Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1128 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619104 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10617413 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10604854 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D5⋊#360 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10604784 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#64903 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #66285 | — | 2 | 1 | no | — |
| 9 | #66266 | — | 2 | 1 | no | — |
| 10 | C5×#576 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #66170 | — | 2 | 1 | no | — |
| 12 | #66109 | — | 2 | 3 | no | — |
| 13 | #66107 | — | 2 | 3 | no | — |
| 14 | #66105 | C4 | 1 | 3 | yes | complemented |
| 15 | D5×#135 | C22 | 1 | 3 | yes | — |
| 16 | #66091 | C4 | 1 | 3 | yes | complemented |
| 17 | C2×#4058 | C22 | 1 | 3 | yes | — |
| 18 | #66087 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | D5×#131 | C22 | 1 | 1 | yes | characteristic |
| 20 | #65791 | — | 2 | 1 | no | — |
| 21 | #65727 | — | 2 | 3 | no | — |
| 22 | #65725 | — | 2 | 3 | no | — |
| 23 | #65721 | C22 | 1 | 3 | yes | complemented |
| 24 | C2×#3993 | C22 | 1 | 3 | yes | complemented |
| 25 | D5⋊M32 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×#3990 | C22 | 1 | 3 | yes | complemented |
| 27 | #64907 | C22 | 1 | 3 | yes | complemented |
| 28 | #64907 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #64903 | C22 | 1 | 6 | yes | complemented |
| 30 | #64903 | C22 | 1 | 3 | yes | complemented |
| 31 | #64903 | C22 | 1 | 3 | yes | complemented |
| 32 | #33388 | — | 5 | 1 | no | maximal, Sylow |
| 33 | C5×H(5,𝔽2) | — | 2 | 1 | no | — |
| 34 | #4150 | — | 2 | 1 | no | — |
| 35 | #4150 | — | 2 | 3 | no | — |
| 36 | #4150 | — | 4 | 1 | no | — |
| 37 | D5×#41 | — | 2 | 3 | no | — |
| 38 | D5×#41 | — | 4 | 1 | no | — |
| 39 | D5×#41 | D4 | 1 | 1 | yes | characteristic |
| 40 | #4144 | — | 2 | 3 | no | — |
| 41 | #4144 | — | 4 | 3 | no | — |
| 42 | C2×#711 | — | 2 | 3 | no | — |
| 43 | C2×#711 | — | 4 | 3 | no | — |
| 44 | Q8×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 45 | D4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 46 | #4130 | — | 2 | 3 | no | — |
| 47 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 48 | C5×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 49 | C5×#135 | C2×C4 | 1 | 3 | yes | complemented |
| 50 | C2×C5×D8 | C2×C4 | 1 | 3 | yes | complemented |
| 51 | C5×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | #4097 | — | 2 | 3 | no | — |
| 53 | #4096 | — | 2 | 3 | no | — |
| 54 | #4094 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×#687 | — | 2 | 3 | no | — |
| 56 | #4078 | — | 2 | 3 | no | — |
| 57 | #4065 | C23 | 1 | 1 | yes | characteristic |
| 58 | D5×Q16 | C2×C4 | 1 | 3 | yes | complemented |
| 59 | #4062 | — | 2 | 3 | no | — |
| 60 | #4061 | — | 2 | 6 | no | — |
| 61 | D5×SD16 | — | 2 | 3 | no | — |
| 62 | #4058 | — | 2 | 3 | no | — |
| 63 | #4058 | — | 2 | 3 | no | — |
| 64 | #4058 | C2×C4 | 1 | 6 | yes | complemented |
| 65 | #4058 | C23 | 1 | 3 | yes | — |
| 66 | #4057 | — | 2 | 6 | no | — |
| 67 | D5×D8 | C2×C4 | 1 | 3 | yes | complemented |
| 68 | #4055 | — | 2 | 3 | no | — |
| 69 | #4053 | D4 | 1 | 3 | yes | — |
| 70 | D5×M16 | D4 | 1 | 3 | yes | — |
| 71 | C2×Dic20 | C2×C4 | 1 | 3 | yes | complemented |
| 72 | #4050 | C2×C4 | 1 | 3 | yes | complemented |
| 73 | #4047 | C2×C4 | 1 | 3 | yes | — |
| 74 | C2×C8×D5 | C23 | 1 | 3 | yes | — |
| 75 | #3998 | — | 2 | 3 | no | — |
| 76 | C2×#674 | — | 2 | 3 | no | — |
| 77 | #3994 | — | 2 | 3 | no | — |
| 78 | #3993 | — | 2 | 3 | no | — |
| 79 | #3993 | C23 | 1 | 3 | yes | — |
| 80 | #3993 | C23 | 1 | 1 | yes | characteristic |
| 81 | #3990 | — | 2 | 3 | no | — |
| 82 | #3990 | C23 | 1 | 1 | yes | characteristic |
| 83 | #3990 | C23 | 1 | 3 | yes | — |
| 84 | D5⋊C16 | — | 2 | 3 | no | — |
| 85 | #3584 | — | 5 | 1 | no | — |
| 86 | #3407 | — | 5 | 1 | no | — |
| 87 | #2912 | — | 5 | 1 | no | — |
| 88 | #2145 | — | 5 | 3 | no | — |
| 89 | #2145 | — | 5 | 3 | no | — |
| 90 | C2×#360 | — | 5 | 3 | no | — |
| 91 | C2×#360 | — | 5 | 3 | no | — |
| 92 | C22×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 93 | C5×#41 | — | 2 | 3 | no | — |
| 94 | C5×#41 | — | 4 | 1 | no | — |
| 95 | C5×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×C5×D4 | — | 2 | 3 | no | — |
| 97 | C2×C5×D4 | — | 4 | 3 | no | — |
| 98 | C2×C22⋊D5 | — | 4 | 3 | no | — |
| 99 | C2×C22⋊D5 | — | 4 | 6 | no | — |
| 100 | C22×Dic5 | — | 4 | 3 | no | — |
| 101 | #713 | — | 2 | 1 | no | — |
| 102 | #713 | SD16 | 1 | 1 | yes | characteristic |
| 103 | Q8×D5 | — | 2 | 3 | no | — |
| 104 | Q8×D5 | — | 4 | 1 | no | — |
| 105 | Q8×D5 | D8 | 1 | 1 | yes | characteristic |
| 106 | #711 | — | 2 | 6 | no | — |
| 107 | #711 | — | 2 | 3 | no | — |
| 108 | #711 | — | 4 | 3 | no | — |
| 109 | #711 | — | 4 | 6 | no | — |
| 110 | #711 | — | 4 | 3 | no | — |
| 111 | #711 | — | 4 | 3 | no | — |
| 112 | #711 | — | 4 | 3 | no | — |
| 113 | #711 | — | 4 | 3 | no | — |
| 114 | #711 | SD16 | 1 | 3 | yes | — |
| 115 | D4×D5 | — | 2 | 3 | no | — |
| 116 | D4×D5 | — | 4 | 3 | no | — |
| 117 | D4×D5 | — | 4 | 3 | no | — |
| 118 | D4×D5 | D8 | 1 | 3 | yes | — |
| 119 | #709 | — | 2 | 3 | no | — |
| 120 | #709 | — | 4 | 3 | no | — |
| 121 | #709 | — | 4 | 3 | no | — |
| 122 | #709 | C22⋊C4 | 1 | 3 | yes | — |
| 123 | C2×C4×D5 | — | 4 | 3 | no | — |
| 124 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 125 | C2×Dic10 | — | 2 | 3 | no | — |
| 126 | C2×Dic10 | — | 4 | 3 | no | — |
| 127 | C22⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 128 | C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 129 | C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 130 | C4⋊AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 131 | C4×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 132 | C5×Q16 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | C5×SD16 | — | 2 | 3 | no | — |
| 134 | C5×D8 | — | 2 | 3 | no | — |
| 135 | C5×D8 | C22×C4 | 1 | 3 | yes | — |
| 136 | C5×M16 | C22⋊C4 | 1 | 3 | yes | — |
| 137 | C2×C5×C8 | C22×C4 | 1 | 3 | yes | — |
| 138 | #689 | — | 2 | 3 | no | — |
| 139 | #688 | — | 2 | 1 | no | — |
| 140 | #687 | — | 2 | 6 | no | — |
| 141 | #687 | — | 2 | 3 | no | — |
| 142 | #686 | — | 2 | 3 | no | — |
| 143 | #681 | C22⋊C4 | 1 | 3 | yes | — |
| 144 | C2×#168 | C2×D4 | 1 | 3 | yes | — |
| 145 | Dic20 | — | 2 | 3 | no | — |
| 146 | Dic20 | C22×C4 | 1 | 3 | yes | — |
| 147 | D40 | C22×C4 | 1 | 1 | yes | characteristic |
| 148 | #677 | — | 2 | 3 | no | — |
| 149 | #676 | C22⋊C4 | 1 | 6 | yes | — |
| 150 | C8×D5 | C22×C4 | 1 | 3 | yes | — |
| 151 | C8×D5 | C2×D4 | 1 | 3 | yes | — |
| 152 | C8×D5 | C2×D4 | 1 | 3 | yes | — |
| 153 | C8×D5 | C24 | 1 | 1 | yes | characteristic |
| 154 | #674 | — | 2 | 3 | no | — |
| 155 | #674 | — | 2 | 1 | no | — |
| 156 | #585 | — | 10 | 1 | no | — |
| 157 | #578 | — | 5 | 3 | no | — |
| 158 | #578 | — | 5 | 1 | no | — |
| 159 | #577 | — | 10 | 3 | no | — |
| 160 | #577 | — | 10 | 1 | no | — |
| 161 | #576 | — | 5 | 3 | no | — |
| 162 | #576 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 163 | #575 | — | 10 | 3 | no | — |
| 164 | C2×#135 | — | 5 | 3 | no | — |
| 165 | C2×#135 | — | 5 | 3 | no | — |
| 166 | C2×#131 | — | 5 | 1 | no | — |
| 167 | #520 | — | 10 | 1 | no | — |
| 168 | #504 | — | 10 | 3 | no | — |
| 169 | #504 | — | 10 | 1 | no | — |
| 170 | C2×M32 | — | 5 | 3 | no | — |
| 171 | C2×M32 | — | 5 | 3 | no | — |
| 172 | #428 | — | 10 | 3 | no | — |
| 173 | #427 | — | 5 | 3 | no | — |
| 174 | C2×#106 | — | 5 | 3 | no | — |
| 175 | #360 | — | 5 | 6 | no | — |
| 176 | #360 | — | 5 | 3 | no | — |
| 177 | #360 | — | 5 | 3 | no | — |
| 178 | #360 | — | 5 | 3 | no | — |
| 179 | #360 | — | 5 | 1 | no | — |
| 180 | C23×C5 | — | 4 | 3 | no | — |
| 181 | C22×D5 | — | 4 | 3 | no | — |
| 182 | C22×D5 | C2×D8 | 1 | 3 | yes | — |
| 183 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 184 | C2×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 185 | C2×AGL(1,𝔽5) | — | 16 | 3 | no | — |
| 186 | C5×Q8 | — | 2 | 1 | no | — |
| 187 | C5×Q8 | #102 | 1 | 1 | yes | characteristic |
| 188 | C5×D4 | — | 2 | 3 | no | — |
| 189 | C5×D4 | — | 4 | 3 | no | — |
| 190 | C5×D4 | — | 4 | 3 | no | — |
| 191 | C5×D4 | #102 | 1 | 3 | yes | — |
| 192 | C2×C4×C5 | — | 4 | 3 | no | — |
| 193 | C2×C4×C5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 194 | C22⋊D5 | — | 4 | 3 | no | — |
| 195 | C22⋊D5 | — | 4 | 3 | no | — |
| 196 | C22⋊D5 | — | 4 | 6 | no | — |
| 197 | C22⋊D5 | — | 4 | 3 | no | — |
| 198 | C22⋊D5 | #102 | 1 | 6 | yes | — |
| 199 | C2×Dic5 | — | 4 | 3 | no | — |
| 200 | C2×Dic5 | — | 4 | 3 | no | — |
| 201 | C2×Dic5 | — | 4 | 6 | no | — |
| 202 | C2×Dic5 | C2×SD16 | 1 | 3 | yes | — |
| 203 | D20 | — | 2 | 1 | no | — |
| 204 | D20 | — | 4 | 1 | no | — |
| 205 | D20 | #102 | 1 | 3 | yes | — |
| 206 | C4×D5 | — | 4 | 3 | no | — |
| 207 | C4×D5 | — | 4 | 3 | no | — |
| 208 | C4×D5 | — | 4 | 1 | no | — |
| 209 | C4×D5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 210 | C4×D5 | C2×D8 | 1 | 3 | yes | — |
| 211 | C4×D5 | C2×SD16 | 1 | 3 | yes | — |
| 212 | C4×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 213 | Dic10 | — | 2 | 3 | no | — |
| 214 | Dic10 | — | 4 | 3 | no | — |
| 215 | Dic10 | — | 4 | 3 | no | — |
| 216 | Dic10 | #102 | 1 | 3 | yes | — |
| 217 | C5×C8 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 218 | C5×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 219 | #168 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 220 | #168 | C22×D4 | 1 | 1 | yes | characteristic |
| 221 | 2−1+4 | — | 10 | 3 | no | — |
| 222 | 2−1+4 | — | 10 | 1 | no | — |
| 223 | 2−1+4 | — | 20 | 1 | no | — |
| 224 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 225 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 226 | H(5,𝔽2) | — | 20 | 3 | no | — |
| 227 | C2×#41 | — | 5 | 1 | no | — |
| 228 | C2×#41 | — | 10 | 3 | no | — |
| 229 | C2×#41 | — | 10 | 3 | no | — |
| 230 | C2×#41 | — | 20 | 3 | no | — |
| 231 | C2×#41 | — | 20 | 1 | no | — |
| 232 | #137 | — | 10 | 6 | no | — |
| 233 | #137 | — | 10 | 3 | no | — |
| 234 | #137 | — | 10 | 3 | no | — |
| 235 | AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 236 | AGL(1,ℤ/8) | — | 10 | 6 | no | — |
| 237 | AGL(1,ℤ/8) | — | 10 | 3 | no | — |
| 238 | #135 | — | 5 | 1 | no | — |
| 239 | #135 | — | 5 | 3 | no | — |
| 240 | #135 | — | 5 | 6 | no | — |
| 241 | #135 | — | 5 | 3 | no | — |
| 242 | #135 | — | 10 | 3 | no | — |
| 243 | #135 | — | 10 | 3 | no | — |
| 244 | #135 | — | 10 | 3 | no | — |
| 245 | #135 | — | 10 | 3 | no | — |
| 246 | #135 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 247 | C2×Q16 | — | 5 | 3 | no | — |
| 248 | C2×Q16 | — | 5 | 3 | no | — |
| 249 | C2×SD16 | — | 10 | 3 | no | — |
| 250 | C2×SD16 | — | 10 | 3 | no | — |
| 251 | C2×D8 | — | 5 | 3 | no | — |
| 252 | C2×D8 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 253 | #131 | — | 5 | 1 | no | — |
| 254 | #131 | — | 5 | 3 | no | — |
| 255 | #131 | — | 5 | 3 | no | — |
| 256 | #131 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 257 | C2×M16 | — | 5 | 3 | no | — |
| 258 | C22×C8 | — | 5 | 3 | no | — |
| 259 | C4×Q8 | — | 20 | 1 | no | — |
| 260 | C4×D4 | — | 20 | 3 | no | — |
| 261 | #117 | — | 10 | 3 | no | — |
| 262 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 263 | M32 | — | 5 | 1 | no | — |
| 264 | M32 | — | 5 | 3 | no | — |
| 265 | M32 | — | 10 | 3 | no | — |
| 266 | M32 | — | 10 | 3 | no | — |
| 267 | C2×C16 | — | 10 | 3 | no | — |
| 268 | C2×C16 | — | 10 | 3 | no | — |
| 269 | #107 | — | 10 | 3 | no | — |
| 270 | #106 | — | 5 | 3 | no | — |
| 271 | #106 | — | 5 | 1 | no | — |
| 272 | #106 | — | 10 | 3 | no | — |
| 273 | C22×C5 | — | 4 | 3 | no | — |
| 274 | C22×C5 | — | 16 | 3 | no | — |
| 275 | C22×C5 | C2×#102 | 1 | 3 | yes | — |
| 276 | C2×D5 | — | 4 | 3 | no | — |
| 277 | C2×D5 | — | 4 | 1 | no | — |
| 278 | C2×D5 | — | 16 | 3 | no | — |
| 279 | C2×D5 | C2×#102 | 1 | 3 | yes | — |
| 280 | C2×D5 | C22×D8 | 1 | 1 | yes | characteristic |
| 281 | AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 282 | AGL(1,𝔽5) | — | 8 | 3 | no | — |
| 283 | C4×C5 | — | 4 | 1 | no | — |
| 284 | C4×C5 | C2×#102 | 1 | 3 | yes | — |
| 285 | C4×C5 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 286 | Dic5 | — | 4 | 3 | no | — |
| 287 | Dic5 | C2×#102 | 1 | 3 | yes | — |
| 288 | Dic5 | C22×SD16 | 1 | 1 | yes | characteristic |
| 289 | #41 | — | 2 | 3 | no | — |
| 290 | #41 | — | 4 | 1 | no | — |
| 291 | #41 | — | 5 | 1 | no | — |
| 292 | #41 | — | 5 | 3 | no | — |
| 293 | #41 | — | 5 | 3 | no | — |
| 294 | #41 | — | 10 | 3 | no | — |
| 295 | #41 | — | 10 | 6 | no | — |
| 296 | #41 | — | 10 | 1 | no | — |
| 297 | #41 | — | 10 | 3 | no | — |
| 298 | #41 | — | 20 | 3 | no | — |
| 299 | #41 | — | 20 | 3 | no | — |
| 300 | #41 | — | 20 | 3 | no | — |
| 301 | #41 | — | 20 | 3 | no | — |
| 302 | #41 | — | 20 | 3 | no | — |
| 303 | #41 | — | 20 | 6 | no | — |
| 304 | #41 | — | 20 | 3 | no | — |
| 305 | #41 | — | 20 | 3 | no | — |
| 306 | #41 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 307 | C2×Q8 | — | 5 | 1 | no | — |
| 308 | C2×Q8 | — | 10 | 3 | no | — |
| 309 | C2×Q8 | — | 10 | 3 | no | — |
| 310 | C2×Q8 | — | 20 | 3 | no | — |
| 311 | C2×Q8 | — | 20 | 1 | no | — |
| 312 | C2×D4 | — | 2 | 3 | no | — |
| 313 | C2×D4 | — | 4 | 3 | no | — |
| 314 | C2×D4 | — | 5 | 3 | no | — |
| 315 | C2×D4 | — | 10 | 3 | no | — |
| 316 | C2×D4 | — | 20 | 3 | no | — |
| 317 | C2×D4 | — | 20 | 3 | no | — |
| 318 | C2×D4 | — | 20 | 6 | no | — |
| 319 | C2×D4 | — | 20 | 3 | no | — |
| 320 | C22×C4 | — | 5 | 3 | no | — |
| 321 | C22×C4 | — | 20 | 3 | no | — |
| 322 | C22×C4 | — | 20 | 3 | no | — |
| 323 | C22×C4 | — | 20 | 3 | no | — |
| 324 | Q16 | — | 5 | 3 | no | — |
| 325 | Q16 | — | 10 | 3 | no | — |
| 326 | Q16 | — | 10 | 3 | no | — |
| 327 | Q16 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 328 | SD16 | — | 2 | 3 | no | — |
| 329 | SD16 | — | 10 | 3 | no | — |
| 330 | SD16 | — | 10 | 6 | no | — |
| 331 | SD16 | — | 10 | 1 | no | — |
| 332 | SD16 | — | 10 | 3 | no | — |
| 333 | D8 | — | 2 | 3 | no | — |
| 334 | D8 | — | 5 | 1 | no | — |
| 335 | D8 | — | 10 | 3 | no | — |
| 336 | D8 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 337 | M16 | — | 5 | 3 | no | — |
| 338 | M16 | — | 5 | 6 | no | — |
| 339 | M16 | C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 340 | C2×C8 | — | 5 | 3 | no | — |
| 341 | C2×C8 | — | 5 | 3 | no | — |
| 342 | C2×C8 | — | 5 | 3 | no | — |
| 343 | C2×C8 | — | 5 | 1 | no | — |
| 344 | C2×C8 | — | 5 | 3 | no | — |
| 345 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 346 | C4⋊C4 | — | 10 | 3 | no | — |
| 347 | C4⋊C4 | — | 10 | 1 | no | — |
| 348 | C4⋊C4 | — | 20 | 3 | no | — |
| 349 | C22⋊C4 | — | 20 | 3 | no | — |
| 350 | C42 | — | 20 | 3 | no | — |
| 351 | C16 | — | 10 | 3 | no | — |
| 352 | C16 | — | 10 | 1 | no | — |
| 353 | C2×C5 | — | 2 | 3 | no | — |
| 354 | C2×C5 | — | 8 | 3 | no | — |
| 355 | C2×C5 | C22×#102 | 1 | 1 | yes | characteristic |
| 356 | D5 | — | 2 | 1 | no | — |
| 357 | D5 | — | 2 | 3 | no | — |
| 358 | D5 | — | 8 | 1 | no | — |
| 359 | C23 | — | 4 | 3 | no | — |
| 360 | C23 | — | 5 | 3 | no | — |
| 361 | C23 | — | 20 | 3 | no | — |
| 362 | Q8 | — | 2 | 1 | no | — |
| 363 | Q8 | — | 5 | 3 | no | — |
| 364 | Q8 | — | 10 | 3 | no | — |
| 365 | Q8 | — | 20 | 3 | no | — |
| 366 | Q8 | — | 20 | 3 | no | — |
| 367 | Q8 | #4007 | 1 | 1 | yes | characteristic |
| 368 | D4 | — | 2 | 3 | no | — |
| 369 | D4 | — | 4 | 3 | no | — |
| 370 | D4 | — | 4 | 3 | no | — |
| 371 | D4 | — | 5 | 6 | no | — |
| 372 | D4 | — | 5 | 3 | no | — |
| 373 | D4 | — | 10 | 1 | no | — |
| 374 | D4 | — | 20 | 1 | no | — |
| 375 | D4 | — | 20 | 3 | no | — |
| 376 | D4 | — | 20 | 3 | no | — |
| 377 | D4 | — | 20 | 6 | no | — |
| 378 | D4 | — | 20 | 3 | no | — |
| 379 | D4 | #4007 | 1 | 3 | yes | — |
| 380 | C2×C4 | — | 4 | 3 | no | — |
| 381 | C2×C4 | — | 5 | 3 | no | — |
| 382 | C2×C4 | — | 5 | 1 | no | — |
| 383 | C2×C4 | — | 5 | 3 | no | — |
| 384 | C2×C4 | — | 5 | 3 | no | — |
| 385 | C2×C4 | — | 5 | 3 | no | — |
| 386 | C2×C4 | — | 20 | 1 | no | — |
| 387 | C2×C4 | — | 20 | 3 | no | — |
| 388 | C2×C4 | — | 20 | 3 | no | — |
| 389 | C2×C4 | — | 20 | 6 | no | — |
| 390 | C2×C4 | — | 20 | 3 | no | — |
| 391 | C2×C4 | — | 20 | 3 | no | — |
| 392 | C2×C4 | — | 20 | 1 | no | — |
| 393 | C2×C4 | — | 20 | 3 | no | — |
| 394 | C2×C4 | — | 80 | 3 | no | — |
| 395 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 396 | C8 | — | 5 | 1 | no | — |
| 397 | C8 | — | 5 | 3 | no | — |
| 398 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 399 | C8 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 400 | C5 | #33388 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 401 | C22 | — | 4 | 3 | no | — |
| 402 | C22 | — | 5 | 1 | no | — |
| 403 | C22 | — | 5 | 3 | no | — |
| 404 | C22 | — | 16 | 3 | no | — |
| 405 | C22 | — | 20 | 3 | no | — |
| 406 | C22 | — | 20 | 1 | no | — |
| 407 | C22 | — | 80 | 3 | no | — |
| 408 | C22 | C2×#4007 | 1 | 3 | yes | — |
| 409 | C4 | — | 4 | 1 | no | — |
| 410 | C4 | — | 5 | 1 | no | — |
| 411 | C4 | — | 5 | 3 | no | — |
| 412 | C4 | — | 20 | 3 | no | — |
| 413 | C4 | — | 40 | 3 | no | — |
| 414 | C4 | — | 40 | 1 | no | — |
| 415 | C4 | C2×#4007 | 1 | 3 | yes | — |
| 416 | C4 | C22×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 417 | C2 | — | 2 | 3 | no | — |
| 418 | C2 | — | 8 | 3 | no | — |
| 419 | C2 | — | 10 | 1 | no | — |
| 420 | C2 | — | 10 | 3 | no | — |
| 421 | C2 | — | 40 | 1 | no | — |
| 422 | C2 | C22×#4007 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10617416 | C2 | semidirect |
| 3. #10617413 | C2 | semidirect |
| 4. #10604854 | C2 | semidirect |
| 5. D5⋊#360 | C2 | semidirect |
| 6. #10604784 | C2 | semidirect |
| 7. C2×#64903 | C2 | semidirect |
| 10. C5×#576 | C4 | semidirect |
| 14. #66105 | C4 | semidirect |
| 16. #66091 | C4 | semidirect |
| 18. #66087 | C4 | semidirect |
| 23. #65721 | C22 | semidirect |
| 24. C2×#3993 | C22 | semidirect |
| 25. D5⋊M32 | C22 | semidirect |
| 26. C2×#3990 | C22 | semidirect |
| 27. #64907 | C22 | semidirect |
| 28. #64907 | C22 | semidirect |
| 29. #64903 | C22 | semidirect |
| 30. #64903 | C22 | semidirect |
| 31. #64903 | C22 | semidirect |
| 49. C5×#135 | C2×C4 | semidirect |
| 50. C2×C5×D8 | C2×C4 | semidirect |
| 58. D5×Q16 | C2×C4 | semidirect |
| 64. #4058 | C2×C4 | semidirect |
| 67. D5×D8 | C2×C4 | semidirect |
| 71. C2×Dic20 | C2×C4 | semidirect |
| 72. #4050 | C2×C4 | semidirect |
| 162. #576 | AGL(1,𝔽5) | semidirect |
| 246. #135 | C2×AGL(1,𝔽5) | semidirect |
| 252. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 400. C5 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619104 | 2 |
| #10617416 | 2 |
| #10617413 | 2 |
| #10604854 | 2 |
| D5⋊#360 | 2 |
| #10604784 | 2 |
| C2×#64903 | 2 |
| #33388 | 5 |