yes | direct product factor |
| 165 | C2×H(5,𝔽2) | C22×C4 | 1 | 256 | yes | — |
| 166 | C2×H(5,𝔽2) | C22×C4 | 1 | 2304 | yes | complemented |
| 167 | C2×H(5,𝔽2) | C22×C4 | 1 | 1536 | yes | complemented |
| 168 | C2×H(5,𝔽2) | C2×D4 | 1 | 512 | yes | — |
| 169 | C22×#41 | — | 2 | 3072 | no | — |
| 170 | C22×#41 | — | 2 | 1536 | no | — |
| 171 | C22×#41 | — | 2 | 96 | no | — |
| 172 | C22×#41 | — | 2 | 288 | no | — |
| 173 | C22×#41 | — | 2 | 288 | no | — |
| 174 | C22×#41 | C22×C4 | 1 | 96 | yes | — |
| 175 | C22×#41 | C22×C4 | 1 | 96 | yes | complemented |
| 176 | C22×#41 | C22×C4 | 1 | 288 | yes | complemented |
| 177 | C22×#41 | C22×C4 | 1 | 288 | yes | complemented |
| 178 | C22×#41 | C22×C4 | 1 | 1536 | yes | complemented |
| 179 | C22×#41 | C2×D4 | 1 | 192 | yes | — |
| 180 | C22×#41 | C24 | 1 | 144 | yes | — |
| 181 | C22×#41 | C24 | 1 | 144 | yes | — |
| 182 | C22×#41 | C24 | 1 | 48 | yes | — |
| 183 | C22×#41 | C24 | 1 | 48 | yes | — |
| 184 | C23×Q8 | — | 2 | 32 | no | — |
| 185 | C23×Q8 | C22×C4 | 1 | 32 | yes | complemented |
| 186 | C23×Q8 | C24 | 1 | 6 | yes | — |
| 187 | C23×Q8 | C24 | 1 | 16 | yes | — |
| 188 | C23×Q8 | C24 | 1 | 2 | yes | — |
| 189 | C23×D4 | — | 2 | 288 | no | — |
| 190 | C23×D4 | — | 2 | 4608 | no | — |
| 191 | C23×D4 | — | 2 | 288 | no | — |
| 192 | C23×D4 | — | 2 | 576 | no | — |
| 193 | C23×D4 | — | 2 | 2304 | no | — |
| 194 | C23×D4 | — | 2 | 144 | no | — |
| 195 | C23×D4 | C22×C4 | 1 | 144 | yes | — |
| 196 | C23×D4 | C22×C4 | 1 | 288 | yes | complemented |
| 197 | C23×D4 | C22×C4 | 1 | 288 | yes | complemented |
| 198 | C23×D4 | C22×C4 | 1 | 576 | yes | complemented |
| 199 | C23×D4 | C22×C4 | 1 | 144 | yes | complemented |
| 200 | C23×D4 | C22×C4 | 1 | 2304 | yes | complemented |
| 201 | C23×D4 | C2×D4 | 1 | 288 | yes | — |
| 202 | C23×D4 | C24 | 1 | 36 | yes | — |
| 203 | C23×D4 | C24 | 1 | 18 | yes | — |
| 204 | C23×D4 | C24 | 1 | 144 | yes | — |
| 205 | C23×D4 | C24 | 1 | 144 | yes | — |
| 206 | C23×D4 | C24 | 1 | 72 | yes | — |
| 207 | C23×D4 | C24 | 1 | 288 | yes | — |
| 208 | C23×D4 | C24 | 1 | 18 | yes | — |
| 209 | C23×D4 | C24 | 1 | 72 | yes | — |
| 210 | C24×C4 | — | 2 | 144 | no | — |
| 211 | C24×C4 | — | 2 | 96 | no | — |
| 212 | C24×C4 | — | 4 | 48 | no | — |
| 213 | C24×C4 | — | 8 | 24 | no | — |
| 214 | C24×C4 | C22×C4 | 1 | 144 | yes | complemented |
| 215 | C24×C4 | C24 | 1 | 18 | yes | — |
| 216 | C24×C4 | C24 | 1 | 6 | yes | — |
| 217 | C24×C4 | C24 | 1 | 9 | yes | — |
| 218 | C24×C4 | C24 | 1 | 18 | yes | — |
| 219 | C24×C4 | C24 | 1 | 72 | yes | — |
| 220 | C24×C4 | C24 | 1 | 36 | yes | — |
| 221 | C24×C4 | C24 | 1 | 18 | yes | — |
| 222 | C24×C4 | C24 | 1 | 9 | yes | — |
| 223 | C24×C4 | C24 | 1 | 96 | yes | complemented |
| 224 | #520 | — | 2 | 1536 | no | — |
| 225 | #518 | — | 2 | 2304 | no | — |
| 226 | C4×#41 | — | 2 | 1536 | no | — |
| 227 | C2×C4×Q8 | — | 2 | 32 | no | — |
| 228 | C2×C4×Q8 | — | 2 | 96 | no | — |
| 229 | C2×C4×Q8 | C24 | 1 | 32 | yes | complemented |
| 230 | C2×C4×Q8 | C24 | 1 | 96 | yes | complemented |
| 231 | C2×C4×D4 | — | 2 | 288 | no | — |
| 232 | C2×C4×D4 | — | 2 | 576 | no | — |
| 233 | C2×C4×D4 | — | 2 | 2304 | no | — |
| 234 | C2×C4×D4 | — | 2 | 288 | no | — |
| 235 | C2×C4×D4 | C24 | 1 | 288 | yes | complemented |
| 236 | C2×C4×D4 | C24 | 1 | 576 | yes | complemented |
| 237 | C2×C4×D4 | C24 | 1 | 288 | yes | complemented |
| 238 | C2×#117 | — | 2 | 288 | no | — |
| 239 | C2×#117 | C24 | 1 | 288 | yes | complemented |
| 240 | C22×C4⋊C4 | — | 2 | 144 | no | — |
| 241 | C22×C4⋊C4 | C24 | 1 | 36 | yes | — |
| 242 | C22×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 243 | C22×C4⋊C4 | C24 | 1 | 144 | yes | complemented |
| 244 | C22×C22⋊C4 | — | 2 | 288 | no | — |
| 245 | C22×C22⋊C4 | — | 2 | 72 | no | — |
| 246 | C22×C22⋊C4 | — | 4 | 384 | no | — |
| 247 | C22×C22⋊C4 | — | 4 | 144 | no | — |
| 248 | C22×C22⋊C4 | — | 4 | 72 | no | — |
| 249 | C22×C22⋊C4 | — | 4 | 36 | no | — |
| 250 | C22×C22⋊C4 | — | 8 | 72 | no | — |
| 251 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 252 | C22×C22⋊C4 | C24 | 1 | 9 | yes | — |
| 253 | C22×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 254 | C22×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 255 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 256 | C22×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 257 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 258 | C22×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 259 | C22×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 260 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 261 | C22×C22⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 262 | C22×C22⋊C4 | C24 | 1 | 288 | yes | complemented |
| 263 | C22×C22⋊C4 | C24 | 1 | 288 | yes | complemented |
| 264 | C22×C22⋊C4 | C24 | 1 | 288 | yes | complemented |
| 265 | C22×C42 | — | 2 | 144 | no | — |
| 266 | C22×C42 | C24 | 1 | 12 | yes | — |
| 267 | C22×C42 | C24 | 1 | 36 | yes | — |
| 268 | C22×C42 | C24 | 1 | 144 | yes | complemented |
| 269 | #391 | C24 | 1 | 288 | yes | complemented |
| 270 | #391 | C24 | 1 | 96 | yes | complemented |
| 271 | #390 | C24 | 1 | 288 | yes | complemented |
| 272 | #390 | C24 | 1 | 576 | yes | complemented |
| 273 | #390 | C24 | 1 | 288 | yes | complemented |
| 274 | #386 | C24 | 1 | 576 | yes | complemented |
| 275 | #386 | C24 | 1 | 1152 | yes | complemented |
| 276 | #386 | C24 | 1 | 576 | yes | complemented |
| 277 | #381 | C24 | 1 | 288 | yes | complemented |
| 278 | #380 | C24 | 1 | 144 | yes | — |
| 279 | #380 | C24 | 1 | 48 | yes | — |
| 280 | #380 | C24 | 1 | 288 | yes | complemented |
| 281 | #380 | C24 | 1 | 288 | yes | complemented |
| 282 | #379 | C24 | 1 | 288 | yes | — |
| 283 | #379 | C24 | 1 | 576 | yes | complemented |
| 284 | C4×C22⋊C4 | C24 | 1 | 48 | yes | — |
| 285 | C4×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 286 | C4×C22⋊C4 | C24 | 1 | 288 | yes | complemented |
| 287 | C4×C22⋊C4 | C24 | 1 | 288 | yes | complemented |
| 288 | C2×#95 | C24 | 1 | 12 | yes | — |
| 289 | C2×#95 | C24 | 1 | 36 | yes | — |
| 290 | C2×#95 | C24 | 1 | 36 | yes | — |
| 291 | C2×#95 | C24 | 1 | 12 | yes | — |
| 292 | C2×#95 | C24 | 1 | 144 | yes | complemented |
| 293 | C2×#95 | C24 | 1 | 144 | yes | complemented |
| 294 | C25 | — | 2 | 72 | no | — |
| 295 | C25 | — | 2 | 36 | no | — |
| 296 | C25 | — | 2 | 36 | no | — |
| 297 | C25 | — | 2 | 768 | no | — |
| 298 | C25 | — | 2 | 384 | no | — |
| 299 | C25 | — | 2 | 144 | no | — |
| 300 | C25 | — | 4 | 12 | no | — |
| 301 | C25 | — | 4 | 24 | no | — |
| 302 | C25 | — | 4 | 12 | no | — |
| 303 | C25 | — | 4 | 36 | no | — |
| 304 | C25 | — | 4 | 36 | no | — |
| 305 | C25 | — | 4 | 96 | no | — |
| 306 | C25 | — | 4 | 72 | no | — |
| 307 | C25 | — | 4 | 384 | no | — |
| 308 | C25 | — | 4 | 36 | no | — |
| 309 | C25 | — | 4 | 96 | no | — |
| 310 | C25 | — | 8 | 192 | no | — |
| 311 | C25 | — | 8 | 96 | no | — |
| 312 | C25 | — | 8 | 384 | no | — |
| 313 | C25 | — | 8 | 384 | no | — |
| 314 | C25 | C23×C4 | 1 | 72 | yes | — |
| 315 | C25 | C23×C4 | 1 | 144 | yes | — |
| 316 | C25 | C23×C4 | 1 | 48 | yes | — |
| 317 | C25 | C23×C4 | 1 | 384 | yes | complemented |
| 318 | C25 | C22×D4 | 1 | 96 | yes | — |
| 319 | C25 | C25 | 1 | 9 | yes | — |
| 320 | C25 | C25 | 1 | 36 | yes | — |
| 321 | C25 | C25 | 1 | 9 | yes | — |
| 322 | C25 | C25 | 1 | 1 | yes | characteristic |
| 323 | C25 | C25 | 1 | 72 | yes | — |
| 324 | C25 | C25 | 1 | 24 | yes | — |
| 325 | H(5,𝔽2) | — | 2 | 12288 | no | — |
| 326 | H(5,𝔽2) | — | 2 | 18432 | no | — |
| 327 | H(5,𝔽2) | C2×C22⋊C4 | 1 | 4096 | yes | direct product factor |
| 328 | C2×#41 | — | 2 | 12288 | no | — |
| 329 | C2×#41 | — | 2 | 768 | no | — |
| 330 | C2×#41 | — | 2 | 384 | no | — |
| 331 | C2×#41 | — | 2 | 2304 | no | — |
| 332 | C2×#41 | — | 2 | 1152 | no | — |
| 333 | C2×#41 | — | 2 | 2304 | no | — |
| 334 | C2×#41 | — | 2 | 1152 | no | — |
| 335 | C2×#41 | C2×C22⋊C4 | 1 | 1536 | yes | complemented |
| 336 | C2×#41 | C23×C4 | 1 | 384 | yes | — |
| 337 | C2×#41 | C23×C4 | 1 | 384 | yes | complemented |
| 338 | C2×#41 | C23×C4 | 1 | 1152 | yes | complemented |
| 339 | C2×#41 | C23×C4 | 1 | 1152 | yes | complemented |
| 340 | C2×#41 | C22×D4 | 1 | 768 | yes | — |
| 341 | C22×Q8 | — | 2 | 256 | no | — |
| 342 | C22×Q8 | — | 2 | 128 | no | — |
| 343 | C22×Q8 | — | 2 | 48 | no | — |
| 344 | C22×Q8 | C23×C4 | 1 | 48 | yes | — |
| 345 | C22×Q8 | C23×C4 | 1 | 16 | yes | — |
| 346 | C22×Q8 | C23×C4 | 1 | 128 | yes | complemented |
| 347 | C22×Q8 | C22×D4 | 1 | 32 | yes | — |
| 348 | C22×Q8 | C25 | 1 | 24 | yes | — |
| 349 | C22×Q8 | C25 | 1 | 8 | yes | — |
| 350 | C22×D4 | — | 2 | 2304 | no | — |
| 351 | C22×D4 | — | 2 | 288 | no | — |
| 352 | C22×D4 | — | 2 | 1152 | no | — |
| 353 | C22×D4 | — | 2 | 2304 | no | — |
| 354 | C22×D4 | — | 2 | 4608 | no | — |
| 355 | C22×D4 | — | 2 | 18432 | no | — |
| 356 | C22×D4 | — | 2 | 1152 | no | — |
| 357 | C22×D4 | — | 2 | 2304 | no | — |
| 358 | C22×D4 | — | 2 | 1152 | no | — |
| 359 | C22×D4 | — | 2 | 144 | no | — |
| 360 | C22×D4 | — | 2 | 576 | no | — |
| 361 | C22×D4 | C2×C22⋊C4 | 1 | 2304 | yes | complemented |
| 362 | C22×D4 | C23×C4 | 1 | 288 | yes | — |
| 363 | C22×D4 | C23×C4 | 1 | 144 | yes | — |
| 364 | C22×D4 | C23×C4 | 1 | 144 | yes | — |
| 365 | C22×D4 | C23×C4 | 1 | 576 | yes | — |
| 366 | C22×D4 | C23×C4 | 1 | 1152 | yes | complemented |
| 367 | C22×D4 | C23×C4 | 1 | 1152 | yes | complemented |
| 368 | C22×D4 | C23×C4 | 1 | 2304 | yes | complemented |
| 369 | C22×D4 | C23×C4 | 1 | 576 | yes | complemented |
| 370 | C22×D4 | C22×D4 | 1 | 288 | yes | — |
| 371 | C22×D4 | C22×D4 | 1 | 1152 | yes | — |
| 372 | C22×D4 | C25 | 1 | 144 | yes | — |
| 373 | C22×D4 | C25 | 1 | 72 | yes | — |
| 374 | C22×D4 | C25 | 1 | 72 | yes | — |
| 375 | C23×C4 | — | 2 | 72 | no | — |
| 376 | C23×C4 | — | 2 | 1152 | no | — |
| 377 | C23×C4 | — | 2 | 48 | no | — |
| 378 | C23×C4 | — | 2 | 144 | no | — |
| 379 | C23×C4 | — | 2 | 576 | no | — |
| 380 | C23×C4 | — | 2 | 72 | no | — |
| 381 | C23×C4 | — | 2 | 72 | no | — |
| 382 | C23×C4 | — | 2 | 144 | no | — |
| 383 | C23×C4 | — | 2 | 384 | no | — |
| 384 | C23×C4 | — | 2 | 72 | no | — |
| 385 | C23×C4 | — | 4 | 192 | no | — |
| 386 | C23×C4 | — | 4 | 36 | no | — |
| 387 | C23×C4 | — | 4 | 72 | no | — |
| 388 | C23×C4 | — | 4 | 36 | no | — |
| 389 | C23×C4 | — | 4 | 36 | no | — |
| 390 | C23×C4 | — | 4 | 72 | no | — |
| 391 | C23×C4 | — | 8 | 96 | no | — |
| 392 | C23×C4 | — | 8 | 384 | no | — |
| 393 | C23×C4 | C23×C4 | 1 | 48 | yes | — |
| 394 | C23×C4 | C23×C4 | 1 | 72 | yes | — |
| 395 | C23×C4 | C23×C4 | 1 | 144 | yes | — |
| 396 | C23×C4 | C23×C4 | 1 | 72 | yes | — |
| 397 | C23×C4 | C23×C4 | 1 | 576 | yes | complemented |
| 398 | C23×C4 | C22×D4 | 1 | 144 | yes | — |
| 399 | C23×C4 | C25 | 1 | 12 | yes | — |
| 400 | C23×C4 | C25 | 1 | 18 | yes | — |
| 401 | C23×C4 | C25 | 1 | 72 | yes | — |
| 402 | C23×C4 | C25 | 1 | 24 | yes | — |
| 403 | C23×C4 | C25 | 1 | 36 | yes | — |
| 404 | C23×C4 | C25 | 1 | 72 | yes | — |
| 405 | C23×C4 | C25 | 1 | 6 | yes | — |
| 406 | C23×C4 | C25 | 1 | 2 | yes | — |
| 407 | C23×C4 | C25 | 1 | 72 | yes | — |
| 408 | C23×C4 | C25 | 1 | 144 | yes | — |
| 409 | C23×C4 | C25 | 1 | 36 | yes | — |
| 410 | C23×C4 | C25 | 1 | 6 | yes | — |
| 411 | C4×Q8 | — | 2 | 128 | no | — |
| 412 | C4×Q8 | — | 2 | 384 | no | — |
| 413 | C4×D4 | — | 2 | 1152 | no | — |
| 414 | C4×D4 | — | 2 | 2304 | no | — |
| 415 | C4×D4 | — | 2 | 1152 | no | — |
| 416 | #117 | — | 2 | 1152 | no | — |
| 417 | C2×C4⋊C4 | — | 2 | 144 | no | — |
| 418 | C2×C4⋊C4 | — | 2 | 576 | no | — |
| 419 | C2×C4⋊C4 | — | 2 | 48 | no | — |
| 420 | C2×C4⋊C4 | C25 | 1 | 144 | yes | — |
| 421 | C2×C4⋊C4 | C25 | 1 | 48 | yes | — |
| 422 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 423 | C2×C22⋊C4 | — | 2 | 1152 | no | — |
| 424 | C2×C22⋊C4 | — | 2 | 36 | no | — |
| 425 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 426 | C2×C22⋊C4 | — | 2 | 72 | no | — |
| 427 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 428 | C2×C22⋊C4 | — | 4 | 576 | no | — |
| 429 | C2×C22⋊C4 | — | 4 | 288 | no | — |
| 430 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 431 | C2×C22⋊C4 | — | 4 | 72 | no | — |
| 432 | C2×C22⋊C4 | — | 4 | 36 | no | — |
| 433 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 434 | C2×C22⋊C4 | — | 8 | 288 | no | — |
| 435 | C2×C22⋊C4 | H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 436 | C2×C22⋊C4 | C25 | 1 | 36 | yes | — |
| 437 | C2×C22⋊C4 | C25 | 1 | 24 | yes | — |
| 438 | C2×C22⋊C4 | C25 | 1 | 72 | yes | — |
| 439 | C2×C22⋊C4 | C25 | 1 | 288 | yes | — |
| 440 | C2×C22⋊C4 | C25 | 1 | 144 | yes | — |
| 441 | C2×C22⋊C4 | C25 | 1 | 72 | yes | — |
| 442 | C2×C22⋊C4 | C25 | 1 | 288 | yes | — |
| 443 | C2×C22⋊C4 | C25 | 1 | 4 | yes | — |
| 444 | C2×C42 | — | 2 | 144 | no | — |
| 445 | C2×C42 | — | 2 | 48 | no | — |
| 446 | C2×C42 | — | 2 | 576 | no | — |
| 447 | C2×C42 | C25 | 1 | 144 | yes | — |
| 448 | C2×C42 | C25 | 1 | 48 | yes | — |
| 449 | #95 | C25 | 1 | 48 | yes | — |
| 450 | #95 | C25 | 1 | 144 | yes | — |
| 451 | #95 | C25 | 1 | 144 | yes | — |
| 452 | #95 | C25 | 1 | 48 | yes | — |
| 453 | C24 | — | 2 | 4 | no | — |
| 454 | C24 | — | 2 | 18 | no | — |
| 455 | C24 | — | 2 | 18 | no | — |
| 456 | C24 | — | 2 | 36 | no | — |
| 457 | C24 | — | 2 | 4 | no | — |
| 458 | C24 | — | 2 | 144 | no | — |
| 459 | C24 | — | 2 | 36 | no | — |
| 460 | C24 | — | 2 | 72 | no | — |
| 461 | C24 | — | 2 | 18 | no | — |
| 462 | C24 | — | 2 | 72 | no | — |
| 463 | C24 | — | 2 | 18 | no | — |
| 464 | C24 | — | 2 | 36 | no | — |
| 465 | C24 | — | 2 | 288 | no | — |
| 466 | C24 | — | 2 | 288 | no | — |
| 467 | C24 | — | 2 | 288 | no | — |
| 468 | C24 | — | 2 | 576 | no | — |
| 469 | C24 | — | 2 | 1536 | no | — |
| 470 | C24 | — | 4 | 24 | no | — |
| 471 | C24 | — | 4 | 192 | no | — |
| 472 | C24 | — | 4 | 48 | no | — |
| 473 | C24 | — | 4 | 96 | no | — |
| 474 | C24 | — | 4 | 24 | no | — |
| 475 | C24 | — | 4 | 144 | no | — |
| 476 | C24 | — | 4 | 72 | no | — |
| 477 | C24 | — | 4 | 96 | no | — |
| 478 | C24 | — | 4 | 192 | no | — |
| 479 | C24 | — | 4 | 72 | no | — |
| 480 | C24 | — | 4 | 144 | no | — |
| 481 | C24 | — | 4 | 288 | no | — |
| 482 | C24 | — | 4 | 768 | no | — |
| 483 | C24 | — | 4 | 72 | no | — |
| 484 | C24 | — | 4 | 288 | no | — |
| 485 | C24 | — | 4 | 288 | no | — |
| 486 | C24 | — | 4 | 288 | no | — |
| 487 | C24 | — | 8 | 288 | no | — |
| 488 | C24 | — | 8 | 288 | no | — |
| 489 | C24 | — | 8 | 384 | no | — |
| 490 | C24 | — | 8 | 768 | no | — |
| 491 | C24 | — | 8 | 3072 | no | — |
| 492 | C24 | — | 8 | 768 | no | — |
| 493 | C24 | C22×C22⋊C4 | 1 | 384 | yes | complemented |
| 494 | C24 | C24×C4 | 1 | 36 | yes | — |
| 495 | C24 | C24×C4 | 1 | 144 | yes | — |
| 496 | C24 | C24×C4 | 1 | 36 | yes | — |
| 497 | C24 | C24×C4 | 1 | 4 | yes | — |
| 498 | C24 | C24×C4 | 1 | 288 | yes | — |
| 499 | C24 | C24×C4 | 1 | 96 | yes | — |
| 500 | C24 | C23×D4 | 1 | 72 | yes | — |
| 501 | C24 | C23×D4 | 1 | 192 | yes | — |
| 502 | C24 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 503 | C24 | #585 | 1 | 4 | yes | — |
| 504 | C24 | C26 | 1 | 18 | yes | — |
| 505 | C24 | C26 | 1 | 18 | yes | — |
| 506 | C24 | C26 | 1 | 2 | yes | — |
| 507 | C24 | C26 | 1 | 1 | yes | characteristic |
| 508 | #41 | — | 2 | 1536 | no | — |
| 509 | #41 | — | 2 | 4608 | no | — |
| 510 | #41 | — | 2 | 4608 | no | — |
| 511 | #41 | C22×C22⋊C4 | 1 | 3072 | yes | complemented |
| 512 | C2×Q8 | — | 2 | 512 | no | — |
| 513 | C2×Q8 | — | 2 | 96 | no | — |
| 514 | C2×Q8 | — | 2 | 192 | no | — |
| 515 | C2×Q8 | C22×C22⋊C4 | 1 | 128 | yes | complemented |
| 516 | C2×Q8 | C24×C4 | 1 | 96 | yes | — |
| 517 | C2×Q8 | C24×C4 | 1 | 32 | yes | — |
| 518 | C2×Q8 | C23×D4 | 1 | 64 | yes | — |
| 519 | C2×D4 | — | 2 | 576 | no | — |
| 520 | C2×D4 | — | 2 | 1152 | no | — |
| 521 | C2×D4 | — | 2 | 4608 | no | — |
| 522 | C2×D4 | — | 2 | 4608 | no | — |
| 523 | C2×D4 | — | 2 | 9216 | no | — |
| 524 | C2×D4 | — | 2 | 288 | no | — |
| 525 | C2×D4 | — | 2 | 576 | no | — |
| 526 | C2×D4 | — | 2 | 2304 | no | — |
| 527 | C2×D4 | C22×C22⋊C4 | 1 | 1152 | yes | complemented |
| 528 | C2×D4 | C22×C22⋊C4 | 1 | 4608 | yes | complemented |
| 529 | C2×D4 | C24×C4 | 1 | 576 | yes | — |
| 530 | C2×D4 | C24×C4 | 1 | 288 | yes | — |
| 531 | C2×D4 | C24×C4 | 1 | 288 | yes | — |
| 532 | C2×D4 | C23×D4 | 1 | 576 | yes | — |
| 533 | C22×C4 | — | 2 | 4 | no | — |
| 534 | C22×C4 | — | 2 | 24 | no | — |
| 535 | C22×C4 | — | 2 | 144 | no | — |
| 536 | C22×C4 | — | 2 | 4 | no | — |
| 537 | C22×C4 | — | 2 | 288 | no | — |
| 538 | C22×C4 | — | 2 | 96 | no | — |
| 539 | C22×C4 | — | 2 | 288 | no | — |
| 540 | C22×C4 | — | 2 | 192 | no | — |
| 541 | C22×C4 | — | 2 | 576 | no | — |
| 542 | C22×C4 | — | 2 | 2304 | no | — |
| 543 | C22×C4 | — | 2 | 24 | no | — |
| 544 | C22×C4 | — | 2 | 36 | no | — |
| 545 | C22×C4 | — | 2 | 144 | no | — |
| 546 | C22×C4 | — | 2 | 36 | no | — |
| 547 | C22×C4 | — | 2 | 24 | no | — |
| 548 | C22×C4 | — | 2 | 24 | no | — |
| 549 | C22×C4 | — | 2 | 36 | no | — |
| 550 | C22×C4 | — | 2 | 144 | no | — |
| 551 | C22×C4 | — | 2 | 288 | no | — |
| 552 | C22×C4 | — | 2 | 144 | no | — |
| 553 | C22×C4 | — | 4 | 72 | no | — |
| 554 | C22×C4 | — | 4 | 144 | no | — |
| 555 | C22×C4 | — | 4 | 72 | no | — |
| 556 | C22×C4 | — | 4 | 72 | no | — |
| 557 | C22×C4 | — | 4 | 144 | no | — |
| 558 | C22×C4 | — | 4 | 288 | no | — |
| 559 | C22×C4 | — | 8 | 768 | no | — |
| 560 | C22×C4 | — | 8 | 144 | no | — |
| 561 | C22×C4 | — | 8 | 288 | no | — |
| 562 | C22×C4 | C22×C22⋊C4 | 1 | 576 | yes | complemented |
| 563 | C22×C4 | C24×C4 | 1 | 24 | yes | — |
| 564 | C22×C4 | C24×C4 | 1 | 96 | yes | — |
| 565 | C22×C4 | C24×C4 | 1 | 144 | yes | — |
| 566 | C22×C4 | C24×C4 | 1 | 288 | yes | — |
| 567 | C22×C4 | C24×C4 | 1 | 24 | yes | — |
| 568 | C22×C4 | C24×C4 | 1 | 144 | yes | — |
| 569 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 570 | C22×C4 | C23×D4 | 1 | 288 | yes | — |
| 571 | C22×C4 | C2×H(5,𝔽2) | 1 | 8 | yes | complemented |
| 572 | C22×C4 | C26 | 1 | 24 | yes | — |
| 573 | C22×C4 | C26 | 1 | 36 | yes | — |
| 574 | C22×C4 | C26 | 1 | 12 | yes | — |
| 575 | C22×C4 | C26 | 1 | 4 | yes | — |
| 576 | C22×C4 | C26 | 1 | 12 | yes | — |
| 577 | C4⋊C4 | — | 2 | 288 | no | — |
| 578 | C4⋊C4 | — | 2 | 96 | no | — |
| 579 | C22⋊C4 | — | 2 | 576 | no | — |
| 580 | C22⋊C4 | — | 2 | 72 | no | — |
| 581 | C22⋊C4 | — | 2 | 48 | no | — |
| 582 | C22⋊C4 | — | 2 | 144 | no | — |
| 583 | C22⋊C4 | — | 4 | 144 | no | — |
| 584 | C22⋊C4 | — | 4 | 72 | no | — |
| 585 | C22⋊C4 | — | 4 | 288 | no | — |
| 586 | C22⋊C4 | C2×H(5,𝔽2) | 1 | 16 | yes | direct product factor |
| 587 | C42 | — | 2 | 96 | no | — |
| 588 | C42 | — | 2 | 288 | no | — |
| 589 | C23 | — | 2 | 144 | no | — |
| 590 | C23 | — | 2 | 16 | no | — |
| 591 | C23 | — | 2 | 144 | no | — |
| 592 | C23 | — | 2 | 16 | no | — |
| 593 | C23 | — | 2 | 4 | no | — |
| 594 | C23 | — | 2 | 18 | no | — |
| 595 | C23 | — | 2 | 18 | no | — |
| 596 | C23 | — | 2 | 36 | no | — |
| 597 | C23 | — | 2 | 4 | no | — |
| 598 | C23 | — | 2 | 8 | no | — |
| 599 | C23 | — | 2 | 72 | no | — |
| 600 | C23 | — | 2 | 8 | no | — |
| 601 | C23 | — | 2 | 72 | no | — |
| 602 | C23 | — | 2 | 36 | no | — |
| 603 | C23 | — | 2 | 18 | no | — |
| 604 | C23 | — | 2 | 18 | no | — |
| 605 | C23 | — | 2 | 36 | no | — |
| 606 | C23 | — | 2 | 288 | no | — |
| 607 | C23 | — | 2 | 72 | no | — |
| 608 | C23 | — | 2 | 72 | no | — |
| 609 | C23 | — | 2 | 288 | no | — |
| 610 | C23 | — | 2 | 72 | no | — |
| 611 | C23 | — | 2 | 576 | no | — |
| 612 | C23 | — | 4 | 192 | no | — |
| 613 | C23 | — | 4 | 96 | no | — |
| 614 | C23 | — | 4 | 144 | no | — |
| 615 | C23 | — | 4 | 768 | no | — |
| 616 | C23 | — | 4 | 96 | no | — |
| 617 | C23 | — | 4 | 192 | no | — |
| 618 | C23 | — | 4 | 288 | no | — |
| 619 | C23 | — | 4 | 288 | no | — |
| 620 | C23 | — | 4 | 1152 | no | — |
| 621 | C23 | — | 4 | 288 | no | — |
| 622 | C23 | — | 4 | 288 | no | — |
| 623 | C23 | — | 4 | 72 | no | — |
| 624 | C23 | — | 4 | 72 | no | — |
| 625 | C23 | — | 8 | 1152 | no | — |
| 626 | C23 | — | 8 | 288 | no | — |
| 627 | C23 | — | 8 | 288 | no | — |
| 628 | C23 | — | 8 | 3072 | no | — |
| 629 | C23 | C23×C22⋊C4 | 1 | 144 | yes | — |
| 630 | C23 | C23×C22⋊C4 | 1 | 384 | yes | complemented |
| 631 | C23 | C4×H(5,𝔽2) | 1 | 16 | yes | complemented |
| 632 | C23 | C25×C4 | 1 | 36 | yes | — |
| 633 | C23 | C25×C4 | 1 | 36 | yes | — |
| 634 | C23 | C25×C4 | 1 | 4 | yes | — |
| 635 | C23 | C25×C4 | 1 | 2 | yes | — |
| 636 | C23 | C24×D4 | 1 | 72 | yes | — |
| 637 | C23 | C24×D4 | 1 | 4 | yes | — |
| 638 | C23 | C22×H(5,𝔽2) | 1 | 4 | yes | — |
| 639 | C23 | C22×H(5,𝔽2) | 1 | 2 | yes | — |
| 640 | C23 | C2×#585 | 1 | 4 | yes | — |
| 641 | C23 | C2×#585 | 1 | 2 | yes | — |
| 642 | C23 | H(7,𝔽2) | 1 | 4 | yes | — |
| 643 | C23 | C27 | 1 | 1 | yes | characteristic |
| 644 | Q8 | — | 2 | 192 | no | — |
| 645 | Q8 | C23×C22⋊C4 | 1 | 128 | yes | complemented |
| 646 | D4 | — | 2 | 1152 | no | — |
| 647 | D4 | — | 2 | 576 | no | — |
| 648 | D4 | C23×C22⋊C4 | 1 | 1152 | yes | complemented |
| 649 | C2×C4 | — | 2 | 16 | no | — |
| 650 | C2×C4 | — | 2 | 4 | no | — |
| 651 | C2×C4 | — | 2 | 24 | no | — |
| 652 | C2×C4 | — | 2 | 4 | no | — |
| 653 | C2×C4 | — | 2 | 48 | no | — |
| 654 | C2×C4 | — | 2 | 288 | no | — |
| 655 | C2×C4 | — | 2 | 192 | no | — |
| 656 | C2×C4 | — | 2 | 576 | no | — |
| 657 | C2×C4 | — | 2 | 24 | no | — |
| 658 | C2×C4 | — | 2 | 36 | no | — |
| 659 | C2×C4 | — | 2 | 36 | no | — |
| 660 | C2×C4 | — | 2 | 24 | no | — |
| 661 | C2×C4 | — | 2 | 24 | no | — |
| 662 | C2×C4 | — | 2 | 36 | no | — |
| 663 | C2×C4 | — | 4 | 288 | no | — |
| 664 | C2×C4 | — | 4 | 72 | no | — |
| 665 | C2×C4 | — | 4 | 48 | no | — |
| 666 | C2×C4 | — | 8 | 144 | no | — |
| 667 | C2×C4 | — | 8 | 288 | no | — |
| 668 | C2×C4 | C23×C22⋊C4 | 1 | 96 | yes | — |
| 669 | C2×C4 | C23×C22⋊C4 | 1 | 576 | yes | complemented |
| 670 | C2×C4 | C25×C4 | 1 | 24 | yes | — |
| 671 | C2×C4 | C25×C4 | 1 | 24 | yes | — |
| 672 | C2×C4 | C24×D4 | 1 | 48 | yes | — |
| 673 | C2×C4 | C22×H(5,𝔽2) | 1 | 8 | yes | complemented |
| 674 | C22 | — | 2 | 4 | no | — |
| 675 | C22 | — | 2 | 36 | no | — |
| 676 | C22 | — | 2 | 4 | no | — |
| 677 | C22 | — | 2 | 36 | no | — |
| 678 | C22 | — | 2 | 32 | no | — |
| 679 | C22 | — | 2 | 288 | no | — |
| 680 | C22 | — | 2 | 72 | no | — |
| 681 | C22 | — | 2 | 8 | no | — |
| 682 | C22 | — | 2 | 72 | no | — |
| 683 | C22 | — | 2 | 8 | no | — |
| 684 | C22 | — | 2 | 36 | no | — |
| 685 | C22 | — | 2 | 36 | no | — |
| 686 | C22 | — | 2 | 36 | no | — |
| 687 | C22 | — | 4 | 384 | no | — |
| 688 | C22 | — | 4 | 576 | no | — |
| 689 | C22 | — | 4 | 144 | no | — |
| 690 | C22 | — | 4 | 36 | no | — |
| 691 | C22 | — | 4 | 36 | no | — |
| 692 | C22 | — | 8 | 576 | no | — |
| 693 | C22 | C24×C22⋊C4 | 1 | 72 | yes | — |
| 694 | C22 | C24×C22⋊C4 | 1 | 4 | yes | — |
| 695 | C22 | C2×C4×H(5,𝔽2) | 1 | 4 | yes | — |
| 696 | C22 | C2×C4×H(5,𝔽2) | 1 | 8 | yes | complemented |
| 697 | C22 | #62652 | 1 | 4 | yes | — |
| 698 | C22 | D4×H(5,𝔽2) | 1 | 8 | yes | — |
| 699 | C22 | #62987 | 1 | 8 | yes | — |
| 700 | C22 | C26×C4 | 1 | 1 | yes | characteristic |
| 701 | C22 | C25×D4 | 1 | 2 | yes | — |
| 702 | C22 | C23×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 703 | C22 | C22×#585 | 1 | 1 | yes | characteristic |
| 704 | C22 | C2×H(7,𝔽2) | 1 | 2 | yes | — |
| 705 | C4 | — | 2 | 24 | no | — |
| 706 | C4 | — | 2 | 8 | no | — |
| 707 | C4 | — | 4 | 36 | no | — |
| 708 | C4 | — | 4 | 24 | no | — |
| 709 | C4 | C24×C22⋊C4 | 1 | 48 | yes | — |
| 710 | C2 | — | 2 | 8 | no | — |
| 711 | C2 | — | 2 | 72 | no | — |
| 712 | C2 | — | 4 | 36 | no | — |
| 713 | C2 | C22⋊C4×H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 714 | C2 | C25×C22⋊C4 | 1 | 1 | yes | characteristic |
| 715 | C2 | C22×C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 716 | C2 | C2×#62652 | 1 | 1 | yes | characteristic |
| 717 | C2 | C2×D4×H(5,𝔽2) | 1 | 2 | yes | — |
| 718 | C2 | C2×#62987 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 2. C22×C4×H(5,𝔽2) | C2 | semidirect |
| 3. C22⋊C4×H(5,𝔽2) | C2 | direct (N × H) |
| 4. C2×#34258 | C2 | semidirect |
| 5. C2×#34256 | C2 | semidirect |
| 6. C2×#34175 | C2 | semidirect |
| 7. C2×#34171 | C2 | semidirect |
| 8. C2×C22⋊C4×#41 | C2 | semidirect |
| 9. C22×D4×C22⋊C4 | C2 | semidirect |
| 11. C23×H(5,𝔽2) | C4 | semidirect |
| 19. C2×C4×H(5,𝔽2) | C22 | semidirect |
| 20. C22×#520 | C22 | semidirect |
| 21. C22×#518 | C22 | semidirect |
| 22. C22×C4×#41 | C22 | semidirect |
| 23. C23×C4×D4 | C22 | semidirect |
| 24. C24×C22⋊C4 | C22 | semidirect |
| 25. #34258 | C22 | semidirect |
| 26. #34256 | C22 | semidirect |
| 27. #34175 | C22 | semidirect |
| 28. #34171 | C22 | semidirect |
| 29. C22⋊C4×#41 | C22 | semidirect |
| 30. C2×#2341 | C22 | semidirect |
| 31. C2×#2341 | C22 | semidirect |
| 32. C2×Q8×C22⋊C4 | C22 | semidirect |
| 33. C2×Q8×C22⋊C4 | C22 | semidirect |
| 34. C2×#2339 | C22 | semidirect |
| 35. C2×#2339 | C22 | semidirect |
| 36. C2×D4×C22⋊C4 | C22 | semidirect |
| 37. C2×D4×C22⋊C4 | C22 | semidirect |
| 38. C2×D4×C22⋊C4 | C22 | semidirect |
| 39. C2×D4×C22⋊C4 | C22 | semidirect |
| 40. C2×D4×C22⋊C4 | C22 | semidirect |
| 41. C2×D4×C22⋊C4 | C22 | semidirect |
| 42. C2×#2311 | C22 | semidirect |
| 43. C2×#2309 | C22 | semidirect |
| 44. C2×#2308 | C22 | semidirect |
| 45. C2×#2297 | C22 | semidirect |
| 46. C22×#390 | C22 | semidirect |
| 47. C22×#386 | C22 | semidirect |
| 48. C2×#2280 | C22 | semidirect |
| 49. C22×#380 | C22 | semidirect |
| 50. C22×#379 | C22 | semidirect |
| 51. C22×C4×C22⋊C4 | C22 | semidirect |
| 58. C22×H(5,𝔽2) | C2×C4 | semidirect |
| 59. C22×H(5,𝔽2) | C2×C4 | semidirect |
| 60. C22×H(5,𝔽2) | C2×C4 | semidirect |
| 66. C23×#41 | C2×C4 | semidirect |
| 74. C24×D4 | C2×C4 | semidirect |
| 82. C25×C4 | C23 | semidirect |
| 85. C2×#520 | C23 | semidirect |
| 87. C2×#518 | C23 | semidirect |
| 89. C2×C4×#41 | C23 | semidirect |
| 90. C22×C4×Q8 | C23 | semidirect |
| 91. C22×C4×Q8 | C23 | semidirect |
| 93. C22×C4×D4 | C23 | semidirect |
| 94. C22×C4×D4 | C23 | semidirect |
| 95. C22×C4×D4 | C23 | semidirect |
| 96. C22×C4×D4 | C23 | semidirect |
| 97. C22×#117 | C23 | semidirect |
| 98. C23×C4⋊C4 | C23 | semidirect |
| 103. C23×C22⋊C4 | C23 | semidirect |
| 104. C23×C22⋊C4 | C23 | semidirect |
| 105. C23×C22⋊C4 | C23 | semidirect |
| 106. C23×C22⋊C4 | C23 | semidirect |
| 107. C23×C42 | C23 | semidirect |
| 108. #2341 | C23 | semidirect |
| 109. #2341 | C23 | semidirect |
| 110. Q8×C22⋊C4 | C23 | semidirect |
| 111. Q8×C22⋊C4 | C23 | semidirect |
| 112. #2339 | C23 | semidirect |
| 113. #2339 | C23 | semidirect |
| 114. D4×C22⋊C4 | C23 | semidirect |
| 115. D4×C22⋊C4 | C23 | semidirect |
| 116. D4×C22⋊C4 | C23 | semidirect |
| 117. D4×C22⋊C4 | C23 | semidirect |
| 118. D4×C22⋊C4 | C23 | semidirect |
| 119. #2311 | C23 | semidirect |
| 120. #2309 | C23 | semidirect |
| 121. #2308 | C23 | semidirect |
| 122. #2297 | C23 | semidirect |
| 123. C2×#391 | C23 | semidirect |
| 124. C2×#391 | C23 | semidirect |
| 125. C2×#390 | C23 | semidirect |
| 126. C2×#390 | C23 | semidirect |
| 127. C2×#390 | C23 | semidirect |
| 128. C2×#390 | C23 | semidirect |
| 129. C2×#386 | C23 | semidirect |
| 130. C2×#386 | C23 | semidirect |
| 131. C2×#386 | C23 | semidirect |
| 132. C2×#386 | C23 | semidirect |
| 133. #2280 | C23 | semidirect |
| 134. C2×#381 | C23 | semidirect |
| 137. C2×#380 | C23 | semidirect |
| 138. C2×#380 | C23 | semidirect |
| 139. C2×#380 | C23 | semidirect |
| 141. C2×#379 | C23 | semidirect |
| 142. C2×#379 | C23 | semidirect |
| 145. C2×C4×C22⋊C4 | C23 | semidirect |
| 146. C2×C4×C22⋊C4 | C23 | semidirect |
| 147. C2×C4×C22⋊C4 | C23 | semidirect |
| 148. C22×#95 | C23 | semidirect |
| 149. C22×#95 | C23 | semidirect |
| 154. C26 | C22×C4 | semidirect |
| 164. C2×H(5,𝔽2) | C22⋊C4 | direct (N × H) |
| 166. C2×H(5,𝔽2) | C22×C4 | semidirect |
| 167. C2×H(5,𝔽2) | C22×C4 | semidirect |
| 175. C22×#41 | C22×C4 | semidirect |
| 176. C22×#41 | C22×C4 | semidirect |
| 177. C22×#41 | C22×C4 | semidirect |
| 178. C22×#41 | C22×C4 | semidirect |
| 185. C23×Q8 | C22×C4 | semidirect |
| 196. C23×D4 | C22×C4 | semidirect |
| 197. C23×D4 | C22×C4 | semidirect |
| 198. C23×D4 | C22×C4 | semidirect |
| 199. C23×D4 | C22×C4 | semidirect |
| 200. C23×D4 | C22×C4 | semidirect |
| 214. C24×C4 | C22×C4 | semidirect |
| 223. C24×C4 | C24 | semidirect |
| 229. C2×C4×Q8 | C24 | semidirect |
| 230. C2×C4×Q8 | C24 | semidirect |
| 235. C2×C4×D4 | C24 | semidirect |
| 236. C2×C4×D4 | C24 | semidirect |
| 237. C2×C4×D4 | C24 | semidirect |
| 239. C2×#117 | C24 | semidirect |
| 243. C22×C4⋊C4 | C24 | semidirect |
| 262. C22×C22⋊C4 | C24 | semidirect |
| 263. C22×C22⋊C4 | C24 | semidirect |
| 264. C22×C22⋊C4 | C24 | semidirect |
| 268. C22×C42 | C24 | semidirect |
| 269. #391 | C24 | semidirect |
| 270. #391 | C24 | semidirect |
| 271. #390 | C24 | semidirect |
| 272. #390 | C24 | semidirect |
| 273. #390 | C24 | semidirect |
| 274. #386 | C24 | semidirect |
| 275. #386 | C24 | semidirect |
| 276. #386 | C24 | semidirect |
| 277. #381 | C24 | semidirect |
| 280. #380 | C24 | semidirect |
| 281. #380 | C24 | semidirect |
| 283. #379 | C24 | semidirect |
| 286. C4×C22⋊C4 | C24 | semidirect |
| 287. C4×C22⋊C4 | C24 | semidirect |
| 292. C2×#95 | C24 | semidirect |
| 293. C2×#95 | C24 | semidirect |
| 317. C25 | C23×C4 | semidirect |
| 327. H(5,𝔽2) | C2×C22⋊C4 | direct (N × H) |
| 335. C2×#41 | C2×C22⋊C4 | semidirect |
| 337. C2×#41 | C23×C4 | semidirect |
| 338. C2×#41 | C23×C4 | semidirect |
| 339. C2×#41 | C23×C4 | semidirect |
| 346. C22×Q8 | C23×C4 | semidirect |
| 361. C22×D4 | C2×C22⋊C4 | semidirect |
| 366. C22×D4 | C23×C4 | semidirect |
| 367. C22×D4 | C23×C4 | semidirect |
| 368. C22×D4 | C23×C4 | semidirect |
| 369. C22×D4 | C23×C4 | semidirect |
| 397. C23×C4 | C23×C4 | semidirect |
| 435. C2×C22⋊C4 | H(5,𝔽2) | direct (N × H) |
| 493. C24 | C22×C22⋊C4 | semidirect |
| 511. #41 | C22×C22⋊C4 | semidirect |
| 515. C2×Q8 | C22×C22⋊C4 | semidirect |
| 527. C2×D4 | C22×C22⋊C4 | semidirect |
| 528. C2×D4 | C22×C22⋊C4 | semidirect |
| 562. C22×C4 | C22×C22⋊C4 | semidirect |
| 571. C22×C4 | C2×H(5,𝔽2) | semidirect |
| 586. C22⋊C4 | C2×H(5,𝔽2) | direct (N × H) |
| 630. C23 | C23×C22⋊C4 | semidirect |
| 631. C23 | C4×H(5,𝔽2) | semidirect |
| 645. Q8 | C23×C22⋊C4 | semidirect |
| 648. D4 | C23×C22⋊C4 | semidirect |
| 669. C2×C4 | C23×C22⋊C4 | semidirect |
| 673. C2×C4 | C22×H(5,𝔽2) | semidirect |
| 696. C22 | C2×C4×H(5,𝔽2) | semidirect |
| 713. C2 | C22⋊C4×H(5,𝔽2) | 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