Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
494 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 84 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 | #10617440 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#509 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | D5⋊#359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10604806 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#64904 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598674 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598673 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #66266 | — | 2 | 1 | no | — |
| 9 | D5×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×D5×D8 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65793 | — | 2 | 1 | no | — |
| 12 | D5⋊#100 | — | 2 | 1 | no | — |
| 13 | #65767 | — | 2 | 1 | no | — |
| 14 | Q16×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 15 | #65735 | — | 2 | 2 | no | — |
| 16 | D8×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 17 | D5⋊#108 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3994 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65718 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×D5⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#509 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #65482 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #65436 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #65203 | — | 2 | 1 | no | — |
| 25 | D5×SD32 | — | 2 | 1 | no | — |
| 26 | #65200 | — | 2 | 1 | no | — |
| 27 | D5×D16 | — | 2 | 1 | no | — |
| 28 | #65197 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | D5×M32 | C22 | 1 | 1 | yes | characteristic |
| 30 | #64909 | — | 2 | 1 | no | — |
| 31 | #64905 | — | 2 | 1 | no | — |
| 32 | #64904 | — | 2 | 2 | no | — |
| 33 | #13022 | — | 5 | 1 | no | maximal, Sylow |
| 34 | D5×#41 | — | 2 | 1 | no | — |
| 35 | C2×D4×D5 | — | 2 | 1 | no | — |
| 36 | Q8×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 37 | D4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 38 | D4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 39 | #4130 | — | 4 | 1 | no | — |
| 40 | #4130 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 42 | C2×C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 43 | D5⋊M16 | — | 2 | 1 | no | — |
| 44 | D5⋊M16 | D4 | 1 | 1 | yes | characteristic |
| 45 | C5×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×C5×D8 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 47 | #4096 | — | 2 | 1 | no | — |
| 48 | C2×#686 | — | 2 | 1 | no | — |
| 49 | #4065 | D4 | 1 | 1 | yes | characteristic |
| 50 | D5×Q16 | D4 | 1 | 1 | yes | characteristic |
| 51 | #4062 | — | 2 | 1 | no | — |
| 52 | D5×SD16 | — | 2 | 1 | no | — |
| 53 | #4058 | D4 | 1 | 1 | yes | characteristic |
| 54 | D5×D8 | — | 2 | 1 | no | — |
| 55 | D5×D8 | — | 2 | 1 | no | — |
| 56 | D5×D8 | — | 2 | 1 | no | — |
| 57 | D5×D8 | — | 2 | 1 | no | — |
| 58 | D5×D8 | D4 | 1 | 1 | yes | characteristic |
| 59 | #4050 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×D40 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 62 | #4013 | — | 4 | 2 | no | — |
| 63 | #4009 | — | 2 | 2 | no | — |
| 64 | #4007 | — | 2 | 2 | no | — |
| 65 | #4007 | — | 4 | 1 | no | — |
| 66 | #4007 | — | 4 | 1 | no | — |
| 67 | C2×#674 | — | 2 | 1 | no | — |
| 68 | #3996 | — | 2 | 1 | no | — |
| 69 | #3995 | — | 2 | 1 | no | — |
| 70 | #3994 | — | 2 | 1 | no | — |
| 71 | #3994 | D4 | 1 | 2 | yes | — |
| 72 | #3992 | — | 2 | 1 | no | — |
| 73 | C8×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 74 | D5⋊C16 | — | 2 | 1 | no | — |
| 75 | D5⋊C16 | — | 2 | 1 | no | — |
| 76 | C5×SD32 | — | 2 | 1 | no | — |
| 77 | C5×D16 | — | 2 | 1 | no | — |
| 78 | C5×M32 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 79 | #3960 | — | 2 | 1 | no | — |
| 80 | #3959 | — | 2 | 1 | no | — |
| 81 | #3958 | — | 2 | 1 | no | — |
| 82 | #3958 | — | 2 | 1 | no | — |
| 83 | #3944 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 84 | #3932 | — | 2 | 1 | no | — |
| 85 | D80 | — | 2 | 1 | no | — |
| 86 | #3930 | — | 2 | 1 | no | — |
| 87 | D5×C16 | — | 2 | 1 | no | — |
| 88 | C2×#509 | — | 5 | 1 | no | — |
| 89 | #2951 | — | 5 | 1 | no | — |
| 90 | C2×#359 | — | 5 | 1 | no | — |
| 91 | C2×#357 | — | 5 | 1 | no | — |
| 92 | #1978 | — | 5 | 1 | no | — |
| 93 | #1387 | — | 5 | 1 | no | — |
| 94 | #1379 | — | 5 | 1 | no | — |
| 95 | C23×D5 | — | 4 | 1 | no | — |
| 96 | C22×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 97 | C22×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 98 | C5×#41 | — | 2 | 1 | no | — |
| 99 | C2×C5×D4 | — | 2 | 1 | no | — |
| 100 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 101 | #713 | — | 2 | 1 | no | — |
| 102 | Q8×D5 | — | 2 | 1 | no | — |
| 103 | #711 | — | 2 | 1 | no | — |
| 104 | #711 | — | 4 | 1 | no | — |
| 105 | D4×D5 | — | 2 | 1 | no | — |
| 106 | D4×D5 | — | 4 | 1 | no | — |
| 107 | D4×D5 | — | 4 | 1 | no | — |
| 108 | D4×D5 | — | 4 | 1 | no | — |
| 109 | D4×D5 | — | 4 | 1 | no | — |
| 110 | D4×D5 | — | 4 | 1 | no | — |
| 111 | #709 | — | 2 | 1 | no | — |
| 112 | #709 | — | 4 | 1 | no | — |
| 113 | C2×D20 | — | 2 | 1 | no | — |
| 114 | C2×C4×D5 | — | 4 | 1 | no | — |
| 115 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 117 | C22⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 118 | #704 | — | 2 | 1 | no | — |
| 119 | #704 | — | 4 | 1 | no | — |
| 120 | C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 121 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 122 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 123 | C4⋊AGL(1,𝔽5) | D8 | 1 | 1 | yes | characteristic |
| 124 | C4⋊AGL(1,𝔽5) | D8 | 1 | 1 | yes | characteristic |
| 125 | C4×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 126 | C4×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 127 | #700 | — | 2 | 1 | no | — |
| 128 | #700 | — | 4 | 1 | no | — |
| 129 | D5⋊C8 | — | 2 | 1 | no | — |
| 130 | D5⋊C8 | — | 4 | 1 | no | — |
| 131 | C5×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 132 | C5×SD16 | — | 2 | 1 | no | — |
| 133 | C5×D8 | — | 2 | 1 | no | — |
| 134 | C5×D8 | — | 2 | 1 | no | — |
| 135 | C5×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 137 | #689 | — | 2 | 1 | no | — |
| 138 | #688 | — | 2 | 1 | no | — |
| 139 | #687 | — | 2 | 1 | no | — |
| 140 | #686 | — | 2 | 1 | no | — |
| 141 | #686 | — | 4 | 1 | no | — |
| 142 | #686 | — | 4 | 1 | no | — |
| 143 | C2×#168 | #41 | 1 | 1 | yes | characteristic |
| 144 | Dic20 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 145 | D40 | — | 2 | 1 | no | — |
| 146 | D40 | — | 2 | 1 | no | — |
| 147 | D40 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | #677 | — | 2 | 1 | no | — |
| 149 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C8×D5 | #41 | 1 | 1 | yes | characteristic |
| 153 | #674 | — | 4 | 1 | no | — |
| 154 | C5×C16 | — | 2 | 1 | no | — |
| 155 | #672 | — | 2 | 1 | no | — |
| 156 | C2×#135 | — | 5 | 1 | no | — |
| 157 | C22×D8 | — | 5 | 1 | no | — |
| 158 | #520 | — | 10 | 1 | no | — |
| 159 | #509 | — | 5 | 1 | no | — |
| 160 | #509 | — | 5 | 1 | no | — |
| 161 | #509 | — | 5 | 1 | no | — |
| 162 | #509 | — | 10 | 1 | no | — |
| 163 | #509 | — | 10 | 1 | no | — |
| 164 | #509 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 165 | C2×SD32 | — | 10 | 1 | no | — |
| 166 | C2×D16 | — | 10 | 1 | no | — |
| 167 | C2×M32 | — | 5 | 1 | no | — |
| 168 | C22×C16 | — | 5 | 1 | no | — |
| 169 | #440 | — | 10 | 2 | no | — |
| 170 | C4×Q16 | — | 10 | 1 | no | — |
| 171 | C4×D8 | — | 10 | 1 | no | — |
| 172 | C2×#108 | — | 5 | 1 | no | — |
| 173 | C2×#107 | — | 5 | 1 | no | — |
| 174 | #418 | — | 10 | 1 | no | — |
| 175 | #417 | — | 10 | 1 | no | — |
| 176 | C2×#100 | — | 10 | 1 | no | — |
| 177 | #405 | — | 5 | 1 | no | — |
| 178 | #359 | — | 10 | 1 | no | — |
| 179 | #359 | — | 10 | 1 | no | — |
| 180 | #357 | — | 10 | 2 | no | — |
| 181 | C23×C5 | — | 4 | 1 | no | — |
| 182 | C22×D5 | — | 4 | 1 | no | — |
| 183 | C22×D5 | — | 4 | 1 | no | — |
| 184 | C22×D5 | — | 8 | 1 | no | — |
| 185 | C22×D5 | — | 8 | 1 | no | — |
| 186 | C22×D5 | — | 16 | 1 | no | — |
| 187 | C22×D5 | — | 16 | 1 | no | — |
| 188 | C22×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 189 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 190 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 191 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 192 | C2×AGL(1,𝔽5) | — | 16 | 2 | no | — |
| 193 | C2×AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 194 | C5×Q8 | — | 2 | 1 | no | — |
| 195 | C5×D4 | — | 2 | 1 | no | — |
| 196 | C5×D4 | — | 4 | 1 | no | — |
| 197 | C5×D4 | — | 4 | 1 | no | — |
| 198 | C5×D4 | — | 4 | 1 | no | — |
| 199 | C2×C4×C5 | — | 4 | 1 | no | — |
| 200 | C2×C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 201 | C22⋊D5 | — | 4 | 1 | no | — |
| 202 | C22⋊D5 | — | 4 | 1 | no | — |
| 203 | C22⋊D5 | — | 4 | 1 | no | — |
| 204 | C22⋊D5 | — | 8 | 1 | no | — |
| 205 | C22⋊D5 | — | 8 | 1 | no | — |
| 206 | C2×Dic5 | — | 4 | 1 | no | — |
| 207 | C2×Dic5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 208 | D20 | — | 2 | 1 | no | — |
| 209 | D20 | — | 4 | 1 | no | — |
| 210 | D20 | — | 4 | 1 | no | — |
| 211 | D20 | — | 4 | 1 | no | — |
| 212 | C4×D5 | — | 4 | 1 | no | — |
| 213 | C4×D5 | — | 4 | 1 | no | — |
| 214 | C4×D5 | — | 4 | 1 | no | — |
| 215 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 216 | C4×D5 | #121 | 1 | 1 | yes | characteristic |
| 217 | C4×D5 | C2×D8 | 1 | 1 | yes | characteristic |
| 218 | C4×D5 | #135 | 1 | 1 | yes | characteristic |
| 219 | Dic10 | — | 2 | 1 | no | — |
| 220 | Dic10 | — | 4 | 1 | no | — |
| 221 | #170 | — | 4 | 1 | no | — |
| 222 | #170 | — | 8 | 1 | no | — |
| 223 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 224 | C5×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 225 | #168 | #121 | 1 | 1 | yes | characteristic |
| 226 | #168 | #123 | 1 | 1 | yes | characteristic |
| 227 | C2×#41 | — | 10 | 1 | no | — |
| 228 | C22×D4 | — | 10 | 1 | no | — |
| 229 | #135 | — | 5 | 1 | no | — |
| 230 | #135 | — | 5 | 1 | no | — |
| 231 | #135 | — | 5 | 1 | no | — |
| 232 | #135 | — | 10 | 1 | no | — |
| 233 | #135 | — | 10 | 1 | no | — |
| 234 | #135 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 235 | C2×Q16 | — | 5 | 1 | no | — |
| 236 | C2×SD16 | — | 10 | 1 | no | — |
| 237 | C2×D8 | — | 5 | 1 | no | — |
| 238 | C2×D8 | — | 5 | 1 | no | — |
| 239 | C2×D8 | — | 10 | 1 | no | — |
| 240 | C2×D8 | — | 10 | 1 | no | — |
| 241 | C2×D8 | — | 10 | 1 | no | — |
| 242 | C2×D8 | — | 10 | 1 | no | — |
| 243 | C2×D8 | — | 10 | 1 | no | — |
| 244 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 245 | C2×M16 | — | 5 | 1 | no | — |
| 246 | C2×M16 | — | 10 | 1 | no | — |
| 247 | C22×C8 | — | 5 | 1 | no | — |
| 248 | C4×Q8 | — | 10 | 2 | no | — |
| 249 | C4×D4 | — | 10 | 2 | no | — |
| 250 | C4×D4 | — | 20 | 2 | no | — |
| 251 | #117 | — | 5 | 1 | no | — |
| 252 | #117 | — | 20 | 1 | no | — |
| 253 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 254 | C2×C4⋊C4 | — | 20 | 1 | no | — |
| 255 | SD32 | — | 2 | 1 | no | — |
| 256 | SD32 | — | 10 | 1 | no | — |
| 257 | SD32 | — | 10 | 1 | no | — |
| 258 | SD32 | — | 10 | 1 | no | — |
| 259 | D16 | — | 2 | 1 | no | — |
| 260 | D16 | — | 10 | 1 | no | — |
| 261 | D16 | — | 10 | 1 | no | — |
| 262 | D16 | — | 10 | 1 | no | — |
| 263 | M32 | — | 5 | 1 | no | — |
| 264 | M32 | — | 10 | 1 | no | — |
| 265 | M32 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 266 | C2×C16 | — | 10 | 1 | no | — |
| 267 | C2×C16 | — | 10 | 1 | no | — |
| 268 | C2×C16 | — | 10 | 1 | no | — |
| 269 | C2×C16 | — | 10 | 1 | no | — |
| 270 | #108 | — | 10 | 1 | no | — |
| 271 | #108 | — | 10 | 1 | no | — |
| 272 | #107 | — | 5 | 2 | no | — |
| 273 | #107 | — | 10 | 1 | no | — |
| 274 | #103 | — | 10 | 2 | no | — |
| 275 | #102 | — | 10 | 2 | no | — |
| 276 | #102 | — | 20 | 1 | no | — |
| 277 | #102 | — | 20 | 1 | no | — |
| 278 | #100 | — | 20 | 2 | no | — |
| 279 | #97 | — | 10 | 1 | no | — |
| 280 | C4×C8 | — | 10 | 1 | no | — |
| 281 | C22×C5 | — | 4 | 1 | no | — |
| 282 | C22×C5 | — | 8 | 1 | no | — |
| 283 | C22×C5 | — | 16 | 1 | no | — |
| 284 | C22×C5 | #442 | 1 | 1 | yes | characteristic |
| 285 | C2×D5 | — | 2 | 1 | no | — |
| 286 | C2×D5 | — | 2 | 1 | no | — |
| 287 | C2×D5 | — | 4 | 1 | no | — |
| 288 | C2×D5 | — | 8 | 1 | no | — |
| 289 | C2×D5 | — | 8 | 1 | no | — |
| 290 | C2×D5 | — | 8 | 1 | no | — |
| 291 | C2×D5 | — | 16 | 2 | no | — |
| 292 | C2×D5 | — | 16 | 1 | no | — |
| 293 | C2×D5 | — | 16 | 1 | no | — |
| 294 | C2×D5 | — | 16 | 1 | no | — |
| 295 | C2×D5 | #447 | 1 | 1 | yes | characteristic |
| 296 | C2×D5 | #463 | 1 | 1 | yes | characteristic |
| 297 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 298 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 299 | AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 300 | C4×C5 | — | 4 | 1 | no | — |
| 301 | C4×C5 | #386 | 1 | 1 | yes | characteristic |
| 302 | C4×C5 | C4×D8 | 1 | 1 | yes | characteristic |
| 303 | Dic5 | — | 4 | 1 | no | — |
| 304 | Dic5 | #449 | 1 | 1 | yes | characteristic |
| 305 | Dic5 | #459 | 1 | 1 | yes | characteristic |
| 306 | C24 | — | 20 | 1 | no | — |
| 307 | #41 | — | 2 | 1 | no | — |
| 308 | #41 | — | 10 | 1 | no | — |
| 309 | #41 | — | 10 | 1 | no | — |
| 310 | #41 | — | 10 | 1 | no | — |
| 311 | #41 | — | 20 | 1 | no | — |
| 312 | #41 | — | 20 | 1 | no | — |
| 313 | C2×Q8 | — | 10 | 1 | no | — |
| 314 | C2×D4 | — | 2 | 1 | no | — |
| 315 | C2×D4 | — | 10 | 1 | no | — |
| 316 | C2×D4 | — | 10 | 1 | no | — |
| 317 | C2×D4 | — | 20 | 1 | no | — |
| 318 | C2×D4 | — | 20 | 1 | no | — |
| 319 | C2×D4 | — | 20 | 1 | no | — |
| 320 | C2×D4 | — | 20 | 1 | no | — |
| 321 | C2×D4 | — | 20 | 1 | no | — |
| 322 | C2×D4 | — | 20 | 1 | no | — |
| 323 | C22×C4 | — | 5 | 1 | no | — |
| 324 | C22×C4 | — | 20 | 1 | no | — |
| 325 | C22×C4 | — | 20 | 2 | no | — |
| 326 | C22×C4 | — | 20 | 1 | no | — |
| 327 | Q16 | — | 5 | 1 | no | — |
| 328 | Q16 | — | 10 | 1 | no | — |
| 329 | Q16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 330 | SD16 | — | 2 | 1 | no | — |
| 331 | SD16 | — | 10 | 1 | no | — |
| 332 | SD16 | — | 10 | 1 | no | — |
| 333 | SD16 | — | 10 | 1 | no | — |
| 334 | D8 | — | 2 | 1 | no | — |
| 335 | D8 | — | 2 | 1 | no | — |
| 336 | D8 | — | 5 | 1 | no | — |
| 337 | D8 | — | 10 | 1 | no | — |
| 338 | D8 | — | 10 | 1 | no | — |
| 339 | D8 | — | 10 | 1 | no | — |
| 340 | D8 | — | 20 | 1 | no | — |
| 341 | D8 | — | 20 | 1 | no | — |
| 342 | D8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 343 | M16 | — | 10 | 1 | no | — |
| 344 | M16 | — | 10 | 1 | no | — |
| 345 | M16 | — | 20 | 1 | no | — |
| 346 | M16 | — | 20 | 1 | no | — |
| 347 | C2×C8 | — | 5 | 1 | no | — |
| 348 | C2×C8 | — | 5 | 1 | no | — |
| 349 | C2×C8 | — | 5 | 1 | no | — |
| 350 | C2×C8 | — | 5 | 1 | no | — |
| 351 | C2×C8 | — | 5 | 1 | no | — |
| 352 | C2×C8 | — | 10 | 1 | no | — |
| 353 | C2×C8 | — | 20 | 1 | no | — |
| 354 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 355 | C4⋊C4 | — | 5 | 1 | no | — |
| 356 | C4⋊C4 | — | 5 | 1 | no | — |
| 357 | C4⋊C4 | — | 10 | 2 | no | — |
| 358 | C4⋊C4 | — | 20 | 1 | no | — |
| 359 | C4⋊C4 | — | 20 | 2 | no | — |
| 360 | C22⋊C4 | — | 10 | 1 | no | — |
| 361 | C22⋊C4 | — | 20 | 2 | no | — |
| 362 | C42 | — | 10 | 1 | no | — |
| 363 | C42 | — | 20 | 2 | no | — |
| 364 | C16 | — | 2 | 1 | no | — |
| 365 | C16 | — | 10 | 1 | no | — |
| 366 | C16 | — | 20 | 1 | no | — |
| 367 | C2×C5 | — | 2 | 1 | no | — |
| 368 | C2×C5 | — | 8 | 1 | no | — |
| 369 | C2×C5 | — | 16 | 1 | no | — |
| 370 | C2×C5 | #1879 | 1 | 1 | yes | characteristic |
| 371 | D5 | — | 2 | 1 | no | — |
| 372 | D5 | — | 8 | 1 | no | — |
| 373 | D5 | — | 16 | 1 | no | — |
| 374 | D5 | #2192 | 1 | 1 | yes | characteristic |
| 375 | D5 | #2193 | 1 | 1 | yes | characteristic |
| 376 | C23 | — | 4 | 1 | no | — |
| 377 | C23 | — | 5 | 1 | no | — |
| 378 | C23 | — | 20 | 1 | no | — |
| 379 | C23 | — | 20 | 1 | no | — |
| 380 | C23 | — | 40 | 1 | no | — |
| 381 | C23 | — | 40 | 1 | no | — |
| 382 | C23 | — | 80 | 1 | no | — |
| 383 | C23 | — | 80 | 1 | no | — |
| 384 | Q8 | — | 2 | 1 | no | — |
| 385 | Q8 | — | 10 | 1 | no | — |
| 386 | Q8 | — | 20 | 1 | no | — |
| 387 | D4 | — | 2 | 1 | no | — |
| 388 | D4 | — | 4 | 1 | no | — |
| 389 | D4 | — | 4 | 1 | no | — |
| 390 | D4 | — | 4 | 1 | no | — |
| 391 | D4 | — | 10 | 1 | no | — |
| 392 | D4 | — | 20 | 1 | no | — |
| 393 | D4 | — | 20 | 1 | no | — |
| 394 | D4 | — | 20 | 1 | no | — |
| 395 | D4 | — | 20 | 1 | no | — |
| 396 | D4 | — | 20 | 1 | no | — |
| 397 | D4 | — | 20 | 1 | no | — |
| 398 | D4 | — | 40 | 1 | no | — |
| 399 | D4 | — | 40 | 1 | no | — |
| 400 | C2×C4 | — | 4 | 1 | no | — |
| 401 | C2×C4 | — | 5 | 1 | no | — |
| 402 | C2×C4 | — | 5 | 1 | no | — |
| 403 | C2×C4 | — | 5 | 1 | no | — |
| 404 | C2×C4 | — | 5 | 1 | no | — |
| 405 | C2×C4 | — | 5 | 1 | no | — |
| 406 | C2×C4 | — | 10 | 1 | no | — |
| 407 | C2×C4 | — | 10 | 1 | no | — |
| 408 | C2×C4 | — | 20 | 1 | no | — |
| 409 | C2×C4 | — | 20 | 1 | no | — |
| 410 | C2×C4 | — | 20 | 1 | no | — |
| 411 | C2×C4 | — | 20 | 1 | no | — |
| 412 | C2×C4 | — | 20 | 2 | no | — |
| 413 | C2×C4 | — | 80 | 2 | no | — |
| 414 | C2×C4 | — | 80 | 1 | no | — |
| 415 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 416 | C8 | — | 5 | 1 | no | — |
| 417 | C8 | — | 5 | 1 | no | — |
| 418 | C8 | — | 20 | 1 | no | — |
| 419 | C8 | — | 40 | 1 | no | — |
| 420 | C8 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 421 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 422 | C5 | #13022 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 423 | C22 | — | 4 | 1 | no | — |
| 424 | C22 | — | 5 | 1 | no | — |
| 425 | C22 | — | 5 | 1 | no | — |
| 426 | C22 | — | 8 | 1 | no | — |
| 427 | C22 | — | 10 | 1 | no | — |
| 428 | C22 | — | 10 | 1 | no | — |
| 429 | C22 | — | 16 | 1 | no | — |
| 430 | C22 | — | 20 | 1 | no | — |
| 431 | C22 | — | 40 | 1 | no | — |
| 432 | C22 | — | 40 | 1 | no | — |
| 433 | C22 | — | 40 | 1 | no | — |
| 434 | C22 | — | 80 | 1 | no | — |
| 435 | C22 | — | 80 | 1 | no | — |
| 436 | C22 | — | 80 | 1 | no | — |
| 437 | C22 | — | 80 | 2 | no | — |
| 438 | C22 | #65731 | 1 | 1 | yes | characteristic |
| 439 | C4 | — | 4 | 1 | no | — |
| 440 | C4 | — | 5 | 1 | no | — |
| 441 | C4 | — | 5 | 1 | no | — |
| 442 | C4 | — | 20 | 1 | no | — |
| 443 | C4 | — | 20 | 1 | no | — |
| 444 | C4 | — | 20 | 1 | no | — |
| 445 | C4 | — | 40 | 2 | no | — |
| 446 | C4 | D8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 447 | C4 | #65779 | 1 | 1 | yes | characteristic |
| 448 | C2 | — | 2 | 1 | no | — |
| 449 | C2 | — | 5 | 1 | no | — |
| 450 | C2 | — | 5 | 1 | no | — |
| 451 | C2 | — | 8 | 1 | no | — |
| 452 | C2 | — | 10 | 1 | no | — |
| 453 | C2 | — | 16 | 1 | no | — |
| 454 | C2 | — | 40 | 1 | no | — |
| 455 | C2 | — | 80 | 1 | no | — |
| 456 | C2 | #10604799 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617440 | C2 | semidirect |
| 3. D5⋊#359 | C2 | semidirect |
| 4. #10604806 | C2 | semidirect |
| 5. C2×#64904 | C2 | semidirect |
| 6. #10598674 | C2 | semidirect |
| 7. #10598673 | C2 | semidirect |
| 21. C5×#509 | C4 | semidirect |
| 22. #65482 | C4 | semidirect |
| 23. #65436 | C4 | semidirect |
| 28. #65197 | C4 | semidirect |
| 46. C2×C5×D8 | C2×C4 | semidirect |
| 60. C2×D40 | C2×C4 | semidirect |
| 78. C5×M32 | C2×C4 | semidirect |
| 83. #3944 | C2×C4 | semidirect |
| 164. #509 | AGL(1,𝔽5) | semidirect |
| 244. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 265. M32 | C2×AGL(1,𝔽5) | semidirect |
| 422. C5 | #13022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617440 | 2 |
| D5×#509 | 2 |
| D5⋊#359 | 2 |
| #10604806 | 2 |
| C2×#64904 | 2 |
| #10598674 | 2 |
| #10598673 | 2 |
| #13022 | 5 |