| 1 | C5×#5196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5194 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×#4895 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×C5×#359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#4510 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#4502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×#4493 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C5×#2179 | — | 3 | 1 | no | maximal, Hall |
| 9 | C3×C5×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | C5×#948 | — | 2 | 1 | no | — |
| 11 | C5×#907 | — | 2 | 1 | no | — |
| 12 | C5×#904 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×C5×C16 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C5×#108 | C22 | 1 | 1 | yes | characteristic |
| 15 | C5×#837 | — | 2 | 1 | no | — |
| 16 | C5×#829 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C5×#828 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C5×#827 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | C5×#826 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C5×#825 | — | 2 | 1 | no | — |
| 21 | C5×#819 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×C8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C5×C3⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 24 | #69239 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 25 | C5×#508 | — | 3 | 1 | no | — |
| 26 | C5×#443 | — | 3 | 1 | no | — |
| 27 | C5×#443 | — | 3 | 1 | no | — |
| 28 | C5×#368 | — | 3 | 1 | no | — |
| 29 | C5×#359 | — | 3 | 1 | no | — |
| 30 | C5×#359 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | C5×#346 | — | 3 | 1 | no | — |
| 32 | C3×C5×#41 | — | 2 | 1 | no | — |
| 33 | C5×#235 | — | 2 | 1 | no | — |
| 34 | C3×C5×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C3×C5×SD16 | — | 2 | 1 | no | — |
| 36 | C3×C5×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C3×C5×M16 | — | 2 | 1 | no | — |
| 38 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 39 | C4×C5×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 40 | C5×#208 | — | 2 | 1 | no | — |
| 41 | C5×#208 | — | 4 | 1 | no | — |
| 42 | C2×C5×C3⋊C8 | — | 4 | 1 | no | — |
| 43 | C2×C5×C3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 44 | C5×Dic12 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C5×D24 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C5×#204 | — | 2 | 1 | no | — |
| 47 | C5×ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 48 | C5×D3×C8 | — | 4 | 1 | no | — |
| 49 | C3×C5×C16 | — | 2 | 1 | no | — |
| 50 | C5×C3⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C5×C3⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | #5196 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5194 | C2×C5 | 1 | 1 | yes | characteristic |
| 54 | #4895 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 55 | C3×#359 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 56 | #4510 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 57 | #4502 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 58 | #4493 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 59 | C5×#135 | — | 3 | 1 | no | — |
| 60 | C5×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C5×#131 | — | 6 | 1 | no | — |
| 62 | C5×#131 | — | 6 | 1 | no | — |
| 63 | C5×Q32 | — | 3 | 1 | no | — |
| 64 | C5×SD32 | — | 3 | 1 | no | — |
| 65 | C5×SD32 | — | 3 | 1 | no | — |
| 66 | C5×D16 | — | 3 | 1 | no | — |
| 67 | C2×C5×C16 | — | 3 | 1 | no | — |
| 68 | C2×C5×C16 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C5×#108 | — | 3 | 1 | no | — |
| 70 | C5×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 71 | C5×#104 | — | 6 | 1 | no | — |
| 72 | C5×#104 | — | 6 | 1 | no | — |
| 73 | C4×C5×C8 | — | 3 | 1 | no | — |
| 74 | #2179 | — | 3 | 1 | no | Sylow |
| 75 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 76 | C3×C5×D4 | — | 2 | 1 | no | — |
| 77 | C3×C5×D4 | — | 4 | 1 | no | — |
| 78 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 79 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C5×#67 | — | 4 | 1 | no | — |
| 81 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 82 | C5×D12 | — | 2 | 1 | no | — |
| 83 | C4×C5×D3 | — | 4 | 1 | no | — |
| 84 | C5×Dic6 | — | 2 | 1 | no | — |
| 85 | C3×C5×C8 | — | 4 | 1 | no | — |
| 86 | C3×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 87 | C3×C5×C8 | #41 | 1 | 1 | yes | characteristic |
| 88 | C5×C3⋊C8 | — | 4 | 1 | no | — |
| 89 | C5×C3⋊C8 | D8 | 1 | 1 | yes | characteristic |
| 90 | C5×C3⋊C8 | D8 | 1 | 1 | yes | characteristic |
| 91 | C3×#135 | C22×C5 | 1 | 1 | yes | characteristic |
| 92 | #948 | — | 2 | 1 | no | — |
| 93 | #907 | — | 2 | 1 | no | — |
| 94 | #904 | C22×C5 | 1 | 1 | yes | characteristic |
| 95 | C2×C3×C16 | C22×C5 | 1 | 1 | yes | characteristic |
| 96 | C3×#108 | C22×C5 | 1 | 1 | yes | characteristic |
| 97 | #837 | — | 2 | 1 | no | — |
| 98 | #829 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 99 | #828 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 100 | #827 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 101 | #826 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 102 | #825 | — | 2 | 1 | no | — |
| 103 | #819 | C22×C5 | 1 | 1 | yes | characteristic |
| 104 | C8×Dic3 | C22×C5 | 1 | 1 | yes | characteristic |
| 105 | C2×C3⋊C16 | C22×C5 | 1 | 1 | yes | characteristic |
| 106 | C5×#41 | — | 2 | 1 | no | — |
| 107 | C5×#41 | — | 6 | 1 | no | — |
| 108 | C5×Q16 | — | 3 | 1 | no | — |
| 109 | C5×Q16 | C4×D3 | 1 | 1 | yes | characteristic |
| 110 | C5×SD16 | — | 2 | 1 | no | — |
| 111 | C5×SD16 | — | 6 | 1 | no | — |
| 112 | C5×D8 | — | 3 | 1 | no | — |
| 113 | C5×D8 | C4×D3 | 1 | 1 | yes | characteristic |
| 114 | C5×M16 | — | 2 | 1 | no | — |
| 115 | C5×M16 | — | 6 | 1 | no | — |
| 116 | C5×M16 | — | 12 | 1 | no | — |
| 117 | C5×M16 | — | 12 | 1 | no | — |
| 118 | C2×C5×C8 | — | 3 | 1 | no | — |
| 119 | C2×C5×C8 | — | 12 | 1 | no | — |
| 120 | C2×C5×C8 | — | 12 | 1 | no | — |
| 121 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 122 | C42×C5 | — | 3 | 1 | no | — |
| 123 | C5×C16 | — | 2 | 1 | no | — |
| 124 | C5×C16 | — | 3 | 1 | no | — |
| 125 | C5×C16 | — | 3 | 1 | no | — |
| 126 | #508 | — | 3 | 1 | no | — |
| 127 | #443 | — | 3 | 1 | no | — |
| 128 | #443 | — | 3 | 1 | no | — |
| 129 | #368 | — | 3 | 1 | no | — |
| 130 | #359 | — | 3 | 1 | no | — |
| 131 | #359 | C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 132 | #346 | — | 3 | 1 | no | — |
| 133 | C22×C3×C5 | — | 4 | 1 | no | — |
| 134 | C22×C3×C5 | #135 | 1 | 1 | yes | characteristic |
| 135 | C2×C5×D3 | — | 4 | 1 | no | — |
| 136 | C3×C4×C5 | — | 4 | 1 | no | — |
| 137 | C3×C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 138 | C3×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 139 | C5×Dic3 | — | 4 | 1 | no | — |
| 140 | C5×Dic3 | — | 4 | 1 | no | — |
| 141 | C3×#41 | — | 2 | 1 | no | — |
| 142 | #235 | — | 2 | 1 | no | — |
| 143 | C3×Q16 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 144 | C3×SD16 | — | 2 | 1 | no | — |
| 145 | C3×D8 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 146 | C3×M16 | — | 2 | 1 | no | — |
| 147 | C2×C3×C8 | C23×C5 | 1 | 1 | yes | characteristic |
| 148 | C4×Dic3 | C5×D4 | 1 | 1 | yes | characteristic |
| 149 | #208 | — | 2 | 1 | no | — |
| 150 | #208 | — | 4 | 1 | no | — |
| 151 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 152 | C2×C3⋊C8 | C5×D4 | 1 | 1 | yes | characteristic |
| 153 | Dic12 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 154 | D24 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 155 | #204 | — | 2 | 1 | no | — |
| 156 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 157 | D3×C8 | — | 4 | 1 | no | — |
| 158 | C3×C16 | — | 2 | 1 | no | — |
| 159 | C3⋊C16 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 160 | C3⋊C16 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 161 | C5×Q8 | — | 2 | 1 | no | — |
| 162 | C5×Q8 | — | 6 | 1 | no | — |
| 163 | C5×D4 | — | 2 | 1 | no | — |
| 164 | C5×D4 | — | 4 | 1 | no | — |
| 165 | C5×D4 | — | 6 | 1 | no | — |
| 166 | C5×D4 | — | 12 | 1 | no | — |
| 167 | C2×C4×C5 | — | 4 | 1 | no | — |
| 168 | C2×C4×C5 | — | 6 | 1 | no | — |
| 169 | C2×C4×C5 | — | 12 | 1 | no | — |
| 170 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 171 | C5×C8 | — | 3 | 1 | no | — |
| 172 | C5×C8 | — | 3 | 1 | no | — |
| 173 | C5×C8 | — | 4 | 1 | no | — |
| 174 | C5×C8 | — | 12 | 1 | no | — |
| 175 | C5×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 176 | C5×C8 | #237 | 1 | 1 | yes | characteristic |
| 177 | #135 | — | 3 | 1 | no | — |
| 178 | #135 | C2×C5×D3 | 1 | 1 | yes | characteristic |
| 179 | #131 | — | 6 | 1 | no | — |
| 180 | #131 | — | 6 | 1 | no | — |
| 181 | Q32 | — | 3 | 1 | no | — |
| 182 | SD32 | — | 3 | 1 | no | — |
| 183 | SD32 | — | 3 | 1 | no | — |
| 184 | D16 | — | 3 | 1 | no | — |
| 185 | C2×C16 | — | 3 | 1 | no | — |
| 186 | C2×C16 | C2×C5×D3 | 1 | 1 | yes | characteristic |
| 187 | #108 | — | 3 | 1 | no | — |
| 188 | #108 | C2×C5×D3 | 1 | 1 | yes | characteristic |
| 189 | #104 | — | 6 | 1 | no | — |
| 190 | #104 | — | 6 | 1 | no | — |
| 191 | C4×C8 | — | 3 | 1 | no | — |
| 192 | C2×C3×C5 | — | 2 | 1 | no | — |
| 193 | C2×C3×C5 | — | 8 | 1 | no | — |
| 194 | C2×C3×C5 | C4×D8 | 1 | 1 | yes | characteristic |
| 195 | C5×D3 | — | 8 | 1 | no | — |
| 196 | C3×Q8 | — | 2 | 1 | no | — |
| 197 | C3×D4 | — | 2 | 1 | no | — |
| 198 | C3×D4 | — | 4 | 1 | no | — |
| 199 | C2×C3×C4 | — | 4 | 1 | no | — |
| 200 | C2×C3×C4 | C2×C5×D4 | 1 | 1 | yes | characteristic |
| 201 | #67 | — | 4 | 1 | no | — |
| 202 | C2×Dic3 | — | 2 | 1 | no | — |
| 203 | D12 | — | 2 | 1 | no | — |
| 204 | C4×D3 | — | 4 | 1 | no | — |
| 205 | Dic6 | — | 2 | 1 | no | — |
| 206 | C3×C8 | — | 4 | 1 | no | — |
| 207 | C3×C8 | C22×C4×C5 | 1 | 1 | yes | characteristic |
| 208 | C3×C8 | C5×#41 | 1 | 1 | yes | characteristic |
| 209 | C3⋊C8 | — | 4 | 1 | no | — |
| 210 | C3⋊C8 | C5×D8 | 1 | 1 | yes | characteristic |
| 211 | C3⋊C8 | C5×D8 | 1 | 1 | yes | characteristic |
| 212 | C22×C5 | — | 4 | 1 | no | — |
| 213 | C22×C5 | — | 12 | 1 | no | — |
| 214 | C22×C5 | #916 | 1 | 1 | yes | characteristic |
| 215 | C4×C5 | — | 4 | 1 | no | — |
| 216 | C4×C5 | — | 12 | 1 | no | — |
| 217 | C4×C5 | — | 12 | 1 | no | — |
| 218 | C4×C5 | #67⋊C4 | 1 | 1 | yes | characteristic |
| 219 | C4×C5 | D3×D8 | 1 | 1 | yes | characteristic |
| 220 | #41 | — | 2 | 1 | no | — |
| 221 | #41 | — | 6 | 1 | no | — |
| 222 | Q16 | — | 3 | 1 | no | — |
| 223 | Q16 | C4×C5×D3 | 1 | 1 | yes | characteristic |
| 224 | SD16 | — | 2 | 1 | no | — |
| 225 | SD16 | — | 6 | 1 | no | — |
| 226 | D8 | — | 3 | 1 | no | — |
| 227 | D8 | C4×C5×D3 | 1 | 1 | yes | characteristic |
| 228 | M16 | — | 2 | 1 | no | — |
| 229 | M16 | — | 6 | 1 | no | — |
| 230 | M16 | — | 12 | 1 | no | — |
| 231 | M16 | — | 12 | 1 | no | — |
| 232 | C2×C8 | — | 3 | 1 | no | — |
| 233 | C2×C8 | — | 12 | 1 | no | — |
| 234 | C2×C8 | — | 12 | 1 | no | — |
| 235 | C2×C8 | C22×C5×D3 | 1 | 1 | yes | characteristic |
| 236 | C42 | — | 3 | 1 | no | — |
| 237 | C16 | — | 2 | 1 | no | — |
| 238 | C16 | — | 3 | 1 | no | — |
| 239 | C16 | — | 3 | 1 | no | — |
| 240 | C3×C5 | #2179 | 1 | 1 | yes | characteristic, complemented, Hall |
| 241 | C22×C3 | — | 4 | 1 | no | — |
| 242 | C22×C3 | C5×#135 | 1 | 1 | yes | characteristic |
| 243 | C2×D3 | — | 4 | 1 | no | — |
| 244 | C3×C4 | — | 4 | 1 | no | — |
| 245 | C3×C4 | C4×C5×D4 | 1 | 1 | yes | characteristic |
| 246 | C3×C4 | C2×C5×D8 | 1 | 1 | yes | characteristic |
| 247 | Dic3 | — | 4 | 1 | no | — |
| 248 | Dic3 | — | 4 | 1 | no | — |
| 249 | C2×C5 | — | 2 | 1 | no | — |
| 250 | C2×C5 | — | 8 | 1 | no | — |
| 251 | C2×C5 | — | 24 | 1 | no | — |
| 252 | C2×C5 | #4756 | 1 | 1 | yes | characteristic |
| 253 | Q8 | — | 2 | 1 | no | — |
| 254 | Q8 | — | 6 | 1 | no | — |
| 255 | D4 | — | 2 | 1 | no | — |
| 256 | D4 | — | 4 | 1 | no | — |
| 257 | D4 | — | 6 | 1 | no | — |
| 258 | D4 | — | 12 | 1 | no | — |
| 259 | C2×C4 | — | 4 | 1 | no | — |
| 260 | C2×C4 | — | 6 | 1 | no | — |
| 261 | C2×C4 | — | 12 | 1 | no | — |
| 262 | C2×C4 | C5×D3×D4 | 1 | 1 | yes | characteristic |
| 263 | C8 | — | 3 | 1 | no | — |
| 264 | C8 | — | 3 | 1 | no | — |
| 265 | C8 | — | 4 | 1 | no | — |
| 266 | C8 | — | 12 | 1 | no | — |
| 267 | C8 | C2×C4×C5×D3 | 1 | 1 | yes | characteristic |
| 268 | C8 | C5×#237 | 1 | 1 | yes | characteristic |
| 269 | C2×C3 | — | 2 | 1 | no | — |
| 270 | C2×C3 | — | 8 | 1 | no | — |
| 271 | C2×C3 | C4×C5×D8 | 1 | 1 | yes | characteristic |
| 272 | D3 | — | 8 | 1 | no | — |
| 273 | C5 | #69239 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 274 | C22 | — | 4 | 1 | no | — |
| 275 | C22 | — | 12 | 1 | no | — |
| 276 | C22 | C5×#916 | 1 | 1 | yes | characteristic |
| 277 | C4 | — | 4 | 1 | no | — |
| 278 | C4 | — | 12 | 1 | no | — |
| 279 | C4 | — | 12 | 1 | no | — |
| 280 | C4 | C5×#67⋊C4 | 1 | 1 | yes | characteristic |
| 281 | C4 | C5×D3×D8 | 1 | 1 | yes | characteristic |
| 282 | C3 | C5×#2179 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 283 | C2 | — | 2 | 1 | no | — |
| 284 | C2 | — | 8 | 1 | no | — |
| 285 | C2 | — | 24 | 1 | no | — |
| 286 | C2 | C5×#4756 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta