Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
976 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619184 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10605013 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10604998 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10604996 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10604940 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×C5×H(5,𝔽2) | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#4150 | C22 | 1 | 1 | yes | characteristic |
| 8 | #66166 | — | 2 | 1 | no | — |
| 9 | #66166 | C22 | 1 | 1 | yes | characteristic |
| 10 | #66165 | — | 2 | 2 | no | — |
| 11 | #41×Dic5 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #66159 | — | 2 | 1 | no | — |
| 13 | #66159 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #66140 | — | 2 | 2 | no | — |
| 15 | #66140 | — | 2 | 4 | no | — |
| 16 | #66139 | — | 2 | 1 | no | — |
| 17 | #66139 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#4082 | — | 2 | 1 | no | — |
| 19 | C2×#4082 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #65782 | — | 2 | 2 | no | — |
| 21 | #65769 | — | 2 | 2 | no | — |
| 22 | #65761 | C22 | 1 | 2 | yes | complemented |
| 23 | #65745 | C22 | 1 | 2 | yes | complemented |
| 24 | #64934 | — | 2 | 4 | no | — |
| 25 | #64929 | — | 2 | 1 | no | — |
| 26 | #64928 | — | 2 | 1 | no | — |
| 27 | #64923 | — | 2 | 1 | no | — |
| 28 | #64922 | — | 2 | 1 | no | — |
| 29 | #12715 | — | 5 | 1 | no | maximal, Sylow |
| 30 | C5×H(5,𝔽2) | — | 4 | 2 | no | — |
| 31 | C5×H(5,𝔽2) | — | 4 | 2 | no | — |
| 32 | C2×C5×#41 | — | 2 | 1 | no | — |
| 33 | C2×C5×#41 | — | 2 | 1 | no | — |
| 34 | C2×C5×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×C5×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C22×C5×D4 | — | 2 | 2 | no | — |
| 37 | C22×C5×D4 | — | 2 | 1 | no | — |
| 38 | C22×C5×D4 | — | 2 | 1 | no | — |
| 39 | C22×C5×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | #4150 | — | 4 | 2 | no | — |
| 41 | #4150 | — | 4 | 2 | no | — |
| 42 | C2×Q8×D5 | D4 | 1 | 2 | yes | — |
| 43 | C2×#711 | — | 2 | 2 | no | — |
| 44 | C2×#711 | D4 | 1 | 2 | yes | — |
| 45 | C2×#709 | — | 2 | 1 | no | — |
| 46 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 47 | C22×Dic10 | — | 2 | 1 | no | — |
| 48 | C22×Dic10 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #4130 | — | 2 | 2 | no | — |
| 50 | D5⋊M16 | — | 2 | 2 | no | — |
| 51 | #4099 | — | 2 | 4 | no | — |
| 52 | #4099 | D4 | 1 | 4 | yes | — |
| 53 | C2×C22⋊Dic5 | — | 2 | 4 | no | — |
| 54 | C2×C22⋊Dic5 | — | 2 | 2 | no | — |
| 55 | #4093 | D4 | 1 | 1 | yes | characteristic |
| 56 | Q8×Dic5 | — | 2 | 1 | no | — |
| 57 | #4090 | — | 2 | 1 | no | — |
| 58 | #4090 | D4 | 1 | 1 | yes | characteristic |
| 59 | #4086 | — | 2 | 1 | no | — |
| 60 | #4086 | D4 | 1 | 1 | yes | characteristic |
| 61 | #4085 | — | 2 | 4 | no | — |
| 62 | #4085 | — | 2 | 2 | no | — |
| 63 | #4084 | — | 2 | 4 | no | — |
| 64 | #4084 | — | 2 | 2 | no | — |
| 65 | #4082 | — | 2 | 4 | no | — |
| 66 | #4082 | — | 2 | 1 | no | — |
| 67 | #4082 | — | 2 | 2 | no | — |
| 68 | #4082 | — | 2 | 1 | no | — |
| 69 | #4082 | — | 2 | 1 | no | — |
| 70 | #4082 | — | 2 | 1 | no | — |
| 71 | #4082 | D4 | 1 | 1 | yes | characteristic |
| 72 | #4081 | — | 2 | 4 | no | — |
| 73 | #4081 | — | 2 | 2 | no | — |
| 74 | D4×Dic5 | — | 2 | 1 | no | — |
| 75 | D4×Dic5 | — | 2 | 2 | no | — |
| 76 | C4×C22⋊D5 | — | 2 | 4 | no | — |
| 77 | C4×C22⋊D5 | — | 2 | 2 | no | — |
| 78 | #4072 | — | 2 | 1 | no | — |
| 79 | #4072 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | #4070 | — | 2 | 4 | no | — |
| 81 | #4070 | — | 2 | 2 | no | — |
| 82 | C2×C4×Dic5 | — | 2 | 1 | no | — |
| 83 | C2×C4×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #4013 | — | 2 | 2 | no | — |
| 85 | #4011 | — | 2 | 2 | no | — |
| 86 | #4009 | — | 4 | 4 | no | — |
| 87 | #4008 | — | 4 | 4 | no | — |
| 88 | #4005 | — | 2 | 2 | no | — |
| 89 | #3999 | — | 2 | 2 | no | — |
| 90 | #3500 | — | 5 | 1 | no | — |
| 91 | #2132 | — | 5 | 1 | no | — |
| 92 | #2126 | — | 5 | 1 | no | — |
| 93 | #2122 | — | 5 | 2 | no | — |
| 94 | #1796 | — | 5 | 2 | no | — |
| 95 | C24×C5 | — | 2 | 2 | no | — |
| 96 | C24×C5 | C22⋊C4 | 1 | 2 | yes | — |
| 97 | C5×#41 | — | 2 | 2 | no | — |
| 98 | C5×#41 | — | 2 | 2 | no | — |
| 99 | C5×#41 | — | 4 | 4 | no | — |
| 100 | C5×#41 | — | 4 | 1 | no | — |
| 101 | C5×#41 | — | 4 | 1 | no | — |
| 102 | C5×#41 | — | 4 | 2 | no | — |
| 103 | C5×#41 | — | 4 | 2 | no | — |
| 104 | C2×C5×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C5×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 106 | C2×C5×D4 | — | 2 | 1 | no | — |
| 107 | C2×C5×D4 | — | 2 | 2 | no | — |
| 108 | C2×C5×D4 | — | 2 | 2 | no | — |
| 109 | C2×C5×D4 | — | 2 | 1 | no | — |
| 110 | C2×C5×D4 | — | 2 | 1 | no | — |
| 111 | C2×C5×D4 | — | 2 | 1 | no | — |
| 112 | C2×C5×D4 | — | 4 | 4 | no | — |
| 113 | C2×C5×D4 | — | 4 | 1 | no | — |
| 114 | C2×C5×D4 | — | 4 | 1 | no | — |
| 115 | C2×C5×D4 | — | 4 | 8 | no | — |
| 116 | C2×C5×D4 | — | 4 | 2 | no | — |
| 117 | C2×C5×D4 | — | 4 | 2 | no | — |
| 118 | C2×C5×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 119 | C2×C5×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C22×C4×C5 | — | 2 | 1 | no | — |
| 121 | C22×C4×C5 | — | 2 | 2 | no | — |
| 122 | C22×C4×C5 | — | 2 | 1 | no | — |
| 123 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 125 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 126 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 127 | C2×C22⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 128 | C22×Dic5 | — | 2 | 1 | no | — |
| 129 | C22×Dic5 | — | 2 | 2 | no | — |
| 130 | C22×Dic5 | — | 2 | 1 | no | — |
| 131 | C22×Dic5 | — | 2 | 2 | no | — |
| 132 | Q8×D5 | — | 2 | 4 | no | — |
| 133 | Q8×D5 | — | 4 | 2 | no | — |
| 134 | #711 | — | 2 | 4 | no | — |
| 135 | #711 | — | 4 | 2 | no | — |
| 136 | #711 | — | 4 | 8 | no | — |
| 137 | #709 | — | 4 | 1 | no | — |
| 138 | #709 | — | 4 | 1 | no | — |
| 139 | #709 | — | 4 | 4 | no | — |
| 140 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C4×D5 | — | 2 | 2 | no | — |
| 142 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 143 | C2×Dic10 | — | 2 | 1 | no | — |
| 144 | C2×Dic10 | — | 2 | 2 | no | — |
| 145 | C2×Dic10 | — | 4 | 1 | no | — |
| 146 | C2×Dic10 | — | 4 | 1 | no | — |
| 147 | C2×Dic10 | — | 4 | 4 | no | — |
| 148 | C2×Dic10 | C22⋊C4 | 1 | 2 | yes | — |
| 149 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 151 | #704 | — | 4 | 2 | no | — |
| 152 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 153 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 154 | #700 | — | 4 | 2 | no | — |
| 155 | D5⋊C8 | — | 4 | 2 | no | — |
| 156 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 157 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 158 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 159 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 160 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 161 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 162 | C22⋊Dic5 | C22⋊C4 | 1 | 2 | yes | — |
| 163 | #685 | — | 2 | 2 | no | — |
| 164 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 165 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 166 | #683 | — | 2 | 4 | no | — |
| 167 | #683 | — | 2 | 2 | no | — |
| 168 | C4×Dic5 | — | 2 | 2 | no | — |
| 169 | C4×Dic5 | — | 2 | 1 | no | — |
| 170 | C4×Dic5 | — | 2 | 1 | no | — |
| 171 | C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 173 | C2×2−1+4 | — | 5 | 1 | no | — |
| 174 | C2×H(5,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 175 | #548 | — | 10 | 2 | no | — |
| 176 | #546 | — | 10 | 4 | no | — |
| 177 | #546 | — | 10 | 2 | no | — |
| 178 | #536 | — | 5 | 1 | no | — |
| 179 | #536 | — | 10 | 1 | no | — |
| 180 | #535 | — | 5 | 1 | no | — |
| 181 | #535 | — | 10 | 1 | no | — |
| 182 | #532 | — | 5 | 1 | no | — |
| 183 | #532 | — | 10 | 1 | no | — |
| 184 | C2×#124 | — | 5 | 1 | no | — |
| 185 | C2×#124 | — | 10 | 1 | no | — |
| 186 | C4×#41 | — | 5 | 1 | no | — |
| 187 | #421 | — | 10 | 2 | no | — |
| 188 | #419 | — | 10 | 2 | no | — |
| 189 | #413 | — | 5 | 2 | no | — |
| 190 | #410 | — | 5 | 2 | no | — |
| 191 | #356 | — | 10 | 1 | no | — |
| 192 | #355 | — | 10 | 1 | no | — |
| 193 | #354 | — | 10 | 1 | no | — |
| 194 | #353 | — | 10 | 1 | no | — |
| 195 | AΣL(1,𝔽16) | — | 10 | 4 | no | — |
| 196 | C23×C5 | — | 2 | 1 | no | — |
| 197 | C23×C5 | — | 2 | 2 | no | — |
| 198 | C23×C5 | — | 2 | 1 | no | — |
| 199 | C23×C5 | — | 4 | 4 | no | — |
| 200 | C23×C5 | — | 4 | 2 | no | — |
| 201 | C23×C5 | — | 8 | 2 | no | — |
| 202 | C23×C5 | — | 8 | 4 | no | — |
| 203 | C23×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C22×D5 | #120 | 1 | 2 | yes | — |
| 205 | C2×AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 206 | C5×Q8 | — | 2 | 1 | no | — |
| 207 | C5×Q8 | — | 4 | 1 | no | — |
| 208 | C5×Q8 | #99 | 1 | 2 | yes | — |
| 209 | C5×D4 | — | 2 | 4 | no | — |
| 210 | C5×D4 | — | 2 | 1 | no | — |
| 211 | C5×D4 | — | 4 | 1 | no | — |
| 212 | C5×D4 | — | 4 | 2 | no | — |
| 213 | C5×D4 | — | 4 | 4 | no | — |
| 214 | C5×D4 | — | 4 | 2 | no | — |
| 215 | C5×D4 | — | 4 | 4 | no | — |
| 216 | C5×D4 | — | 4 | 1 | no | — |
| 217 | C5×D4 | — | 4 | 1 | no | — |
| 218 | C5×D4 | #99 | 1 | 2 | yes | — |
| 219 | C2×C4×C5 | — | 2 | 4 | no | — |
| 220 | C2×C4×C5 | — | 2 | 1 | no | — |
| 221 | C2×C4×C5 | — | 2 | 1 | no | — |
| 222 | C2×C4×C5 | — | 2 | 1 | no | — |
| 223 | C2×C4×C5 | — | 2 | 1 | no | — |
| 224 | C2×C4×C5 | — | 4 | 4 | no | — |
| 225 | C2×C4×C5 | — | 4 | 1 | no | — |
| 226 | C2×C4×C5 | — | 4 | 1 | no | — |
| 227 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 229 | C22⋊D5 | — | 4 | 2 | no | — |
| 230 | C22⋊D5 | — | 4 | 4 | no | — |
| 231 | C22⋊D5 | — | 8 | 2 | no | — |
| 232 | C22⋊D5 | — | 8 | 4 | no | — |
| 233 | C2×Dic5 | — | 2 | 1 | no | — |
| 234 | C2×Dic5 | — | 2 | 2 | no | — |
| 235 | C2×Dic5 | — | 2 | 1 | no | — |
| 236 | C2×Dic5 | — | 2 | 2 | no | — |
| 237 | C2×Dic5 | — | 4 | 4 | no | — |
| 238 | C2×Dic5 | — | 4 | 2 | no | — |
| 239 | C2×Dic5 | — | 8 | 1 | no | — |
| 240 | C2×Dic5 | — | 8 | 2 | no | — |
| 241 | C2×Dic5 | #120 | 1 | 2 | yes | — |
| 242 | D20 | — | 4 | 1 | no | — |
| 243 | C4×D5 | — | 2 | 2 | no | — |
| 244 | C4×D5 | — | 2 | 2 | no | — |
| 245 | C4×D5 | — | 4 | 4 | no | — |
| 246 | Dic10 | — | 2 | 2 | no | — |
| 247 | Dic10 | — | 2 | 2 | no | — |
| 248 | Dic10 | — | 4 | 1 | no | — |
| 249 | Dic10 | — | 4 | 4 | no | — |
| 250 | Dic10 | — | 4 | 2 | no | — |
| 251 | #170 | — | 8 | 2 | no | — |
| 252 | 2−1+4 | — | 20 | 2 | no | — |
| 253 | 2−1+4 | — | 20 | 2 | no | — |
| 254 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 255 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 256 | C2×#41 | — | 2 | 1 | no | — |
| 257 | C2×#41 | — | 2 | 1 | no | — |
| 258 | C2×#41 | — | 5 | 1 | no | — |
| 259 | C2×#41 | — | 5 | 2 | no | — |
| 260 | C2×#41 | — | 10 | 1 | no | — |
| 261 | C2×#41 | — | 10 | 2 | no | — |
| 262 | C2×#41 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 263 | C2×#41 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 264 | C22×Q8 | — | 5 | 2 | no | — |
| 265 | C22×Q8 | — | 5 | 1 | no | — |
| 266 | C22×Q8 | — | 10 | 1 | no | — |
| 267 | C22×D4 | — | 2 | 2 | no | — |
| 268 | C22×D4 | — | 2 | 1 | no | — |
| 269 | C22×D4 | — | 2 | 1 | no | — |
| 270 | C22×D4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 271 | C2×M16 | — | 10 | 2 | no | — |
| 272 | C4⋊Q8 | — | 5 | 1 | no | — |
| 273 | C4⋊Q8 | — | 10 | 1 | no | — |
| 274 | #127 | — | 5 | 1 | no | — |
| 275 | #127 | — | 10 | 1 | no | — |
| 276 | #124 | — | 5 | 1 | no | — |
| 277 | #124 | — | 5 | 1 | no | — |
| 278 | #124 | — | 10 | 1 | no | — |
| 279 | #124 | — | 10 | 1 | no | — |
| 280 | #124 | — | 10 | 2 | no | — |
| 281 | #124 | — | 10 | 1 | no | — |
| 282 | #124 | — | 10 | 4 | no | — |
| 283 | #124 | — | 10 | 1 | no | — |
| 284 | #123 | — | 10 | 2 | no | — |
| 285 | #123 | — | 10 | 4 | no | — |
| 286 | C22⋊Q8 | — | 10 | 2 | no | — |
| 287 | C22⋊Q8 | — | 10 | 4 | no | — |
| 288 | #121 | — | 10 | 2 | no | — |
| 289 | #121 | — | 10 | 2 | no | — |
| 290 | #121 | — | 10 | 4 | no | — |
| 291 | #121 | — | 10 | 4 | no | — |
| 292 | #120 | — | 5 | 4 | no | — |
| 293 | #120 | — | 10 | 4 | no | — |
| 294 | C4×Q8 | — | 10 | 1 | no | — |
| 295 | C4×D4 | — | 10 | 2 | no | — |
| 296 | C4×D4 | — | 10 | 2 | no | — |
| 297 | C4×D4 | — | 10 | 4 | no | — |
| 298 | C4×D4 | — | 10 | 1 | no | — |
| 299 | #117 | — | 5 | 1 | no | — |
| 300 | #117 | — | 10 | 1 | no | — |
| 301 | #117 | — | 10 | 2 | no | — |
| 302 | C2×C22⋊C4 | — | 10 | 4 | no | — |
| 303 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 304 | C2×C42 | — | 5 | 1 | no | — |
| 305 | C2×C42 | — | 10 | 1 | no | — |
| 306 | #104 | — | 20 | 4 | no | — |
| 307 | #103 | — | 20 | 4 | no | — |
| 308 | #101 | — | 10 | 2 | no | — |
| 309 | #100 | — | 10 | 2 | no | — |
| 310 | #99 | — | 10 | 2 | no | — |
| 311 | #99 | — | 10 | 2 | no | — |
| 312 | C22×C5 | — | 2 | 1 | no | — |
| 313 | C22×C5 | — | 2 | 2 | no | — |
| 314 | C22×C5 | — | 4 | 1 | no | — |
| 315 | C22×C5 | — | 4 | 2 | no | — |
| 316 | C22×C5 | — | 4 | 4 | no | — |
| 317 | C22×C5 | — | 4 | 2 | no | — |
| 318 | C22×C5 | — | 4 | 2 | no | — |
| 319 | C22×C5 | — | 4 | 1 | no | — |
| 320 | C22×C5 | — | 16 | 2 | no | — |
| 321 | C22×C5 | — | 16 | 4 | no | — |
| 322 | C22×C5 | #379 | 1 | 1 | yes | characteristic |
| 323 | C2×D5 | — | 2 | 2 | no | — |
| 324 | C2×D5 | — | 4 | 2 | no | — |
| 325 | AGL(1,𝔽5) | — | 16 | 2 | no | — |
| 326 | C4×C5 | — | 2 | 1 | no | — |
| 327 | C4×C5 | — | 2 | 2 | no | — |
| 328 | C4×C5 | — | 4 | 1 | no | — |
| 329 | C4×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 330 | C4×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 331 | Dic5 | — | 2 | 2 | no | — |
| 332 | Dic5 | — | 4 | 1 | no | — |
| 333 | Dic5 | — | 4 | 2 | no | — |
| 334 | Dic5 | — | 4 | 1 | no | — |
| 335 | Dic5 | — | 4 | 2 | no | — |
| 336 | C24 | — | 2 | 2 | no | — |
| 337 | C24 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 338 | #41 | — | 2 | 2 | no | — |
| 339 | #41 | — | 2 | 2 | no | — |
| 340 | #41 | — | 4 | 4 | no | — |
| 341 | #41 | — | 4 | 1 | no | — |
| 342 | #41 | — | 4 | 1 | no | — |
| 343 | #41 | — | 4 | 2 | no | — |
| 344 | #41 | — | 4 | 2 | no | — |
| 345 | #41 | — | 10 | 4 | no | — |
| 346 | #41 | — | 20 | 1 | no | — |
| 347 | #41 | — | 20 | 1 | no | — |
| 348 | #41 | — | 20 | 4 | no | — |
| 349 | #41 | — | 20 | 2 | no | — |
| 350 | #41 | — | 20 | 8 | no | — |
| 351 | C2×Q8 | — | 5 | 1 | no | — |
| 352 | C2×Q8 | — | 5 | 2 | no | — |
| 353 | C2×Q8 | — | 10 | 2 | no | — |
| 354 | C2×Q8 | — | 10 | 1 | no | — |
| 355 | C2×Q8 | — | 10 | 4 | no | — |
| 356 | C2×Q8 | — | 20 | 1 | no | — |
| 357 | C2×Q8 | — | 20 | 1 | no | — |
| 358 | C2×Q8 | — | 20 | 4 | no | — |
| 359 | C2×Q8 | — | 20 | 2 | no | — |
| 360 | C2×Q8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 361 | C2×Q8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 362 | C2×D4 | — | 2 | 1 | no | — |
| 363 | C2×D4 | — | 2 | 2 | no | — |
| 364 | C2×D4 | — | 2 | 2 | no | — |
| 365 | C2×D4 | — | 2 | 1 | no | — |
| 366 | C2×D4 | — | 2 | 1 | no | — |
| 367 | C2×D4 | — | 2 | 1 | no | — |
| 368 | C2×D4 | — | 4 | 4 | no | — |
| 369 | C2×D4 | — | 4 | 1 | no | — |
| 370 | C2×D4 | — | 4 | 1 | no | — |
| 371 | C2×D4 | — | 4 | 8 | no | — |
| 372 | C2×D4 | — | 4 | 2 | no | — |
| 373 | C2×D4 | — | 4 | 2 | no | — |
| 374 | C2×D4 | — | 5 | 2 | no | — |
| 375 | C2×D4 | — | 5 | 1 | no | — |
| 376 | C2×D4 | — | 10 | 2 | no | — |
| 377 | C2×D4 | — | 10 | 4 | no | — |
| 378 | C2×D4 | — | 10 | 2 | no | — |
| 379 | C2×D4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 380 | C2×D4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 381 | C22×C4 | — | 2 | 1 | no | — |
| 382 | C22×C4 | — | 2 | 2 | no | — |
| 383 | C22×C4 | — | 2 | 1 | no | — |
| 384 | C22×C4 | — | 5 | 2 | no | — |
| 385 | C22×C4 | — | 10 | 2 | no | — |
| 386 | C22×C4 | — | 10 | 2 | no | — |
| 387 | C22×C4 | — | 10 | 1 | no | — |
| 388 | C22×C4 | — | 10 | 2 | no | — |
| 389 | C22×C4 | — | 10 | 1 | no | — |
| 390 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 391 | M16 | — | 20 | 2 | no | — |
| 392 | M16 | — | 20 | 2 | no | — |
| 393 | C2×C8 | — | 20 | 2 | no | — |
| 394 | C4⋊C4 | — | 10 | 2 | no | — |
| 395 | C4⋊C4 | — | 10 | 2 | no | — |
| 396 | C4⋊C4 | — | 10 | 4 | no | — |
| 397 | C4⋊C4 | — | 10 | 1 | no | — |
| 398 | C4⋊C4 | — | 20 | 2 | no | — |
| 399 | C22⋊C4 | — | 5 | 2 | no | — |
| 400 | C22⋊C4 | — | 10 | 2 | no | — |
| 401 | C22⋊C4 | — | 10 | 2 | no | — |
| 402 | C22⋊C4 | — | 10 | 4 | no | — |
| 403 | C22⋊C4 | — | 10 | 4 | no | — |
| 404 | C22⋊C4 | — | 10 | 4 | no | — |
| 405 | C22⋊C4 | — | 10 | 4 | no | — |
| 406 | C22⋊C4 | — | 10 | 2 | no | — |
| 407 | C22⋊C4 | — | 20 | 2 | no | — |
| 408 | C42 | — | 5 | 1 | no | — |
| 409 | C42 | — | 5 | 1 | no | — |
| 410 | C42 | — | 10 | 2 | no | — |
| 411 | C42 | — | 10 | 1 | no | — |
| 412 | C42 | — | 10 | 1 | no | — |
| 413 | C42 | — | 20 | 2 | no | — |
| 414 | C2×C5 | — | 2 | 1 | no | — |
| 415 | C2×C5 | — | 4 | 2 | no | — |
| 416 | C2×C5 | — | 4 | 1 | no | — |
| 417 | C2×C5 | — | 8 | 2 | no | — |
| 418 | C2×C5 | — | 8 | 1 | no | — |
| 419 | C2×C5 | #1781 | 1 | 1 | yes | characteristic |
| 420 | D5 | — | 4 | 2 | no | — |
| 421 | C23 | — | 2 | 1 | no | — |
| 422 | C23 | — | 2 | 2 | no | — |
| 423 | C23 | — | 2 | 1 | no | — |
| 424 | C23 | — | 4 | 4 | no | — |
| 425 | C23 | — | 4 | 2 | no | — |
| 426 | C23 | — | 5 | 2 | no | — |
| 427 | C23 | — | 8 | 2 | no | — |
| 428 | C23 | — | 8 | 4 | no | — |
| 429 | C23 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 430 | Q8 | — | 2 | 1 | no | — |
| 431 | Q8 | — | 4 | 1 | no | — |
| 432 | Q8 | — | 10 | 2 | no | — |
| 433 | Q8 | — | 10 | 2 | no | — |
| 434 | Q8 | — | 20 | 1 | no | — |
| 435 | Q8 | — | 20 | 4 | no | — |
| 436 | Q8 | — | 20 | 2 | no | — |
| 437 | Q8 | #4011 | 1 | 2 | yes | — |
| 438 | D4 | — | 2 | 4 | no | — |
| 439 | D4 | — | 2 | 1 | no | — |
| 440 | D4 | — | 4 | 1 | no | — |
| 441 | D4 | — | 4 | 2 | no | — |
| 442 | D4 | — | 4 | 4 | no | — |
| 443 | D4 | — | 4 | 2 | no | — |
| 444 | D4 | — | 4 | 4 | no | — |
| 445 | D4 | — | 4 | 1 | no | — |
| 446 | D4 | — | 4 | 1 | no | — |
| 447 | D4 | — | 20 | 1 | no | — |
| 448 | D4 | — | 20 | 2 | no | — |
| 449 | D4 | — | 20 | 4 | no | — |
| 450 | D4 | — | 40 | 4 | no | — |
| 451 | D4 | — | 40 | 2 | no | — |
| 452 | D4 | #4011 | 1 | 2 | yes | — |
| 453 | C2×C4 | — | 2 | 4 | no | — |
| 454 | C2×C4 | — | 2 | 1 | no | — |
| 455 | C2×C4 | — | 2 | 1 | no | — |
| 456 | C2×C4 | — | 2 | 1 | no | — |
| 457 | C2×C4 | — | 2 | 1 | no | — |
| 458 | C2×C4 | — | 4 | 4 | no | — |
| 459 | C2×C4 | — | 4 | 1 | no | — |
| 460 | C2×C4 | — | 4 | 1 | no | — |
| 461 | C2×C4 | — | 5 | 2 | no | — |
| 462 | C2×C4 | — | 10 | 2 | no | — |
| 463 | C2×C4 | — | 10 | 2 | no | — |
| 464 | C2×C4 | — | 10 | 1 | no | — |
| 465 | C2×C4 | — | 10 | 1 | no | — |
| 466 | C2×C4 | — | 10 | 2 | no | — |
| 467 | C2×C4 | — | 10 | 2 | no | — |
| 468 | C2×C4 | — | 20 | 4 | no | — |
| 469 | C2×C4 | — | 20 | 4 | no | — |
| 470 | C2×C4 | — | 20 | 2 | no | — |
| 471 | C2×C4 | — | 40 | 1 | no | — |
| 472 | C2×C4 | — | 40 | 2 | no | — |
| 473 | C2×C4 | — | 40 | 2 | no | — |
| 474 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 475 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 476 | C8 | — | 40 | 2 | no | — |
| 477 | C5 | #12715 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 478 | C22 | — | 2 | 1 | no | — |
| 479 | C22 | — | 2 | 2 | no | — |
| 480 | C22 | — | 4 | 1 | no | — |
| 481 | C22 | — | 4 | 2 | no | — |
| 482 | C22 | — | 4 | 2 | no | — |
| 483 | C22 | — | 4 | 4 | no | — |
| 484 | C22 | — | 4 | 2 | no | — |
| 485 | C22 | — | 4 | 1 | no | — |
| 486 | C22 | — | 10 | 2 | no | — |
| 487 | C22 | — | 16 | 2 | no | — |
| 488 | C22 | — | 16 | 4 | no | — |
| 489 | C22 | — | 20 | 2 | no | — |
| 490 | C22 | #65800 | 1 | 1 | yes | characteristic |
| 491 | C4 | — | 2 | 1 | no | — |
| 492 | C4 | — | 2 | 2 | no | — |
| 493 | C4 | — | 4 | 1 | no | — |
| 494 | C4 | — | 10 | 2 | no | — |
| 495 | C4 | — | 20 | 1 | no | — |
| 496 | C4 | — | 20 | 1 | no | — |
| 497 | C4 | — | 20 | 2 | no | — |
| 498 | C4 | — | 20 | 2 | no | — |
| 499 | C4 | — | 80 | 2 | no | — |
| 500 | C4 | C2×#4011 | 1 | 1 | yes | characteristic |
| 501 | C4 | C2×#4011 | 1 | 1 | yes | characteristic |
| 502 | C2 | — | 2 | 1 | no | — |
| 503 | C2 | — | 4 | 2 | no | — |
| 504 | C2 | — | 4 | 1 | no | — |
| 505 | C2 | — | 8 | 1 | no | — |
| 506 | C2 | — | 8 | 2 | no | — |
| 507 | C2 | — | 20 | 2 | no | — |
| 508 | C2 | #10605024 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10605013 | C2 | semidirect |
| 3. #10604998 | C2 | semidirect |
| 4. #10604996 | C2 | semidirect |
| 5. #10604940 | C2 | semidirect |
| 6. C2×C5×H(5,𝔽2) | C4 | semidirect |
| 11. #41×Dic5 | C4 | semidirect |
| 13. #66159 | C4 | semidirect |
| 19. C2×#4082 | C4 | semidirect |
| 22. #65761 | C22 | semidirect |
| 23. #65745 | C22 | semidirect |
| 174. C2×H(5,𝔽2) | AGL(1,𝔽5) | semidirect |
| 477. C5 | #12715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619184 | 2 |
| #10605013 | 2 |
| #10604998 | 2 |
| #10604996 | 2 |
| #10604940 | 2 |
| #12715 | 5 |