Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
644 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #10617220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10612035 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10605018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10605016 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10604458 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #66285 | C22 | 1 | 1 | yes | characteristic |
| 9 | #65920 | — | 2 | 1 | no | — |
| 10 | #65920 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65798 | — | 2 | 1 | no | — |
| 12 | #65795 | — | 2 | 1 | no | — |
| 13 | #65794 | — | 2 | 1 | no | — |
| 14 | #65777 | — | 2 | 1 | no | — |
| 15 | #65777 | C22 | 1 | 1 | yes | characteristic |
| 16 | #65776 | C22 | 1 | 1 | yes | characteristic |
| 17 | #65775 | — | 2 | 1 | no | — |
| 18 | #65775 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65774 | — | 2 | 1 | no | — |
| 20 | #65773 | — | 2 | 1 | no | — |
| 21 | #65771 | C22 | 1 | 1 | yes | characteristic |
| 22 | #65697 | — | 2 | 1 | no | — |
| 23 | #65695 | — | 2 | 1 | no | — |
| 24 | #65694 | — | 2 | 1 | no | — |
| 25 | C5×B(4,𝔽2) | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #65532 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #65321 | — | 2 | 1 | no | — |
| 28 | #65321 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #65031 | — | 2 | 1 | no | — |
| 30 | #65031 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | #65029 | — | 2 | 1 | no | — |
| 32 | #65029 | C22 | 1 | 1 | yes | characteristic |
| 33 | #64934 | — | 2 | 1 | no | — |
| 34 | #64865 | — | 2 | 1 | no | — |
| 35 | #13046 | — | 5 | 1 | no | maximal, Sylow |
| 36 | C5×H(5,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C23×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 38 | #4150 | — | 2 | 1 | no | — |
| 39 | #4150 | — | 4 | 1 | no | — |
| 40 | D5×#41 | — | 2 | 1 | no | — |
| 41 | D5×#41 | — | 4 | 1 | no | — |
| 42 | #4144 | — | 2 | 1 | no | — |
| 43 | #4144 | — | 2 | 1 | no | — |
| 44 | #4144 | — | 4 | 1 | no | — |
| 45 | #4144 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×#711 | — | 2 | 1 | no | — |
| 47 | C2×#711 | — | 2 | 1 | no | — |
| 48 | C2×#711 | — | 4 | 1 | no | — |
| 49 | C2×#711 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#704 | — | 2 | 1 | no | — |
| 51 | C2×#704 | — | 2 | 1 | no | — |
| 52 | C2×#704 | — | 2 | 1 | no | — |
| 53 | C2×#704 | D4 | 1 | 1 | yes | characteristic, complemented |
| 54 | C22×#170 | D4 | 1 | 1 | yes | characteristic, complemented |
| 55 | #4130 | — | 2 | 1 | no | — |
| 56 | C2×#700 | D4 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×D5⋊C8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | C5×#120 | — | 2 | 1 | no | — |
| 59 | C5×#120 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #4099 | — | 2 | 1 | no | — |
| 61 | #4099 | D4 | 1 | 1 | yes | characteristic |
| 62 | #4085 | — | 2 | 1 | no | — |
| 63 | #4085 | — | 4 | 1 | no | — |
| 64 | #4081 | — | 2 | 1 | no | — |
| 65 | #4081 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | D4×Dic5 | — | 2 | 1 | no | — |
| 67 | D4×Dic5 | — | 4 | 1 | no | — |
| 68 | #4032 | — | 2 | 1 | no | — |
| 69 | #4032 | D4 | 1 | 1 | yes | characteristic |
| 70 | #4027 | — | 2 | 1 | no | — |
| 71 | #4027 | — | 4 | 1 | no | — |
| 72 | #4024 | — | 2 | 1 | no | — |
| 73 | #4024 | — | 4 | 1 | no | — |
| 74 | #4023 | — | 2 | 1 | no | — |
| 75 | #4023 | D4 | 1 | 1 | yes | characteristic |
| 76 | #4013 | — | 2 | 1 | no | — |
| 77 | #4013 | — | 4 | 1 | no | — |
| 78 | C22⋊#170 | — | 2 | 1 | no | — |
| 79 | C22⋊#170 | — | 2 | 1 | no | — |
| 80 | C22⋊#170 | — | 2 | 1 | no | — |
| 81 | C22⋊#170 | — | 2 | 1 | no | — |
| 82 | C22⋊#170 | — | 2 | 1 | no | — |
| 83 | C22⋊#170 | — | 4 | 1 | no | — |
| 84 | #4011 | — | 2 | 1 | no | — |
| 85 | #4011 | — | 2 | 1 | no | — |
| 86 | #4010 | — | 4 | 1 | no | — |
| 87 | #4009 | — | 4 | 1 | no | — |
| 88 | #4008 | — | 4 | 1 | no | — |
| 89 | #4007 | — | 4 | 1 | no | — |
| 90 | #4005 | — | 2 | 1 | no | — |
| 91 | #4005 | — | 4 | 1 | no | — |
| 92 | #4004 | — | 2 | 1 | no | — |
| 93 | #4003 | — | 2 | 1 | no | — |
| 94 | #4003 | — | 4 | 1 | no | — |
| 95 | #4002 | — | 2 | 1 | no | — |
| 96 | C4⋊#170 | — | 2 | 1 | no | — |
| 97 | C4×#170 | — | 2 | 1 | no | — |
| 98 | C5×#99 | — | 2 | 1 | no | — |
| 99 | C5×#99 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | #3966 | — | 2 | 1 | no | — |
| 101 | #3966 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | #3938 | — | 2 | 1 | no | — |
| 103 | #3938 | — | 2 | 1 | no | — |
| 104 | #3938 | — | 2 | 1 | no | — |
| 105 | #3025 | — | 5 | 1 | no | — |
| 106 | #2978 | — | 5 | 1 | no | — |
| 107 | #2120 | — | 5 | 1 | no | — |
| 108 | #1794 | — | 5 | 1 | no | — |
| 109 | #1791 | — | 5 | 1 | no | — |
| 110 | #1395 | — | 5 | 1 | no | — |
| 111 | #1391 | — | 5 | 1 | no | — |
| 112 | C24×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C5×#41 | — | 2 | 1 | no | — |
| 114 | C5×#41 | — | 4 | 1 | no | — |
| 115 | C2×C5×D4 | — | 2 | 1 | no | — |
| 116 | C2×C5×D4 | — | 2 | 1 | no | — |
| 117 | C2×C5×D4 | — | 2 | 1 | no | — |
| 118 | C2×C5×D4 | — | 4 | 1 | no | — |
| 119 | C2×C5×D4 | — | 4 | 1 | no | — |
| 120 | C2×C5×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 121 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 122 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 123 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 124 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 125 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 126 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 127 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 128 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 129 | C2×C22⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×C22⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 131 | C22×Dic5 | — | 2 | 1 | no | — |
| 132 | C22×Dic5 | — | 2 | 1 | no | — |
| 133 | C22×Dic5 | — | 2 | 1 | no | — |
| 134 | C22×Dic5 | — | 2 | 1 | no | — |
| 135 | C22×Dic5 | — | 4 | 1 | no | — |
| 136 | C22×Dic5 | — | 4 | 1 | no | — |
| 137 | C22×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C22×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | #713 | — | 2 | 1 | no | — |
| 141 | Q8×D5 | — | 2 | 1 | no | — |
| 142 | Q8×D5 | — | 4 | 1 | no | — |
| 143 | #711 | — | 2 | 1 | no | — |
| 144 | #711 | — | 4 | 1 | no | — |
| 145 | #711 | — | 4 | 1 | no | — |
| 146 | #711 | — | 4 | 1 | no | — |
| 147 | #711 | — | 4 | 1 | no | — |
| 148 | #711 | — | 4 | 1 | no | — |
| 149 | #711 | — | 4 | 1 | no | — |
| 150 | #711 | — | 4 | 1 | no | — |
| 151 | #711 | — | 4 | 1 | no | — |
| 152 | #711 | — | 4 | 1 | no | — |
| 153 | #711 | — | 4 | 1 | no | — |
| 154 | #711 | — | 4 | 1 | no | — |
| 155 | #711 | — | 4 | 1 | no | — |
| 156 | #711 | — | 4 | 1 | no | — |
| 157 | D4×D5 | — | 2 | 1 | no | — |
| 158 | D4×D5 | — | 4 | 1 | no | — |
| 159 | D4×D5 | — | 4 | 1 | no | — |
| 160 | D4×D5 | — | 4 | 1 | no | — |
| 161 | D4×D5 | — | 4 | 1 | no | — |
| 162 | #709 | — | 2 | 1 | no | — |
| 163 | #709 | — | 4 | 1 | no | — |
| 164 | #709 | — | 4 | 1 | no | — |
| 165 | #709 | — | 4 | 1 | no | — |
| 166 | #709 | — | 4 | 1 | no | — |
| 167 | C2×C4×D5 | — | 2 | 1 | no | — |
| 168 | C2×C4×D5 | — | 2 | 1 | no | — |
| 169 | C2×C4×D5 | — | 4 | 1 | no | — |
| 170 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×Dic10 | — | 2 | 1 | no | — |
| 172 | C2×Dic10 | — | 2 | 1 | no | — |
| 173 | C2×Dic10 | — | 4 | 1 | no | — |
| 174 | C2×Dic10 | #41 | 1 | 1 | yes | characteristic |
| 175 | C22⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 176 | #704 | — | 4 | 1 | no | — |
| 177 | #704 | — | 4 | 1 | no | — |
| 178 | #704 | — | 4 | 1 | no | — |
| 179 | #704 | — | 8 | 1 | no | — |
| 180 | #704 | — | 8 | 1 | no | — |
| 181 | C2×#170 | — | 2 | 1 | no | — |
| 182 | C2×#170 | — | 2 | 1 | no | — |
| 183 | C2×#170 | — | 2 | 1 | no | — |
| 184 | C2×#170 | — | 2 | 1 | no | — |
| 185 | C2×#170 | — | 4 | 1 | no | — |
| 186 | C2×#170 | — | 4 | 1 | no | — |
| 187 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 188 | C4×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 189 | #700 | — | 4 | 1 | no | — |
| 190 | D5⋊C8 | — | 4 | 1 | no | — |
| 191 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 192 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 193 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 194 | C5×C22⋊C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 195 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 196 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 197 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 198 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 199 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 200 | C22⋊Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 201 | #685 | — | 2 | 1 | no | — |
| 202 | #685 | — | 4 | 1 | no | — |
| 203 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 204 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 205 | #683 | — | 2 | 1 | no | — |
| 206 | #683 | — | 2 | 1 | no | — |
| 207 | #683 | — | 4 | 1 | no | — |
| 208 | #683 | — | 4 | 1 | no | — |
| 209 | C4×Dic5 | — | 2 | 1 | no | — |
| 210 | C4×Dic5 | — | 4 | 1 | no | — |
| 211 | #585 | — | 5 | 1 | no | — |
| 212 | #525 | — | 5 | 1 | no | — |
| 213 | #525 | — | 10 | 1 | no | — |
| 214 | #458 | — | 5 | 1 | no | — |
| 215 | #458 | — | 5 | 1 | no | — |
| 216 | #458 | — | 10 | 1 | no | — |
| 217 | B(4,𝔽2) | — | 5 | 1 | no | — |
| 218 | B(4,𝔽2) | — | 10 | 1 | no | — |
| 219 | B(4,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 220 | #436 | — | 10 | 1 | no | — |
| 221 | #436 | — | 10 | 1 | no | — |
| 222 | #435 | — | 10 | 1 | no | — |
| 223 | #435 | — | 10 | 1 | no | — |
| 224 | #433 | — | 10 | 1 | no | — |
| 225 | #421 | — | 10 | 1 | no | — |
| 226 | #416 | — | 10 | 1 | no | — |
| 227 | #413 | — | 5 | 1 | no | — |
| 228 | #413 | — | 10 | 1 | no | — |
| 229 | #410 | — | 5 | 1 | no | — |
| 230 | #410 | — | 5 | 1 | no | — |
| 231 | #410 | — | 10 | 1 | no | — |
| 232 | #408 | — | 5 | 1 | no | — |
| 233 | #408 | — | 5 | 1 | no | — |
| 234 | #408 | — | 10 | 1 | no | — |
| 235 | #407 | — | 10 | 1 | no | — |
| 236 | #352 | — | 10 | 1 | no | — |
| 237 | AΣL(1,𝔽16) | — | 10 | 1 | no | — |
| 238 | C23×C5 | — | 2 | 1 | no | — |
| 239 | C23×C5 | — | 2 | 1 | no | — |
| 240 | C23×C5 | — | 2 | 1 | no | — |
| 241 | C23×C5 | — | 4 | 1 | no | — |
| 242 | C23×C5 | — | 8 | 1 | no | — |
| 243 | C23×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 244 | C23×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 245 | C22×D5 | — | 2 | 1 | no | — |
| 246 | C22×D5 | — | 2 | 1 | no | — |
| 247 | C22×D5 | — | 4 | 1 | no | — |
| 248 | C22×D5 | #121 | 1 | 1 | yes | characteristic |
| 249 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 250 | C5×Q8 | — | 2 | 1 | no | — |
| 251 | C5×D4 | — | 2 | 1 | no | — |
| 252 | C5×D4 | — | 4 | 1 | no | — |
| 253 | C5×D4 | — | 4 | 1 | no | — |
| 254 | C5×D4 | — | 4 | 1 | no | — |
| 255 | C5×D4 | — | 4 | 1 | no | — |
| 256 | C5×D4 | — | 8 | 1 | no | — |
| 257 | C5×D4 | — | 8 | 2 | no | — |
| 258 | C2×C4×C5 | — | 2 | 1 | no | — |
| 259 | C2×C4×C5 | — | 2 | 1 | no | — |
| 260 | C2×C4×C5 | — | 2 | 1 | no | — |
| 261 | C2×C4×C5 | — | 4 | 1 | no | — |
| 262 | C2×C4×C5 | — | 4 | 1 | no | — |
| 263 | C2×C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 264 | C22⋊D5 | — | 4 | 1 | no | — |
| 265 | C22⋊D5 | — | 4 | 1 | no | — |
| 266 | C22⋊D5 | — | 4 | 1 | no | — |
| 267 | C22⋊D5 | — | 4 | 1 | no | — |
| 268 | C22⋊D5 | — | 4 | 1 | no | — |
| 269 | C22⋊D5 | — | 4 | 1 | no | — |
| 270 | C22⋊D5 | — | 4 | 1 | no | — |
| 271 | C22⋊D5 | — | 4 | 1 | no | — |
| 272 | C22⋊D5 | — | 4 | 1 | no | — |
| 273 | C22⋊D5 | — | 8 | 1 | no | — |
| 274 | C22⋊D5 | — | 8 | 2 | no | — |
| 275 | C2×Dic5 | — | 2 | 1 | no | — |
| 276 | C2×Dic5 | — | 2 | 1 | no | — |
| 277 | C2×Dic5 | — | 2 | 1 | no | — |
| 278 | C2×Dic5 | — | 2 | 1 | no | — |
| 279 | C2×Dic5 | — | 2 | 1 | no | — |
| 280 | C2×Dic5 | — | 2 | 1 | no | — |
| 281 | C2×Dic5 | — | 2 | 1 | no | — |
| 282 | C2×Dic5 | — | 2 | 1 | no | — |
| 283 | C2×Dic5 | — | 4 | 1 | no | — |
| 284 | C2×Dic5 | — | 4 | 1 | no | — |
| 285 | C2×Dic5 | — | 4 | 1 | 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 | — | 8 | 1 | no | — |
| 291 | C2×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 292 | C2×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 293 | C2×Dic5 | #123 | 1 | 1 | yes | characteristic |
| 294 | D20 | — | 2 | 1 | no | — |
| 295 | D20 | — | 4 | 1 | no | — |
| 296 | C4×D5 | — | 2 | 1 | no | — |
| 297 | C4×D5 | — | 2 | 1 | no | — |
| 298 | C4×D5 | — | 4 | 1 | no | — |
| 299 | C4×D5 | — | 4 | 1 | no | — |
| 300 | C4×D5 | — | 4 | 1 | no | — |
| 301 | C4×D5 | — | 4 | 1 | no | — |
| 302 | C4×D5 | — | 4 | 1 | no | — |
| 303 | Dic10 | — | 2 | 1 | no | — |
| 304 | Dic10 | — | 4 | 1 | no | — |
| 305 | Dic10 | — | 4 | 1 | no | — |
| 306 | Dic10 | — | 4 | 1 | no | — |
| 307 | Dic10 | — | 4 | 1 | no | — |
| 308 | #170 | — | 4 | 1 | no | — |
| 309 | #170 | — | 4 | 1 | no | — |
| 310 | #170 | — | 4 | 1 | no | — |
| 311 | #170 | — | 4 | 1 | no | — |
| 312 | #170 | — | 8 | 1 | no | — |
| 313 | 2−1+4 | — | 10 | 1 | no | — |
| 314 | 2−1+4 | — | 20 | 1 | no | — |
| 315 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 316 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 317 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 318 | H(5,𝔽2) | — | 20 | 1 | no | — |
| 319 | H(5,𝔽2) | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 320 | C2×#41 | — | 5 | 1 | no | — |
| 321 | C2×#41 | — | 10 | 1 | no | — |
| 322 | C2×#41 | — | 10 | 1 | no | — |
| 323 | C2×#41 | — | 10 | 1 | no | — |
| 324 | C2×#41 | — | 20 | 1 | no | — |
| 325 | C2×#41 | — | 20 | 1 | no | — |
| 326 | C23×C4 | — | 5 | 1 | no | — |
| 327 | C2×M16 | — | 5 | 1 | no | — |
| 328 | C2×M16 | — | 5 | 1 | no | — |
| 329 | C2×M16 | — | 10 | 1 | no | — |
| 330 | C2×M16 | — | 10 | 1 | no | — |
| 331 | C2×M16 | — | 10 | 1 | no | — |
| 332 | C22×C8 | — | 5 | 1 | no | — |
| 333 | C22×C8 | — | 5 | 1 | no | — |
| 334 | #123 | — | 5 | 1 | no | — |
| 335 | #123 | — | 5 | 1 | no | — |
| 336 | #123 | — | 10 | 1 | no | — |
| 337 | #123 | — | 10 | 1 | no | — |
| 338 | C22⋊Q8 | — | 10 | 1 | no | — |
| 339 | C22⋊Q8 | — | 20 | 1 | no | — |
| 340 | #121 | — | 10 | 1 | no | — |
| 341 | #121 | — | 20 | 1 | no | — |
| 342 | #120 | — | 2 | 1 | no | — |
| 343 | #120 | — | 5 | 1 | no | — |
| 344 | #120 | — | 10 | 1 | no | — |
| 345 | #120 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 346 | C4×D4 | — | 10 | 1 | no | — |
| 347 | C4×D4 | — | 10 | 1 | no | — |
| 348 | C4×D4 | — | 20 | 1 | no | — |
| 349 | C4×D4 | — | 20 | 1 | no | — |
| 350 | #117 | — | 5 | 1 | no | — |
| 351 | #117 | — | 10 | 1 | no | — |
| 352 | #117 | — | 10 | 1 | no | — |
| 353 | C4⋊C8 | — | 10 | 1 | no | — |
| 354 | C4⋊C8 | — | 10 | 1 | no | — |
| 355 | #104 | — | 20 | 1 | no | — |
| 356 | #104 | — | 20 | 1 | no | — |
| 357 | #103 | — | 20 | 1 | no | — |
| 358 | #102 | — | 20 | 1 | no | — |
| 359 | #101 | — | 10 | 1 | no | — |
| 360 | #101 | — | 20 | 1 | no | — |
| 361 | #100 | — | 10 | 1 | no | — |
| 362 | #100 | — | 20 | 1 | no | — |
| 363 | #99 | — | 2 | 1 | no | — |
| 364 | #99 | — | 5 | 1 | no | — |
| 365 | #99 | — | 10 | 1 | no | — |
| 366 | #99 | — | 10 | 1 | no | — |
| 367 | #99 | — | 10 | 1 | no | — |
| 368 | #99 | — | 10 | 1 | no | — |
| 369 | #99 | — | 10 | 1 | no | — |
| 370 | #99 | — | 10 | 1 | no | — |
| 371 | #99 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 372 | C22⋊C8 | — | 10 | 1 | no | — |
| 373 | C22⋊C8 | — | 10 | 1 | no | — |
| 374 | C22⋊C8 | — | 10 | 1 | no | — |
| 375 | C22⋊C8 | — | 10 | 1 | no | — |
| 376 | C22⋊C8 | — | 10 | 1 | no | — |
| 377 | C22⋊C8 | — | 10 | 1 | no | — |
| 378 | C22⋊C8 | — | 20 | 1 | no | — |
| 379 | C22⋊C8 | — | 20 | 1 | no | — |
| 380 | #97 | — | 10 | 1 | no | — |
| 381 | C4×C8 | — | 10 | 1 | no | — |
| 382 | C22×C5 | — | 2 | 1 | no | — |
| 383 | C22×C5 | — | 2 | 1 | no | — |
| 384 | C22×C5 | — | 4 | 1 | no | — |
| 385 | C22×C5 | — | 4 | 1 | no | — |
| 386 | C22×C5 | — | 4 | 1 | no | — |
| 387 | C22×C5 | — | 4 | 1 | no | — |
| 388 | C22×C5 | — | 4 | 2 | no | — |
| 389 | C22×C5 | — | 4 | 1 | no | — |
| 390 | C22×C5 | — | 4 | 1 | no | — |
| 391 | C22×C5 | — | 8 | 1 | no | — |
| 392 | C22×C5 | — | 8 | 1 | no | — |
| 393 | C22×C5 | — | 8 | 1 | no | — |
| 394 | C22×C5 | #386 | 1 | 1 | yes | characteristic |
| 395 | C2×D5 | — | 2 | 1 | no | — |
| 396 | C2×D5 | — | 4 | 1 | no | — |
| 397 | C2×D5 | — | 4 | 1 | no | — |
| 398 | C2×D5 | — | 8 | 1 | no | — |
| 399 | C2×D5 | — | 8 | 1 | no | — |
| 400 | C2×D5 | — | 16 | 1 | no | — |
| 401 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 402 | C4×C5 | — | 2 | 1 | no | — |
| 403 | C4×C5 | — | 4 | 1 | no | — |
| 404 | C4×C5 | — | 4 | 1 | no | — |
| 405 | C4×C5 | — | 8 | 1 | no | — |
| 406 | Dic5 | — | 2 | 1 | no | — |
| 407 | Dic5 | — | 2 | 1 | no | — |
| 408 | Dic5 | — | 4 | 1 | no | — |
| 409 | Dic5 | — | 4 | 1 | no | — |
| 410 | Dic5 | — | 4 | 1 | no | — |
| 411 | Dic5 | — | 8 | 1 | no | — |
| 412 | Dic5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 413 | Dic5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 414 | C24 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 415 | #41 | — | 2 | 1 | no | — |
| 416 | #41 | — | 4 | 1 | no | — |
| 417 | #41 | — | 10 | 1 | no | — |
| 418 | #41 | — | 10 | 1 | no | — |
| 419 | #41 | — | 10 | 1 | no | — |
| 420 | #41 | — | 20 | 1 | no | — |
| 421 | #41 | — | 20 | 1 | no | — |
| 422 | #41 | — | 20 | 1 | no | — |
| 423 | #41 | — | 20 | 1 | no | — |
| 424 | #41 | — | 20 | 1 | no | — |
| 425 | #41 | — | 20 | 1 | no | — |
| 426 | #41 | — | 20 | 1 | no | — |
| 427 | #41 | — | 20 | 1 | no | — |
| 428 | #41 | — | 20 | 1 | no | — |
| 429 | #41 | — | 20 | 1 | no | — |
| 430 | #41 | — | 20 | 1 | no | — |
| 431 | #41 | — | 20 | 1 | no | — |
| 432 | #41 | — | 20 | 1 | no | — |
| 433 | #41 | — | 20 | 1 | no | — |
| 434 | #41 | — | 20 | 1 | no | — |
| 435 | #41 | — | 20 | 1 | no | — |
| 436 | #41 | — | 20 | 1 | no | — |
| 437 | C2×Q8 | — | 5 | 1 | no | — |
| 438 | C2×Q8 | — | 10 | 1 | no | — |
| 439 | C2×Q8 | — | 10 | 1 | no | — |
| 440 | C2×Q8 | — | 10 | 1 | no | — |
| 441 | C2×Q8 | — | 20 | 1 | no | — |
| 442 | C2×Q8 | — | 20 | 1 | no | — |
| 443 | C2×D4 | — | 2 | 1 | no | — |
| 444 | C2×D4 | — | 2 | 1 | no | — |
| 445 | C2×D4 | — | 2 | 1 | no | — |
| 446 | C2×D4 | — | 4 | 1 | no | — |
| 447 | C2×D4 | — | 4 | 1 | no | — |
| 448 | C2×D4 | — | 5 | 1 | no | — |
| 449 | C2×D4 | — | 5 | 1 | no | — |
| 450 | C2×D4 | — | 10 | 1 | no | — |
| 451 | C2×D4 | — | 10 | 1 | no | — |
| 452 | C2×D4 | — | 10 | 1 | no | — |
| 453 | C2×D4 | — | 10 | 1 | no | — |
| 454 | C2×D4 | — | 10 | 1 | no | — |
| 455 | C2×D4 | — | 10 | 1 | no | — |
| 456 | C2×D4 | — | 20 | 1 | no | — |
| 457 | C2×D4 | — | 20 | 1 | no | — |
| 458 | C2×D4 | — | 20 | 1 | no | — |
| 459 | C2×D4 | — | 20 | 1 | no | — |
| 460 | C2×D4 | — | 20 | 1 | no | — |
| 461 | C2×D4 | — | 20 | 1 | no | — |
| 462 | C2×D4 | — | 20 | 1 | no | — |
| 463 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 464 | C22×C4 | — | 5 | 1 | no | — |
| 465 | C22×C4 | — | 5 | 1 | no | — |
| 466 | C22×C4 | — | 5 | 1 | no | — |
| 467 | C22×C4 | — | 5 | 1 | no | — |
| 468 | C22×C4 | — | 10 | 1 | no | — |
| 469 | C22×C4 | — | 10 | 1 | no | — |
| 470 | C22×C4 | — | 10 | 1 | no | — |
| 471 | C22×C4 | — | 10 | 1 | no | — |
| 472 | C22×C4 | — | 10 | 1 | no | — |
| 473 | C22×C4 | — | 10 | 1 | no | — |
| 474 | C22×C4 | — | 20 | 1 | no | — |
| 475 | C22×C4 | — | 20 | 1 | no | — |
| 476 | C22×C4 | — | 20 | 1 | no | — |
| 477 | M16 | — | 20 | 1 | no | — |
| 478 | M16 | — | 20 | 1 | no | — |
| 479 | M16 | — | 20 | 1 | no | — |
| 480 | M16 | — | 20 | 1 | no | — |
| 481 | M16 | — | 40 | 1 | no | — |
| 482 | M16 | — | 40 | 1 | no | — |
| 483 | C2×C8 | — | 10 | 1 | no | — |
| 484 | C2×C8 | — | 10 | 1 | no | — |
| 485 | C2×C8 | — | 10 | 1 | no | — |
| 486 | C2×C8 | — | 10 | 1 | no | — |
| 487 | C2×C8 | — | 20 | 1 | no | — |
| 488 | C2×C8 | — | 20 | 1 | no | — |
| 489 | C2×C8 | — | 20 | 1 | no | — |
| 490 | C4⋊C4 | — | 10 | 1 | no | — |
| 491 | C4⋊C4 | — | 10 | 1 | no | — |
| 492 | C4⋊C4 | — | 10 | 1 | no | — |
| 493 | C4⋊C4 | — | 20 | 1 | no | — |
| 494 | C4⋊C4 | — | 20 | 1 | no | — |
| 495 | C4⋊C4 | — | 20 | 1 | no | — |
| 496 | C4⋊C4 | — | 20 | 1 | no | — |
| 497 | C22⋊C4 | — | 2 | 1 | no | — |
| 498 | C22⋊C4 | — | 2 | 1 | no | — |
| 499 | C22⋊C4 | — | 4 | 1 | no | — |
| 500 | C22⋊C4 | — | 5 | 1 | no | — |
| 501 | C22⋊C4 | — | 10 | 1 | no | — |
| 502 | C22⋊C4 | — | 10 | 1 | no | — |
| 503 | C22⋊C4 | — | 10 | 1 | no | — |
| 504 | C22⋊C4 | — | 10 | 1 | no | — |
| 505 | C22⋊C4 | — | 20 | 1 | no | — |
| 506 | C22⋊C4 | — | 20 | 1 | no | — |
| 507 | C22⋊C4 | — | 20 | 1 | no | — |
| 508 | C22⋊C4 | — | 20 | 1 | no | — |
| 509 | C22⋊C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 510 | C42 | — | 10 | 1 | no | — |
| 511 | C42 | — | 20 | 1 | no | — |
| 512 | C42 | — | 20 | 1 | no | — |
| 513 | C2×C5 | — | 2 | 1 | no | — |
| 514 | C2×C5 | — | 4 | 1 | no | — |
| 515 | C2×C5 | — | 4 | 1 | no | — |
| 516 | C2×C5 | — | 8 | 1 | no | — |
| 517 | C2×C5 | — | 8 | 1 | no | — |
| 518 | C2×C5 | #1889 | 1 | 1 | yes | characteristic |
| 519 | D5 | — | 4 | 1 | no | — |
| 520 | D5 | — | 8 | 1 | no | — |
| 521 | C23 | — | 2 | 1 | no | — |
| 522 | C23 | — | 2 | 1 | no | — |
| 523 | C23 | — | 2 | 1 | no | — |
| 524 | C23 | — | 4 | 1 | no | — |
| 525 | C23 | — | 5 | 1 | no | — |
| 526 | C23 | — | 8 | 1 | no | — |
| 527 | C23 | — | 10 | 1 | no | — |
| 528 | C23 | — | 10 | 1 | no | — |
| 529 | C23 | — | 20 | 1 | no | — |
| 530 | C23 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 531 | C23 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 532 | Q8 | — | 2 | 1 | no | — |
| 533 | Q8 | — | 10 | 1 | no | — |
| 534 | Q8 | — | 20 | 1 | no | — |
| 535 | Q8 | — | 20 | 1 | no | — |
| 536 | Q8 | — | 20 | 1 | no | — |
| 537 | Q8 | — | 20 | 1 | no | — |
| 538 | D4 | — | 2 | 1 | no | — |
| 539 | D4 | — | 4 | 1 | no | — |
| 540 | D4 | — | 4 | 1 | no | — |
| 541 | D4 | — | 4 | 1 | no | — |
| 542 | D4 | — | 4 | 1 | no | — |
| 543 | D4 | — | 8 | 1 | no | — |
| 544 | D4 | — | 8 | 2 | no | — |
| 545 | D4 | — | 10 | 1 | no | — |
| 546 | D4 | — | 20 | 1 | no | — |
| 547 | D4 | — | 20 | 1 | no | — |
| 548 | D4 | — | 20 | 1 | no | — |
| 549 | D4 | — | 20 | 1 | no | — |
| 550 | D4 | — | 20 | 1 | no | — |
| 551 | D4 | — | 20 | 1 | no | — |
| 552 | D4 | — | 20 | 1 | no | — |
| 553 | D4 | — | 20 | 1 | no | — |
| 554 | D4 | — | 20 | 1 | no | — |
| 555 | D4 | — | 20 | 1 | no | — |
| 556 | D4 | — | 40 | 1 | no | — |
| 557 | D4 | — | 40 | 2 | no | — |
| 558 | C2×C4 | — | 2 | 1 | no | — |
| 559 | C2×C4 | — | 2 | 1 | no | — |
| 560 | C2×C4 | — | 2 | 1 | no | — |
| 561 | C2×C4 | — | 4 | 1 | no | — |
| 562 | C2×C4 | — | 4 | 1 | no | — |
| 563 | C2×C4 | — | 5 | 1 | no | — |
| 564 | C2×C4 | — | 5 | 1 | no | — |
| 565 | C2×C4 | — | 5 | 1 | no | — |
| 566 | C2×C4 | — | 10 | 1 | no | — |
| 567 | C2×C4 | — | 10 | 1 | no | — |
| 568 | C2×C4 | — | 10 | 1 | no | — |
| 569 | C2×C4 | — | 10 | 1 | no | — |
| 570 | C2×C4 | — | 10 | 1 | no | — |
| 571 | C2×C4 | — | 10 | 1 | no | — |
| 572 | C2×C4 | — | 10 | 1 | no | — |
| 573 | C2×C4 | — | 10 | 1 | no | — |
| 574 | C2×C4 | — | 10 | 1 | no | — |
| 575 | C2×C4 | — | 10 | 1 | no | — |
| 576 | C2×C4 | — | 20 | 1 | no | — |
| 577 | C2×C4 | — | 20 | 1 | no | — |
| 578 | C2×C4 | — | 20 | 1 | no | — |
| 579 | C2×C4 | — | 20 | 1 | no | — |
| 580 | C2×C4 | — | 20 | 1 | no | — |
| 581 | C2×C4 | — | 20 | 1 | no | — |
| 582 | C2×C4 | — | 20 | 1 | no | — |
| 583 | C2×C4 | — | 20 | 1 | no | — |
| 584 | C2×C4 | — | 20 | 1 | no | — |
| 585 | C2×C4 | — | 20 | 1 | no | — |
| 586 | C2×C4 | — | 20 | 1 | no | — |
| 587 | C2×C4 | — | 20 | 1 | no | — |
| 588 | C2×C4 | — | 40 | 1 | no | — |
| 589 | C2×C4 | — | 40 | 1 | no | — |
| 590 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 591 | C8 | — | 20 | 1 | no | — |
| 592 | C8 | — | 20 | 1 | no | — |
| 593 | C8 | — | 20 | 1 | no | — |
| 594 | C8 | — | 20 | 1 | no | — |
| 595 | C8 | — | 40 | 1 | no | — |
| 596 | C5 | #13046 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 597 | C22 | — | 2 | 1 | no | — |
| 598 | C22 | — | 2 | 1 | no | — |
| 599 | C22 | — | 4 | 1 | no | — |
| 600 | C22 | — | 4 | 1 | no | — |
| 601 | C22 | — | 4 | 1 | no | — |
| 602 | C22 | — | 4 | 1 | no | — |
| 603 | C22 | — | 4 | 2 | no | — |
| 604 | C22 | — | 4 | 1 | no | — |
| 605 | C22 | — | 4 | 1 | no | — |
| 606 | C22 | — | 8 | 1 | no | — |
| 607 | C22 | — | 8 | 1 | no | — |
| 608 | C22 | — | 8 | 1 | no | — |
| 609 | C22 | — | 10 | 1 | no | — |
| 610 | C22 | — | 20 | 1 | no | — |
| 611 | C22 | — | 20 | 1 | no | — |
| 612 | C22 | — | 40 | 1 | no | — |
| 613 | C22 | — | 40 | 1 | no | — |
| 614 | C22 | — | 80 | 1 | no | — |
| 615 | C22 | #65779 | 1 | 1 | yes | characteristic |
| 616 | C4 | — | 2 | 1 | no | — |
| 617 | C4 | — | 4 | 1 | no | — |
| 618 | C4 | — | 4 | 1 | no | — |
| 619 | C4 | — | 5 | 1 | no | — |
| 620 | C4 | — | 5 | 1 | no | — |
| 621 | C4 | — | 8 | 1 | no | — |
| 622 | C4 | — | 10 | 1 | no | — |
| 623 | C4 | — | 10 | 1 | no | — |
| 624 | C4 | — | 20 | 1 | no | — |
| 625 | C4 | — | 20 | 1 | no | — |
| 626 | C4 | — | 20 | 1 | no | — |
| 627 | C4 | — | 40 | 1 | no | — |
| 628 | C4 | — | 80 | 1 | no | — |
| 629 | C2 | — | 2 | 1 | no | — |
| 630 | C2 | — | 4 | 1 | no | — |
| 631 | C2 | — | 4 | 1 | no | — |
| 632 | C2 | — | 8 | 1 | no | — |
| 633 | C2 | — | 8 | 1 | no | — |
| 634 | C2 | — | 20 | 1 | no | — |
| 635 | C2 | — | 40 | 1 | no | — |
| 636 | C2 | #10604461 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617220 | C2 | semidirect |
| 3. #10605018 | C2 | semidirect |
| 4. #10605016 | C2 | semidirect |
| 5. #10604458 | C2 | semidirect |
| 6. #10598570 | C2 | semidirect |
| 7. #10598569 | C2 | semidirect |
| 25. C5×B(4,𝔽2) | C4 | semidirect |
| 26. #65532 | C4 | semidirect |
| 28. #65321 | C4 | semidirect |
| 30. #65031 | C4 | semidirect |
| 53. C2×#704 | D4 | semidirect |
| 54. C22×#170 | D4 | semidirect |
| 56. C2×#700 | D4 | semidirect |
| 57. C2×D5⋊C8 | D4 | semidirect |
| 219. B(4,𝔽2) | AGL(1,𝔽5) | semidirect |
| 596. C5 | #13046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617220 | 2 |
| #10612035 | 2 |
| #10605018 | 2 |
| #10605016 | 2 |
| #10604458 | 2 |
| #10598570 | 2 |
| #10598569 | 2 |
| #13046 | 5 |