Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
928 conjugacy classes of subgroups.
The subgroup lattice has 708 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D5×#576 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10604860 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10604854 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#64906 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10604786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10604779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10604776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D5×H(5,𝔽2) | — | 2 | 1 | no | — |
| 9 | C5×#576 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #66169 | — | 2 | 1 | no | — |
| 11 | #66108 | — | 2 | 2 | no | — |
| 12 | #66108 | — | 2 | 1 | no | — |
| 13 | D5×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 14 | D5×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 15 | #66103 | — | 2 | 1 | no | — |
| 16 | #66103 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | D5×#135 | — | 2 | 1 | no | — |
| 18 | D5×#135 | C22 | 1 | 1 | yes | characteristic |
| 19 | #66091 | — | 2 | 1 | no | — |
| 20 | #66091 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×D5×D8 | — | 2 | 1 | no | — |
| 22 | C2×D5×D8 | C22 | 1 | 1 | yes | characteristic |
| 23 | #66086 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | D5×#131 | C22 | 1 | 1 | yes | characteristic |
| 25 | #65795 | — | 2 | 1 | no | — |
| 26 | C2×#3995 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #65721 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | D5⋊M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#3990 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #64932 | — | 2 | 1 | no | — |
| 31 | #64910 | — | 2 | 1 | no | — |
| 32 | #64907 | — | 2 | 1 | no | — |
| 33 | #64906 | — | 2 | 1 | no | — |
| 34 | #64906 | — | 2 | 2 | no | — |
| 35 | #64904 | — | 2 | 2 | no | — |
| 36 | #64903 | — | 2 | 1 | no | — |
| 37 | #64902 | — | 2 | 1 | no | — |
| 38 | #64898 | — | 2 | 1 | no | — |
| 39 | #12750 | — | 5 | 1 | no | maximal, Sylow |
| 40 | C5×H(5,𝔽2) | — | 2 | 1 | no | — |
| 41 | #4149 | — | 2 | 1 | no | — |
| 42 | #4149 | — | 2 | 2 | no | — |
| 43 | #4149 | — | 2 | 1 | no | — |
| 44 | #4149 | — | 4 | 1 | no | — |
| 45 | D5×#41 | — | 2 | 2 | no | — |
| 46 | D5×#41 | — | 2 | 1 | no | — |
| 47 | D5×#41 | — | 4 | 1 | no | — |
| 48 | D5×#41 | D4 | 1 | 1 | yes | characteristic |
| 49 | #4144 | — | 2 | 2 | no | — |
| 50 | #4144 | — | 2 | 1 | no | — |
| 51 | #4144 | — | 4 | 2 | no | — |
| 52 | #4144 | — | 4 | 1 | no | — |
| 53 | C2×D4×D5 | — | 2 | 2 | no | — |
| 54 | C2×D4×D5 | — | 2 | 1 | no | — |
| 55 | C2×D4×D5 | — | 4 | 2 | no | — |
| 56 | C2×D4×D5 | — | 4 | 1 | no | — |
| 57 | #4130 | — | 2 | 1 | no | — |
| 58 | C2×#700 | — | 2 | 1 | no | — |
| 59 | C5×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 60 | C5×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 61 | C5×#135 | — | 2 | 1 | no | — |
| 62 | C5×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C2×C5×D8 | — | 2 | 1 | no | — |
| 64 | C2×C5×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C5×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | #4096 | — | 2 | 2 | no | — |
| 67 | #4096 | — | 2 | 1 | no | — |
| 68 | #4095 | — | 2 | 2 | no | — |
| 69 | #4095 | — | 2 | 1 | no | — |
| 70 | #4094 | D4 | 1 | 1 | yes | characteristic |
| 71 | #4078 | — | 2 | 2 | no | — |
| 72 | #4078 | — | 2 | 1 | no | — |
| 73 | C2×#686 | — | 2 | 2 | no | — |
| 74 | C2×#686 | — | 2 | 1 | no | — |
| 75 | #4065 | — | 2 | 1 | no | — |
| 76 | #4065 | D4 | 1 | 1 | yes | characteristic |
| 77 | D5×Q16 | D4 | 1 | 1 | yes | characteristic |
| 78 | #4062 | — | 2 | 2 | no | — |
| 79 | #4062 | — | 2 | 1 | no | — |
| 80 | #4060 | — | 2 | 2 | no | — |
| 81 | #4060 | — | 2 | 2 | no | — |
| 82 | #4060 | — | 2 | 2 | no | — |
| 83 | D5×SD16 | — | 2 | 2 | no | — |
| 84 | D5×SD16 | — | 2 | 1 | no | — |
| 85 | #4058 | — | 2 | 1 | no | — |
| 86 | #4058 | D4 | 1 | 1 | yes | characteristic |
| 87 | #4057 | — | 2 | 2 | no | — |
| 88 | #4057 | — | 2 | 2 | no | — |
| 89 | #4057 | — | 2 | 2 | no | — |
| 90 | D5×D8 | — | 2 | 2 | no | — |
| 91 | D5×D8 | — | 2 | 2 | no | — |
| 92 | D5×D8 | — | 2 | 1 | no | — |
| 93 | D5×D8 | — | 2 | 1 | no | — |
| 94 | D5×D8 | — | 2 | 1 | no | — |
| 95 | D5×D8 | — | 2 | 1 | no | — |
| 96 | D5×D8 | D4 | 1 | 1 | yes | characteristic |
| 97 | D5×D8 | D4 | 1 | 2 | yes | — |
| 98 | D5×D8 | D4 | 1 | 2 | yes | — |
| 99 | #4054 | — | 2 | 1 | no | — |
| 100 | #4054 | — | 2 | 2 | no | — |
| 101 | #4053 | — | 2 | 1 | no | — |
| 102 | #4053 | D4 | 1 | 1 | yes | characteristic |
| 103 | D5×M16 | — | 2 | 1 | no | — |
| 104 | D5×M16 | D4 | 1 | 1 | yes | characteristic |
| 105 | #4050 | — | 2 | 1 | no | — |
| 106 | #4050 | C2×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×D40 | — | 2 | 1 | no | — |
| 108 | C2×D40 | C2×C4 | 1 | 1 | yes | characteristic |
| 109 | #4047 | — | 2 | 1 | no | — |
| 110 | #4047 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×C8×D5 | — | 2 | 1 | no | — |
| 112 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 113 | #4010 | — | 4 | 1 | no | — |
| 114 | #4008 | — | 4 | 1 | no | — |
| 115 | #3998 | — | 2 | 1 | no | — |
| 116 | C2×#674 | — | 2 | 1 | no | — |
| 117 | #3995 | — | 2 | 1 | no | — |
| 118 | #3995 | — | 2 | 1 | no | — |
| 119 | #3994 | — | 2 | 1 | no | — |
| 120 | #3993 | — | 2 | 1 | no | — |
| 121 | #3990 | — | 2 | 1 | no | — |
| 122 | #3990 | — | 2 | 1 | no | — |
| 123 | #3990 | — | 2 | 1 | no | — |
| 124 | D5⋊C16 | — | 2 | 1 | no | — |
| 125 | C2×#576 | — | 5 | 1 | no | — |
| 126 | #2148 | — | 5 | 1 | no | — |
| 127 | C2×#361 | — | 5 | 1 | no | — |
| 128 | #2145 | — | 5 | 1 | no | — |
| 129 | #2140 | — | 5 | 1 | no | — |
| 130 | #2117 | — | 5 | 1 | no | — |
| 131 | #1814 | — | 5 | 1 | no | — |
| 132 | C23×D5 | — | 4 | 2 | no | — |
| 133 | C23×D5 | — | 4 | 1 | no | — |
| 134 | C5×#41 | — | 2 | 2 | no | — |
| 135 | C5×#41 | — | 2 | 1 | no | — |
| 136 | C5×#41 | — | 4 | 1 | no | — |
| 137 | C5×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C2×C5×D4 | — | 2 | 2 | no | — |
| 139 | C2×C5×D4 | — | 2 | 1 | no | — |
| 140 | C2×C5×D4 | — | 4 | 2 | no | — |
| 141 | C2×C5×D4 | — | 4 | 1 | no | — |
| 142 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 143 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 144 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 145 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 146 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 147 | #713 | — | 2 | 2 | no | — |
| 148 | #713 | — | 2 | 1 | no | — |
| 149 | #713 | — | 4 | 1 | no | — |
| 150 | #713 | D8 | 1 | 1 | yes | characteristic |
| 151 | Q8×D5 | — | 2 | 1 | no | — |
| 152 | Q8×D5 | SD16 | 1 | 1 | yes | characteristic |
| 153 | #711 | — | 2 | 1 | no | — |
| 154 | #711 | — | 2 | 2 | no | — |
| 155 | #711 | — | 2 | 1 | no | — |
| 156 | #711 | — | 4 | 2 | no | — |
| 157 | #711 | — | 4 | 2 | no | — |
| 158 | #711 | — | 4 | 1 | no | — |
| 159 | #711 | — | 4 | 1 | no | — |
| 160 | #711 | D8 | 1 | 1 | yes | characteristic |
| 161 | D4×D5 | — | 2 | 1 | no | — |
| 162 | D4×D5 | — | 2 | 2 | no | — |
| 163 | D4×D5 | — | 2 | 2 | no | — |
| 164 | D4×D5 | — | 2 | 1 | no | — |
| 165 | D4×D5 | — | 2 | 2 | no | — |
| 166 | D4×D5 | — | 2 | 2 | no | — |
| 167 | D4×D5 | — | 4 | 2 | no | — |
| 168 | D4×D5 | — | 4 | 2 | no | — |
| 169 | D4×D5 | — | 4 | 2 | no | — |
| 170 | D4×D5 | — | 4 | 2 | no | — |
| 171 | D4×D5 | — | 4 | 2 | no | — |
| 172 | D4×D5 | — | 4 | 2 | no | — |
| 173 | D4×D5 | — | 4 | 2 | no | — |
| 174 | D4×D5 | — | 4 | 2 | no | — |
| 175 | D4×D5 | — | 4 | 1 | no | — |
| 176 | D4×D5 | — | 4 | 1 | no | — |
| 177 | D4×D5 | — | 4 | 1 | no | — |
| 178 | D4×D5 | — | 4 | 1 | no | — |
| 179 | D4×D5 | — | 4 | 1 | no | — |
| 180 | D4×D5 | SD16 | 1 | 1 | yes | characteristic |
| 181 | #709 | — | 2 | 1 | no | — |
| 182 | #709 | — | 2 | 2 | no | — |
| 183 | #709 | — | 2 | 1 | no | — |
| 184 | #709 | — | 4 | 2 | no | — |
| 185 | #709 | — | 4 | 2 | no | — |
| 186 | #709 | — | 4 | 1 | no | — |
| 187 | #709 | — | 4 | 1 | no | — |
| 188 | #709 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 189 | C2×D20 | — | 2 | 2 | no | — |
| 190 | C2×D20 | — | 2 | 1 | no | — |
| 191 | C2×D20 | — | 4 | 2 | no | — |
| 192 | C2×D20 | — | 4 | 1 | no | — |
| 193 | C2×C4×D5 | — | 2 | 1 | no | — |
| 194 | C2×C4×D5 | — | 4 | 2 | no | — |
| 195 | C2×C4×D5 | — | 4 | 1 | no | — |
| 196 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C22⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 198 | C2×#170 | — | 4 | 1 | no | — |
| 199 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 200 | C4×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 201 | #700 | — | 4 | 1 | no | — |
| 202 | #700 | — | 4 | 1 | no | — |
| 203 | C5×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C5×SD16 | — | 2 | 2 | no | — |
| 205 | C5×SD16 | — | 2 | 1 | no | — |
| 206 | C5×D8 | — | 2 | 2 | no | — |
| 207 | C5×D8 | — | 2 | 1 | no | — |
| 208 | C5×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 209 | C5×D8 | C22⋊C4 | 1 | 2 | yes | — |
| 210 | C5×M16 | — | 2 | 1 | no | — |
| 211 | C5×M16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 212 | C2×C5×C8 | — | 2 | 1 | no | — |
| 213 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 214 | #689 | — | 2 | 1 | no | — |
| 215 | #688 | — | 2 | 2 | no | — |
| 216 | #688 | — | 2 | 1 | no | — |
| 217 | #687 | — | 2 | 2 | no | — |
| 218 | #687 | — | 2 | 1 | no | — |
| 219 | #686 | — | 2 | 2 | no | — |
| 220 | #686 | — | 2 | 2 | no | — |
| 221 | #686 | — | 2 | 2 | no | — |
| 222 | #686 | — | 2 | 1 | no | — |
| 223 | #686 | — | 2 | 2 | no | — |
| 224 | #681 | — | 2 | 1 | no | — |
| 225 | #681 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 226 | C2×#168 | — | 2 | 1 | no | — |
| 227 | C2×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | Dic20 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 229 | D40 | — | 2 | 2 | no | — |
| 230 | D40 | — | 2 | 1 | no | — |
| 231 | D40 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 232 | D40 | C22⋊C4 | 1 | 2 | yes | — |
| 233 | #677 | — | 2 | 2 | no | — |
| 234 | #677 | — | 2 | 1 | no | — |
| 235 | #676 | — | 2 | 1 | no | — |
| 236 | #676 | — | 2 | 1 | no | — |
| 237 | #676 | — | 2 | 1 | no | — |
| 238 | C8×D5 | — | 2 | 1 | no | — |
| 239 | C8×D5 | — | 2 | 1 | no | — |
| 240 | C8×D5 | — | 2 | 1 | no | — |
| 241 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | #674 | — | 4 | 1 | no | — |
| 246 | #674 | — | 4 | 1 | no | — |
| 247 | C2×H(5,𝔽2) | — | 10 | 1 | no | — |
| 248 | #576 | — | 5 | 1 | no | — |
| 249 | #576 | — | 5 | 1 | no | — |
| 250 | #576 | — | 5 | 1 | no | — |
| 251 | #576 | — | 10 | 1 | no | — |
| 252 | #576 | — | 10 | 1 | no | — |
| 253 | #576 | — | 10 | 1 | no | — |
| 254 | #576 | — | 10 | 2 | no | — |
| 255 | #576 | — | 10 | 1 | no | — |
| 256 | #576 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 257 | C2×AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 258 | C2×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 259 | C2×#135 | — | 5 | 1 | no | — |
| 260 | C2×#135 | — | 10 | 1 | no | — |
| 261 | C22×D8 | — | 5 | 1 | no | — |
| 262 | C22×D8 | — | 10 | 1 | no | — |
| 263 | C2×#131 | — | 5 | 1 | no | — |
| 264 | C2×M32 | — | 5 | 1 | no | — |
| 265 | C2×M32 | — | 5 | 1 | no | — |
| 266 | C2×#108 | — | 5 | 1 | no | — |
| 267 | #427 | — | 5 | 1 | no | — |
| 268 | #421 | — | 10 | 1 | no | — |
| 269 | #362 | — | 10 | 1 | no | — |
| 270 | #361 | — | 10 | 2 | no | — |
| 271 | #361 | — | 10 | 1 | no | — |
| 272 | #360 | — | 10 | 1 | no | — |
| 273 | #360 | — | 10 | 1 | no | — |
| 274 | #357 | — | 10 | 2 | no | — |
| 275 | #350 | — | 10 | 1 | no | — |
| 276 | #350 | — | 10 | 1 | no | — |
| 277 | #344 | — | 10 | 1 | no | — |
| 278 | C23×C5 | — | 4 | 2 | no | — |
| 279 | C23×C5 | — | 4 | 1 | no | — |
| 280 | C22×D5 | — | 2 | 1 | no | — |
| 281 | C22×D5 | — | 4 | 2 | no | — |
| 282 | C22×D5 | — | 4 | 2 | no | — |
| 283 | C22×D5 | — | 4 | 2 | no | — |
| 284 | C22×D5 | — | 4 | 1 | no | — |
| 285 | C22×D5 | — | 4 | 2 | no | — |
| 286 | C22×D5 | — | 4 | 1 | no | — |
| 287 | C22×D5 | — | 4 | 2 | no | — |
| 288 | C22×D5 | — | 16 | 2 | no | — |
| 289 | C22×D5 | — | 16 | 4 | no | — |
| 290 | C22×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 291 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 292 | C5×Q8 | — | 2 | 1 | no | — |
| 293 | C5×Q8 | #102 | 1 | 1 | yes | characteristic |
| 294 | C5×D4 | — | 2 | 1 | no | — |
| 295 | C5×D4 | — | 2 | 1 | no | — |
| 296 | C5×D4 | — | 2 | 2 | no | — |
| 297 | C5×D4 | — | 4 | 2 | no | — |
| 298 | C5×D4 | — | 4 | 2 | no | — |
| 299 | C5×D4 | — | 4 | 1 | no | — |
| 300 | C5×D4 | — | 4 | 1 | no | — |
| 301 | C5×D4 | #102 | 1 | 1 | yes | characteristic |
| 302 | C2×C4×C5 | — | 2 | 1 | no | — |
| 303 | C2×C4×C5 | — | 4 | 2 | no | — |
| 304 | C2×C4×C5 | — | 4 | 1 | no | — |
| 305 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 306 | C22⋊D5 | — | 2 | 1 | no | — |
| 307 | C22⋊D5 | — | 2 | 1 | no | — |
| 308 | C22⋊D5 | — | 2 | 1 | no | — |
| 309 | C22⋊D5 | — | 4 | 2 | no | — |
| 310 | C22⋊D5 | — | 4 | 2 | no | — |
| 311 | C22⋊D5 | — | 4 | 2 | no | — |
| 312 | C22⋊D5 | — | 4 | 2 | no | — |
| 313 | C22⋊D5 | — | 4 | 1 | no | — |
| 314 | C22⋊D5 | — | 4 | 1 | no | — |
| 315 | C22⋊D5 | — | 4 | 2 | no | — |
| 316 | C22⋊D5 | — | 4 | 1 | no | — |
| 317 | C22⋊D5 | — | 4 | 2 | no | — |
| 318 | C2×Dic5 | — | 2 | 1 | no | — |
| 319 | C2×Dic5 | — | 4 | 2 | no | — |
| 320 | C2×Dic5 | — | 4 | 1 | no | — |
| 321 | C2×Dic5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 322 | D20 | — | 2 | 1 | no | — |
| 323 | D20 | — | 2 | 2 | no | — |
| 324 | D20 | — | 2 | 1 | no | — |
| 325 | D20 | — | 4 | 2 | no | — |
| 326 | D20 | — | 4 | 2 | no | — |
| 327 | D20 | — | 4 | 1 | no | — |
| 328 | D20 | — | 4 | 1 | no | — |
| 329 | D20 | #102 | 1 | 1 | yes | characteristic |
| 330 | C4×D5 | — | 2 | 1 | no | — |
| 331 | C4×D5 | — | 2 | 1 | no | — |
| 332 | C4×D5 | — | 2 | 1 | no | — |
| 333 | C4×D5 | — | 4 | 2 | no | — |
| 334 | C4×D5 | — | 4 | 2 | no | — |
| 335 | C4×D5 | — | 4 | 1 | no | — |
| 336 | C4×D5 | — | 4 | 1 | no | — |
| 337 | C4×D5 | — | 4 | 1 | no | — |
| 338 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 339 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 340 | C4×D5 | C2×D8 | 1 | 1 | yes | characteristic |
| 341 | C4×D5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 342 | Dic10 | — | 2 | 1 | no | — |
| 343 | Dic10 | — | 2 | 1 | no | — |
| 344 | Dic10 | — | 4 | 1 | no | — |
| 345 | Dic10 | #102 | 1 | 1 | yes | characteristic |
| 346 | #170 | — | 8 | 1 | no | — |
| 347 | C5×C8 | — | 2 | 1 | no | — |
| 348 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 349 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 350 | #168 | — | 2 | 1 | no | — |
| 351 | #168 | #120 | 1 | 1 | yes | characteristic |
| 352 | #168 | #120 | 1 | 1 | yes | characteristic |
| 353 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 354 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 355 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 356 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 357 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 358 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 359 | H(5,𝔽2) | — | 20 | 1 | no | — |
| 360 | H(5,𝔽2) | — | 20 | 2 | no | — |
| 361 | H(5,𝔽2) | — | 20 | 1 | no | — |
| 362 | C2×#41 | — | 5 | 1 | no | — |
| 363 | C2×#41 | — | 10 | 1 | no | — |
| 364 | C2×#41 | — | 10 | 2 | no | — |
| 365 | C2×#41 | — | 20 | 1 | no | — |
| 366 | C22×D4 | — | 10 | 1 | no | — |
| 367 | C22×D4 | — | 10 | 2 | no | — |
| 368 | C22×D4 | — | 20 | 1 | no | — |
| 369 | C22×D4 | — | 20 | 2 | no | — |
| 370 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 371 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 372 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 373 | AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 374 | AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 375 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 376 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 377 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 378 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 379 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 380 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 381 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 383 | AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 384 | #135 | — | 2 | 1 | no | — |
| 385 | #135 | — | 5 | 1 | no | — |
| 386 | #135 | — | 5 | 1 | no | — |
| 387 | #135 | — | 5 | 1 | no | — |
| 388 | #135 | — | 10 | 1 | no | — |
| 389 | #135 | — | 10 | 1 | no | — |
| 390 | #135 | — | 10 | 1 | no | — |
| 391 | #135 | — | 10 | 1 | no | — |
| 392 | #135 | — | 10 | 2 | no | — |
| 393 | #135 | — | 10 | 2 | no | — |
| 394 | #135 | — | 10 | 1 | no | — |
| 395 | #135 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 396 | C2×Q16 | — | 5 | 1 | no | — |
| 397 | C2×SD16 | — | 10 | 1 | no | — |
| 398 | C2×SD16 | — | 10 | 2 | no | — |
| 399 | C2×D8 | — | 2 | 1 | no | — |
| 400 | C2×D8 | — | 5 | 2 | no | — |
| 401 | C2×D8 | — | 5 | 2 | no | — |
| 402 | C2×D8 | — | 5 | 1 | no | — |
| 403 | C2×D8 | — | 5 | 1 | no | — |
| 404 | C2×D8 | — | 10 | 1 | no | — |
| 405 | C2×D8 | — | 10 | 1 | no | — |
| 406 | C2×D8 | — | 10 | 1 | no | — |
| 407 | C2×D8 | — | 10 | 1 | no | — |
| 408 | C2×D8 | — | 10 | 1 | no | — |
| 409 | C2×D8 | — | 10 | 2 | no | — |
| 410 | C2×D8 | — | 10 | 2 | no | — |
| 411 | C2×D8 | — | 10 | 2 | no | — |
| 412 | C2×D8 | — | 10 | 1 | no | — |
| 413 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 414 | #131 | — | 5 | 1 | no | — |
| 415 | #131 | — | 5 | 1 | no | — |
| 416 | #131 | — | 5 | 1 | no | — |
| 417 | #131 | — | 10 | 1 | no | — |
| 418 | #131 | — | 10 | 1 | no | — |
| 419 | #131 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 420 | C2×M16 | — | 5 | 1 | no | — |
| 421 | C2×M16 | — | 10 | 1 | no | — |
| 422 | C2×M16 | — | 10 | 1 | no | — |
| 423 | C22×C8 | — | 5 | 1 | no | — |
| 424 | C22×C8 | — | 10 | 1 | no | — |
| 425 | #117 | — | 10 | 1 | no | — |
| 426 | M32 | — | 10 | 1 | no | — |
| 427 | M32 | — | 10 | 1 | no | — |
| 428 | M32 | — | 10 | 1 | no | — |
| 429 | M32 | — | 10 | 1 | no | — |
| 430 | C2×C16 | — | 10 | 1 | no | — |
| 431 | C2×C16 | — | 10 | 1 | no | — |
| 432 | #108 | — | 10 | 1 | no | — |
| 433 | #108 | — | 10 | 1 | no | — |
| 434 | #107 | — | 10 | 1 | no | — |
| 435 | #106 | — | 10 | 1 | no | — |
| 436 | #104 | — | 20 | 1 | no | — |
| 437 | #104 | — | 20 | 1 | no | — |
| 438 | C22×C5 | — | 2 | 1 | no | — |
| 439 | C22×C5 | — | 4 | 2 | no | — |
| 440 | C22×C5 | — | 4 | 1 | no | — |
| 441 | C22×C5 | — | 16 | 1 | no | — |
| 442 | C22×C5 | — | 16 | 2 | no | — |
| 443 | C22×C5 | #418 | 1 | 1 | yes | characteristic |
| 444 | C2×D5 | — | 2 | 1 | no | — |
| 445 | C2×D5 | — | 4 | 1 | no | — |
| 446 | C2×D5 | — | 4 | 2 | no | — |
| 447 | C2×D5 | — | 4 | 2 | no | — |
| 448 | C2×D5 | — | 4 | 1 | no | — |
| 449 | C2×D5 | — | 8 | 4 | no | — |
| 450 | C2×D5 | — | 8 | 2 | no | — |
| 451 | C2×D5 | — | 16 | 2 | no | — |
| 452 | C2×D5 | — | 16 | 2 | no | — |
| 453 | C2×D5 | — | 16 | 2 | no | — |
| 454 | C2×D5 | — | 16 | 1 | no | — |
| 455 | C2×D5 | — | 16 | 2 | no | — |
| 456 | C2×D5 | #447 | 1 | 1 | yes | characteristic |
| 457 | C2×D5 | #450 | 1 | 1 | yes | characteristic |
| 458 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 459 | C4×C5 | — | 2 | 1 | no | — |
| 460 | C4×C5 | — | 4 | 1 | no | — |
| 461 | C4×C5 | #379 | 1 | 1 | yes | characteristic |
| 462 | C4×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 463 | Dic5 | — | 2 | 1 | no | — |
| 464 | Dic5 | — | 4 | 1 | no | — |
| 465 | Dic5 | #447 | 1 | 1 | yes | characteristic |
| 466 | Dic5 | #450 | 1 | 1 | yes | characteristic |
| 467 | C24 | — | 20 | 1 | no | — |
| 468 | C24 | — | 20 | 2 | no | — |
| 469 | #41 | — | 2 | 2 | no | — |
| 470 | #41 | — | 2 | 1 | no | — |
| 471 | #41 | — | 4 | 1 | no | — |
| 472 | #41 | — | 5 | 1 | no | — |
| 473 | #41 | — | 5 | 1 | no | — |
| 474 | #41 | — | 5 | 1 | no | — |
| 475 | #41 | — | 10 | 1 | no | — |
| 476 | #41 | — | 10 | 2 | no | — |
| 477 | #41 | — | 10 | 1 | no | — |
| 478 | #41 | — | 10 | 1 | no | — |
| 479 | #41 | — | 10 | 1 | no | — |
| 480 | #41 | — | 10 | 2 | no | — |
| 481 | #41 | — | 10 | 2 | no | — |
| 482 | #41 | — | 10 | 1 | no | — |
| 483 | #41 | — | 20 | 1 | no | — |
| 484 | #41 | — | 20 | 2 | no | — |
| 485 | #41 | — | 20 | 1 | no | — |
| 486 | #41 | — | 20 | 2 | no | — |
| 487 | #41 | — | 20 | 1 | no | — |
| 488 | #41 | — | 20 | 2 | no | — |
| 489 | #41 | — | 20 | 1 | no | — |
| 490 | #41 | — | 20 | 2 | no | — |
| 491 | #41 | — | 20 | 1 | no | — |
| 492 | #41 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 493 | C2×Q8 | — | 5 | 1 | no | — |
| 494 | C2×Q8 | — | 10 | 1 | no | — |
| 495 | C2×D4 | — | 2 | 2 | no | — |
| 496 | C2×D4 | — | 2 | 1 | no | — |
| 497 | C2×D4 | — | 4 | 2 | no | — |
| 498 | C2×D4 | — | 4 | 1 | no | — |
| 499 | C2×D4 | — | 5 | 1 | no | — |
| 500 | C2×D4 | — | 10 | 2 | no | — |
| 501 | C2×D4 | — | 10 | 2 | no | — |
| 502 | C2×D4 | — | 10 | 1 | no | — |
| 503 | C2×D4 | — | 10 | 2 | no | — |
| 504 | C2×D4 | — | 10 | 1 | no | — |
| 505 | C2×D4 | — | 10 | 2 | no | — |
| 506 | C2×D4 | — | 10 | 2 | no | — |
| 507 | C2×D4 | — | 10 | 1 | no | — |
| 508 | C2×D4 | — | 20 | 1 | no | — |
| 509 | C2×D4 | — | 20 | 2 | no | — |
| 510 | C2×D4 | — | 20 | 1 | no | — |
| 511 | C2×D4 | — | 20 | 1 | no | — |
| 512 | C2×D4 | — | 20 | 1 | no | — |
| 513 | C2×D4 | — | 20 | 2 | no | — |
| 514 | C2×D4 | — | 20 | 2 | no | — |
| 515 | C2×D4 | — | 20 | 2 | no | — |
| 516 | C2×D4 | — | 20 | 2 | no | — |
| 517 | C2×D4 | — | 20 | 1 | no | — |
| 518 | C2×D4 | — | 20 | 2 | no | — |
| 519 | C2×D4 | — | 20 | 2 | no | — |
| 520 | C2×D4 | — | 20 | 2 | no | — |
| 521 | C2×D4 | — | 20 | 2 | no | — |
| 522 | C2×D4 | — | 20 | 1 | no | — |
| 523 | C2×D4 | — | 20 | 2 | no | — |
| 524 | C2×D4 | — | 20 | 2 | no | — |
| 525 | C2×D4 | — | 20 | 2 | no | — |
| 526 | C2×D4 | — | 20 | 2 | no | — |
| 527 | C2×D4 | — | 20 | 1 | no | — |
| 528 | C22×C4 | — | 5 | 1 | no | — |
| 529 | C22×C4 | — | 10 | 1 | no | — |
| 530 | C22×C4 | — | 20 | 1 | no | — |
| 531 | C22×C4 | — | 20 | 2 | no | — |
| 532 | Q16 | — | 5 | 1 | no | — |
| 533 | Q16 | — | 10 | 1 | no | — |
| 534 | Q16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 535 | SD16 | — | 2 | 2 | no | — |
| 536 | SD16 | — | 2 | 1 | no | — |
| 537 | SD16 | — | 10 | 2 | no | — |
| 538 | SD16 | — | 10 | 1 | no | — |
| 539 | SD16 | — | 10 | 1 | no | — |
| 540 | SD16 | — | 10 | 2 | no | — |
| 541 | SD16 | — | 10 | 2 | no | — |
| 542 | SD16 | — | 10 | 1 | no | — |
| 543 | D8 | — | 2 | 2 | no | — |
| 544 | D8 | — | 2 | 1 | no | — |
| 545 | D8 | — | 5 | 2 | no | — |
| 546 | D8 | — | 5 | 1 | no | — |
| 547 | D8 | — | 10 | 2 | no | — |
| 548 | D8 | — | 10 | 2 | no | — |
| 549 | D8 | — | 10 | 1 | no | — |
| 550 | D8 | — | 10 | 2 | no | — |
| 551 | D8 | — | 10 | 2 | no | — |
| 552 | D8 | — | 10 | 2 | no | — |
| 553 | D8 | — | 10 | 1 | no | — |
| 554 | D8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 555 | D8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 556 | M16 | — | 2 | 1 | no | — |
| 557 | M16 | — | 5 | 1 | no | — |
| 558 | M16 | — | 10 | 1 | no | — |
| 559 | M16 | — | 10 | 1 | no | — |
| 560 | M16 | — | 10 | 1 | no | — |
| 561 | M16 | — | 10 | 1 | no | — |
| 562 | M16 | — | 20 | 1 | no | — |
| 563 | M16 | — | 20 | 1 | no | — |
| 564 | M16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 565 | C2×C8 | — | 2 | 1 | no | — |
| 566 | C2×C8 | — | 5 | 1 | no | — |
| 567 | C2×C8 | — | 5 | 1 | no | — |
| 568 | C2×C8 | — | 5 | 1 | no | — |
| 569 | C2×C8 | — | 5 | 1 | no | — |
| 570 | C2×C8 | — | 5 | 1 | no | — |
| 571 | C2×C8 | — | 10 | 1 | no | — |
| 572 | C2×C8 | — | 10 | 1 | no | — |
| 573 | C2×C8 | — | 10 | 1 | no | — |
| 574 | C2×C8 | — | 10 | 1 | no | — |
| 575 | C2×C8 | — | 20 | 1 | no | — |
| 576 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 577 | C4⋊C4 | — | 20 | 1 | no | — |
| 578 | C22⋊C4 | — | 20 | 1 | no | — |
| 579 | C42 | — | 20 | 1 | no | — |
| 580 | C16 | — | 20 | 1 | no | — |
| 581 | C16 | — | 20 | 1 | no | — |
| 582 | C2×C5 | — | 2 | 1 | no | — |
| 583 | C2×C5 | — | 4 | 1 | no | — |
| 584 | C2×C5 | — | 8 | 2 | no | — |
| 585 | C2×C5 | — | 8 | 1 | no | — |
| 586 | C2×C5 | #1786 | 1 | 1 | yes | characteristic |
| 587 | D5 | — | 2 | 1 | no | — |
| 588 | D5 | — | 2 | 1 | no | — |
| 589 | D5 | — | 4 | 1 | no | — |
| 590 | D5 | — | 8 | 2 | no | — |
| 591 | D5 | — | 8 | 1 | no | — |
| 592 | C23 | — | 4 | 2 | no | — |
| 593 | C23 | — | 4 | 1 | no | — |
| 594 | C23 | — | 5 | 1 | no | — |
| 595 | C23 | — | 10 | 1 | no | — |
| 596 | C23 | — | 20 | 2 | no | — |
| 597 | C23 | — | 20 | 1 | no | — |
| 598 | C23 | — | 20 | 2 | no | — |
| 599 | C23 | — | 20 | 2 | no | — |
| 600 | C23 | — | 20 | 2 | no | — |
| 601 | C23 | — | 20 | 2 | no | — |
| 602 | C23 | — | 20 | 1 | no | — |
| 603 | C23 | — | 80 | 2 | no | — |
| 604 | C23 | — | 80 | 4 | no | — |
| 605 | Q8 | — | 2 | 1 | no | — |
| 606 | Q8 | — | 5 | 1 | no | — |
| 607 | Q8 | — | 10 | 1 | no | — |
| 608 | Q8 | — | 10 | 1 | no | — |
| 609 | Q8 | — | 20 | 1 | no | — |
| 610 | Q8 | #4007 | 1 | 1 | yes | characteristic |
| 611 | D4 | — | 2 | 1 | no | — |
| 612 | D4 | — | 2 | 1 | no | — |
| 613 | D4 | — | 2 | 2 | no | — |
| 614 | D4 | — | 4 | 2 | no | — |
| 615 | D4 | — | 4 | 2 | no | — |
| 616 | D4 | — | 4 | 1 | no | — |
| 617 | D4 | — | 4 | 1 | no | — |
| 618 | D4 | — | 5 | 1 | no | — |
| 619 | D4 | — | 10 | 1 | no | — |
| 620 | D4 | — | 10 | 1 | no | — |
| 621 | D4 | — | 10 | 1 | no | — |
| 622 | D4 | — | 10 | 1 | no | — |
| 623 | D4 | — | 10 | 2 | no | — |
| 624 | D4 | — | 10 | 1 | no | — |
| 625 | D4 | — | 20 | 2 | no | — |
| 626 | D4 | — | 20 | 1 | no | — |
| 627 | D4 | — | 20 | 2 | no | — |
| 628 | D4 | — | 20 | 2 | no | — |
| 629 | D4 | — | 20 | 1 | no | — |
| 630 | D4 | — | 20 | 2 | no | — |
| 631 | D4 | — | 20 | 2 | no | — |
| 632 | D4 | — | 20 | 2 | no | — |
| 633 | D4 | — | 20 | 2 | no | — |
| 634 | D4 | — | 20 | 1 | no | — |
| 635 | D4 | — | 20 | 2 | no | — |
| 636 | D4 | — | 20 | 1 | no | — |
| 637 | D4 | — | 20 | 1 | no | — |
| 638 | D4 | #4007 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | — | 2 | 1 | no | — |
| 640 | C2×C4 | — | 4 | 2 | no | — |
| 641 | C2×C4 | — | 4 | 1 | no | — |
| 642 | C2×C4 | — | 5 | 1 | no | — |
| 643 | C2×C4 | — | 5 | 1 | no | — |
| 644 | C2×C4 | — | 5 | 1 | no | — |
| 645 | C2×C4 | — | 5 | 1 | no | — |
| 646 | C2×C4 | — | 5 | 1 | no | — |
| 647 | C2×C4 | — | 10 | 1 | no | — |
| 648 | C2×C4 | — | 10 | 1 | no | — |
| 649 | C2×C4 | — | 10 | 1 | no | — |
| 650 | C2×C4 | — | 10 | 1 | no | — |
| 651 | C2×C4 | — | 20 | 2 | no | — |
| 652 | C2×C4 | — | 20 | 1 | no | — |
| 653 | C2×C4 | — | 20 | 2 | no | — |
| 654 | C2×C4 | — | 20 | 1 | no | — |
| 655 | C2×C4 | — | 20 | 1 | no | — |
| 656 | C2×C4 | — | 20 | 2 | no | — |
| 657 | C2×C4 | — | 20 | 1 | no | — |
| 658 | C2×C4 | — | 40 | 1 | no | — |
| 659 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 660 | C8 | — | 2 | 1 | no | — |
| 661 | C8 | — | 5 | 1 | no | — |
| 662 | C8 | — | 5 | 1 | no | — |
| 663 | C8 | — | 10 | 1 | no | — |
| 664 | C8 | — | 40 | 1 | no | — |
| 665 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 666 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 667 | C5 | #12750 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 668 | C22 | — | 2 | 1 | no | — |
| 669 | C22 | — | 4 | 2 | no | — |
| 670 | C22 | — | 4 | 1 | no | — |
| 671 | C22 | — | 5 | 1 | no | — |
| 672 | C22 | — | 5 | 1 | no | — |
| 673 | C22 | — | 10 | 1 | no | — |
| 674 | C22 | — | 16 | 1 | no | — |
| 675 | C22 | — | 16 | 2 | no | — |
| 676 | C22 | — | 20 | 1 | no | — |
| 677 | C22 | — | 20 | 2 | no | — |
| 678 | C22 | — | 20 | 2 | no | — |
| 679 | C22 | — | 20 | 1 | no | — |
| 680 | C22 | — | 40 | 4 | no | — |
| 681 | C22 | — | 40 | 2 | no | — |
| 682 | C22 | — | 80 | 1 | no | — |
| 683 | C22 | — | 80 | 2 | no | — |
| 684 | C22 | — | 80 | 2 | no | — |
| 685 | C22 | — | 80 | 2 | no | — |
| 686 | C22 | — | 80 | 2 | no | — |
| 687 | C22 | #65767 | 1 | 1 | yes | characteristic |
| 688 | C4 | — | 2 | 1 | no | — |
| 689 | C4 | — | 4 | 1 | no | — |
| 690 | C4 | — | 5 | 1 | no | — |
| 691 | C4 | — | 5 | 1 | no | — |
| 692 | C4 | — | 10 | 1 | no | — |
| 693 | C4 | — | 20 | 1 | no | — |
| 694 | C4 | — | 80 | 1 | no | — |
| 695 | C4 | C2×#4007 | 1 | 1 | yes | characteristic |
| 696 | C4 | #65800 | 1 | 1 | yes | characteristic |
| 697 | C2 | — | 2 | 1 | no | — |
| 698 | C2 | — | 4 | 1 | no | — |
| 699 | C2 | — | 8 | 2 | no | — |
| 700 | C2 | — | 8 | 1 | no | — |
| 701 | C2 | — | 10 | 1 | no | — |
| 702 | C2 | — | 10 | 1 | no | — |
| 703 | C2 | — | 20 | 1 | no | — |
| 704 | C2 | — | 40 | 2 | no | — |
| 705 | C2 | — | 40 | 1 | no | — |
| 706 | C2 | #10604928 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10604860 | C2 | semidirect |
| 3. #10604854 | C2 | semidirect |
| 4. C2×#64906 | C2 | semidirect |
| 5. #10604786 | C2 | semidirect |
| 6. #10604779 | C2 | semidirect |
| 7. #10604776 | C2 | semidirect |
| 9. C5×#576 | C4 | semidirect |
| 16. #66103 | C4 | semidirect |
| 20. #66091 | C4 | semidirect |
| 23. #66086 | C4 | semidirect |
| 26. C2×#3995 | C22 | semidirect |
| 27. #65721 | C22 | semidirect |
| 28. D5⋊M32 | C22 | semidirect |
| 29. C2×#3990 | C22 | semidirect |
| 256. #576 | AGL(1,𝔽5) | semidirect |
| 667. C5 | #12750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#576 | 2 |
| #10604860 | 2 |
| #10604854 | 2 |
| C2×#64906 | 2 |
| #10604786 | 2 |
| #10604779 | 2 |
| #10604776 | 2 |
| #12750 | 5 |