Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1016 conjugacy classes of subgroups.
The subgroup lattice has 594 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617560 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10617449 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10612008 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10604864 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10604618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10604611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10604008 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | AGL(1,𝔽5)×#104 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10603924 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #66285 | C22 | 1 | 1 | yes | characteristic |
| 11 | #41×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 12 | #66264 | C22 | 1 | 2 | yes | — |
| 13 | #66256 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #66107 | C22 | 1 | 2 | yes | — |
| 15 | #66050 | C22 | 1 | 1 | yes | characteristic |
| 16 | #65795 | — | 2 | 2 | no | — |
| 17 | #65795 | C22 | 1 | 2 | yes | — |
| 18 | D5⋊#104 | — | 2 | 2 | no | — |
| 19 | D5⋊#104 | C22 | 1 | 2 | yes | — |
| 20 | #65771 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #65769 | — | 2 | 2 | no | — |
| 22 | #65769 | C22 | 1 | 2 | yes | — |
| 23 | C2×#4008 | — | 2 | 2 | no | — |
| 24 | C2×#4008 | C22 | 1 | 2 | yes | — |
| 25 | C2×#4008 | C22 | 1 | 2 | yes | complemented |
| 26 | #65737 | — | 2 | 2 | no | — |
| 27 | #65736 | — | 2 | 2 | no | — |
| 28 | #65733 | — | 2 | 2 | no | — |
| 29 | #65732 | — | 2 | 2 | no | — |
| 30 | #65729 | C22 | 1 | 2 | yes | complemented |
| 31 | M16×AGL(1,𝔽5) | C22 | 1 | 2 | yes | complemented |
| 32 | C42×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #65681 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C5×#453 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | #65531 | C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | #65490 | C4 | 1 | 2 | yes | complemented |
| 37 | #65366 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | #65115 | C4 | 1 | 2 | yes | complemented |
| 39 | D5×#104 | C22 | 1 | 2 | yes | — |
| 40 | #65035 | C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | #65034 | C22 | 1 | 1 | yes | characteristic |
| 42 | #64902 | C22 | 1 | 2 | yes | complemented |
| 43 | #64900 | C22 | 1 | 2 | yes | complemented |
| 44 | #64862 | C22 | 1 | 2 | yes | complemented |
| 45 | #22899 | — | 5 | 1 | no | maximal, Sylow |
| 46 | C5×H(5,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #4150 | — | 2 | 2 | no | — |
| 48 | #4150 | C2×C4 | 1 | 2 | yes | — |
| 49 | D5×#41 | — | 2 | 2 | no | — |
| 50 | D5×#41 | C23 | 1 | 2 | yes | — |
| 51 | #4144 | — | 2 | 2 | no | — |
| 52 | #4144 | — | 4 | 1 | no | — |
| 53 | #4144 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×#711 | — | 2 | 2 | no | — |
| 55 | C2×#711 | — | 4 | 1 | no | — |
| 56 | C2×#711 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×#711 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×#704 | — | 4 | 1 | no | — |
| 59 | Q8×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 60 | #4133 | — | 2 | 2 | no | — |
| 61 | D4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 62 | D4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 63 | #4131 | — | 2 | 2 | no | — |
| 64 | #4131 | — | 2 | 2 | no | — |
| 65 | #4131 | — | 2 | 2 | no | — |
| 66 | #4131 | — | 4 | 2 | no | — |
| 67 | #4130 | — | 2 | 2 | no | — |
| 68 | #4130 | C23 | 1 | 2 | yes | — |
| 69 | C2×C4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 70 | C2×C4×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 71 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 72 | D5⋊M16 | — | 2 | 2 | no | — |
| 73 | D5⋊M16 | C23 | 1 | 2 | yes | — |
| 74 | C2×#700 | — | 2 | 2 | no | — |
| 75 | C2×#700 | C23 | 1 | 2 | yes | — |
| 76 | C5×AGL(1,ℤ/8) | C2×C4 | 1 | 2 | yes | complemented |
| 77 | C5×#127 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 78 | #4097 | C2×C4 | 1 | 2 | yes | complemented |
| 79 | #4084 | — | 4 | 1 | no | — |
| 80 | #4082 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 81 | #4082 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 82 | D4×Dic5 | — | 4 | 1 | no | — |
| 83 | #4078 | C2×C4 | 1 | 2 | yes | complemented |
| 84 | #4062 | — | 2 | 2 | no | — |
| 85 | #4061 | — | 2 | 2 | no | — |
| 86 | #4058 | — | 2 | 2 | no | — |
| 87 | #4057 | — | 2 | 2 | no | — |
| 88 | #4055 | C2×C4 | 1 | 2 | yes | complemented |
| 89 | D5×M16 | C23 | 1 | 2 | yes | — |
| 90 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 91 | #4015 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 92 | #4011 | — | 4 | 1 | no | — |
| 93 | #4010 | — | 2 | 2 | no | — |
| 94 | #4010 | D4 | 1 | 2 | yes | complemented |
| 95 | #4010 | D4 | 1 | 2 | yes | complemented |
| 96 | #4008 | — | 2 | 2 | no | — |
| 97 | #4008 | — | 2 | 2 | no | — |
| 98 | #4008 | — | 2 | 2 | no | — |
| 99 | #4008 | — | 2 | 2 | no | — |
| 100 | #4008 | — | 2 | 2 | no | — |
| 101 | #4008 | — | 2 | 2 | no | — |
| 102 | #4008 | — | 2 | 2 | no | — |
| 103 | #4008 | D4 | 1 | 2 | yes | complemented |
| 104 | #4008 | D4 | 1 | 2 | yes | complemented |
| 105 | C4⋊#170 | — | 4 | 1 | no | — |
| 106 | #3996 | — | 2 | 2 | no | — |
| 107 | #3995 | — | 2 | 2 | no | — |
| 108 | #3992 | — | 2 | 2 | no | — |
| 109 | C8×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 110 | C5×#104 | C2×C4 | 1 | 2 | yes | complemented |
| 111 | C5×#100 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 112 | #3969 | C2×C4 | 1 | 2 | yes | complemented |
| 113 | #3965 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 114 | #3957 | C2×C4 | 1 | 2 | yes | complemented |
| 115 | #3956 | C2×C4 | 1 | 2 | yes | complemented |
| 116 | #3937 | C2×C4 | 1 | 2 | yes | complemented |
| 117 | #3018 | — | 5 | 1 | no | — |
| 118 | #2956 | — | 5 | 2 | no | — |
| 119 | #2901 | — | 5 | 2 | no | — |
| 120 | #1962 | — | 5 | 1 | no | — |
| 121 | #1932 | — | 5 | 2 | no | — |
| 122 | #1906 | — | 5 | 2 | no | — |
| 123 | #1884 | — | 5 | 1 | no | — |
| 124 | #1861 | — | 5 | 2 | no | — |
| 125 | C4×#104 | — | 5 | 2 | no | — |
| 126 | C22×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 127 | C22×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 128 | C5×#41 | — | 2 | 2 | no | — |
| 129 | C5×#41 | C22×C4 | 1 | 2 | yes | — |
| 130 | C2×C5×D4 | — | 2 | 2 | no | — |
| 131 | C2×C5×D4 | — | 4 | 1 | no | — |
| 132 | C2×C5×D4 | — | 4 | 1 | no | — |
| 133 | C2×C5×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | C2×C5×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 135 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 136 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 137 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 138 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 139 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 140 | C22×Dic5 | — | 2 | 1 | no | — |
| 141 | C22×Dic5 | — | 2 | 1 | no | — |
| 142 | C22×Dic5 | — | 4 | 1 | no | — |
| 143 | #713 | C2×D4 | 1 | 2 | yes | — |
| 144 | Q8×D5 | — | 2 | 2 | no | — |
| 145 | Q8×D5 | #41 | 1 | 2 | yes | — |
| 146 | #711 | — | 2 | 2 | no | — |
| 147 | #711 | — | 2 | 2 | no | — |
| 148 | #711 | — | 2 | 2 | no | — |
| 149 | #711 | — | 2 | 2 | no | — |
| 150 | #711 | — | 2 | 2 | no | — |
| 151 | #711 | — | 2 | 2 | no | — |
| 152 | #711 | — | 2 | 2 | no | — |
| 153 | #711 | — | 4 | 2 | no | — |
| 154 | #711 | — | 4 | 2 | no | — |
| 155 | #711 | — | 4 | 2 | no | — |
| 156 | #711 | — | 4 | 2 | no | — |
| 157 | #711 | C2×D4 | 1 | 2 | yes | — |
| 158 | D4×D5 | — | 2 | 2 | no | — |
| 159 | D4×D5 | — | 2 | 2 | no | — |
| 160 | D4×D5 | — | 4 | 2 | no | — |
| 161 | D4×D5 | #41 | 1 | 2 | yes | — |
| 162 | #709 | — | 2 | 2 | no | — |
| 163 | #709 | — | 2 | 2 | no | — |
| 164 | #709 | — | 4 | 2 | no | — |
| 165 | #709 | C22×C4 | 1 | 2 | yes | — |
| 166 | C2×C4×D5 | — | 2 | 2 | no | — |
| 167 | C2×C4×D5 | — | 2 | 1 | no | — |
| 168 | C2×C4×D5 | — | 4 | 1 | no | — |
| 169 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 170 | C2×Dic10 | — | 2 | 2 | no | — |
| 171 | C2×Dic10 | — | 4 | 1 | no | — |
| 172 | C2×Dic10 | C22×C4 | 1 | 1 | yes | characteristic |
| 173 | C2×Dic10 | C22×C4 | 1 | 1 | yes | characteristic |
| 174 | C22⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 175 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 176 | #704 | — | 2 | 2 | no | — |
| 177 | #704 | — | 4 | 2 | no | — |
| 178 | #704 | — | 4 | 2 | no | — |
| 179 | C2×#170 | — | 2 | 2 | no | — |
| 180 | C2×#170 | — | 4 | 1 | no | — |
| 181 | C2×#170 | — | 4 | 1 | no | — |
| 182 | C2×#170 | — | 4 | 2 | no | — |
| 183 | C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 184 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 185 | C4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 186 | C4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 187 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 188 | C4×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 189 | C4×AGL(1,𝔽5) | C2×D4 | 1 | 2 | yes | — |
| 190 | C4×AGL(1,𝔽5) | C2×D4 | 1 | 2 | yes | — |
| 191 | #700 | — | 2 | 2 | no | — |
| 192 | #700 | — | 2 | 2 | no | — |
| 193 | #700 | — | 4 | 2 | no | — |
| 194 | #700 | C2×D4 | 1 | 2 | yes | — |
| 195 | #700 | C2×D4 | 1 | 2 | yes | — |
| 196 | D5⋊C8 | — | 2 | 2 | no | — |
| 197 | D5⋊C8 | — | 4 | 2 | no | — |
| 198 | C5×SD16 | — | 2 | 2 | no | — |
| 199 | C5×D8 | — | 2 | 2 | no | — |
| 200 | C5×M16 | C22×C4 | 1 | 2 | yes | — |
| 201 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 202 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 203 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 204 | #689 | — | 2 | 2 | no | — |
| 205 | #687 | — | 2 | 2 | no | — |
| 206 | #687 | — | 2 | 2 | no | — |
| 207 | #686 | — | 2 | 2 | no | — |
| 208 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 209 | C4×Dic5 | — | 2 | 1 | no | — |
| 210 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 211 | #681 | C22×C4 | 1 | 2 | yes | — |
| 212 | Dic20 | — | 2 | 2 | no | — |
| 213 | #677 | — | 2 | 2 | no | — |
| 214 | #676 | — | 2 | 2 | no | — |
| 215 | C8×D5 | — | 2 | 2 | no | — |
| 216 | #585 | — | 5 | 1 | no | — |
| 217 | #575 | — | 5 | 2 | no | — |
| 218 | #568 | — | 5 | 2 | no | — |
| 219 | #568 | — | 5 | 1 | no | — |
| 220 | #532 | — | 5 | 1 | no | — |
| 221 | C4×#41 | — | 5 | 2 | no | — |
| 222 | #456 | — | 5 | 2 | no | — |
| 223 | #455 | — | 5 | 1 | no | — |
| 224 | #455 | — | 5 | 1 | no | — |
| 225 | #454 | — | 5 | 2 | no | — |
| 226 | #453 | — | 5 | 1 | no | — |
| 227 | #453 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 228 | #444 | — | 10 | 2 | no | — |
| 229 | #444 | — | 10 | 2 | no | — |
| 230 | #443 | — | 10 | 2 | no | — |
| 231 | #443 | — | 10 | 2 | no | — |
| 232 | #430 | — | 5 | 2 | no | — |
| 233 | #423 | — | 5 | 1 | no | — |
| 234 | #421 | — | 5 | 2 | no | — |
| 235 | #421 | — | 5 | 2 | no | — |
| 236 | #421 | — | 10 | 2 | no | — |
| 237 | #421 | — | 10 | 2 | no | — |
| 238 | C2×#104 | — | 5 | 2 | no | — |
| 239 | C2×#104 | — | 5 | 2 | no | — |
| 240 | C2×#104 | — | 5 | 2 | no | — |
| 241 | C2×#104 | — | 5 | 2 | no | — |
| 242 | C2×#104 | — | 10 | 2 | no | — |
| 243 | C2×#104 | — | 10 | 2 | no | — |
| 244 | #413 | — | 5 | 1 | no | — |
| 245 | #410 | — | 5 | 1 | no | — |
| 246 | C4×M16 | — | 5 | 2 | no | — |
| 247 | C43 | — | 5 | 1 | no | — |
| 248 | #344 | — | 5 | 2 | no | — |
| 249 | #339 | — | 5 | 2 | no | — |
| 250 | #339 | — | 5 | 2 | no | — |
| 251 | C23×C5 | — | 2 | 1 | no | — |
| 252 | C23×C5 | — | 2 | 1 | no | — |
| 253 | C23×C5 | — | 4 | 1 | no | — |
| 254 | C22×D5 | — | 2 | 2 | no | — |
| 255 | C22×D5 | — | 4 | 1 | no | — |
| 256 | C22×D5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 257 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 258 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 259 | C2×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 260 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 261 | C2×AGL(1,𝔽5) | — | 8 | 4 | no | — |
| 262 | C5×Q8 | C4×D4 | 1 | 2 | yes | — |
| 263 | C5×D4 | — | 2 | 2 | no | — |
| 264 | C5×D4 | — | 2 | 2 | no | — |
| 265 | C5×D4 | — | 2 | 2 | no | — |
| 266 | C5×D4 | — | 4 | 2 | no | — |
| 267 | C5×D4 | — | 8 | 2 | no | — |
| 268 | C5×D4 | C4×D4 | 1 | 2 | yes | — |
| 269 | C2×C4×C5 | — | 2 | 1 | no | — |
| 270 | C2×C4×C5 | — | 2 | 2 | no | — |
| 271 | C2×C4×C5 | — | 4 | 1 | no | — |
| 272 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 273 | C22⋊D5 | — | 2 | 2 | no | — |
| 274 | C22⋊D5 | — | 2 | 2 | no | — |
| 275 | C22⋊D5 | — | 2 | 2 | no | — |
| 276 | C22⋊D5 | — | 4 | 2 | no | — |
| 277 | C22⋊D5 | — | 4 | 2 | no | — |
| 278 | C22⋊D5 | — | 4 | 2 | no | — |
| 279 | C22⋊D5 | — | 4 | 2 | no | — |
| 280 | C2×Dic5 | — | 2 | 2 | no | — |
| 281 | C2×Dic5 | — | 2 | 1 | no | — |
| 282 | C2×Dic5 | — | 2 | 1 | no | — |
| 283 | C2×Dic5 | — | 2 | 1 | no | — |
| 284 | C2×Dic5 | — | 4 | 1 | no | — |
| 285 | C2×Dic5 | — | 4 | 2 | no | — |
| 286 | C2×Dic5 | — | 4 | 1 | no | — |
| 287 | C2×Dic5 | — | 4 | 1 | no | — |
| 288 | C2×Dic5 | — | 4 | 1 | no | — |
| 289 | C2×Dic5 | — | 4 | 1 | no | — |
| 290 | C2×Dic5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 291 | D20 | — | 2 | 2 | no | — |
| 292 | D20 | C4×D4 | 1 | 2 | yes | — |
| 293 | C4×D5 | — | 2 | 2 | no | — |
| 294 | C4×D5 | — | 2 | 2 | no | — |
| 295 | C4×D5 | — | 2 | 2 | no | — |
| 296 | C4×D5 | — | 4 | 2 | no | — |
| 297 | C4×D5 | — | 4 | 2 | no | — |
| 298 | C4×D5 | C22×D4 | 1 | 2 | yes | — |
| 299 | C4×D5 | C2×#41 | 1 | 2 | yes | — |
| 300 | Dic10 | — | 2 | 2 | no | — |
| 301 | Dic10 | — | 2 | 2 | no | — |
| 302 | Dic10 | — | 2 | 2 | no | — |
| 303 | Dic10 | — | 4 | 2 | no | — |
| 304 | Dic10 | C4×D4 | 1 | 2 | yes | — |
| 305 | #170 | — | 2 | 2 | no | — |
| 306 | #170 | — | 2 | 2 | no | — |
| 307 | #170 | — | 4 | 2 | no | — |
| 308 | C5×C8 | — | 2 | 2 | no | — |
| 309 | #168 | — | 2 | 2 | no | — |
| 310 | 2−1+4 | — | 5 | 2 | no | — |
| 311 | 2−1+4 | — | 10 | 2 | no | — |
| 312 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 313 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 314 | H(5,𝔽2) | — | 20 | 1 | no | — |
| 315 | H(5,𝔽2) | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 316 | C2×#41 | — | 5 | 2 | no | — |
| 317 | C2×#41 | — | 5 | 1 | no | — |
| 318 | C2×#41 | — | 5 | 1 | no | — |
| 319 | C2×#41 | — | 10 | 2 | no | — |
| 320 | C2×#41 | — | 10 | 2 | no | — |
| 321 | C2×#41 | — | 20 | 1 | no | — |
| 322 | #137 | — | 5 | 2 | no | — |
| 323 | #137 | — | 5 | 2 | no | — |
| 324 | #137 | — | 10 | 2 | no | — |
| 325 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 326 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 327 | AGL(1,ℤ/8) | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 328 | #135 | — | 10 | 2 | no | — |
| 329 | #135 | — | 10 | 2 | no | — |
| 330 | #131 | — | 10 | 2 | no | — |
| 331 | #131 | — | 10 | 2 | no | — |
| 332 | #131 | — | 10 | 2 | no | — |
| 333 | #131 | — | 10 | 2 | no | — |
| 334 | #131 | — | 20 | 2 | no | — |
| 335 | C2×M16 | — | 5 | 2 | no | — |
| 336 | C2×M16 | — | 5 | 2 | no | — |
| 337 | C2×M16 | — | 5 | 2 | no | — |
| 338 | C2×M16 | — | 10 | 2 | no | — |
| 339 | C2×M16 | — | 10 | 2 | no | — |
| 340 | C2×M16 | — | 20 | 1 | no | — |
| 341 | C4⋊Q8 | — | 5 | 1 | no | — |
| 342 | #127 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 343 | #124 | — | 5 | 1 | no | — |
| 344 | #124 | — | 5 | 1 | no | — |
| 345 | #121 | — | 20 | 1 | no | — |
| 346 | C4×Q8 | — | 10 | 2 | no | — |
| 347 | C4×D4 | — | 10 | 2 | no | — |
| 348 | C4×D4 | — | 20 | 1 | no | — |
| 349 | C4×D4 | — | 20 | 2 | no | — |
| 350 | #117 | — | 5 | 2 | no | — |
| 351 | #117 | — | 10 | 2 | no | — |
| 352 | C2×C42 | — | 5 | 2 | no | — |
| 353 | C2×C42 | — | 5 | 1 | no | — |
| 354 | C2×C42 | — | 10 | 2 | no | — |
| 355 | C2×C42 | — | 20 | 1 | no | — |
| 356 | #108 | — | 10 | 2 | no | — |
| 357 | #108 | — | 10 | 2 | no | — |
| 358 | C4⋊C8 | — | 20 | 1 | no | — |
| 359 | #104 | — | 5 | 2 | no | — |
| 360 | #104 | — | 5 | 2 | no | — |
| 361 | #104 | — | 5 | 2 | no | — |
| 362 | #104 | — | 5 | 2 | no | — |
| 363 | #104 | — | 5 | 2 | no | — |
| 364 | #104 | — | 5 | 2 | no | — |
| 365 | #104 | — | 5 | 2 | no | — |
| 366 | #104 | — | 10 | 2 | no | — |
| 367 | #104 | — | 10 | 2 | no | — |
| 368 | #104 | — | 10 | 2 | no | — |
| 369 | #104 | — | 10 | 2 | no | — |
| 370 | #104 | — | 10 | 2 | no | — |
| 371 | #104 | — | 10 | 2 | no | — |
| 372 | #104 | — | 10 | 2 | no | — |
| 373 | #104 | — | 10 | 2 | no | — |
| 374 | #104 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 375 | #101 | — | 5 | 2 | no | — |
| 376 | #100 | — | 5 | 1 | no | — |
| 377 | #100 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 378 | #99 | — | 20 | 1 | no | — |
| 379 | #97 | — | 10 | 2 | no | — |
| 380 | C4×C8 | — | 10 | 2 | no | — |
| 381 | C22×C5 | — | 2 | 2 | no | — |
| 382 | C22×C5 | — | 4 | 1 | no | — |
| 383 | C22×C5 | — | 4 | 1 | no | — |
| 384 | C22×C5 | — | 8 | 1 | no | — |
| 385 | C22×C5 | — | 8 | 1 | no | — |
| 386 | C22×C5 | — | 16 | 1 | no | — |
| 387 | C22×C5 | #518 | 1 | 1 | yes | characteristic |
| 388 | C2×D5 | — | 2 | 2 | no | — |
| 389 | C2×D5 | — | 4 | 1 | no | — |
| 390 | C2×D5 | — | 8 | 2 | no | — |
| 391 | C2×D5 | — | 16 | 1 | no | — |
| 392 | C2×D5 | #546 | 1 | 2 | yes | — |
| 393 | AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 394 | AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 395 | AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 396 | C4×C5 | — | 2 | 2 | no | — |
| 397 | C4×C5 | — | 2 | 2 | no | — |
| 398 | C4×C5 | C2×C4×D4 | 1 | 2 | yes | — |
| 399 | Dic5 | — | 2 | 2 | no | — |
| 400 | Dic5 | — | 4 | 1 | no | — |
| 401 | Dic5 | — | 4 | 1 | no | — |
| 402 | Dic5 | — | 4 | 1 | no | — |
| 403 | Dic5 | D42 | 1 | 1 | yes | characteristic |
| 404 | Dic5 | #551 | 1 | 1 | yes | characteristic |
| 405 | #41 | — | 2 | 2 | no | — |
| 406 | #41 | — | 5 | 2 | no | — |
| 407 | #41 | — | 5 | 2 | no | — |
| 408 | #41 | — | 5 | 2 | no | — |
| 409 | #41 | — | 10 | 2 | no | — |
| 410 | #41 | — | 10 | 2 | no | — |
| 411 | #41 | — | 10 | 2 | no | — |
| 412 | #41 | — | 10 | 2 | no | — |
| 413 | #41 | — | 10 | 2 | no | — |
| 414 | #41 | — | 10 | 2 | no | — |
| 415 | #41 | — | 10 | 2 | no | — |
| 416 | #41 | — | 10 | 2 | no | — |
| 417 | #41 | — | 10 | 2 | no | — |
| 418 | #41 | — | 20 | 2 | no | — |
| 419 | #41 | — | 20 | 2 | no | — |
| 420 | #41 | — | 20 | 2 | no | — |
| 421 | #41 | — | 20 | 2 | no | — |
| 422 | #41 | — | 20 | 2 | no | — |
| 423 | #41 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 424 | C2×Q8 | — | 5 | 2 | no | — |
| 425 | C2×Q8 | — | 5 | 1 | no | — |
| 426 | C2×Q8 | — | 5 | 1 | no | — |
| 427 | C2×Q8 | — | 10 | 2 | no | — |
| 428 | C2×Q8 | — | 10 | 2 | no | — |
| 429 | C2×Q8 | — | 20 | 1 | no | — |
| 430 | C2×D4 | — | 2 | 2 | no | — |
| 431 | C2×D4 | — | 4 | 1 | no | — |
| 432 | C2×D4 | — | 4 | 1 | no | — |
| 433 | C2×D4 | — | 5 | 2 | no | — |
| 434 | C2×D4 | — | 10 | 2 | no | — |
| 435 | C2×D4 | — | 10 | 2 | no | — |
| 436 | C2×D4 | — | 10 | 1 | no | — |
| 437 | C2×D4 | — | 10 | 1 | no | — |
| 438 | C2×D4 | — | 20 | 2 | no | — |
| 439 | C2×D4 | — | 20 | 1 | no | — |
| 440 | C2×D4 | — | 20 | 1 | no | — |
| 441 | C2×D4 | — | 20 | 2 | no | — |
| 442 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 443 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 444 | C22×C4 | — | 5 | 1 | no | — |
| 445 | C22×C4 | — | 10 | 2 | no | — |
| 446 | C22×C4 | — | 10 | 1 | no | — |
| 447 | C22×C4 | — | 10 | 1 | no | — |
| 448 | C22×C4 | — | 10 | 1 | no | — |
| 449 | C22×C4 | — | 10 | 2 | no | — |
| 450 | C22×C4 | — | 20 | 1 | no | — |
| 451 | C22×C4 | — | 20 | 1 | no | — |
| 452 | C22×C4 | — | 20 | 2 | no | — |
| 453 | Q16 | — | 10 | 2 | no | — |
| 454 | Q16 | — | 10 | 2 | no | — |
| 455 | SD16 | — | 2 | 2 | no | — |
| 456 | SD16 | — | 10 | 2 | no | — |
| 457 | SD16 | — | 10 | 2 | no | — |
| 458 | SD16 | — | 10 | 2 | no | — |
| 459 | D8 | — | 2 | 2 | no | — |
| 460 | D8 | — | 10 | 2 | no | — |
| 461 | M16 | — | 5 | 2 | no | — |
| 462 | M16 | — | 5 | 2 | no | — |
| 463 | M16 | — | 5 | 2 | no | — |
| 464 | M16 | — | 10 | 2 | no | — |
| 465 | M16 | — | 10 | 2 | no | — |
| 466 | M16 | — | 10 | 2 | no | — |
| 467 | M16 | — | 10 | 2 | no | — |
| 468 | M16 | — | 20 | 2 | no | — |
| 469 | M16 | — | 20 | 2 | no | — |
| 470 | M16 | — | 20 | 2 | no | — |
| 471 | M16 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 472 | C2×C8 | — | 10 | 2 | no | — |
| 473 | C2×C8 | — | 10 | 2 | no | — |
| 474 | C2×C8 | — | 10 | 2 | no | — |
| 475 | C2×C8 | — | 20 | 1 | no | — |
| 476 | C2×C8 | — | 20 | 1 | no | — |
| 477 | C2×C8 | — | 20 | 2 | no | — |
| 478 | C2×C8 | — | 20 | 2 | no | — |
| 479 | C4⋊C4 | — | 10 | 2 | no | — |
| 480 | C4⋊C4 | — | 20 | 1 | no | — |
| 481 | C4⋊C4 | — | 20 | 2 | no | — |
| 482 | C22⋊C4 | — | 10 | 2 | no | — |
| 483 | C22⋊C4 | — | 20 | 1 | no | — |
| 484 | C22⋊C4 | — | 20 | 1 | no | — |
| 485 | C22⋊C4 | — | 20 | 2 | no | — |
| 486 | C42 | — | 5 | 2 | no | — |
| 487 | C42 | — | 5 | 2 | no | — |
| 488 | C42 | — | 5 | 1 | no | — |
| 489 | C42 | — | 10 | 1 | no | — |
| 490 | C42 | — | 10 | 2 | no | — |
| 491 | C42 | — | 10 | 2 | no | — |
| 492 | C42 | — | 20 | 2 | no | — |
| 493 | C42 | — | 20 | 4 | no | — |
| 494 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 495 | C2×C5 | — | 2 | 1 | no | — |
| 496 | C2×C5 | — | 4 | 2 | no | — |
| 497 | C2×C5 | — | 8 | 1 | no | — |
| 498 | C2×C5 | — | 8 | 1 | no | — |
| 499 | C2×C5 | #2358 | 1 | 1 | yes | characteristic |
| 500 | D5 | — | 2 | 2 | no | — |
| 501 | D5 | — | 4 | 2 | no | — |
| 502 | C23 | — | 2 | 1 | no | — |
| 503 | C23 | — | 2 | 1 | no | — |
| 504 | C23 | — | 4 | 1 | no | — |
| 505 | C23 | — | 5 | 1 | no | — |
| 506 | C23 | — | 10 | 2 | no | — |
| 507 | C23 | — | 20 | 1 | no | — |
| 508 | Q8 | — | 5 | 2 | no | — |
| 509 | Q8 | — | 10 | 2 | no | — |
| 510 | Q8 | — | 10 | 2 | no | — |
| 511 | Q8 | — | 10 | 2 | no | — |
| 512 | Q8 | — | 20 | 2 | no | — |
| 513 | Q8 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 514 | D4 | — | 2 | 2 | no | — |
| 515 | D4 | — | 2 | 2 | no | — |
| 516 | D4 | — | 2 | 2 | no | — |
| 517 | D4 | — | 4 | 2 | no | — |
| 518 | D4 | — | 5 | 2 | no | — |
| 519 | D4 | — | 8 | 2 | no | — |
| 520 | D4 | — | 10 | 2 | no | — |
| 521 | D4 | — | 10 | 2 | no | — |
| 522 | D4 | — | 10 | 2 | no | — |
| 523 | D4 | — | 10 | 2 | no | — |
| 524 | D4 | — | 20 | 2 | no | — |
| 525 | D4 | — | 20 | 2 | no | — |
| 526 | D4 | — | 20 | 2 | no | — |
| 527 | D4 | — | 20 | 2 | no | — |
| 528 | D4 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 2 | 2 | no | — |
| 531 | C2×C4 | — | 4 | 1 | no | — |
| 532 | C2×C4 | — | 5 | 1 | no | — |
| 533 | C2×C4 | — | 5 | 2 | no | — |
| 534 | C2×C4 | — | 5 | 2 | no | — |
| 535 | C2×C4 | — | 10 | 2 | no | — |
| 536 | C2×C4 | — | 10 | 2 | no | — |
| 537 | C2×C4 | — | 10 | 2 | no | — |
| 538 | C2×C4 | — | 10 | 2 | no | — |
| 539 | C2×C4 | — | 10 | 2 | no | — |
| 540 | C2×C4 | — | 10 | 2 | no | — |
| 541 | C2×C4 | — | 10 | 1 | no | — |
| 542 | C2×C4 | — | 10 | 1 | no | — |
| 543 | C2×C4 | — | 10 | 1 | no | — |
| 544 | C2×C4 | — | 20 | 2 | no | — |
| 545 | C2×C4 | — | 20 | 2 | no | — |
| 546 | C2×C4 | — | 20 | 1 | no | — |
| 547 | C2×C4 | — | 20 | 1 | no | — |
| 548 | C2×C4 | — | 20 | 1 | no | — |
| 549 | C2×C4 | — | 20 | 1 | no | — |
| 550 | C2×C4 | — | 20 | 1 | no | — |
| 551 | C2×C4 | — | 20 | 2 | no | — |
| 552 | C2×C4 | — | 20 | 4 | no | — |
| 553 | C2×C4 | — | 20 | 2 | no | — |
| 554 | C2×C4 | — | 40 | 4 | no | — |
| 555 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 556 | C8 | — | 2 | 2 | no | — |
| 557 | C8 | — | 10 | 2 | no | — |
| 558 | C8 | — | 10 | 2 | no | — |
| 559 | C8 | — | 10 | 2 | no | — |
| 560 | C8 | — | 20 | 2 | no | — |
| 561 | C5 | #22899 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 562 | C22 | — | 2 | 2 | no | — |
| 563 | C22 | — | 4 | 1 | no | — |
| 564 | C22 | — | 4 | 1 | no | — |
| 565 | C22 | — | 5 | 2 | no | — |
| 566 | C22 | — | 8 | 1 | no | — |
| 567 | C22 | — | 8 | 1 | no | — |
| 568 | C22 | — | 10 | 2 | no | — |
| 569 | C22 | — | 16 | 1 | no | — |
| 570 | C22 | — | 20 | 1 | no | — |
| 571 | C22 | — | 40 | 2 | no | — |
| 572 | C22 | — | 80 | 1 | no | — |
| 573 | C22 | #66258 | 1 | 1 | yes | characteristic |
| 574 | C4 | — | 2 | 2 | no | — |
| 575 | C4 | — | 2 | 2 | no | — |
| 576 | C4 | — | 5 | 1 | no | — |
| 577 | C4 | — | 5 | 1 | no | — |
| 578 | C4 | — | 10 | 4 | no | — |
| 579 | C4 | — | 10 | 2 | no | — |
| 580 | C4 | — | 20 | 1 | no | — |
| 581 | C4 | — | 20 | 2 | no | — |
| 582 | C4 | — | 20 | 1 | no | — |
| 583 | C4 | — | 20 | 1 | no | — |
| 584 | C4 | — | 40 | 2 | no | — |
| 585 | C4 | C2×D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 586 | C2 | — | 2 | 1 | no | — |
| 587 | C2 | — | 4 | 2 | no | — |
| 588 | C2 | — | 8 | 1 | no | — |
| 589 | C2 | — | 8 | 1 | no | — |
| 590 | C2 | — | 10 | 2 | no | — |
| 591 | C2 | — | 20 | 2 | no | — |
| 592 | C2 | #10617223 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617560 | C2 | semidirect |
| 2. #10617449 | C2 | semidirect |
| 4. #10604864 | C2 | semidirect |
| 5. #10604618 | C2 | semidirect |
| 6. #10604611 | C2 | semidirect |
| 7. #10604008 | C2 | semidirect |
| 8. AGL(1,𝔽5)×#104 | C2 | semidirect |
| 9. #10603924 | C2 | semidirect |
| 13. #66256 | C22 | semidirect |
| 20. #65771 | C22 | semidirect |
| 25. C2×#4008 | C22 | semidirect |
| 30. #65729 | C22 | semidirect |
| 31. M16×AGL(1,𝔽5) | C22 | semidirect |
| 32. C42×AGL(1,𝔽5) | C22 | semidirect |
| 33. #65681 | C22 | semidirect |
| 34. C5×#453 | C4 | semidirect |
| 35. #65531 | C4 | semidirect |
| 36. #65490 | C4 | semidirect |
| 37. #65366 | C4 | semidirect |
| 38. #65115 | C4 | semidirect |
| 40. #65035 | C4 | semidirect |
| 42. #64902 | C22 | semidirect |
| 43. #64900 | C22 | semidirect |
| 44. #64862 | C22 | semidirect |
| 76. C5×AGL(1,ℤ/8) | C2×C4 | semidirect |
| 77. C5×#127 | C2×C4 | semidirect |
| 78. #4097 | C2×C4 | semidirect |
| 80. #4082 | C2×C4 | semidirect |
| 81. #4082 | C2×C4 | semidirect |
| 83. #4078 | C2×C4 | semidirect |
| 88. #4055 | C2×C4 | semidirect |
| 91. #4015 | C2×C4 | semidirect |
| 94. #4010 | D4 | semidirect |
| 95. #4010 | D4 | semidirect |
| 103. #4008 | D4 | semidirect |
| 104. #4008 | D4 | semidirect |
| 110. C5×#104 | C2×C4 | semidirect |
| 111. C5×#100 | C2×C4 | semidirect |
| 112. #3969 | C2×C4 | semidirect |
| 113. #3965 | C2×C4 | semidirect |
| 114. #3957 | C2×C4 | semidirect |
| 115. #3956 | C2×C4 | semidirect |
| 116. #3937 | C2×C4 | semidirect |
| 227. #453 | AGL(1,𝔽5) | semidirect |
| 327. AGL(1,ℤ/8) | C2×AGL(1,𝔽5) | semidirect |
| 342. #127 | C2×AGL(1,𝔽5) | semidirect |
| 374. #104 | C2×AGL(1,𝔽5) | semidirect |
| 377. #100 | C2×AGL(1,𝔽5) | semidirect |
| 561. C5 | #22899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617560 | 2 |
| #10617449 | 2 |
| #10612008 | 2 |
| #10604864 | 2 |
| #10604618 | 2 |
| #10604611 | 2 |
| #10604008 | 2 |
| AGL(1,𝔽5)×#104 | 2 |
| #10603924 | 2 |
| #22899 | 5 |