Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
882 conjugacy classes of subgroups.
The subgroup lattice has 694 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D5×#578 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D5⋊#359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10604856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D5⋊#362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#64908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10604782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D5⋊#350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D5×2−1+4 | — | 2 | 1 | no | — |
| 9 | C5×#578 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #66172 | — | 2 | 1 | no | — |
| 11 | #66113 | — | 2 | 2 | no | — |
| 12 | #66113 | — | 2 | 1 | no | — |
| 13 | D5×#137 | — | 2 | 2 | no | — |
| 14 | D5×#137 | — | 2 | 1 | no | — |
| 15 | #66105 | — | 2 | 1 | no | — |
| 16 | #66105 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | D5×#135 | — | 2 | 1 | no | — |
| 18 | D5×#135 | C22 | 1 | 1 | yes | characteristic |
| 19 | #66100 | — | 2 | 1 | no | — |
| 20 | #66100 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×D5×Q16 | — | 2 | 1 | no | — |
| 22 | C2×D5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 23 | #66087 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | D5×#131 | C22 | 1 | 1 | yes | characteristic |
| 25 | #65793 | — | 2 | 1 | no | — |
| 26 | D5⋊#108 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#3994 | C22 | 1 | 1 | yes | characteristic |
| 28 | D5⋊M32 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×D5⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 30 | #64932 | — | 2 | 1 | no | — |
| 31 | #64910 | — | 2 | 2 | no | — |
| 32 | #64909 | — | 2 | 1 | no | — |
| 33 | #64908 | — | 2 | 2 | no | — |
| 34 | #64908 | — | 2 | 1 | no | — |
| 35 | #64905 | — | 2 | 1 | no | — |
| 36 | #64904 | — | 2 | 1 | no | — |
| 37 | #64899 | — | 2 | 1 | no | — |
| 38 | #64898 | — | 2 | 1 | no | — |
| 39 | #12749 | — | 5 | 1 | no | maximal, Sylow |
| 40 | C5×2−1+4 | — | 2 | 1 | no | — |
| 41 | #4150 | — | 2 | 1 | no | — |
| 42 | #4150 | — | 2 | 2 | no | — |
| 43 | #4150 | — | 2 | 1 | no | — |
| 44 | #4150 | — | 4 | 2 | no | — |
| 45 | #4150 | — | 4 | 1 | no | — |
| 46 | D5×#41 | — | 2 | 2 | no | — |
| 47 | D5×#41 | — | 2 | 1 | no | — |
| 48 | D5×#41 | — | 4 | 2 | no | — |
| 49 | D5×#41 | — | 4 | 1 | no | — |
| 50 | D5×#41 | D4 | 1 | 1 | yes | characteristic |
| 51 | #4147 | — | 2 | 2 | no | — |
| 52 | #4147 | — | 2 | 1 | no | — |
| 53 | #4147 | — | 4 | 1 | no | — |
| 54 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 55 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 56 | C2×Q8×D5 | — | 4 | 1 | no | — |
| 57 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 58 | D5⋊M16 | — | 2 | 1 | no | — |
| 59 | C5×#137 | — | 2 | 2 | no | — |
| 60 | C5×#137 | — | 2 | 1 | no | — |
| 61 | C5×#135 | — | 2 | 1 | no | — |
| 62 | C5×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 64 | C2×C5×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C5×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | #4097 | — | 2 | 2 | no | — |
| 67 | #4097 | — | 2 | 1 | no | — |
| 68 | #4096 | — | 2 | 2 | no | — |
| 69 | #4096 | — | 2 | 1 | no | — |
| 70 | #4094 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×#689 | — | 2 | 2 | no | — |
| 72 | C2×#689 | — | 2 | 1 | no | — |
| 73 | #4088 | — | 2 | 2 | no | — |
| 74 | #4088 | — | 2 | 1 | no | — |
| 75 | #4065 | — | 2 | 1 | no | — |
| 76 | #4065 | D4 | 1 | 1 | yes | characteristic |
| 77 | #4064 | — | 2 | 2 | no | — |
| 78 | #4064 | — | 2 | 2 | no | — |
| 79 | #4064 | — | 2 | 2 | no | — |
| 80 | D5×Q16 | — | 2 | 2 | no | — |
| 81 | D5×Q16 | — | 2 | 2 | no | — |
| 82 | D5×Q16 | — | 2 | 1 | no | — |
| 83 | D5×Q16 | — | 2 | 1 | no | — |
| 84 | D5×Q16 | — | 2 | 1 | no | — |
| 85 | D5×Q16 | — | 2 | 1 | no | — |
| 86 | D5×Q16 | D4 | 1 | 1 | yes | characteristic |
| 87 | D5×Q16 | D4 | 1 | 2 | yes | — |
| 88 | D5×Q16 | D4 | 1 | 2 | yes | — |
| 89 | #4062 | — | 2 | 2 | no | — |
| 90 | #4062 | — | 2 | 1 | no | — |
| 91 | #4061 | — | 2 | 2 | no | — |
| 92 | #4061 | — | 2 | 2 | no | — |
| 93 | #4061 | — | 2 | 2 | no | — |
| 94 | D5×SD16 | — | 2 | 2 | no | — |
| 95 | D5×SD16 | — | 2 | 1 | no | — |
| 96 | #4058 | — | 2 | 1 | no | — |
| 97 | #4058 | D4 | 1 | 1 | yes | characteristic |
| 98 | D5×D8 | D4 | 1 | 1 | yes | characteristic |
| 99 | #4055 | — | 2 | 1 | no | — |
| 100 | #4055 | — | 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 | C2×Dic20 | — | 2 | 1 | no | — |
| 106 | C2×Dic20 | C2×C4 | 1 | 1 | yes | characteristic |
| 107 | #4050 | — | 2 | 1 | no | — |
| 108 | #4050 | 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 | #4009 | — | 4 | 1 | no | — |
| 114 | #4007 | — | 4 | 1 | no | — |
| 115 | #3998 | — | 2 | 1 | no | — |
| 116 | C2×#674 | — | 2 | 1 | no | — |
| 117 | #3996 | — | 2 | 1 | no | — |
| 118 | #3995 | — | 2 | 1 | no | — |
| 119 | #3994 | — | 2 | 1 | no | — |
| 120 | #3994 | — | 2 | 1 | no | — |
| 121 | #3990 | — | 2 | 1 | no | — |
| 122 | D5⋊C16 | — | 2 | 1 | no | — |
| 123 | D5⋊C16 | — | 2 | 1 | no | — |
| 124 | D5⋊C16 | — | 2 | 1 | no | — |
| 125 | C2×#578 | — | 5 | 1 | no | — |
| 126 | C2×#362 | — | 5 | 1 | no | — |
| 127 | C2×#359 | — | 5 | 1 | no | — |
| 128 | #2139 | — | 5 | 1 | no | — |
| 129 | C2×#358 | — | 5 | 1 | no | — |
| 130 | C2×#350 | — | 5 | 1 | no | — |
| 131 | #1816 | — | 5 | 1 | no | — |
| 132 | C22×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 133 | C5×#41 | — | 2 | 2 | no | — |
| 134 | C5×#41 | — | 2 | 1 | no | — |
| 135 | C5×#41 | — | 4 | 2 | no | — |
| 136 | C5×#41 | — | 4 | 1 | no | — |
| 137 | C5×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 139 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 140 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 141 | #713 | — | 2 | 2 | no | — |
| 142 | #713 | — | 2 | 1 | no | — |
| 143 | #713 | — | 4 | 2 | no | — |
| 144 | #713 | — | 4 | 1 | no | — |
| 145 | #713 | SD16 | 1 | 1 | yes | characteristic |
| 146 | Q8×D5 | — | 2 | 2 | no | — |
| 147 | Q8×D5 | — | 2 | 2 | no | — |
| 148 | Q8×D5 | — | 2 | 1 | no | — |
| 149 | Q8×D5 | — | 2 | 2 | no | — |
| 150 | Q8×D5 | — | 2 | 2 | no | — |
| 151 | Q8×D5 | — | 4 | 2 | no | — |
| 152 | Q8×D5 | — | 4 | 2 | no | — |
| 153 | Q8×D5 | — | 4 | 2 | no | — |
| 154 | Q8×D5 | — | 4 | 1 | no | — |
| 155 | Q8×D5 | — | 4 | 1 | no | — |
| 156 | Q8×D5 | — | 4 | 1 | no | — |
| 157 | Q8×D5 | — | 4 | 1 | no | — |
| 158 | Q8×D5 | D8 | 1 | 1 | yes | characteristic |
| 159 | #711 | — | 2 | 1 | no | — |
| 160 | #711 | — | 2 | 2 | no | — |
| 161 | #711 | — | 2 | 1 | no | — |
| 162 | #711 | — | 4 | 2 | no | — |
| 163 | #711 | — | 4 | 2 | no | — |
| 164 | #711 | — | 4 | 2 | no | — |
| 165 | #711 | — | 4 | 2 | no | — |
| 166 | #711 | — | 4 | 2 | no | — |
| 167 | #711 | — | 4 | 1 | no | — |
| 168 | #711 | — | 4 | 1 | no | — |
| 169 | #711 | SD16 | 1 | 1 | yes | characteristic |
| 170 | D4×D5 | — | 2 | 1 | no | — |
| 171 | D4×D5 | — | 2 | 1 | no | — |
| 172 | D4×D5 | — | 4 | 2 | no | — |
| 173 | D4×D5 | — | 4 | 1 | no | — |
| 174 | D4×D5 | D8 | 1 | 1 | yes | characteristic |
| 175 | #709 | — | 2 | 1 | no | — |
| 176 | #709 | — | 2 | 2 | no | — |
| 177 | #709 | — | 2 | 1 | no | — |
| 178 | #709 | — | 4 | 2 | no | — |
| 179 | #709 | — | 4 | 2 | no | — |
| 180 | #709 | — | 4 | 2 | no | — |
| 181 | #709 | — | 4 | 2 | no | — |
| 182 | #709 | — | 4 | 2 | no | — |
| 183 | #709 | — | 4 | 1 | no | — |
| 184 | #709 | — | 4 | 1 | no | — |
| 185 | #709 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×D5 | — | 2 | 1 | no | — |
| 187 | C2×C4×D5 | — | 4 | 2 | no | — |
| 188 | C2×C4×D5 | — | 4 | 2 | no | — |
| 189 | C2×C4×D5 | — | 4 | 1 | no | — |
| 190 | C2×C4×D5 | — | 4 | 1 | no | — |
| 191 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×Dic10 | — | 2 | 2 | no | — |
| 193 | C2×Dic10 | — | 2 | 1 | no | — |
| 194 | C2×Dic10 | — | 4 | 2 | no | — |
| 195 | C2×Dic10 | — | 4 | 2 | no | — |
| 196 | C2×Dic10 | — | 4 | 1 | no | — |
| 197 | C2×Dic10 | — | 4 | 1 | no | — |
| 198 | #704 | — | 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 | D5⋊C8 | — | 4 | 1 | no | — |
| 203 | C5×Q16 | — | 2 | 2 | no | — |
| 204 | C5×Q16 | — | 2 | 1 | no | — |
| 205 | C5×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 206 | C5×Q16 | C22⋊C4 | 1 | 2 | yes | — |
| 207 | C5×SD16 | — | 2 | 2 | no | — |
| 208 | C5×SD16 | — | 2 | 1 | no | — |
| 209 | C5×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 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 | 2 | no | — |
| 215 | #689 | — | 2 | 2 | no | — |
| 216 | #689 | — | 2 | 2 | no | — |
| 217 | #689 | — | 2 | 1 | no | — |
| 218 | #689 | — | 2 | 2 | no | — |
| 219 | #688 | — | 2 | 2 | no | — |
| 220 | #688 | — | 2 | 1 | no | — |
| 221 | #687 | — | 2 | 2 | no | — |
| 222 | #687 | — | 2 | 1 | no | — |
| 223 | #686 | — | 2 | 1 | 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 | — | 2 | 2 | no | — |
| 229 | Dic20 | — | 2 | 1 | no | — |
| 230 | Dic20 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 231 | Dic20 | C22⋊C4 | 1 | 2 | yes | — |
| 232 | D40 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 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 | C2×2−1+4 | — | 10 | 1 | no | — |
| 248 | #578 | — | 5 | 1 | no | — |
| 249 | #578 | — | 5 | 1 | no | — |
| 250 | #578 | — | 5 | 1 | no | — |
| 251 | #578 | — | 10 | 1 | no | — |
| 252 | #578 | — | 10 | 1 | no | — |
| 253 | #578 | — | 10 | 1 | no | — |
| 254 | #578 | — | 10 | 2 | no | — |
| 255 | #578 | — | 10 | 1 | no | — |
| 256 | #578 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 257 | C2×#137 | — | 10 | 1 | no | — |
| 258 | C2×#137 | — | 10 | 2 | no | — |
| 259 | C2×#135 | — | 5 | 1 | no | — |
| 260 | C2×#135 | — | 10 | 1 | no | — |
| 261 | C22×Q16 | — | 5 | 1 | no | — |
| 262 | C22×Q16 | — | 10 | 1 | no | — |
| 263 | C2×#131 | — | 5 | 1 | no | — |
| 264 | C2×M32 | — | 5 | 1 | no | — |
| 265 | C22×C16 | — | 5 | 1 | no | — |
| 266 | C2×#108 | — | 5 | 1 | no | — |
| 267 | C2×#107 | — | 5 | 1 | no | — |
| 268 | #417 | — | 10 | 1 | no | — |
| 269 | #362 | — | 10 | 2 | no | — |
| 270 | #359 | — | 10 | 1 | no | — |
| 271 | #359 | — | 10 | 1 | no | — |
| 272 | #358 | — | 10 | 2 | no | — |
| 273 | #358 | — | 10 | 1 | no | — |
| 274 | #357 | — | 10 | 1 | no | — |
| 275 | #350 | — | 10 | 1 | no | — |
| 276 | #350 | — | 10 | 1 | no | — |
| 277 | #343 | — | 10 | 1 | no | — |
| 278 | C22×D5 | — | 2 | 1 | no | — |
| 279 | C22×D5 | — | 4 | 1 | no | — |
| 280 | C22×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 281 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 282 | C2×AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 283 | C5×Q8 | — | 2 | 2 | no | — |
| 284 | C5×Q8 | — | 2 | 1 | no | — |
| 285 | C5×Q8 | — | 4 | 2 | no | — |
| 286 | C5×Q8 | — | 4 | 1 | no | — |
| 287 | C5×Q8 | #102 | 1 | 1 | yes | characteristic |
| 288 | C5×D4 | — | 2 | 1 | no | — |
| 289 | C5×D4 | — | 2 | 1 | no | — |
| 290 | C5×D4 | — | 4 | 2 | no | — |
| 291 | C5×D4 | — | 4 | 1 | no | — |
| 292 | C5×D4 | #102 | 1 | 1 | yes | characteristic |
| 293 | C2×C4×C5 | — | 2 | 1 | no | — |
| 294 | C2×C4×C5 | — | 4 | 2 | no | — |
| 295 | C2×C4×C5 | — | 4 | 2 | no | — |
| 296 | C2×C4×C5 | — | 4 | 1 | no | — |
| 297 | C2×C4×C5 | — | 4 | 1 | no | — |
| 298 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 299 | C22⋊D5 | — | 2 | 1 | no | — |
| 300 | C22⋊D5 | — | 2 | 1 | no | — |
| 301 | C22⋊D5 | — | 2 | 1 | no | — |
| 302 | C22⋊D5 | — | 4 | 2 | no | — |
| 303 | C22⋊D5 | — | 4 | 2 | no | — |
| 304 | C22⋊D5 | — | 4 | 1 | no | — |
| 305 | C22⋊D5 | — | 4 | 1 | no | — |
| 306 | C22⋊D5 | — | 4 | 1 | no | — |
| 307 | C2×Dic5 | — | 2 | 1 | no | — |
| 308 | C2×Dic5 | — | 4 | 2 | no | — |
| 309 | C2×Dic5 | — | 4 | 2 | no | — |
| 310 | C2×Dic5 | — | 4 | 1 | no | — |
| 311 | C2×Dic5 | — | 4 | 1 | no | — |
| 312 | C2×Dic5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 313 | D20 | — | 2 | 1 | no | — |
| 314 | D20 | — | 2 | 1 | no | — |
| 315 | D20 | — | 4 | 2 | no | — |
| 316 | D20 | — | 4 | 1 | no | — |
| 317 | D20 | #102 | 1 | 1 | yes | characteristic |
| 318 | C4×D5 | — | 2 | 1 | no | — |
| 319 | C4×D5 | — | 2 | 1 | no | — |
| 320 | C4×D5 | — | 2 | 1 | no | — |
| 321 | C4×D5 | — | 4 | 2 | no | — |
| 322 | C4×D5 | — | 4 | 2 | no | — |
| 323 | C4×D5 | — | 4 | 2 | no | — |
| 324 | C4×D5 | — | 4 | 2 | no | — |
| 325 | C4×D5 | — | 4 | 2 | no | — |
| 326 | C4×D5 | — | 4 | 1 | no | — |
| 327 | C4×D5 | — | 4 | 2 | no | — |
| 328 | C4×D5 | — | 4 | 1 | no | — |
| 329 | C4×D5 | — | 4 | 1 | no | — |
| 330 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 331 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 332 | C4×D5 | C2×D8 | 1 | 1 | yes | characteristic |
| 333 | C4×D5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 334 | Dic10 | — | 2 | 1 | no | — |
| 335 | Dic10 | — | 2 | 2 | no | — |
| 336 | Dic10 | — | 2 | 1 | no | — |
| 337 | Dic10 | — | 4 | 2 | no | — |
| 338 | Dic10 | — | 4 | 2 | no | — |
| 339 | Dic10 | — | 4 | 2 | no | — |
| 340 | Dic10 | — | 4 | 1 | no | — |
| 341 | Dic10 | — | 4 | 2 | no | — |
| 342 | Dic10 | — | 4 | 1 | no | — |
| 343 | Dic10 | — | 4 | 2 | no | — |
| 344 | Dic10 | #102 | 1 | 1 | yes | characteristic |
| 345 | #170 | — | 8 | 1 | no | — |
| 346 | C5×C8 | — | 2 | 1 | no | — |
| 347 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 348 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 349 | #168 | — | 2 | 1 | no | — |
| 350 | #168 | #120 | 1 | 1 | yes | characteristic |
| 351 | #168 | #120 | 1 | 1 | yes | characteristic |
| 352 | 2−1+4 | — | 2 | 1 | no | — |
| 353 | 2−1+4 | — | 10 | 1 | no | — |
| 354 | 2−1+4 | — | 10 | 2 | no | — |
| 355 | 2−1+4 | — | 10 | 1 | no | — |
| 356 | 2−1+4 | — | 10 | 2 | no | — |
| 357 | 2−1+4 | — | 10 | 1 | no | — |
| 358 | 2−1+4 | — | 20 | 1 | no | — |
| 359 | 2−1+4 | — | 20 | 1 | no | — |
| 360 | 2−1+4 | — | 20 | 2 | no | — |
| 361 | C2×#41 | — | 5 | 1 | no | — |
| 362 | C2×#41 | — | 10 | 1 | no | — |
| 363 | C2×#41 | — | 10 | 2 | no | — |
| 364 | C2×#41 | — | 20 | 1 | no | — |
| 365 | C2×#41 | — | 20 | 2 | no | — |
| 366 | C22×Q8 | — | 10 | 1 | no | — |
| 367 | C22×Q8 | — | 10 | 2 | no | — |
| 368 | C22×Q8 | — | 20 | 1 | no | — |
| 369 | #137 | — | 2 | 2 | no | — |
| 370 | #137 | — | 2 | 1 | no | — |
| 371 | #137 | — | 10 | 2 | no | — |
| 372 | #137 | — | 10 | 1 | no | — |
| 373 | #137 | — | 10 | 1 | no | — |
| 374 | #137 | — | 10 | 2 | no | — |
| 375 | #137 | — | 10 | 2 | no | — |
| 376 | #137 | — | 10 | 2 | no | — |
| 377 | #137 | — | 10 | 2 | no | — |
| 378 | #137 | — | 10 | 2 | no | — |
| 379 | #137 | — | 10 | 2 | no | — |
| 380 | #137 | — | 10 | 2 | no | — |
| 381 | #137 | — | 10 | 2 | no | — |
| 382 | #137 | — | 10 | 1 | no | — |
| 383 | #135 | — | 2 | 1 | no | — |
| 384 | #135 | — | 5 | 1 | no | — |
| 385 | #135 | — | 5 | 1 | no | — |
| 386 | #135 | — | 5 | 1 | no | — |
| 387 | #135 | — | 10 | 1 | no | — |
| 388 | #135 | — | 10 | 1 | no | — |
| 389 | #135 | — | 10 | 1 | no | — |
| 390 | #135 | — | 10 | 1 | no | — |
| 391 | #135 | — | 10 | 2 | no | — |
| 392 | #135 | — | 10 | 2 | no | — |
| 393 | #135 | — | 10 | 1 | no | — |
| 394 | #135 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 395 | C2×Q16 | — | 2 | 1 | no | — |
| 396 | C2×Q16 | — | 5 | 2 | no | — |
| 397 | C2×Q16 | — | 5 | 2 | no | — |
| 398 | C2×Q16 | — | 5 | 1 | no | — |
| 399 | C2×Q16 | — | 5 | 1 | no | — |
| 400 | C2×Q16 | — | 10 | 1 | no | — |
| 401 | C2×Q16 | — | 10 | 1 | no | — |
| 402 | C2×Q16 | — | 10 | 1 | no | — |
| 403 | C2×Q16 | — | 10 | 1 | no | — |
| 404 | C2×Q16 | — | 10 | 1 | no | — |
| 405 | C2×Q16 | — | 10 | 2 | no | — |
| 406 | C2×Q16 | — | 10 | 2 | no | — |
| 407 | C2×Q16 | — | 10 | 2 | no | — |
| 408 | C2×Q16 | — | 10 | 1 | no | — |
| 409 | C2×Q16 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 410 | C2×SD16 | — | 10 | 1 | no | — |
| 411 | C2×SD16 | — | 10 | 2 | no | — |
| 412 | C2×D8 | — | 5 | 1 | no | — |
| 413 | #131 | — | 5 | 1 | no | — |
| 414 | #131 | — | 5 | 1 | no | — |
| 415 | #131 | — | 5 | 1 | no | — |
| 416 | #131 | — | 10 | 1 | no | — |
| 417 | #131 | — | 10 | 1 | no | — |
| 418 | #131 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 419 | C2×M16 | — | 5 | 1 | no | — |
| 420 | C2×M16 | — | 10 | 1 | no | — |
| 421 | C2×M16 | — | 10 | 1 | no | — |
| 422 | C22×C8 | — | 5 | 1 | no | — |
| 423 | C22×C8 | — | 10 | 1 | no | — |
| 424 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 425 | M32 | — | 10 | 1 | no | — |
| 426 | M32 | — | 10 | 1 | no | — |
| 427 | C2×C16 | — | 10 | 1 | no | — |
| 428 | C2×C16 | — | 10 | 1 | no | — |
| 429 | C2×C16 | — | 10 | 1 | no | — |
| 430 | C2×C16 | — | 10 | 1 | no | — |
| 431 | #108 | — | 10 | 1 | no | — |
| 432 | #108 | — | 10 | 1 | no | — |
| 433 | #107 | — | 10 | 1 | no | — |
| 434 | #107 | — | 10 | 1 | no | — |
| 435 | #103 | — | 20 | 1 | no | — |
| 436 | #102 | — | 20 | 1 | no | — |
| 437 | C22×C5 | — | 2 | 1 | no | — |
| 438 | C22×C5 | — | 4 | 1 | no | — |
| 439 | C22×C5 | #418 | 1 | 1 | yes | characteristic |
| 440 | C2×D5 | — | 2 | 1 | no | — |
| 441 | C2×D5 | — | 2 | 1 | no | — |
| 442 | C2×D5 | — | 2 | 1 | no | — |
| 443 | C2×D5 | — | 4 | 1 | no | — |
| 444 | C2×D5 | — | 4 | 1 | no | — |
| 445 | C2×D5 | — | 4 | 1 | no | — |
| 446 | C2×D5 | — | 8 | 1 | no | — |
| 447 | C2×D5 | — | 8 | 1 | no | — |
| 448 | C2×D5 | #447 | 1 | 1 | yes | characteristic |
| 449 | C2×D5 | #450 | 1 | 1 | yes | characteristic |
| 450 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 451 | C4×C5 | — | 2 | 1 | no | — |
| 452 | C4×C5 | — | 4 | 1 | no | — |
| 453 | C4×C5 | — | 4 | 2 | no | — |
| 454 | C4×C5 | #379 | 1 | 1 | yes | characteristic |
| 455 | C4×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 456 | Dic5 | — | 2 | 1 | no | — |
| 457 | Dic5 | — | 4 | 1 | no | — |
| 458 | Dic5 | — | 4 | 2 | no | — |
| 459 | Dic5 | #447 | 1 | 1 | yes | characteristic |
| 460 | Dic5 | #450 | 1 | 1 | yes | characteristic |
| 461 | #41 | — | 2 | 2 | no | — |
| 462 | #41 | — | 2 | 1 | no | — |
| 463 | #41 | — | 4 | 2 | no | — |
| 464 | #41 | — | 4 | 1 | no | — |
| 465 | #41 | — | 5 | 1 | no | — |
| 466 | #41 | — | 5 | 1 | no | — |
| 467 | #41 | — | 5 | 1 | no | — |
| 468 | #41 | — | 10 | 1 | no | — |
| 469 | #41 | — | 10 | 2 | no | — |
| 470 | #41 | — | 10 | 1 | no | — |
| 471 | #41 | — | 10 | 1 | no | — |
| 472 | #41 | — | 10 | 1 | no | — |
| 473 | #41 | — | 10 | 2 | no | — |
| 474 | #41 | — | 10 | 2 | no | — |
| 475 | #41 | — | 10 | 1 | no | — |
| 476 | #41 | — | 20 | 1 | no | — |
| 477 | #41 | — | 20 | 2 | no | — |
| 478 | #41 | — | 20 | 1 | no | — |
| 479 | #41 | — | 20 | 2 | no | — |
| 480 | #41 | — | 20 | 2 | no | — |
| 481 | #41 | — | 20 | 2 | no | — |
| 482 | #41 | — | 20 | 2 | no | — |
| 483 | #41 | — | 20 | 1 | no | — |
| 484 | #41 | — | 20 | 2 | no | — |
| 485 | #41 | — | 20 | 2 | no | — |
| 486 | #41 | — | 20 | 2 | no | — |
| 487 | #41 | — | 20 | 2 | 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 | — | 2 | 2 | no | — |
| 494 | C2×Q8 | — | 2 | 1 | no | — |
| 495 | C2×Q8 | — | 4 | 1 | no | — |
| 496 | C2×Q8 | — | 5 | 1 | no | — |
| 497 | C2×Q8 | — | 10 | 2 | no | — |
| 498 | C2×Q8 | — | 10 | 1 | no | — |
| 499 | C2×Q8 | — | 10 | 2 | no | — |
| 500 | C2×Q8 | — | 10 | 2 | no | — |
| 501 | C2×Q8 | — | 10 | 2 | no | — |
| 502 | C2×Q8 | — | 10 | 2 | no | — |
| 503 | C2×Q8 | — | 10 | 1 | no | — |
| 504 | C2×Q8 | — | 20 | 1 | no | — |
| 505 | C2×Q8 | — | 20 | 2 | no | — |
| 506 | C2×Q8 | — | 20 | 1 | no | — |
| 507 | C2×Q8 | — | 20 | 2 | no | — |
| 508 | C2×Q8 | — | 20 | 1 | no | — |
| 509 | C2×Q8 | — | 20 | 1 | no | — |
| 510 | C2×Q8 | — | 20 | 2 | no | — |
| 511 | C2×Q8 | — | 20 | 2 | no | — |
| 512 | C2×Q8 | — | 20 | 1 | no | — |
| 513 | C2×Q8 | — | 20 | 2 | no | — |
| 514 | C2×Q8 | — | 20 | 1 | no | — |
| 515 | C2×D4 | — | 5 | 1 | no | — |
| 516 | C2×D4 | — | 10 | 1 | no | — |
| 517 | C2×D4 | — | 10 | 1 | no | — |
| 518 | C2×D4 | — | 20 | 1 | no | — |
| 519 | C2×D4 | — | 20 | 2 | no | — |
| 520 | C22×C4 | — | 5 | 1 | no | — |
| 521 | C22×C4 | — | 10 | 1 | no | — |
| 522 | C22×C4 | — | 20 | 1 | no | — |
| 523 | C22×C4 | — | 20 | 2 | no | — |
| 524 | C22×C4 | — | 20 | 1 | no | — |
| 525 | C22×C4 | — | 20 | 2 | no | — |
| 526 | C22×C4 | — | 20 | 1 | no | — |
| 527 | Q16 | — | 2 | 2 | no | — |
| 528 | Q16 | — | 2 | 1 | no | — |
| 529 | Q16 | — | 5 | 2 | no | — |
| 530 | Q16 | — | 5 | 1 | no | — |
| 531 | Q16 | — | 10 | 2 | no | — |
| 532 | Q16 | — | 10 | 2 | no | — |
| 533 | Q16 | — | 10 | 1 | no | — |
| 534 | Q16 | — | 10 | 2 | no | — |
| 535 | Q16 | — | 10 | 2 | no | — |
| 536 | Q16 | — | 10 | 2 | no | — |
| 537 | Q16 | — | 10 | 1 | no | — |
| 538 | Q16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 539 | Q16 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 540 | SD16 | — | 2 | 2 | no | — |
| 541 | SD16 | — | 2 | 1 | no | — |
| 542 | SD16 | — | 10 | 2 | no | — |
| 543 | SD16 | — | 10 | 1 | no | — |
| 544 | SD16 | — | 10 | 1 | no | — |
| 545 | SD16 | — | 10 | 2 | no | — |
| 546 | SD16 | — | 10 | 2 | no | — |
| 547 | SD16 | — | 10 | 1 | no | — |
| 548 | D8 | — | 5 | 1 | no | — |
| 549 | D8 | — | 10 | 1 | no | — |
| 550 | D8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 551 | M16 | — | 2 | 1 | no | — |
| 552 | M16 | — | 5 | 1 | no | — |
| 553 | M16 | — | 10 | 1 | no | — |
| 554 | M16 | — | 10 | 1 | no | — |
| 555 | M16 | — | 10 | 1 | no | — |
| 556 | M16 | — | 10 | 1 | no | — |
| 557 | M16 | — | 20 | 1 | no | — |
| 558 | M16 | — | 20 | 1 | no | — |
| 559 | M16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 560 | C2×C8 | — | 2 | 1 | no | — |
| 561 | C2×C8 | — | 5 | 1 | no | — |
| 562 | C2×C8 | — | 5 | 1 | no | — |
| 563 | C2×C8 | — | 5 | 1 | no | — |
| 564 | C2×C8 | — | 5 | 1 | no | — |
| 565 | C2×C8 | — | 5 | 1 | no | — |
| 566 | C2×C8 | — | 10 | 1 | no | — |
| 567 | C2×C8 | — | 10 | 1 | no | — |
| 568 | C2×C8 | — | 10 | 1 | no | — |
| 569 | C2×C8 | — | 10 | 1 | no | — |
| 570 | C2×C8 | — | 20 | 1 | no | — |
| 571 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 572 | C4⋊C4 | — | 20 | 1 | no | — |
| 573 | C4⋊C4 | — | 20 | 1 | no | — |
| 574 | C16 | — | 20 | 1 | no | — |
| 575 | C16 | — | 20 | 1 | no | — |
| 576 | C2×C5 | — | 2 | 1 | no | — |
| 577 | C2×C5 | — | 4 | 1 | no | — |
| 578 | C2×C5 | — | 8 | 1 | no | — |
| 579 | C2×C5 | #1786 | 1 | 1 | yes | characteristic |
| 580 | D5 | — | 2 | 1 | no | — |
| 581 | D5 | — | 4 | 1 | no | — |
| 582 | D5 | — | 8 | 1 | no | — |
| 583 | D5 | #2193 | 1 | 1 | yes | characteristic |
| 584 | D5 | #2195 | 1 | 1 | yes | characteristic |
| 585 | C23 | — | 5 | 1 | no | — |
| 586 | C23 | — | 10 | 1 | no | — |
| 587 | C23 | — | 20 | 1 | no | — |
| 588 | Q8 | — | 2 | 2 | no | — |
| 589 | Q8 | — | 2 | 1 | no | — |
| 590 | Q8 | — | 4 | 2 | no | — |
| 591 | Q8 | — | 4 | 1 | no | — |
| 592 | Q8 | — | 5 | 1 | no | — |
| 593 | Q8 | — | 10 | 1 | no | — |
| 594 | Q8 | — | 10 | 2 | no | — |
| 595 | Q8 | — | 10 | 1 | no | — |
| 596 | Q8 | — | 20 | 2 | no | — |
| 597 | Q8 | — | 20 | 2 | no | — |
| 598 | Q8 | — | 20 | 2 | no | — |
| 599 | Q8 | — | 20 | 1 | no | — |
| 600 | Q8 | — | 20 | 2 | no | — |
| 601 | Q8 | — | 20 | 2 | no | — |
| 602 | Q8 | — | 20 | 1 | no | — |
| 603 | Q8 | #4007 | 1 | 1 | yes | characteristic |
| 604 | D4 | — | 2 | 1 | no | — |
| 605 | D4 | — | 2 | 1 | no | — |
| 606 | D4 | — | 4 | 2 | no | — |
| 607 | D4 | — | 4 | 1 | no | — |
| 608 | D4 | — | 5 | 1 | no | — |
| 609 | D4 | — | 10 | 1 | no | — |
| 610 | D4 | — | 10 | 1 | no | — |
| 611 | D4 | — | 10 | 1 | no | — |
| 612 | D4 | — | 10 | 1 | no | — |
| 613 | D4 | — | 10 | 1 | no | — |
| 614 | D4 | — | 20 | 1 | no | — |
| 615 | D4 | — | 20 | 2 | no | — |
| 616 | D4 | — | 20 | 1 | no | — |
| 617 | D4 | — | 20 | 2 | no | — |
| 618 | D4 | — | 20 | 1 | no | — |
| 619 | D4 | — | 20 | 2 | no | — |
| 620 | D4 | — | 20 | 1 | no | — |
| 621 | D4 | #4007 | 1 | 1 | yes | characteristic |
| 622 | C2×C4 | — | 2 | 1 | no | — |
| 623 | C2×C4 | — | 4 | 2 | no | — |
| 624 | C2×C4 | — | 4 | 2 | no | — |
| 625 | C2×C4 | — | 4 | 1 | no | — |
| 626 | C2×C4 | — | 4 | 1 | no | — |
| 627 | C2×C4 | — | 5 | 1 | no | — |
| 628 | C2×C4 | — | 5 | 1 | no | — |
| 629 | C2×C4 | — | 5 | 1 | no | — |
| 630 | C2×C4 | — | 5 | 1 | no | — |
| 631 | C2×C4 | — | 5 | 1 | no | — |
| 632 | C2×C4 | — | 10 | 1 | no | — |
| 633 | C2×C4 | — | 10 | 1 | no | — |
| 634 | C2×C4 | — | 10 | 1 | no | — |
| 635 | C2×C4 | — | 10 | 1 | no | — |
| 636 | C2×C4 | — | 20 | 2 | no | — |
| 637 | C2×C4 | — | 20 | 1 | no | — |
| 638 | C2×C4 | — | 20 | 2 | no | — |
| 639 | C2×C4 | — | 20 | 1 | no | — |
| 640 | C2×C4 | — | 20 | 2 | no | — |
| 641 | C2×C4 | — | 20 | 2 | no | — |
| 642 | C2×C4 | — | 20 | 2 | no | — |
| 643 | C2×C4 | — | 20 | 2 | no | — |
| 644 | C2×C4 | — | 20 | 1 | no | — |
| 645 | C2×C4 | — | 20 | 2 | no | — |
| 646 | C2×C4 | — | 20 | 2 | no | — |
| 647 | C2×C4 | — | 20 | 1 | no | — |
| 648 | C2×C4 | — | 20 | 1 | no | — |
| 649 | C2×C4 | — | 40 | 1 | no | — |
| 650 | C2×C4 | — | 80 | 1 | no | — |
| 651 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 652 | C8 | — | 2 | 1 | no | — |
| 653 | C8 | — | 5 | 1 | no | — |
| 654 | C8 | — | 5 | 1 | no | — |
| 655 | C8 | — | 10 | 1 | no | — |
| 656 | C8 | — | 40 | 1 | no | — |
| 657 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 658 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 659 | C5 | #12749 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 660 | C22 | — | 2 | 1 | no | — |
| 661 | C22 | — | 4 | 1 | no | — |
| 662 | C22 | — | 5 | 1 | no | — |
| 663 | C22 | — | 5 | 1 | no | — |
| 664 | C22 | — | 10 | 1 | no | — |
| 665 | C22 | — | 10 | 1 | no | — |
| 666 | C22 | — | 10 | 1 | no | — |
| 667 | C22 | — | 20 | 1 | no | — |
| 668 | C22 | — | 20 | 1 | no | — |
| 669 | C22 | — | 20 | 1 | no | — |
| 670 | C22 | — | 40 | 1 | no | — |
| 671 | C22 | — | 40 | 1 | no | — |
| 672 | C22 | #65767 | 1 | 1 | yes | characteristic |
| 673 | C4 | — | 2 | 1 | no | — |
| 674 | C4 | — | 4 | 2 | no | — |
| 675 | C4 | — | 4 | 1 | no | — |
| 676 | C4 | — | 5 | 1 | no | — |
| 677 | C4 | — | 5 | 1 | no | — |
| 678 | C4 | — | 10 | 1 | no | — |
| 679 | C4 | — | 20 | 2 | no | — |
| 680 | C4 | — | 20 | 1 | no | — |
| 681 | C4 | — | 80 | 1 | no | — |
| 682 | C4 | C2×#4007 | 1 | 1 | yes | characteristic |
| 683 | C4 | #65800 | 1 | 1 | yes | characteristic |
| 684 | C2 | — | 2 | 1 | no | — |
| 685 | C2 | — | 4 | 1 | no | — |
| 686 | C2 | — | 5 | 1 | no | — |
| 687 | C2 | — | 5 | 1 | no | — |
| 688 | C2 | — | 8 | 1 | no | — |
| 689 | C2 | — | 10 | 1 | no | — |
| 690 | C2 | — | 20 | 1 | no | — |
| 691 | C2 | — | 40 | 1 | no | — |
| 692 | C2 | #10604928 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D5⋊#359 | C2 | semidirect |
| 3. #10604856 | C2 | semidirect |
| 4. D5⋊#362 | C2 | semidirect |
| 5. C2×#64908 | C2 | semidirect |
| 6. #10604782 | C2 | semidirect |
| 7. D5⋊#350 | C2 | semidirect |
| 9. C5×#578 | C4 | semidirect |
| 16. #66105 | C4 | semidirect |
| 20. #66100 | C4 | semidirect |
| 23. #66087 | C4 | semidirect |
| 256. #578 | AGL(1,𝔽5) | semidirect |
| 659. C5 | #12749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#578 | 2 |
| D5⋊#359 | 2 |
| #10604856 | 2 |
| D5⋊#362 | 2 |
| C2×#64908 | 2 |
| #10604782 | 2 |
| D5⋊#350 | 2 |
| #12749 | 5 |