Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1328 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 212 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 | #10619413 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10617215 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10612035 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10605018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10604463 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10603921 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10603920 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #66285 | C22 | 1 | 1 | yes | characteristic |
| 9 | C23×#170 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #66264 | — | 2 | 3 | no | — |
| 11 | D5⋊#131 | — | 2 | 3 | no | — |
| 12 | #66256 | — | 2 | 3 | no | — |
| 13 | #66256 | C22 | 1 | 3 | yes | — |
| 14 | C2×#4131 | — | 2 | 3 | no | — |
| 15 | C2×#4131 | C22 | 1 | 3 | yes | — |
| 16 | #65920 | C22 | 1 | 3 | yes | — |
| 17 | #65798 | C22 | 1 | 3 | yes | complemented |
| 18 | #65777 | C22 | 1 | 3 | yes | — |
| 19 | #65775 | C22 | 1 | 3 | yes | — |
| 20 | #65773 | — | 2 | 3 | no | — |
| 21 | D4×#170 | — | 2 | 3 | no | — |
| 22 | #65696 | C22 | 1 | 3 | yes | complemented |
| 23 | #65693 | — | 2 | 3 | no | — |
| 24 | #65692 | — | 2 | 3 | no | — |
| 25 | #65691 | C22 | 1 | 3 | yes | complemented |
| 26 | C5×B(4,𝔽2) | C4 | 1 | 1 | yes | characteristic |
| 27 | #65532 | C4 | 1 | 1 | yes | characteristic |
| 28 | #65321 | C4 | 1 | 3 | yes | — |
| 29 | #65031 | C4 | 1 | 3 | yes | — |
| 30 | #65029 | C22 | 1 | 3 | yes | — |
| 31 | #64867 | C22 | 1 | 6 | yes | complemented |
| 32 | #21483 | — | 5 | 1 | no | maximal, Sylow |
| 33 | C5×H(5,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C23×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 35 | #4150 | — | 2 | 3 | no | — |
| 36 | D5×#41 | — | 2 | 3 | no | — |
| 37 | #4144 | — | 2 | 3 | no | — |
| 38 | #4144 | C2×C4 | 1 | 3 | yes | — |
| 39 | C2×#711 | — | 2 | 3 | no | — |
| 40 | C2×#711 | C23 | 1 | 3 | yes | — |
| 41 | C2×#704 | — | 2 | 3 | no | — |
| 42 | C2×#704 | — | 2 | 3 | no | — |
| 43 | C2×#704 | D4 | 1 | 3 | yes | complemented |
| 44 | C2×#704 | C23 | 1 | 3 | yes | — |
| 45 | C2×#704 | C23 | 1 | 3 | yes | — |
| 46 | C22×#170 | — | 2 | 1 | no | — |
| 47 | C22×#170 | — | 2 | 3 | no | — |
| 48 | C22×#170 | — | 2 | 3 | no | — |
| 49 | C22×#170 | D4 | 1 | 3 | yes | complemented |
| 50 | C22×#170 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×#170 | C23 | 1 | 1 | yes | characteristic |
| 52 | #4133 | — | 2 | 1 | no | — |
| 53 | #4133 | — | 2 | 3 | no | — |
| 54 | #4131 | — | 2 | 3 | no | — |
| 55 | #4131 | — | 2 | 6 | no | — |
| 56 | #4131 | — | 2 | 3 | no | — |
| 57 | #4131 | — | 2 | 6 | no | — |
| 58 | #4131 | — | 2 | 6 | no | — |
| 59 | #4131 | — | 2 | 6 | no | — |
| 60 | #4131 | — | 2 | 6 | no | — |
| 61 | D5⋊M16 | — | 2 | 6 | no | — |
| 62 | D5⋊M16 | — | 2 | 3 | no | — |
| 63 | C2×#700 | — | 2 | 3 | no | — |
| 64 | C2×#700 | D4 | 1 | 3 | yes | complemented |
| 65 | C2×D5⋊C8 | — | 2 | 3 | no | — |
| 66 | C2×D5⋊C8 | D4 | 1 | 3 | yes | complemented |
| 67 | C5×#120 | C2×C4 | 1 | 3 | yes | — |
| 68 | #4099 | C2×C4 | 1 | 3 | yes | — |
| 69 | #4085 | — | 2 | 3 | no | — |
| 70 | #4081 | C2×C4 | 1 | 3 | yes | — |
| 71 | D4×Dic5 | — | 2 | 3 | no | — |
| 72 | #4032 | C2×C4 | 1 | 3 | yes | — |
| 73 | #4027 | — | 2 | 3 | no | — |
| 74 | #4024 | — | 2 | 3 | no | — |
| 75 | #4023 | C23 | 1 | 3 | yes | — |
| 76 | #4013 | — | 2 | 3 | no | — |
| 77 | C22⋊#170 | — | 2 | 3 | no | — |
| 78 | C22⋊#170 | — | 2 | 3 | no | — |
| 79 | C22⋊#170 | — | 2 | 3 | no | — |
| 80 | #4005 | — | 2 | 3 | no | — |
| 81 | #4004 | — | 2 | 3 | no | — |
| 82 | #4003 | — | 2 | 3 | no | — |
| 83 | #4002 | — | 2 | 3 | no | — |
| 84 | C4⋊#170 | — | 2 | 3 | no | — |
| 85 | C4×#170 | — | 2 | 3 | no | — |
| 86 | C5×#99 | C2×C4 | 1 | 3 | yes | — |
| 87 | #3966 | C2×C4 | 1 | 3 | yes | — |
| 88 | #3938 | C2×C4 | 1 | 6 | yes | — |
| 89 | #3573 | — | 5 | 1 | no | — |
| 90 | #3025 | — | 5 | 1 | no | — |
| 91 | #2929 | — | 5 | 3 | no | — |
| 92 | #1891 | — | 5 | 3 | no | — |
| 93 | #1868 | — | 5 | 3 | no | — |
| 94 | #1791 | — | 5 | 1 | no | — |
| 95 | #1757 | — | 5 | 3 | no | — |
| 96 | C24×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C5×#41 | — | 2 | 3 | no | — |
| 98 | C2×C5×D4 | — | 2 | 3 | no | — |
| 99 | C2×C5×D4 | — | 2 | 3 | no | — |
| 100 | C2×C5×D4 | C22×C4 | 1 | 3 | yes | — |
| 101 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 102 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 103 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 104 | C2×C22⋊D5 | C22×C4 | 1 | 3 | yes | — |
| 105 | C2×C22⋊D5 | #41 | 1 | 3 | yes | — |
| 106 | C22×Dic5 | — | 2 | 1 | no | — |
| 107 | C22×Dic5 | — | 2 | 3 | no | — |
| 108 | C22×Dic5 | — | 2 | 3 | no | — |
| 109 | C22×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C22×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 111 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 112 | #713 | — | 2 | 1 | no | — |
| 113 | Q8×D5 | — | 2 | 3 | no | — |
| 114 | #711 | — | 2 | 3 | no | — |
| 115 | #711 | — | 2 | 6 | no | — |
| 116 | #711 | — | 2 | 6 | no | — |
| 117 | #711 | — | 2 | 6 | no | — |
| 118 | #711 | — | 2 | 6 | no | — |
| 119 | D4×D5 | — | 2 | 3 | no | — |
| 120 | D4×D5 | — | 2 | 6 | no | — |
| 121 | #709 | — | 2 | 6 | no | — |
| 122 | #709 | — | 2 | 3 | no | — |
| 123 | C2×C4×D5 | — | 2 | 3 | no | — |
| 124 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 125 | C2×Dic10 | — | 2 | 3 | no | — |
| 126 | C2×Dic10 | #41 | 1 | 3 | yes | — |
| 127 | #704 | — | 2 | 6 | no | — |
| 128 | #704 | — | 2 | 6 | no | — |
| 129 | #704 | — | 2 | 6 | no | — |
| 130 | #704 | — | 2 | 6 | no | — |
| 131 | C2×#170 | — | 2 | 3 | no | — |
| 132 | C2×#170 | — | 2 | 3 | no | — |
| 133 | C2×#170 | — | 2 | 3 | no | — |
| 134 | C2×#170 | — | 2 | 3 | no | — |
| 135 | C2×#170 | — | 2 | 3 | no | — |
| 136 | C2×#170 | — | 2 | 3 | no | — |
| 137 | C2×#170 | — | 4 | 1 | no | — |
| 138 | C2×#170 | — | 4 | 3 | no | — |
| 139 | C2×#170 | C2×D4 | 1 | 3 | yes | — |
| 140 | C2×#170 | C2×D4 | 1 | 3 | yes | — |
| 141 | C2×#170 | C2×D4 | 1 | 3 | yes | — |
| 142 | C2×#170 | C2×D4 | 1 | 3 | yes | — |
| 143 | #700 | — | 2 | 3 | no | — |
| 144 | #700 | — | 2 | 3 | no | — |
| 145 | #700 | — | 2 | 6 | no | — |
| 146 | D5⋊C8 | — | 2 | 6 | no | — |
| 147 | D5⋊C8 | — | 2 | 3 | no | — |
| 148 | D5⋊C8 | — | 2 | 3 | no | — |
| 149 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 150 | C5×C22⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 151 | C22⋊Dic5 | — | 2 | 3 | no | — |
| 152 | C22⋊Dic5 | — | 2 | 3 | no | — |
| 153 | C22⋊Dic5 | C22×C4 | 1 | 3 | yes | — |
| 154 | #685 | — | 2 | 3 | no | — |
| 155 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 156 | #683 | — | 2 | 3 | no | — |
| 157 | #683 | — | 2 | 3 | no | — |
| 158 | C4×Dic5 | — | 2 | 3 | no | — |
| 159 | #585 | — | 5 | 1 | no | — |
| 160 | #568 | — | 5 | 3 | no | — |
| 161 | #568 | — | 10 | 3 | no | — |
| 162 | #568 | — | 10 | 3 | no | — |
| 163 | C2×#131 | — | 5 | 3 | no | — |
| 164 | C2×#131 | — | 10 | 3 | no | — |
| 165 | C2×#131 | — | 10 | 3 | no | — |
| 166 | C23×C8 | — | 5 | 1 | no | — |
| 167 | #525 | — | 5 | 3 | no | — |
| 168 | #458 | — | 5 | 1 | no | — |
| 169 | #458 | — | 5 | 3 | no | — |
| 170 | B(4,𝔽2) | — | 5 | 3 | no | — |
| 171 | B(4,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 172 | #435 | — | 10 | 3 | no | — |
| 173 | #435 | — | 10 | 3 | no | — |
| 174 | C8×D4 | — | 10 | 3 | no | — |
| 175 | C8×D4 | — | 10 | 3 | no | — |
| 176 | #424 | — | 5 | 3 | no | — |
| 177 | #413 | — | 5 | 3 | no | — |
| 178 | #410 | — | 5 | 3 | no | — |
| 179 | #408 | — | 5 | 3 | no | — |
| 180 | #407 | — | 5 | 3 | no | — |
| 181 | #405 | — | 5 | 3 | no | — |
| 182 | #344 | — | 5 | 6 | no | — |
| 183 | C23×C5 | — | 2 | 1 | no | — |
| 184 | C23×C5 | — | 2 | 3 | no | — |
| 185 | C23×C5 | — | 4 | 2 | no | — |
| 186 | C23×C5 | C4×D4 | 1 | 3 | yes | — |
| 187 | C23×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 188 | C22×D5 | — | 2 | 3 | no | — |
| 189 | C22×D5 | C4×D4 | 1 | 3 | yes | — |
| 190 | C5×Q8 | — | 2 | 1 | no | — |
| 191 | C5×D4 | — | 2 | 3 | no | — |
| 192 | C5×D4 | — | 2 | 6 | no | — |
| 193 | C5×D4 | — | 4 | 6 | no | — |
| 194 | C2×C4×C5 | — | 2 | 3 | no | — |
| 195 | C2×C4×C5 | — | 2 | 3 | no | — |
| 196 | C2×C4×C5 | C4×D4 | 1 | 3 | yes | — |
| 197 | C22⋊D5 | — | 2 | 6 | no | — |
| 198 | C22⋊D5 | — | 2 | 6 | no | — |
| 199 | C22⋊D5 | — | 2 | 6 | no | — |
| 200 | C22⋊D5 | — | 4 | 6 | no | — |
| 201 | C2×Dic5 | — | 2 | 3 | no | — |
| 202 | C2×Dic5 | — | 2 | 3 | no | — |
| 203 | C2×Dic5 | — | 2 | 3 | no | — |
| 204 | C2×Dic5 | — | 2 | 3 | no | — |
| 205 | C2×Dic5 | — | 2 | 3 | no | — |
| 206 | C2×Dic5 | — | 4 | 1 | no | — |
| 207 | C2×Dic5 | — | 4 | 3 | no | — |
| 208 | C2×Dic5 | C4×D4 | 1 | 3 | yes | — |
| 209 | C2×Dic5 | C22×D4 | 1 | 3 | yes | — |
| 210 | C2×Dic5 | C2×#41 | 1 | 3 | yes | — |
| 211 | D20 | — | 2 | 3 | no | — |
| 212 | C4×D5 | — | 2 | 6 | no | — |
| 213 | C4×D5 | — | 2 | 3 | no | — |
| 214 | C4×D5 | — | 2 | 3 | no | — |
| 215 | Dic10 | — | 2 | 3 | no | — |
| 216 | Dic10 | — | 2 | 6 | no | — |
| 217 | #170 | — | 2 | 3 | no | — |
| 218 | #170 | — | 2 | 3 | no | — |
| 219 | #170 | — | 4 | 1 | no | — |
| 220 | #170 | — | 4 | 3 | no | — |
| 221 | #170 | #120 | 1 | 1 | yes | characteristic |
| 222 | #170 | #120 | 1 | 3 | yes | — |
| 223 | 2−1+4 | — | 10 | 3 | no | — |
| 224 | H(5,𝔽2) | — | 5 | 3 | no | — |
| 225 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 226 | H(5,𝔽2) | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 227 | C2×#41 | — | 5 | 3 | no | — |
| 228 | C2×#41 | — | 10 | 3 | no | — |
| 229 | C2×#41 | — | 10 | 3 | no | — |
| 230 | C23×C4 | — | 5 | 1 | no | — |
| 231 | #131 | — | 10 | 6 | no | — |
| 232 | #131 | — | 10 | 6 | no | — |
| 233 | #131 | — | 10 | 6 | no | — |
| 234 | #131 | — | 10 | 6 | no | — |
| 235 | #131 | — | 10 | 3 | no | — |
| 236 | #131 | — | 10 | 3 | no | — |
| 237 | #131 | — | 10 | 6 | no | — |
| 238 | #131 | — | 10 | 1 | no | — |
| 239 | #131 | — | 10 | 3 | no | — |
| 240 | C2×M16 | — | 5 | 3 | no | — |
| 241 | C2×M16 | — | 5 | 3 | no | — |
| 242 | C2×M16 | — | 5 | 3 | no | — |
| 243 | C2×M16 | — | 5 | 3 | no | — |
| 244 | C2×M16 | — | 10 | 3 | no | — |
| 245 | C2×M16 | — | 10 | 3 | no | — |
| 246 | C2×M16 | — | 10 | 3 | no | — |
| 247 | C2×M16 | — | 10 | 6 | no | — |
| 248 | C2×M16 | — | 10 | 3 | no | — |
| 249 | C22×C8 | — | 5 | 1 | no | — |
| 250 | C22×C8 | — | 5 | 3 | no | — |
| 251 | C22×C8 | — | 5 | 3 | no | — |
| 252 | C22×C8 | — | 5 | 1 | no | — |
| 253 | C22×C8 | — | 10 | 3 | no | — |
| 254 | C22×C8 | — | 10 | 3 | no | — |
| 255 | C22×C8 | — | 10 | 3 | no | — |
| 256 | C22×C8 | — | 10 | 1 | no | — |
| 257 | #123 | — | 5 | 3 | no | — |
| 258 | #123 | — | 5 | 3 | no | — |
| 259 | C22⋊Q8 | — | 10 | 3 | no | — |
| 260 | #121 | — | 10 | 3 | no | — |
| 261 | #120 | — | 5 | 3 | no | — |
| 262 | #120 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 263 | C4×D4 | — | 10 | 3 | no | — |
| 264 | C4×D4 | — | 10 | 3 | no | — |
| 265 | #117 | — | 5 | 3 | no | — |
| 266 | C4⋊C8 | — | 10 | 3 | no | — |
| 267 | C4⋊C8 | — | 10 | 3 | no | — |
| 268 | #101 | — | 10 | 3 | no | — |
| 269 | #100 | — | 10 | 3 | no | — |
| 270 | #99 | — | 5 | 3 | no | — |
| 271 | #99 | — | 5 | 6 | no | — |
| 272 | #99 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 273 | C22⋊C8 | — | 10 | 3 | no | — |
| 274 | C22⋊C8 | — | 10 | 3 | no | — |
| 275 | C22⋊C8 | — | 10 | 3 | no | — |
| 276 | C22⋊C8 | — | 10 | 3 | no | — |
| 277 | #97 | — | 10 | 3 | no | — |
| 278 | C4×C8 | — | 10 | 3 | no | — |
| 279 | C22×C5 | — | 2 | 6 | no | — |
| 280 | C22×C5 | — | 2 | 3 | no | — |
| 281 | C22×C5 | — | 4 | 1 | no | — |
| 282 | C22×C5 | — | 4 | 3 | no | — |
| 283 | C22×C5 | — | 4 | 3 | no | — |
| 284 | C22×C5 | — | 4 | 1 | no | — |
| 285 | C22×C5 | — | 8 | 1 | no | — |
| 286 | C22×C5 | C2×C4×D4 | 1 | 3 | yes | — |
| 287 | C2×D5 | — | 2 | 3 | no | — |
| 288 | C2×D5 | — | 4 | 3 | no | — |
| 289 | C2×D5 | — | 8 | 3 | no | — |
| 290 | C4×C5 | — | 2 | 3 | no | — |
| 291 | C4×C5 | — | 4 | 3 | no | — |
| 292 | Dic5 | — | 2 | 3 | no | — |
| 293 | Dic5 | — | 4 | 3 | no | — |
| 294 | Dic5 | — | 4 | 1 | no | — |
| 295 | Dic5 | C2×#120 | 1 | 1 | yes | characteristic |
| 296 | Dic5 | #525 | 1 | 3 | yes | — |
| 297 | C24 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 298 | #41 | — | 2 | 3 | no | — |
| 299 | #41 | — | 10 | 6 | no | — |
| 300 | #41 | — | 10 | 6 | no | — |
| 301 | #41 | — | 10 | 6 | no | — |
| 302 | #41 | — | 10 | 6 | no | — |
| 303 | #41 | — | 10 | 3 | no | — |
| 304 | #41 | — | 10 | 6 | no | — |
| 305 | #41 | — | 10 | 1 | no | — |
| 306 | #41 | — | 10 | 3 | no | — |
| 307 | C2×Q8 | — | 5 | 3 | no | — |
| 308 | C2×Q8 | — | 10 | 3 | no | — |
| 309 | C2×Q8 | — | 10 | 3 | no | — |
| 310 | C2×D4 | — | 2 | 3 | no | — |
| 311 | C2×D4 | — | 2 | 3 | no | — |
| 312 | C2×D4 | — | 5 | 3 | no | — |
| 313 | C2×D4 | — | 5 | 3 | no | — |
| 314 | C2×D4 | — | 10 | 6 | no | — |
| 315 | C2×D4 | — | 10 | 3 | no | — |
| 316 | C2×D4 | — | 10 | 3 | no | — |
| 317 | C2×D4 | — | 10 | 3 | no | — |
| 318 | C2×D4 | — | 10 | 3 | no | — |
| 319 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 320 | C22×C4 | — | 5 | 1 | no | — |
| 321 | C22×C4 | — | 5 | 3 | no | — |
| 322 | C22×C4 | — | 5 | 3 | no | — |
| 323 | C22×C4 | — | 5 | 1 | no | — |
| 324 | C22×C4 | — | 10 | 3 | no | — |
| 325 | C22×C4 | — | 10 | 3 | no | — |
| 326 | C22×C4 | — | 10 | 3 | no | — |
| 327 | C22×C4 | — | 10 | 1 | no | — |
| 328 | M16 | — | 10 | 6 | no | — |
| 329 | M16 | — | 10 | 6 | no | — |
| 330 | M16 | — | 10 | 6 | no | — |
| 331 | M16 | — | 10 | 3 | no | — |
| 332 | M16 | — | 10 | 3 | no | — |
| 333 | M16 | — | 10 | 6 | no | — |
| 334 | M16 | — | 10 | 6 | no | — |
| 335 | C2×C8 | — | 5 | 3 | no | — |
| 336 | C2×C8 | — | 5 | 3 | no | — |
| 337 | C2×C8 | — | 5 | 3 | no | — |
| 338 | C2×C8 | — | 5 | 3 | no | — |
| 339 | C2×C8 | — | 10 | 3 | no | — |
| 340 | C2×C8 | — | 10 | 3 | no | — |
| 341 | C2×C8 | — | 10 | 3 | no | — |
| 342 | C2×C8 | — | 10 | 3 | no | — |
| 343 | C2×C8 | — | 10 | 6 | no | — |
| 344 | C2×C8 | — | 10 | 3 | no | — |
| 345 | C2×C8 | — | 10 | 3 | no | — |
| 346 | C2×C8 | — | 10 | 3 | no | — |
| 347 | C2×C8 | — | 10 | 3 | no | — |
| 348 | C2×C8 | — | 20 | 1 | no | — |
| 349 | C2×C8 | — | 20 | 3 | no | — |
| 350 | C4⋊C4 | — | 10 | 3 | no | — |
| 351 | C4⋊C4 | — | 10 | 3 | no | — |
| 352 | C4⋊C4 | — | 10 | 3 | no | — |
| 353 | C22⋊C4 | — | 2 | 3 | no | — |
| 354 | C22⋊C4 | — | 5 | 3 | no | — |
| 355 | C22⋊C4 | — | 10 | 3 | no | — |
| 356 | C22⋊C4 | — | 10 | 3 | no | — |
| 357 | C22⋊C4 | — | 10 | 3 | no | — |
| 358 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 359 | C42 | — | 10 | 3 | no | — |
| 360 | C2×C5 | — | 2 | 3 | no | — |
| 361 | C2×C5 | — | 4 | 3 | no | — |
| 362 | C2×C5 | — | 4 | 2 | no | — |
| 363 | C2×C5 | C4×#120 | 1 | 1 | yes | characteristic |
| 364 | D5 | — | 4 | 3 | no | — |
| 365 | C23 | — | 2 | 1 | no | — |
| 366 | C23 | — | 2 | 3 | no | — |
| 367 | C23 | — | 4 | 2 | no | — |
| 368 | C23 | — | 5 | 3 | no | — |
| 369 | C23 | — | 10 | 3 | no | — |
| 370 | C23 | D4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 371 | C23 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 372 | Q8 | — | 2 | 1 | no | — |
| 373 | Q8 | — | 10 | 6 | no | — |
| 374 | Q8 | — | 10 | 3 | no | — |
| 375 | D4 | — | 2 | 3 | no | — |
| 376 | D4 | — | 2 | 6 | no | — |
| 377 | D4 | — | 4 | 6 | no | — |
| 378 | D4 | — | 10 | 3 | no | — |
| 379 | D4 | — | 10 | 6 | no | — |
| 380 | D4 | — | 10 | 6 | no | — |
| 381 | D4 | — | 10 | 6 | no | — |
| 382 | D4 | — | 20 | 6 | no | — |
| 383 | C2×C4 | — | 2 | 3 | no | — |
| 384 | C2×C4 | — | 2 | 3 | no | — |
| 385 | C2×C4 | — | 5 | 3 | no | — |
| 386 | C2×C4 | — | 5 | 3 | no | — |
| 387 | C2×C4 | — | 5 | 3 | no | — |
| 388 | C2×C4 | — | 10 | 3 | no | — |
| 389 | C2×C4 | — | 10 | 3 | no | — |
| 390 | C2×C4 | — | 10 | 6 | no | — |
| 391 | C2×C4 | — | 10 | 3 | no | — |
| 392 | C2×C4 | — | 10 | 3 | no | — |
| 393 | C2×C4 | — | 10 | 3 | no | — |
| 394 | C2×C4 | — | 10 | 3 | no | — |
| 395 | C2×C4 | — | 10 | 3 | no | — |
| 396 | C2×C4 | — | 20 | 1 | no | — |
| 397 | C2×C4 | — | 20 | 3 | no | — |
| 398 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 399 | C8 | — | 5 | 1 | no | — |
| 400 | C8 | — | 5 | 3 | no | — |
| 401 | C8 | — | 10 | 3 | no | — |
| 402 | C8 | — | 10 | 3 | no | — |
| 403 | C8 | — | 20 | 1 | no | — |
| 404 | C8 | — | 20 | 3 | no | — |
| 405 | C5 | #21483 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 406 | C22 | — | 2 | 6 | no | — |
| 407 | C22 | — | 2 | 3 | no | — |
| 408 | C22 | — | 4 | 1 | no | — |
| 409 | C22 | — | 4 | 3 | no | — |
| 410 | C22 | — | 4 | 3 | no | — |
| 411 | C22 | — | 4 | 1 | no | — |
| 412 | C22 | — | 8 | 1 | no | — |
| 413 | C22 | — | 10 | 3 | no | — |
| 414 | C22 | — | 20 | 3 | no | — |
| 415 | C22 | — | 40 | 3 | no | — |
| 416 | C22 | C2×D4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 417 | C4 | — | 2 | 3 | no | — |
| 418 | C4 | — | 4 | 3 | no | — |
| 419 | C4 | — | 5 | 1 | no | — |
| 420 | C4 | — | 5 | 3 | no | — |
| 421 | C4 | — | 10 | 3 | no | — |
| 422 | C4 | — | 20 | 3 | no | — |
| 423 | C4 | — | 20 | 1 | no | — |
| 424 | C2 | — | 2 | 3 | no | — |
| 425 | C2 | — | 4 | 2 | no | — |
| 426 | C2 | — | 4 | 3 | no | — |
| 427 | C2 | — | 20 | 3 | no | — |
| 428 | C2 | AGL(1,𝔽5)×#120 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619413 | C2 | semidirect |
| 2. #10617215 | C2 | semidirect |
| 4. #10605018 | C2 | semidirect |
| 5. #10604463 | C2 | semidirect |
| 6. #10603921 | C2 | semidirect |
| 7. #10603920 | C2 | semidirect |
| 9. C23×#170 | C22 | semidirect |
| 17. #65798 | C22 | semidirect |
| 22. #65696 | C22 | semidirect |
| 25. #65691 | C22 | semidirect |
| 31. #64867 | C22 | semidirect |
| 43. C2×#704 | D4 | semidirect |
| 49. C22×#170 | D4 | semidirect |
| 64. C2×#700 | D4 | semidirect |
| 66. C2×D5⋊C8 | D4 | semidirect |
| 405. C5 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619413 | 2 |
| #10617215 | 2 |
| #10612035 | 2 |
| #10605018 | 2 |
| #10604463 | 2 |
| #10603921 | 2 |
| #10603920 | 2 |
| #21483 | 5 |