Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
880 conjugacy classes of subgroups.
The subgroup lattice has 484 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617437 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10617431 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10613600 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10604847 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10604821 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10604676 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10604569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10604568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10603885 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #66260 | C22 | 1 | 1 | yes | characteristic |
| 11 | #66260 | C22 | 1 | 2 | yes | — |
| 12 | #66256 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#4065 | C22 | 1 | 2 | yes | — |
| 14 | C2×#4062 | C22 | 1 | 2 | yes | — |
| 15 | #66059 | C22 | 1 | 1 | yes | characteristic |
| 16 | #66002 | C22 | 1 | 1 | yes | characteristic |
| 17 | #65785 | C22 | 1 | 2 | yes | — |
| 18 | #65785 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65784 | C22 | 1 | 2 | yes | — |
| 20 | #65784 | C22 | 1 | 2 | yes | — |
| 21 | #65784 | C22 | 1 | 2 | yes | — |
| 22 | #65771 | C22 | 1 | 1 | yes | characteristic |
| 23 | #65769 | C22 | 1 | 2 | yes | — |
| 24 | #65741 | — | 2 | 4 | no | — |
| 25 | #65740 | — | 2 | 4 | no | — |
| 26 | #65737 | — | 2 | 4 | no | — |
| 27 | #65736 | — | 2 | 4 | no | — |
| 28 | D5⋊#108 | C22 | 1 | 2 | yes | — |
| 29 | #65721 | C22 | 1 | 2 | yes | — |
| 30 | #65718 | C22 | 1 | 2 | yes | — |
| 31 | #65718 | C22 | 1 | 2 | yes | — |
| 32 | C5×#497 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #65479 | C4 | 1 | 2 | yes | complemented |
| 34 | #65465 | C4 | 1 | 2 | yes | complemented |
| 35 | #65375 | C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | #65347 | C4 | 1 | 1 | yes | characteristic, complemented |
| 37 | #65001 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | D5×#97 | C22 | 1 | 1 | yes | characteristic |
| 39 | #64862 | C22 | 1 | 2 | yes | — |
| 40 | #64862 | C22 | 1 | 2 | yes | — |
| 41 | #23197 | — | 5 | 1 | no | maximal, Sylow |
| 42 | C2×#713 | C23 | 1 | 2 | yes | — |
| 43 | C2×#713 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×#711 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×#704 | — | 4 | 1 | no | — |
| 46 | #4133 | — | 2 | 4 | no | — |
| 47 | #4133 | — | 2 | 4 | no | — |
| 48 | #4133 | — | 2 | 4 | no | — |
| 49 | #4131 | — | 2 | 4 | no | — |
| 50 | #4130 | C23 | 1 | 2 | yes | — |
| 51 | #4130 | C23 | 1 | 2 | yes | — |
| 52 | D5⋊M16 | — | 4 | 1 | no | — |
| 53 | D5⋊M16 | — | 4 | 2 | no | — |
| 54 | D5⋊M16 | C23 | 1 | 2 | yes | — |
| 55 | D5⋊M16 | C23 | 1 | 2 | yes | — |
| 56 | C2×C5×Q16 | C2×C4 | 1 | 2 | yes | — |
| 57 | C2×C5×SD16 | C2×C4 | 1 | 2 | yes | — |
| 58 | C5×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C5×#124 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #4093 | C2×C4 | 1 | 2 | yes | — |
| 61 | #4090 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×#689 | C2×C4 | 1 | 2 | yes | — |
| 63 | C2×#688 | C2×C4 | 1 | 2 | yes | — |
| 64 | C2×#688 | C2×C4 | 1 | 2 | yes | — |
| 65 | #4086 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×#686 | C2×C4 | 1 | 2 | yes | — |
| 67 | #4065 | — | 2 | 2 | no | — |
| 68 | #4065 | — | 2 | 2 | no | — |
| 69 | #4065 | — | 2 | 2 | no | — |
| 70 | #4065 | — | 2 | 2 | no | — |
| 71 | #4062 | — | 2 | 2 | no | — |
| 72 | #4062 | — | 2 | 2 | no | — |
| 73 | #4062 | — | 2 | 2 | no | — |
| 74 | #4062 | — | 2 | 2 | no | — |
| 75 | C2×D40 | C2×C4 | 1 | 2 | yes | — |
| 76 | C2×#677 | C2×C4 | 1 | 2 | yes | — |
| 77 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 78 | #4041 | — | 4 | 1 | no | — |
| 79 | #4039 | — | 4 | 1 | no | — |
| 80 | #4030 | — | 4 | 1 | no | — |
| 81 | #4027 | — | 4 | 1 | no | — |
| 82 | #4021 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 85 | #4011 | — | 4 | 1 | no | — |
| 86 | #4010 | — | 2 | 4 | no | — |
| 87 | #4010 | — | 2 | 4 | no | — |
| 88 | #4010 | — | 2 | 4 | no | — |
| 89 | #4008 | — | 2 | 4 | no | — |
| 90 | #3999 | — | 4 | 1 | no | — |
| 91 | #3999 | — | 4 | 2 | no | — |
| 92 | #3996 | D4 | 1 | 4 | yes | complemented |
| 93 | #3995 | D4 | 1 | 4 | yes | complemented |
| 94 | #3994 | — | 2 | 2 | no | — |
| 95 | #3993 | — | 2 | 2 | no | — |
| 96 | #3992 | — | 2 | 2 | no | — |
| 97 | #3992 | — | 2 | 2 | no | — |
| 98 | C8×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 99 | C8×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 100 | C5×#97 | C2×C4 | 1 | 1 | yes | characteristic |
| 101 | #3947 | C2×C4 | 1 | 2 | yes | — |
| 102 | #3935 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | #3150 | — | 5 | 1 | no | — |
| 104 | #2957 | — | 5 | 2 | no | — |
| 105 | #2957 | — | 5 | 2 | no | — |
| 106 | #1976 | — | 5 | 2 | no | — |
| 107 | #1976 | — | 5 | 2 | no | — |
| 108 | #1884 | — | 5 | 1 | no | — |
| 109 | #1884 | — | 5 | 1 | no | — |
| 110 | #1884 | — | 5 | 2 | no | — |
| 111 | #1773 | — | 5 | 2 | no | — |
| 112 | C2×C5×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C5×Q8 | C22×C4 | 1 | 2 | yes | — |
| 114 | C2×C5×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 116 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 117 | C22×Dic5 | — | 2 | 1 | no | — |
| 118 | #713 | — | 2 | 2 | no | — |
| 119 | #713 | — | 2 | 2 | no | — |
| 120 | #713 | — | 2 | 2 | no | — |
| 121 | #713 | — | 2 | 2 | no | — |
| 122 | #713 | — | 2 | 2 | no | — |
| 123 | #713 | — | 2 | 2 | no | — |
| 124 | #711 | — | 2 | 2 | no | — |
| 125 | #711 | — | 2 | 2 | no | — |
| 126 | C2×D20 | — | 2 | 1 | no | — |
| 127 | C2×D20 | — | 2 | 2 | no | — |
| 128 | C2×D20 | — | 4 | 1 | no | — |
| 129 | C2×D20 | C22×C4 | 1 | 2 | yes | — |
| 130 | C2×D20 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×D5 | — | 2 | 1 | no | — |
| 132 | C2×C4×D5 | — | 2 | 2 | no | — |
| 133 | C2×C4×D5 | — | 2 | 1 | no | — |
| 134 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 135 | C2×Dic10 | C22×C4 | 1 | 1 | yes | characteristic |
| 136 | C22⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 137 | C22⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 138 | #704 | — | 2 | 2 | no | — |
| 139 | #704 | — | 2 | 2 | no | — |
| 140 | #704 | — | 4 | 2 | no | — |
| 141 | C2×#170 | — | 4 | 2 | no | — |
| 142 | C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 143 | C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 144 | C4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 145 | C4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 146 | #700 | — | 4 | 2 | no | — |
| 147 | #700 | — | 4 | 4 | no | — |
| 148 | #700 | C2×D4 | 1 | 4 | yes | — |
| 149 | #700 | C2×D4 | 1 | 4 | yes | — |
| 150 | D5⋊C8 | — | 2 | 2 | no | — |
| 151 | D5⋊C8 | — | 2 | 2 | no | — |
| 152 | D5⋊C8 | — | 4 | 2 | no | — |
| 153 | D5⋊C8 | — | 4 | 4 | no | — |
| 154 | C5×Q16 | — | 2 | 2 | no | — |
| 155 | C5×Q16 | — | 2 | 2 | no | — |
| 156 | C5×SD16 | — | 2 | 2 | no | — |
| 157 | C5×SD16 | — | 2 | 2 | no | — |
| 158 | C2×C5×C8 | C22×C4 | 1 | 2 | yes | — |
| 159 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 160 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 161 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 162 | #689 | — | 2 | 2 | no | — |
| 163 | #689 | — | 2 | 2 | no | — |
| 164 | #688 | — | 2 | 2 | no | — |
| 165 | #688 | — | 2 | 2 | no | — |
| 166 | #688 | — | 2 | 2 | no | — |
| 167 | #688 | — | 2 | 2 | no | — |
| 168 | #686 | — | 2 | 2 | no | — |
| 169 | #686 | — | 2 | 2 | no | — |
| 170 | #685 | — | 4 | 1 | no | — |
| 171 | #685 | — | 4 | 2 | no | — |
| 172 | #683 | — | 4 | 1 | no | — |
| 173 | C4×Dic5 | — | 2 | 1 | no | — |
| 174 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 175 | C2×#168 | C22×C4 | 1 | 2 | yes | — |
| 176 | D40 | — | 2 | 2 | no | — |
| 177 | D40 | — | 2 | 2 | no | — |
| 178 | #677 | — | 2 | 2 | no | — |
| 179 | #677 | — | 2 | 2 | no | — |
| 180 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 181 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 182 | C8×D5 | #41 | 1 | 2 | yes | — |
| 183 | C8×D5 | #41 | 1 | 2 | yes | — |
| 184 | C2×#135 | — | 5 | 2 | no | — |
| 185 | C2×#135 | — | 5 | 2 | no | — |
| 186 | #568 | — | 5 | 1 | no | — |
| 187 | #568 | — | 5 | 1 | no | — |
| 188 | #568 | — | 5 | 2 | no | — |
| 189 | #532 | — | 5 | 1 | no | — |
| 190 | #532 | — | 5 | 1 | no | — |
| 191 | #497 | — | 5 | 2 | no | — |
| 192 | #497 | — | 5 | 1 | no | — |
| 193 | #497 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 194 | #496 | — | 5 | 2 | no | — |
| 195 | #496 | — | 5 | 1 | no | — |
| 196 | #496 | — | 5 | 1 | no | — |
| 197 | #444 | — | 10 | 4 | no | — |
| 198 | #444 | — | 10 | 4 | no | — |
| 199 | #443 | — | 10 | 4 | no | — |
| 200 | #443 | — | 10 | 4 | no | — |
| 201 | C2×#108 | — | 5 | 2 | no | — |
| 202 | #427 | — | 5 | 2 | no | — |
| 203 | #421 | — | 5 | 2 | no | — |
| 204 | #421 | — | 5 | 2 | no | — |
| 205 | #421 | — | 5 | 2 | no | — |
| 206 | #421 | — | 5 | 2 | no | — |
| 207 | #410 | — | 5 | 1 | no | — |
| 208 | #410 | — | 5 | 1 | no | — |
| 209 | #410 | — | 5 | 2 | no | — |
| 210 | #405 | — | 5 | 2 | no | — |
| 211 | #405 | — | 5 | 2 | no | — |
| 212 | C2×#97 | — | 5 | 1 | no | — |
| 213 | #339 | — | 5 | 2 | no | — |
| 214 | #339 | — | 5 | 2 | no | — |
| 215 | C23×C5 | — | 2 | 1 | no | — |
| 216 | C22×D5 | — | 2 | 2 | no | — |
| 217 | C22×D5 | — | 2 | 1 | no | — |
| 218 | C22×D5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 219 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 220 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 221 | C5×Q8 | — | 2 | 2 | no | — |
| 222 | C5×Q8 | — | 2 | 2 | no | — |
| 223 | C5×Q8 | — | 2 | 2 | no | — |
| 224 | C5×D4 | — | 2 | 2 | no | — |
| 225 | C2×C4×C5 | — | 2 | 1 | no | — |
| 226 | C2×C4×C5 | — | 2 | 1 | no | — |
| 227 | C2×C4×C5 | — | 2 | 2 | no | — |
| 228 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 229 | C22⋊D5 | — | 4 | 2 | no | — |
| 230 | C22⋊D5 | — | 8 | 2 | no | — |
| 231 | C2×Dic5 | — | 2 | 1 | no | — |
| 232 | C2×Dic5 | — | 2 | 1 | no | — |
| 233 | C2×Dic5 | — | 4 | 1 | no | — |
| 234 | C2×Dic5 | — | 4 | 1 | no | — |
| 235 | C2×Dic5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 236 | D20 | — | 2 | 2 | no | — |
| 237 | D20 | — | 2 | 2 | no | — |
| 238 | D20 | — | 2 | 2 | no | — |
| 239 | D20 | — | 4 | 2 | no | — |
| 240 | D20 | — | 4 | 2 | no | — |
| 241 | D20 | — | 4 | 2 | no | — |
| 242 | D20 | — | 8 | 2 | no | — |
| 243 | C4×D5 | — | 4 | 1 | no | — |
| 244 | C4×D5 | — | 4 | 2 | no | — |
| 245 | C4×D5 | — | 4 | 1 | no | — |
| 246 | C4×D5 | — | 4 | 2 | no | — |
| 247 | C4×D5 | — | 8 | 1 | no | — |
| 248 | C4×D5 | C22×D4 | 1 | 2 | yes | — |
| 249 | C4×D5 | C2×#41 | 1 | 2 | yes | — |
| 250 | Dic10 | — | 2 | 2 | no | — |
| 251 | #170 | — | 2 | 4 | no | — |
| 252 | #170 | — | 2 | 4 | no | — |
| 253 | C5×C8 | C4×D4 | 1 | 2 | yes | — |
| 254 | C5×C8 | C4×D4 | 1 | 2 | yes | — |
| 255 | #168 | C4×D4 | 1 | 2 | yes | — |
| 256 | #168 | C4×D4 | 1 | 2 | yes | — |
| 257 | C2×#41 | — | 5 | 2 | no | — |
| 258 | C2×#41 | — | 5 | 1 | no | — |
| 259 | C2×#41 | — | 5 | 1 | no | — |
| 260 | #135 | — | 10 | 2 | no | — |
| 261 | #135 | — | 10 | 2 | no | — |
| 262 | #135 | — | 10 | 2 | no | — |
| 263 | #135 | — | 10 | 2 | no | — |
| 264 | #135 | — | 10 | 2 | no | — |
| 265 | #135 | — | 10 | 2 | no | — |
| 266 | #135 | — | 10 | 2 | no | — |
| 267 | #135 | — | 10 | 2 | no | — |
| 268 | C2×Q16 | — | 5 | 2 | no | — |
| 269 | C2×Q16 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 270 | C2×SD16 | — | 5 | 2 | no | — |
| 271 | C2×SD16 | — | 5 | 2 | no | — |
| 272 | C2×SD16 | — | 5 | 2 | no | — |
| 273 | C2×SD16 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 274 | C2×D8 | — | 5 | 2 | no | — |
| 275 | C2×D8 | — | 5 | 2 | no | — |
| 276 | #131 | — | 10 | 4 | no | — |
| 277 | #131 | — | 10 | 4 | no | — |
| 278 | #131 | — | 10 | 4 | no | — |
| 279 | #131 | — | 10 | 4 | no | — |
| 280 | C2×M16 | — | 5 | 2 | no | — |
| 281 | C2×M16 | — | 5 | 2 | no | — |
| 282 | C2×M16 | — | 20 | 1 | no | — |
| 283 | C2×M16 | — | 20 | 2 | no | — |
| 284 | C2×M16 | — | 20 | 1 | no | — |
| 285 | C22×C8 | — | 5 | 2 | no | — |
| 286 | C4⋊Q8 | — | 5 | 1 | no | — |
| 287 | C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 288 | #127 | — | 5 | 1 | no | — |
| 289 | #127 | — | 5 | 1 | no | — |
| 290 | #124 | — | 5 | 2 | no | — |
| 291 | #124 | — | 5 | 1 | no | — |
| 292 | #124 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 293 | #121 | — | 20 | 1 | no | — |
| 294 | #121 | — | 20 | 1 | no | — |
| 295 | C4×D4 | — | 20 | 1 | no | — |
| 296 | C4×D4 | — | 20 | 1 | no | — |
| 297 | #117 | — | 5 | 2 | no | — |
| 298 | #117 | — | 5 | 2 | no | — |
| 299 | C2×C42 | — | 5 | 1 | no | — |
| 300 | #108 | — | 5 | 4 | no | — |
| 301 | #108 | — | 5 | 4 | no | — |
| 302 | #107 | — | 10 | 2 | no | — |
| 303 | #106 | — | 10 | 2 | no | — |
| 304 | #104 | — | 10 | 4 | no | — |
| 305 | #104 | — | 10 | 4 | no | — |
| 306 | #104 | — | 10 | 4 | no | — |
| 307 | #104 | — | 10 | 4 | no | — |
| 308 | #99 | — | 20 | 1 | no | — |
| 309 | #99 | — | 20 | 2 | no | — |
| 310 | #99 | — | 20 | 1 | no | — |
| 311 | #97 | — | 5 | 2 | no | — |
| 312 | #97 | — | 5 | 1 | no | — |
| 313 | #97 | — | 10 | 2 | no | — |
| 314 | #97 | — | 10 | 2 | no | — |
| 315 | #97 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 316 | C4×C8 | — | 10 | 2 | no | — |
| 317 | C4×C8 | — | 10 | 2 | no | — |
| 318 | C22×C5 | — | 4 | 1 | no | — |
| 319 | C22×C5 | — | 8 | 1 | no | — |
| 320 | C22×C5 | #518 | 1 | 1 | yes | characteristic |
| 321 | C2×D5 | — | 4 | 1 | no | — |
| 322 | C2×D5 | — | 4 | 2 | no | — |
| 323 | C2×D5 | — | 4 | 1 | no | — |
| 324 | C2×D5 | — | 8 | 2 | no | — |
| 325 | C2×D5 | — | 8 | 1 | no | — |
| 326 | C2×D5 | #550 | 1 | 2 | yes | — |
| 327 | AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 328 | AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 329 | C4×C5 | — | 4 | 1 | no | — |
| 330 | C4×C5 | — | 4 | 1 | no | — |
| 331 | C4×C5 | — | 4 | 2 | no | — |
| 332 | C4×C5 | C2×C4×D4 | 1 | 2 | yes | — |
| 333 | Dic5 | — | 4 | 1 | no | — |
| 334 | Dic5 | — | 4 | 1 | no | — |
| 335 | Dic5 | D42 | 1 | 1 | yes | characteristic |
| 336 | Dic5 | #559 | 1 | 1 | yes | characteristic |
| 337 | #41 | — | 10 | 2 | no | — |
| 338 | #41 | — | 10 | 2 | no | — |
| 339 | #41 | — | 10 | 2 | no | — |
| 340 | #41 | — | 10 | 2 | no | — |
| 341 | #41 | — | 10 | 2 | no | — |
| 342 | #41 | — | 10 | 2 | no | — |
| 343 | #41 | — | 10 | 2 | no | — |
| 344 | #41 | — | 10 | 2 | no | — |
| 345 | C2×Q8 | — | 5 | 1 | no | — |
| 346 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 347 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 348 | C2×D4 | — | 5 | 2 | no | — |
| 349 | C2×D4 | — | 5 | 1 | no | — |
| 350 | C2×D4 | — | 10 | 1 | no | — |
| 351 | C2×D4 | — | 10 | 2 | no | — |
| 352 | C2×D4 | — | 10 | 1 | no | — |
| 353 | C2×D4 | — | 20 | 1 | no | — |
| 354 | C2×D4 | — | 20 | 1 | no | — |
| 355 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 356 | C22×C4 | — | 5 | 1 | no | — |
| 357 | C22×C4 | — | 10 | 1 | no | — |
| 358 | C22×C4 | — | 10 | 2 | no | — |
| 359 | C22×C4 | — | 10 | 1 | no | — |
| 360 | C22×C4 | — | 10 | 1 | no | — |
| 361 | Q16 | — | 2 | 2 | no | — |
| 362 | Q16 | — | 2 | 2 | no | — |
| 363 | Q16 | — | 10 | 2 | no | — |
| 364 | Q16 | — | 10 | 2 | no | — |
| 365 | SD16 | — | 2 | 2 | no | — |
| 366 | SD16 | — | 2 | 2 | no | — |
| 367 | SD16 | — | 10 | 2 | no | — |
| 368 | SD16 | — | 10 | 2 | no | — |
| 369 | SD16 | — | 10 | 2 | no | — |
| 370 | SD16 | — | 10 | 2 | no | — |
| 371 | SD16 | — | 10 | 2 | no | — |
| 372 | SD16 | — | 10 | 2 | no | — |
| 373 | D8 | — | 10 | 2 | no | — |
| 374 | D8 | — | 10 | 2 | no | — |
| 375 | D8 | — | 10 | 2 | no | — |
| 376 | D8 | — | 10 | 2 | no | — |
| 377 | M16 | — | 5 | 4 | no | — |
| 378 | M16 | — | 5 | 4 | no | — |
| 379 | M16 | — | 10 | 2 | no | — |
| 380 | M16 | — | 10 | 2 | no | — |
| 381 | M16 | — | 20 | 2 | no | — |
| 382 | M16 | — | 20 | 4 | no | — |
| 383 | M16 | — | 20 | 2 | no | — |
| 384 | C2×C8 | — | 5 | 2 | no | — |
| 385 | C2×C8 | — | 5 | 2 | no | — |
| 386 | C2×C8 | — | 5 | 2 | no | — |
| 387 | C2×C8 | — | 5 | 2 | no | — |
| 388 | C2×C8 | — | 5 | 2 | no | — |
| 389 | C2×C8 | — | 10 | 2 | no | — |
| 390 | C2×C8 | — | 10 | 2 | no | — |
| 391 | C2×C8 | — | 20 | 2 | no | — |
| 392 | C2×C8 | — | 20 | 4 | no | — |
| 393 | C2×C8 | — | 20 | 2 | no | — |
| 394 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 395 | C4⋊C4 | — | 4 | 1 | no | — |
| 396 | C4⋊C4 | — | 10 | 2 | no | — |
| 397 | C4⋊C4 | — | 10 | 2 | no | — |
| 398 | C4⋊C4 | — | 20 | 1 | no | — |
| 399 | C22⋊C4 | — | 4 | 1 | no | — |
| 400 | C22⋊C4 | — | 10 | 2 | no | — |
| 401 | C22⋊C4 | — | 10 | 2 | no | — |
| 402 | C22⋊C4 | — | 20 | 1 | no | — |
| 403 | C22⋊C4 | — | 20 | 2 | no | — |
| 404 | C42 | — | 5 | 1 | no | — |
| 405 | C42 | — | 10 | 1 | no | — |
| 406 | C42 | — | 10 | 2 | no | — |
| 407 | C42 | — | 10 | 2 | no | — |
| 408 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 409 | C2×C5 | — | 2 | 1 | no | — |
| 410 | C2×C5 | — | 8 | 1 | no | — |
| 411 | C2×C5 | #2366 | 1 | 1 | yes | characteristic |
| 412 | D5 | — | 2 | 2 | no | — |
| 413 | D5 | — | 8 | 2 | no | — |
| 414 | D5 | — | 8 | 1 | no | — |
| 415 | C23 | — | 2 | 1 | no | — |
| 416 | C23 | — | 5 | 1 | no | — |
| 417 | C23 | — | 10 | 2 | no | — |
| 418 | C23 | — | 10 | 1 | no | — |
| 419 | Q8 | — | 2 | 2 | no | — |
| 420 | Q8 | — | 2 | 2 | no | — |
| 421 | Q8 | — | 2 | 2 | no | — |
| 422 | Q8 | — | 10 | 2 | no | — |
| 423 | D4 | — | 2 | 2 | no | — |
| 424 | D4 | — | 10 | 2 | no | — |
| 425 | D4 | — | 10 | 2 | no | — |
| 426 | D4 | — | 10 | 2 | no | — |
| 427 | D4 | — | 20 | 2 | no | — |
| 428 | D4 | — | 20 | 2 | no | — |
| 429 | D4 | — | 20 | 2 | no | — |
| 430 | D4 | — | 20 | 2 | no | — |
| 431 | D4 | — | 40 | 2 | no | — |
| 432 | D4 | — | 40 | 2 | no | — |
| 433 | C2×C4 | — | 2 | 1 | no | — |
| 434 | C2×C4 | — | 2 | 1 | no | — |
| 435 | C2×C4 | — | 2 | 2 | no | — |
| 436 | C2×C4 | — | 5 | 1 | no | — |
| 437 | C2×C4 | — | 5 | 2 | no | — |
| 438 | C2×C4 | — | 5 | 2 | no | — |
| 439 | C2×C4 | — | 10 | 1 | no | — |
| 440 | C2×C4 | — | 10 | 1 | no | — |
| 441 | C2×C4 | — | 20 | 1 | no | — |
| 442 | C2×C4 | — | 20 | 2 | no | — |
| 443 | C2×C4 | — | 20 | 1 | no | — |
| 444 | C2×C4 | — | 20 | 2 | no | — |
| 445 | C2×C4 | — | 20 | 1 | no | — |
| 446 | C2×C4 | — | 20 | 1 | no | — |
| 447 | C2×C4 | — | 20 | 2 | no | — |
| 448 | C2×C4 | — | 20 | 2 | no | — |
| 449 | C2×C4 | — | 40 | 1 | no | — |
| 450 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 451 | C8 | — | 5 | 2 | no | — |
| 452 | C8 | — | 5 | 2 | no | — |
| 453 | C8 | — | 10 | 4 | no | — |
| 454 | C8 | — | 10 | 4 | no | — |
| 455 | C8 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 456 | C8 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 457 | C5 | #23197 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 458 | C22 | — | 4 | 1 | no | — |
| 459 | C22 | — | 5 | 2 | no | — |
| 460 | C22 | — | 8 | 1 | no | — |
| 461 | C22 | — | 20 | 1 | no | — |
| 462 | C22 | — | 20 | 2 | no | — |
| 463 | C22 | — | 20 | 1 | no | — |
| 464 | C22 | — | 40 | 2 | no | — |
| 465 | C22 | — | 40 | 1 | no | — |
| 466 | C22 | #66258 | 1 | 1 | yes | characteristic |
| 467 | C4 | — | 4 | 1 | no | — |
| 468 | C4 | — | 4 | 1 | no | — |
| 469 | C4 | — | 4 | 2 | no | — |
| 470 | C4 | — | 5 | 1 | no | — |
| 471 | C4 | — | 5 | 1 | no | — |
| 472 | C4 | — | 20 | 1 | no | — |
| 473 | C4 | — | 20 | 1 | no | — |
| 474 | C4 | — | 40 | 2 | no | — |
| 475 | C4 | — | 40 | 2 | no | — |
| 476 | C4 | C2×D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 477 | C2 | — | 2 | 1 | no | — |
| 478 | C2 | — | 8 | 1 | no | — |
| 479 | C2 | — | 10 | 2 | no | — |
| 480 | C2 | — | 40 | 2 | no | — |
| 481 | C2 | — | 40 | 1 | no | — |
| 482 | C2 | #10617369 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617437 | C2 | semidirect |
| 2. #10617431 | C2 | semidirect |
| 4. #10604847 | C2 | semidirect |
| 5. #10604821 | C2 | semidirect |
| 6. #10604676 | C2 | semidirect |
| 7. #10604569 | C2 | semidirect |
| 8. #10604568 | C2 | semidirect |
| 9. #10603885 | C2 | semidirect |
| 32. C5×#497 | C4 | semidirect |
| 33. #65479 | C4 | semidirect |
| 34. #65465 | C4 | semidirect |
| 35. #65375 | C4 | semidirect |
| 36. #65347 | C4 | semidirect |
| 37. #65001 | C4 | semidirect |
| 92. #3996 | D4 | semidirect |
| 93. #3995 | D4 | semidirect |
| 193. #497 | AGL(1,𝔽5) | semidirect |
| 457. C5 | #23197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617437 | 2 |
| #10617431 | 2 |
| #10613600 | 2 |
| #10604847 | 2 |
| #10604821 | 2 |
| #10604676 | 2 |
| #10604569 | 2 |
| #10604568 | 2 |
| #10603885 | 2 |
| #23197 | 5 |