Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
930 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C2×#66091 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10604786 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10604784 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10604727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10604713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#4144 | — | 2 | 1 | no | — |
| 7 | C22×C5×D8 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C2×#4078 | — | 2 | 1 | no | — |
| 9 | #66091 | — | 2 | 4 | no | — |
| 10 | #66091 | — | 2 | 4 | no | — |
| 11 | C2×#4058 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#4058 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#4057 | — | 2 | 1 | no | — |
| 14 | C2×#4057 | — | 2 | 1 | no | — |
| 15 | C2×D5×D8 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×D5×D8 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#4050 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65745 | — | 2 | 1 | no | — |
| 20 | #65721 | C22 | 1 | 2 | yes | complemented |
| 21 | D5⋊M32 | C22 | 1 | 2 | yes | complemented |
| 22 | #64912 | — | 2 | 1 | no | — |
| 23 | #64904 | — | 2 | 4 | no | — |
| 24 | #64903 | — | 2 | 4 | no | — |
| 25 | #64895 | — | 2 | 1 | no | — |
| 26 | #64891 | — | 2 | 1 | no | — |
| 27 | #12741 | — | 5 | 1 | no | maximal, Sylow |
| 28 | C22×C5×D4 | — | 2 | 1 | no | — |
| 29 | C22×C22⋊D5 | — | 4 | 1 | no | — |
| 30 | C22×C22⋊D5 | — | 4 | 1 | no | — |
| 31 | #4144 | — | 2 | 8 | no | — |
| 32 | #4144 | — | 4 | 4 | no | — |
| 33 | C2×#711 | — | 2 | 1 | no | — |
| 34 | C2×#711 | — | 2 | 1 | no | — |
| 35 | C2×#711 | — | 4 | 1 | no | — |
| 36 | C2×D4×D5 | — | 2 | 1 | no | — |
| 37 | C2×D4×D5 | — | 2 | 1 | no | — |
| 38 | C2×D4×D5 | — | 4 | 1 | no | — |
| 39 | C2×#709 | — | 2 | 1 | no | — |
| 40 | C2×#709 | D4 | 1 | 1 | yes | characteristic |
| 41 | #4130 | — | 2 | 2 | no | — |
| 42 | C2×C5×D8 | — | 2 | 2 | no | — |
| 43 | C2×C5×D8 | — | 2 | 2 | no | — |
| 44 | C2×C5×D8 | — | 2 | 1 | no | — |
| 45 | C2×C5×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×C5×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C22×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#687 | — | 2 | 1 | no | — |
| 49 | C2×#687 | — | 2 | 1 | no | — |
| 50 | #4078 | — | 2 | 8 | no | — |
| 51 | C2×#686 | — | 2 | 1 | no | — |
| 52 | C2×#686 | — | 2 | 1 | no | — |
| 53 | C2×#681 | D4 | 1 | 1 | yes | characteristic |
| 54 | #4058 | — | 2 | 2 | no | — |
| 55 | #4058 | — | 2 | 2 | no | — |
| 56 | #4058 | — | 2 | 2 | no | — |
| 57 | #4058 | D4 | 1 | 4 | yes | — |
| 58 | #4057 | — | 2 | 8 | no | — |
| 59 | #4057 | — | 2 | 8 | no | — |
| 60 | D5×D8 | — | 2 | 2 | no | — |
| 61 | D5×D8 | — | 2 | 2 | no | — |
| 62 | D5×D8 | — | 2 | 2 | no | — |
| 63 | D5×D8 | D4 | 1 | 4 | yes | — |
| 64 | C2×Dic20 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | #4050 | — | 2 | 2 | no | — |
| 66 | #4050 | — | 2 | 2 | no | — |
| 67 | C2×D40 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×#677 | — | 2 | 1 | no | — |
| 69 | #4047 | — | 2 | 2 | no | — |
| 70 | #4047 | — | 2 | 2 | no | — |
| 71 | C2×#676 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×#676 | D4 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 75 | #4011 | — | 4 | 1 | no | — |
| 76 | #3999 | — | 4 | 1 | no | — |
| 77 | #3998 | — | 2 | 2 | no | — |
| 78 | #3994 | — | 2 | 2 | no | — |
| 79 | #3993 | — | 2 | 2 | no | — |
| 80 | #3990 | — | 2 | 2 | no | — |
| 81 | D5⋊C16 | — | 2 | 2 | no | — |
| 82 | C2×#576 | — | 5 | 1 | no | — |
| 83 | #2145 | — | 5 | 2 | no | — |
| 84 | #2140 | — | 5 | 2 | no | — |
| 85 | #2115 | — | 5 | 1 | no | — |
| 86 | #1812 | — | 5 | 1 | no | — |
| 87 | C24×C5 | — | 4 | 1 | no | — |
| 88 | C23×D5 | — | 4 | 1 | no | — |
| 89 | C23×D5 | — | 4 | 1 | no | — |
| 90 | C2×C5×D4 | — | 2 | 4 | no | — |
| 91 | C2×C5×D4 | — | 2 | 1 | no | — |
| 92 | C2×C5×D4 | — | 2 | 1 | no | — |
| 93 | C2×C5×D4 | — | 4 | 2 | no | — |
| 94 | C2×C5×D4 | — | 4 | 1 | no | — |
| 95 | C22×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×C22⋊D5 | — | 4 | 8 | no | — |
| 97 | C2×C22⋊D5 | — | 4 | 8 | no | — |
| 98 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 99 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 100 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 101 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 102 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 103 | C2×C22⋊D5 | D8 | 1 | 1 | yes | characteristic |
| 104 | C2×C22⋊D5 | SD16 | 1 | 1 | yes | characteristic |
| 105 | C22×Dic5 | — | 4 | 1 | no | — |
| 106 | C22×Dic5 | — | 4 | 1 | no | — |
| 107 | #711 | — | 2 | 4 | no | — |
| 108 | #711 | — | 2 | 4 | no | — |
| 109 | #711 | — | 4 | 8 | no | — |
| 110 | #711 | — | 4 | 2 | no | — |
| 111 | #711 | — | 4 | 2 | no | — |
| 112 | D4×D5 | — | 2 | 4 | no | — |
| 113 | D4×D5 | — | 2 | 4 | no | — |
| 114 | D4×D5 | — | 4 | 2 | no | — |
| 115 | D4×D5 | — | 4 | 8 | no | — |
| 116 | D4×D5 | — | 4 | 2 | no | — |
| 117 | #709 | — | 2 | 2 | no | — |
| 118 | #709 | — | 2 | 2 | no | — |
| 119 | #709 | — | 2 | 4 | no | — |
| 120 | #709 | — | 4 | 2 | no | — |
| 121 | C2×D20 | — | 2 | 1 | no | — |
| 122 | C2×D20 | D8 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×D5 | — | 4 | 1 | no | — |
| 124 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×Dic10 | — | 2 | 1 | no | — |
| 127 | C2×Dic10 | SD16 | 1 | 1 | yes | characteristic |
| 128 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 129 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 130 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 131 | C5×D8 | — | 2 | 4 | no | — |
| 132 | C5×D8 | — | 2 | 1 | no | — |
| 133 | C5×D8 | — | 2 | 1 | no | — |
| 134 | C5×D8 | C22⋊C4 | 1 | 2 | yes | — |
| 135 | C5×D8 | C22⋊C4 | 1 | 2 | yes | — |
| 136 | C2×C5×C8 | — | 2 | 1 | no | — |
| 137 | C2×C5×C8 | — | 2 | 1 | no | — |
| 138 | C2×C5×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 140 | #687 | — | 2 | 4 | no | — |
| 141 | #687 | — | 2 | 4 | no | — |
| 142 | #686 | — | 2 | 4 | no | — |
| 143 | #686 | — | 2 | 4 | no | — |
| 144 | #681 | — | 2 | 2 | no | — |
| 145 | C2×#168 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 146 | C2×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | Dic20 | — | 2 | 1 | no | — |
| 148 | Dic20 | C22⋊C4 | 1 | 2 | yes | — |
| 149 | D40 | — | 2 | 1 | no | — |
| 150 | D40 | C22⋊C4 | 1 | 2 | yes | — |
| 151 | #677 | — | 2 | 4 | no | — |
| 152 | #676 | — | 2 | 2 | no | — |
| 153 | #676 | — | 2 | 2 | no | — |
| 154 | C8×D5 | — | 2 | 1 | no | — |
| 155 | C8×D5 | — | 2 | 1 | no | — |
| 156 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 157 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 158 | #674 | — | 4 | 2 | no | — |
| 159 | C2×H(5,𝔽2) | — | 10 | 1 | no | — |
| 160 | #576 | — | 10 | 4 | no | — |
| 161 | #576 | — | 10 | 4 | no | — |
| 162 | C2×AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 163 | C2×AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 164 | C2×AGL(1,ℤ/8) | — | 10 | 1 | no | — |
| 165 | C2×#135 | — | 5 | 1 | no | — |
| 166 | C2×#135 | — | 5 | 1 | no | — |
| 167 | C2×#135 | — | 5 | 1 | no | — |
| 168 | C22×D8 | — | 5 | 1 | no | — |
| 169 | C22×D8 | — | 5 | 1 | no | — |
| 170 | C22×D8 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 171 | C2×#131 | — | 5 | 1 | no | — |
| 172 | C2×M32 | — | 5 | 2 | no | — |
| 173 | #427 | — | 5 | 2 | no | — |
| 174 | #410 | — | 10 | 1 | no | — |
| 175 | #360 | — | 10 | 4 | no | — |
| 176 | #357 | — | 10 | 4 | no | — |
| 177 | #349 | — | 10 | 1 | no | — |
| 178 | #349 | — | 10 | 1 | no | — |
| 179 | H(3,ℤ/4) | — | 10 | 1 | no | — |
| 180 | C23×C5 | — | 4 | 4 | no | — |
| 181 | C23×C5 | — | 4 | 1 | no | — |
| 182 | C23×C5 | — | 4 | 1 | no | — |
| 183 | C23×C5 | — | 16 | 2 | no | — |
| 184 | C23×C5 | #102 | 1 | 1 | yes | characteristic |
| 185 | C22×D5 | — | 4 | 4 | no | — |
| 186 | C22×D5 | — | 4 | 1 | no | — |
| 187 | C22×D5 | — | 4 | 4 | no | — |
| 188 | C22×D5 | — | 16 | 2 | no | — |
| 189 | C22×D5 | — | 16 | 2 | no | — |
| 190 | C22×D5 | #102 | 1 | 1 | yes | characteristic |
| 191 | C22×D5 | C2×D8 | 1 | 1 | yes | characteristic |
| 192 | C2×AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 193 | C5×D4 | — | 2 | 2 | no | — |
| 194 | C5×D4 | — | 2 | 2 | no | — |
| 195 | C5×D4 | — | 4 | 4 | no | — |
| 196 | C5×D4 | — | 4 | 1 | no | — |
| 197 | C5×D4 | — | 4 | 1 | no | — |
| 198 | C2×C4×C5 | — | 2 | 1 | no | — |
| 199 | C2×C4×C5 | — | 2 | 1 | no | — |
| 200 | C2×C4×C5 | #102 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | C22⋊D5 | — | 2 | 2 | no | — |
| 203 | C22⋊D5 | — | 2 | 2 | no | — |
| 204 | C22⋊D5 | — | 4 | 4 | no | — |
| 205 | C22⋊D5 | — | 4 | 4 | no | — |
| 206 | C22⋊D5 | — | 4 | 4 | no | — |
| 207 | C22⋊D5 | — | 4 | 4 | no | — |
| 208 | C22⋊D5 | — | 4 | 4 | no | — |
| 209 | C2×Dic5 | — | 4 | 4 | no | — |
| 210 | C2×Dic5 | — | 4 | 1 | no | — |
| 211 | C2×Dic5 | — | 4 | 4 | no | — |
| 212 | C2×Dic5 | #102 | 1 | 1 | yes | characteristic |
| 213 | C2×Dic5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 214 | D20 | — | 2 | 2 | no | — |
| 215 | D20 | — | 2 | 2 | no | — |
| 216 | D20 | — | 4 | 1 | no | — |
| 217 | C4×D5 | — | 2 | 1 | no | — |
| 218 | C4×D5 | — | 2 | 1 | no | — |
| 219 | C4×D5 | — | 4 | 4 | no | — |
| 220 | C4×D5 | #120 | 1 | 2 | yes | — |
| 221 | C4×D5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 222 | Dic10 | — | 2 | 2 | no | — |
| 223 | Dic10 | — | 2 | 2 | no | — |
| 224 | Dic10 | — | 4 | 1 | no | — |
| 225 | C5×C8 | — | 2 | 1 | no | — |
| 226 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 227 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 228 | #168 | — | 2 | 1 | no | — |
| 229 | #168 | #120 | 1 | 2 | yes | — |
| 230 | H(5,𝔽2) | — | 10 | 8 | no | — |
| 231 | H(5,𝔽2) | — | 20 | 4 | no | — |
| 232 | C2×#41 | — | 5 | 1 | no | — |
| 233 | C2×#41 | — | 10 | 1 | no | — |
| 234 | C2×#41 | — | 10 | 1 | no | — |
| 235 | C2×#41 | — | 10 | 1 | no | — |
| 236 | C2×#41 | — | 20 | 1 | no | — |
| 237 | C22×D4 | — | 2 | 1 | no | — |
| 238 | C22×D4 | — | 10 | 1 | no | — |
| 239 | C22×D4 | — | 10 | 1 | no | — |
| 240 | C22×D4 | — | 20 | 1 | no | — |
| 241 | C22×D4 | — | 20 | 1 | no | — |
| 242 | C22×D4 | — | 20 | 1 | no | — |
| 243 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 244 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 245 | AGL(1,ℤ/8) | — | 10 | 8 | no | — |
| 246 | #135 | — | 5 | 4 | no | — |
| 247 | #135 | — | 10 | 2 | no | — |
| 248 | #135 | — | 10 | 2 | no | — |
| 249 | #135 | — | 10 | 2 | no | — |
| 250 | #135 | — | 10 | 2 | no | — |
| 251 | #135 | — | 10 | 2 | no | — |
| 252 | C2×Q16 | — | 5 | 1 | no | — |
| 253 | C2×SD16 | — | 10 | 1 | no | — |
| 254 | C2×SD16 | — | 10 | 1 | no | — |
| 255 | C2×SD16 | — | 10 | 1 | no | — |
| 256 | C2×D8 | — | 2 | 2 | no | — |
| 257 | C2×D8 | — | 2 | 2 | no | — |
| 258 | C2×D8 | — | 2 | 1 | no | — |
| 259 | C2×D8 | — | 5 | 4 | no | — |
| 260 | C2×D8 | — | 5 | 1 | no | — |
| 261 | C2×D8 | — | 10 | 2 | no | — |
| 262 | C2×D8 | — | 10 | 1 | no | — |
| 263 | C2×D8 | — | 10 | 1 | no | — |
| 264 | C2×D8 | — | 10 | 2 | no | — |
| 265 | C2×D8 | — | 10 | 2 | no | — |
| 266 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 267 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 268 | #131 | — | 10 | 2 | no | — |
| 269 | #131 | — | 10 | 2 | no | — |
| 270 | C2×M16 | — | 5 | 1 | no | — |
| 271 | C2×M16 | — | 5 | 1 | no | — |
| 272 | C2×M16 | — | 5 | 1 | no | — |
| 273 | C22×C8 | — | 5 | 1 | no | — |
| 274 | C22×C8 | — | 5 | 1 | no | — |
| 275 | C22×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 276 | #117 | — | 10 | 2 | no | — |
| 277 | M32 | — | 10 | 2 | no | — |
| 278 | M32 | — | 10 | 2 | no | — |
| 279 | C2×C16 | — | 10 | 2 | no | — |
| 280 | #107 | — | 10 | 2 | no | — |
| 281 | #106 | — | 10 | 2 | no | — |
| 282 | #99 | — | 20 | 1 | no | — |
| 283 | #99 | — | 20 | 1 | no | — |
| 284 | C22×C5 | — | 2 | 1 | no | — |
| 285 | C22×C5 | — | 4 | 1 | no | — |
| 286 | C22×C5 | — | 4 | 2 | no | — |
| 287 | C22×C5 | — | 4 | 2 | no | — |
| 288 | C22×C5 | — | 8 | 2 | no | — |
| 289 | C22×C5 | — | 8 | 2 | no | — |
| 290 | C22×C5 | — | 16 | 4 | no | — |
| 291 | C22×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 292 | C2×D5 | — | 2 | 1 | no | — |
| 293 | C2×D5 | — | 4 | 1 | no | — |
| 294 | C2×D5 | — | 4 | 1 | no | — |
| 295 | C2×D5 | — | 4 | 2 | no | — |
| 296 | C2×D5 | — | 8 | 2 | no | — |
| 297 | C2×D5 | — | 16 | 4 | no | — |
| 298 | C2×D5 | — | 16 | 4 | no | — |
| 299 | C2×D5 | #447 | 1 | 2 | yes | — |
| 300 | AGL(1,𝔽5) | — | 16 | 2 | no | — |
| 301 | C4×C5 | — | 2 | 1 | no | — |
| 302 | C4×C5 | #379 | 1 | 1 | yes | characteristic |
| 303 | C4×C5 | #418 | 1 | 1 | yes | characteristic |
| 304 | Dic5 | — | 2 | 1 | no | — |
| 305 | Dic5 | — | 4 | 2 | no | — |
| 306 | Dic5 | #450 | 1 | 2 | yes | — |
| 307 | C24 | — | 4 | 1 | no | — |
| 308 | C24 | — | 20 | 1 | no | — |
| 309 | C24 | — | 20 | 1 | no | — |
| 310 | #41 | — | 10 | 2 | no | — |
| 311 | #41 | — | 10 | 2 | no | — |
| 312 | #41 | — | 10 | 4 | no | — |
| 313 | #41 | — | 10 | 4 | no | — |
| 314 | #41 | — | 10 | 4 | no | — |
| 315 | #41 | — | 20 | 2 | no | — |
| 316 | #41 | — | 20 | 2 | no | — |
| 317 | #41 | — | 20 | 2 | no | — |
| 318 | #41 | — | 20 | 8 | no | — |
| 319 | C2×Q8 | — | 5 | 1 | no | — |
| 320 | C2×Q8 | — | 10 | 1 | no | — |
| 321 | C2×D4 | — | 2 | 4 | no | — |
| 322 | C2×D4 | — | 2 | 1 | no | — |
| 323 | C2×D4 | — | 2 | 1 | no | — |
| 324 | C2×D4 | — | 4 | 2 | no | — |
| 325 | C2×D4 | — | 4 | 1 | no | — |
| 326 | C2×D4 | — | 5 | 1 | no | — |
| 327 | C2×D4 | — | 5 | 1 | no | — |
| 328 | C2×D4 | — | 5 | 1 | no | — |
| 329 | C2×D4 | — | 10 | 4 | no | — |
| 330 | C2×D4 | — | 10 | 4 | no | — |
| 331 | C2×D4 | — | 10 | 1 | no | — |
| 332 | C2×D4 | — | 20 | 2 | no | — |
| 333 | C2×D4 | — | 20 | 1 | no | — |
| 334 | C2×D4 | — | 20 | 1 | no | — |
| 335 | C2×D4 | — | 20 | 2 | no | — |
| 336 | C2×D4 | — | 20 | 8 | no | — |
| 337 | C2×D4 | — | 20 | 8 | no | — |
| 338 | C2×D4 | — | 20 | 8 | no | — |
| 339 | C2×D4 | — | 20 | 1 | no | — |
| 340 | C2×D4 | — | 20 | 1 | no | — |
| 341 | C2×D4 | — | 20 | 1 | no | — |
| 342 | C22×C4 | — | 5 | 1 | no | — |
| 343 | C22×C4 | — | 5 | 1 | no | — |
| 344 | C22×C4 | — | 20 | 1 | no | — |
| 345 | C22×C4 | — | 20 | 1 | no | — |
| 346 | C22×C4 | — | 20 | 1 | no | — |
| 347 | C22×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 348 | Q16 | — | 5 | 2 | no | — |
| 349 | Q16 | — | 10 | 1 | no | — |
| 350 | SD16 | — | 10 | 4 | no | — |
| 351 | SD16 | — | 10 | 4 | no | — |
| 352 | SD16 | — | 10 | 4 | no | — |
| 353 | D8 | — | 2 | 4 | no | — |
| 354 | D8 | — | 2 | 1 | no | — |
| 355 | D8 | — | 2 | 1 | no | — |
| 356 | D8 | — | 5 | 2 | no | — |
| 357 | D8 | — | 10 | 4 | no | — |
| 358 | D8 | — | 10 | 4 | no | — |
| 359 | D8 | — | 10 | 1 | no | — |
| 360 | D8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 361 | D8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 362 | M16 | — | 10 | 2 | no | — |
| 363 | M16 | — | 10 | 2 | no | — |
| 364 | M16 | — | 10 | 2 | no | — |
| 365 | C2×C8 | — | 2 | 1 | no | — |
| 366 | C2×C8 | — | 2 | 1 | no | — |
| 367 | C2×C8 | — | 5 | 1 | no | — |
| 368 | C2×C8 | — | 5 | 2 | no | — |
| 369 | C2×C8 | — | 5 | 2 | no | — |
| 370 | C2×C8 | — | 5 | 1 | no | — |
| 371 | C2×C8 | — | 10 | 1 | no | — |
| 372 | C2×C8 | — | 10 | 1 | no | — |
| 373 | C2×C8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 374 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 375 | C4⋊C4 | — | 20 | 2 | no | — |
| 376 | C22⋊C4 | — | 20 | 2 | no | — |
| 377 | C42 | — | 20 | 2 | no | — |
| 378 | C16 | — | 20 | 2 | no | — |
| 379 | C2×C5 | — | 2 | 1 | no | — |
| 380 | C2×C5 | — | 4 | 1 | no | — |
| 381 | C2×C5 | — | 8 | 2 | no | — |
| 382 | C2×C5 | — | 8 | 2 | no | — |
| 383 | C2×C5 | #1786 | 1 | 1 | yes | characteristic |
| 384 | D5 | — | 2 | 2 | no | — |
| 385 | D5 | — | 4 | 1 | no | — |
| 386 | D5 | — | 8 | 2 | no | — |
| 387 | C23 | — | 4 | 4 | no | — |
| 388 | C23 | — | 4 | 1 | no | — |
| 389 | C23 | — | 4 | 1 | no | — |
| 390 | C23 | — | 5 | 1 | no | — |
| 391 | C23 | — | 5 | 1 | no | — |
| 392 | C23 | — | 16 | 2 | no | — |
| 393 | C23 | — | 20 | 4 | no | — |
| 394 | C23 | — | 20 | 4 | no | — |
| 395 | C23 | — | 20 | 1 | no | — |
| 396 | C23 | — | 80 | 2 | no | — |
| 397 | C23 | — | 80 | 2 | no | — |
| 398 | C23 | #4007 | 1 | 1 | yes | characteristic |
| 399 | Q8 | — | 10 | 2 | no | — |
| 400 | Q8 | — | 10 | 2 | no | — |
| 401 | Q8 | — | 20 | 1 | no | — |
| 402 | D4 | — | 2 | 2 | no | — |
| 403 | D4 | — | 2 | 2 | no | — |
| 404 | D4 | — | 4 | 4 | no | — |
| 405 | D4 | — | 4 | 1 | no | — |
| 406 | D4 | — | 4 | 1 | no | — |
| 407 | D4 | — | 10 | 2 | no | — |
| 408 | D4 | — | 10 | 2 | no | — |
| 409 | D4 | — | 10 | 2 | no | — |
| 410 | D4 | — | 10 | 2 | no | — |
| 411 | D4 | — | 20 | 4 | no | — |
| 412 | D4 | — | 20 | 4 | no | — |
| 413 | D4 | — | 20 | 4 | no | — |
| 414 | D4 | — | 20 | 4 | no | — |
| 415 | D4 | — | 20 | 4 | no | — |
| 416 | D4 | — | 20 | 1 | no | — |
| 417 | C2×C4 | — | 2 | 1 | no | — |
| 418 | C2×C4 | — | 2 | 1 | no | — |
| 419 | C2×C4 | — | 5 | 1 | no | — |
| 420 | C2×C4 | — | 5 | 2 | no | — |
| 421 | C2×C4 | — | 5 | 2 | no | — |
| 422 | C2×C4 | — | 5 | 1 | no | — |
| 423 | C2×C4 | — | 10 | 1 | no | — |
| 424 | C2×C4 | — | 10 | 1 | no | — |
| 425 | C2×C4 | — | 20 | 4 | no | — |
| 426 | C2×C4 | — | 20 | 4 | no | — |
| 427 | C2×C4 | — | 20 | 4 | no | — |
| 428 | C2×C4 | — | 20 | 1 | no | — |
| 429 | C2×C4 | — | 40 | 2 | no | — |
| 430 | C2×C4 | #4007 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 432 | C8 | — | 2 | 1 | no | — |
| 433 | C8 | — | 5 | 2 | no | — |
| 434 | C8 | — | 10 | 1 | no | — |
| 435 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 436 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 437 | C5 | #12741 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 438 | C22 | — | 2 | 1 | no | — |
| 439 | C22 | — | 4 | 1 | no | — |
| 440 | C22 | — | 4 | 2 | no | — |
| 441 | C22 | — | 4 | 2 | no | — |
| 442 | C22 | — | 5 | 2 | no | — |
| 443 | C22 | — | 8 | 2 | no | — |
| 444 | C22 | — | 8 | 2 | no | — |
| 445 | C22 | — | 10 | 1 | no | — |
| 446 | C22 | — | 16 | 4 | no | — |
| 447 | C22 | — | 20 | 1 | no | — |
| 448 | C22 | — | 20 | 1 | no | — |
| 449 | C22 | — | 20 | 2 | no | — |
| 450 | C22 | — | 40 | 2 | no | — |
| 451 | C22 | — | 80 | 4 | no | — |
| 452 | C22 | — | 80 | 4 | no | — |
| 453 | C22 | C2×#4007 | 1 | 1 | yes | characteristic |
| 454 | C4 | — | 2 | 1 | no | — |
| 455 | C4 | — | 5 | 2 | no | — |
| 456 | C4 | — | 10 | 1 | no | — |
| 457 | C4 | — | 20 | 2 | no | — |
| 458 | C4 | — | 80 | 2 | no | — |
| 459 | C4 | #65767 | 1 | 1 | yes | characteristic |
| 460 | C4 | #65800 | 1 | 1 | yes | characteristic |
| 461 | C2 | — | 2 | 1 | no | — |
| 462 | C2 | — | 4 | 1 | no | — |
| 463 | C2 | — | 8 | 2 | no | — |
| 464 | C2 | — | 8 | 2 | no | — |
| 465 | C2 | — | 10 | 2 | no | — |
| 466 | C2 | — | 20 | 1 | no | — |
| 467 | C2 | — | 40 | 2 | no | — |
| 468 | C2 | #10604928 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10604786 | C2 | semidirect |
| 3. #10604784 | C2 | semidirect |
| 4. #10604727 | C2 | semidirect |
| 5. #10604713 | C2 | semidirect |
| 7. C22×C5×D8 | C4 | semidirect |
| 11. C2×#4058 | C4 | semidirect |
| 15. C2×D5×D8 | C4 | semidirect |
| 17. C2×#4050 | C4 | semidirect |
| 20. #65721 | C22 | semidirect |
| 21. D5⋊M32 | C22 | semidirect |
| 170. C22×D8 | AGL(1,𝔽5) | semidirect |
| 437. C5 | #12741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66091 | 2 |
| #10604786 | 2 |
| #10604784 | 2 |
| #10604727 | 2 |
| #10604713 | 2 |
| #12741 | 5 |