Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2794 conjugacy classes of subgroups.
The subgroup lattice has 528 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#65940 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C5×#2656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10614441 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10614410 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | Dic5×#121 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10609789 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10609748 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10608439 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10608396 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10605092 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#64955 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#711 | C22 | 1 | 2 | yes | — |
| 13 | C23×C4×D5 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C5×#121 | C22 | 1 | 4 | yes | — |
| 15 | C2×C5×#121 | C22 | 1 | 2 | yes | — |
| 16 | C2×#4084 | C22 | 1 | 2 | yes | — |
| 17 | C2×#4083 | C22 | 1 | 4 | yes | — |
| 18 | C2×D4×Dic5 | C22 | 1 | 4 | yes | — |
| 19 | C2×D4×Dic5 | C22 | 1 | 4 | yes | complemented |
| 20 | C22×#685 | C22 | 1 | 2 | yes | — |
| 21 | C2×#4070 | C22 | 1 | 2 | yes | — |
| 22 | C22×C4×Dic5 | C22 | 1 | 2 | yes | — |
| 23 | #65940 | — | 2 | 16 | no | — |
| 24 | C2×#4043 | C22 | 1 | 2 | yes | — |
| 25 | C2×#4038 | C22 | 1 | 2 | yes | — |
| 26 | C2×#4029 | C22 | 1 | 4 | yes | — |
| 27 | C2×#4027 | C22 | 1 | 4 | yes | — |
| 28 | C5×#399 | C22 | 1 | 4 | yes | complemented |
| 29 | C5×#392 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×C5×#95 | C22 | 1 | 1 | yes | characteristic |
| 31 | #65512 | C22 | 1 | 8 | yes | — |
| 32 | #65511 | C22 | 1 | 4 | yes | complemented |
| 33 | #65510 | C22 | 1 | 4 | yes | complemented |
| 34 | #65509 | C22 | 1 | 8 | yes | — |
| 35 | #65501 | C22 | 1 | 4 | yes | — |
| 36 | C2×#3963 | C22 | 1 | 1 | yes | characteristic |
| 37 | #65282 | C22 | 1 | 8 | yes | — |
| 38 | #65274 | C22 | 1 | 4 | yes | complemented |
| 39 | #65271 | C22 | 1 | 4 | yes | complemented |
| 40 | C4⋊C4×Dic5 | C22 | 1 | 4 | yes | complemented |
| 41 | #65250 | C22 | 1 | 8 | yes | — |
| 42 | #65250 | C22 | 1 | 8 | yes | — |
| 43 | #65242 | C22 | 1 | 4 | yes | complemented |
| 44 | #65240 | C22 | 1 | 8 | yes | complemented |
| 45 | #65236 | C22 | 1 | 4 | yes | complemented |
| 46 | C22⋊C4×Dic5 | C22 | 1 | 8 | yes | complemented |
| 47 | #64955 | C22 | 1 | 4 | yes | — |
| 48 | #64955 | C22 | 1 | 4 | yes | — |
| 49 | #64950 | C22 | 1 | 4 | yes | complemented |
| 50 | #64945 | C22 | 1 | 4 | yes | complemented |
| 51 | #34575 | — | 5 | 1 | no | maximal, Sylow |
| 52 | C24×D5 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C5×D4 | C23 | 1 | 4 | yes | — |
| 54 | C22×C5×D4 | C23 | 1 | 4 | yes | — |
| 55 | C22×C5×D4 | C23 | 1 | 2 | yes | — |
| 56 | C23×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 57 | C23×C4×C5 | C23 | 1 | 2 | yes | — |
| 58 | C22×C22⋊D5 | C23 | 1 | 4 | yes | — |
| 59 | C22×C22⋊D5 | C23 | 1 | 4 | yes | — |
| 60 | C23×Dic5 | C23 | 1 | 4 | yes | — |
| 61 | C23×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 62 | C23×Dic5 | C23 | 1 | 2 | yes | — |
| 63 | C2×#711 | — | 2 | 8 | no | — |
| 64 | C2×#711 | — | 4 | 8 | no | — |
| 65 | C22×C4×D5 | — | 4 | 4 | no | — |
| 66 | C22×C4×D5 | D4 | 1 | 8 | yes | complemented |
| 67 | C22×C4×D5 | C23 | 1 | 2 | yes | — |
| 68 | C22×C4×D5 | C23 | 1 | 2 | yes | — |
| 69 | C22×Dic10 | C23 | 1 | 2 | yes | — |
| 70 | C5×#121 | — | 2 | 8 | no | — |
| 71 | C5×#121 | — | 2 | 16 | no | — |
| 72 | C2×C5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 73 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 74 | C2×C5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 75 | C2×C5×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 76 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 77 | C2×C22⋊Dic5 | C23 | 1 | 4 | yes | — |
| 78 | C2×C22⋊Dic5 | C23 | 1 | 8 | yes | — |
| 79 | C2×C22⋊Dic5 | C23 | 1 | 8 | yes | — |
| 80 | #4084 | — | 2 | 8 | no | — |
| 81 | #4083 | — | 2 | 16 | no | — |
| 82 | D4×Dic5 | — | 2 | 16 | no | — |
| 83 | D4×Dic5 | — | 4 | 8 | no | — |
| 84 | C2×#685 | — | 2 | 8 | no | — |
| 85 | C2×#685 | C23 | 1 | 4 | yes | — |
| 86 | C2×#685 | C23 | 1 | 4 | yes | — |
| 87 | C2×#685 | C23 | 1 | 8 | yes | — |
| 88 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 89 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 90 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 91 | C2×C4⋊Dic5 | C23 | 1 | 4 | yes | — |
| 92 | #4070 | — | 2 | 8 | no | — |
| 93 | C2×#683 | C23 | 1 | 4 | yes | — |
| 94 | C2×C4×Dic5 | — | 4 | 4 | no | — |
| 95 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 96 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 97 | C2×C4×Dic5 | C23 | 1 | 4 | yes | — |
| 98 | #4043 | — | 2 | 8 | no | — |
| 99 | #4038 | — | 2 | 8 | no | — |
| 100 | #4029 | — | 2 | 16 | no | — |
| 101 | #4027 | — | 2 | 16 | no | — |
| 102 | C5×#95 | C23 | 1 | 4 | yes | — |
| 103 | #3963 | C23 | 1 | 8 | yes | — |
| 104 | #3963 | C23 | 1 | 8 | yes | — |
| 105 | #3963 | C23 | 1 | 8 | yes | — |
| 106 | #3963 | C23 | 1 | 4 | yes | — |
| 107 | C2×#525 | — | 5 | 2 | no | — |
| 108 | #2663 | — | 5 | 4 | no | — |
| 109 | #2661 | — | 5 | 4 | no | — |
| 110 | #2659 | — | 5 | 1 | no | — |
| 111 | #2656 | D5 | 1 | 1 | yes | characteristic, complemented |
| 112 | #2639 | — | 5 | 2 | no | — |
| 113 | #2617 | — | 5 | 4 | no | — |
| 114 | #2395 | — | 5 | 4 | no | — |
| 115 | #2388 | — | 5 | 4 | no | — |
| 116 | C4×#121 | — | 5 | 4 | no | — |
| 117 | C2×C4×C22⋊C4 | — | 5 | 1 | no | — |
| 118 | C24×C5 | C24 | 1 | 4 | yes | — |
| 119 | C24×C5 | C24 | 1 | 1 | yes | characteristic |
| 120 | C23×D5 | — | 2 | 4 | no | — |
| 121 | C23×D5 | — | 4 | 2 | no | — |
| 122 | C23×D5 | — | 4 | 1 | no | — |
| 123 | C23×D5 | — | 4 | 1 | no | — |
| 124 | C23×D5 | C2×D4 | 1 | 4 | yes | — |
| 125 | C23×D5 | C24 | 1 | 2 | yes | — |
| 126 | C2×C5×D4 | — | 2 | 8 | no | — |
| 127 | C2×C5×D4 | — | 2 | 16 | no | — |
| 128 | C2×C5×D4 | — | 2 | 4 | no | — |
| 129 | C2×C5×D4 | — | 2 | 8 | no | — |
| 130 | C2×C5×D4 | — | 4 | 4 | no | — |
| 131 | C2×C5×D4 | — | 4 | 4 | no | — |
| 132 | C2×C5×D4 | — | 4 | 4 | no | — |
| 133 | C22×C4×C5 | — | 4 | 2 | no | — |
| 134 | C22×C4×C5 | — | 4 | 2 | no | — |
| 135 | C22×C4×C5 | — | 4 | 2 | no | — |
| 136 | C22×C4×C5 | C2×D4 | 1 | 4 | yes | — |
| 137 | C22×C4×C5 | #41 | 1 | 8 | yes | complemented |
| 138 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 139 | C22×C4×C5 | C24 | 1 | 2 | yes | — |
| 140 | C22×C4×C5 | C24 | 1 | 4 | yes | — |
| 141 | C2×C22⋊D5 | — | 2 | 8 | no | — |
| 142 | C2×C22⋊D5 | — | 2 | 8 | no | — |
| 143 | C2×C22⋊D5 | — | 4 | 8 | no | — |
| 144 | C2×C22⋊D5 | — | 4 | 4 | no | — |
| 145 | C2×C22⋊D5 | — | 4 | 4 | no | — |
| 146 | C22×Dic5 | — | 2 | 4 | no | — |
| 147 | C22×Dic5 | — | 2 | 4 | no | — |
| 148 | C22×Dic5 | — | 2 | 8 | no | — |
| 149 | C22×Dic5 | — | 2 | 16 | no | — |
| 150 | C22×Dic5 | — | 4 | 2 | no | — |
| 151 | C22×Dic5 | — | 4 | 2 | no | — |
| 152 | C22×Dic5 | C2×D4 | 1 | 4 | yes | — |
| 153 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 154 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 155 | C22×Dic5 | C24 | 1 | 4 | yes | — |
| 156 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 157 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 158 | #711 | — | 4 | 32 | no | — |
| 159 | C2×C4×D5 | — | 2 | 8 | no | — |
| 160 | C2×C4×D5 | — | 4 | 16 | no | — |
| 161 | C2×C4×D5 | — | 4 | 4 | no | — |
| 162 | C2×C4×D5 | C2×D4 | 1 | 8 | yes | — |
| 163 | C2×C4×D5 | C2×D4 | 1 | 8 | yes | — |
| 164 | C2×Dic10 | — | 2 | 4 | no | — |
| 165 | C2×Dic10 | — | 4 | 4 | no | — |
| 166 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 167 | C5×C4⋊C4 | — | 2 | 8 | no | — |
| 168 | C5×C22⋊C4 | — | 2 | 8 | no | — |
| 169 | C5×C22⋊C4 | — | 2 | 16 | no | — |
| 170 | C22⋊Dic5 | — | 2 | 8 | no | — |
| 171 | C22⋊Dic5 | — | 2 | 8 | no | — |
| 172 | C22⋊Dic5 | — | 4 | 8 | no | — |
| 173 | C22⋊Dic5 | — | 4 | 8 | no | — |
| 174 | #685 | — | 2 | 8 | no | — |
| 175 | #685 | — | 2 | 8 | no | — |
| 176 | #685 | — | 2 | 16 | no | — |
| 177 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 178 | C4⋊Dic5 | — | 2 | 8 | no | — |
| 179 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 180 | C4⋊Dic5 | — | 4 | 4 | no | — |
| 181 | #683 | — | 2 | 8 | no | — |
| 182 | C4×Dic5 | — | 2 | 8 | no | — |
| 183 | C4×Dic5 | — | 2 | 8 | no | — |
| 184 | C4×Dic5 | — | 4 | 4 | no | — |
| 185 | C22×#41 | — | 5 | 2 | no | — |
| 186 | C24×C4 | — | 5 | 1 | no | — |
| 187 | #525 | — | 10 | 16 | no | — |
| 188 | C2×#123 | — | 5 | 4 | no | — |
| 189 | C2×C22⋊Q8 | — | 5 | 2 | no | — |
| 190 | C2×C22⋊Q8 | — | 5 | 2 | no | — |
| 191 | C2×#121 | — | 5 | 2 | no | — |
| 192 | C2×#121 | C2×D5 | 1 | 4 | yes | — |
| 193 | C2×#121 | C2×D5 | 1 | 2 | yes | — |
| 194 | C2×#120 | — | 5 | 4 | no | — |
| 195 | C2×C4×D4 | — | 5 | 4 | no | — |
| 196 | C2×C4×D4 | — | 5 | 4 | no | — |
| 197 | C2×C4×D4 | — | 5 | 4 | no | — |
| 198 | C2×#117 | — | 5 | 2 | no | — |
| 199 | C22×C22⋊C4 | — | 5 | 2 | no | — |
| 200 | C22×C42 | — | 5 | 2 | no | — |
| 201 | #400 | — | 5 | 4 | no | — |
| 202 | #399 | C2×D5 | 1 | 4 | yes | complemented |
| 203 | #398 | — | 5 | 4 | no | — |
| 204 | #397 | — | 5 | 8 | no | — |
| 205 | #397 | — | 5 | 4 | no | — |
| 206 | #395 | — | 5 | 4 | no | — |
| 207 | #394 | — | 5 | 4 | no | — |
| 208 | #394 | — | 5 | 8 | no | — |
| 209 | #394 | — | 5 | 8 | no | — |
| 210 | #393 | — | 5 | 4 | no | — |
| 211 | #392 | — | 5 | 8 | no | — |
| 212 | #392 | C2×D5 | 1 | 4 | yes | complemented |
| 213 | #390 | — | 5 | 4 | no | — |
| 214 | #389 | — | 5 | 4 | no | — |
| 215 | #388 | — | 5 | 8 | no | — |
| 216 | #386 | — | 5 | 8 | no | — |
| 217 | #380 | — | 5 | 4 | no | — |
| 218 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 219 | C4×C22⋊C4 | — | 5 | 8 | no | — |
| 220 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 221 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 222 | C2×#95 | — | 5 | 1 | no | — |
| 223 | C2×#95 | C2×D5 | 1 | 1 | yes | characteristic |
| 224 | C23×C5 | — | 2 | 2 | no | — |
| 225 | C23×C5 | — | 2 | 1 | no | — |
| 226 | C23×C5 | — | 2 | 1 | no | — |
| 227 | C23×C5 | — | 2 | 4 | no | — |
| 228 | C23×C5 | — | 2 | 8 | no | — |
| 229 | C23×C5 | — | 2 | 8 | no | — |
| 230 | C23×C5 | — | 2 | 4 | no | — |
| 231 | C23×C5 | — | 2 | 4 | no | — |
| 232 | C23×C5 | C22×D4 | 1 | 2 | yes | — |
| 233 | C23×C5 | C2×#41 | 1 | 4 | yes | — |
| 234 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 235 | C22×D5 | — | 2 | 8 | no | — |
| 236 | C22×D5 | — | 2 | 4 | no | — |
| 237 | C22×D5 | — | 2 | 4 | no | — |
| 238 | C22×D5 | — | 2 | 2 | no | — |
| 239 | C22×D5 | — | 2 | 2 | no | — |
| 240 | C22×D5 | — | 4 | 4 | no | — |
| 241 | C22×D5 | — | 4 | 4 | no | — |
| 242 | C22×D5 | — | 4 | 8 | no | — |
| 243 | C22×D5 | — | 4 | 8 | no | — |
| 244 | C22×D5 | C22×D4 | 1 | 4 | yes | — |
| 245 | C5×D4 | — | 4 | 8 | no | — |
| 246 | C5×D4 | — | 4 | 16 | no | — |
| 247 | C5×D4 | — | 4 | 16 | no | — |
| 248 | C2×C4×C5 | — | 2 | 4 | no | — |
| 249 | C2×C4×C5 | — | 2 | 4 | no | — |
| 250 | C2×C4×C5 | — | 2 | 4 | no | — |
| 251 | C2×C4×C5 | — | 2 | 4 | no | — |
| 252 | C2×C4×C5 | — | 2 | 8 | no | — |
| 253 | C2×C4×C5 | — | 4 | 4 | no | — |
| 254 | C2×C4×C5 | — | 4 | 8 | no | — |
| 255 | C2×C4×C5 | C22×D4 | 1 | 4 | yes | — |
| 256 | C2×C4×C5 | C2×#41 | 1 | 8 | yes | — |
| 257 | C22⋊D5 | — | 4 | 16 | no | — |
| 258 | C22⋊D5 | — | 4 | 16 | no | — |
| 259 | C2×Dic5 | — | 2 | 2 | no | — |
| 260 | C2×Dic5 | — | 2 | 8 | no | — |
| 261 | C2×Dic5 | — | 2 | 4 | no | — |
| 262 | C2×Dic5 | — | 2 | 4 | no | — |
| 263 | C2×Dic5 | — | 2 | 4 | no | — |
| 264 | C2×Dic5 | — | 2 | 4 | no | — |
| 265 | C2×Dic5 | — | 2 | 8 | no | — |
| 266 | C2×Dic5 | — | 2 | 4 | no | — |
| 267 | C2×Dic5 | — | 2 | 4 | no | — |
| 268 | C2×Dic5 | — | 2 | 4 | no | — |
| 269 | C2×Dic5 | — | 4 | 8 | no | — |
| 270 | C2×Dic5 | — | 4 | 16 | no | — |
| 271 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 272 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 273 | C2×Dic5 | H(5,𝔽2) | 1 | 4 | yes | — |
| 274 | C4×D5 | — | 2 | 16 | no | — |
| 275 | C4×D5 | — | 4 | 8 | no | — |
| 276 | Dic10 | — | 4 | 8 | no | — |
| 277 | C25 | — | 5 | 1 | no | — |
| 278 | C2×#41 | — | 10 | 8 | no | — |
| 279 | C2×#41 | — | 20 | 8 | no | — |
| 280 | C22×Q8 | — | 5 | 2 | no | — |
| 281 | C22×D4 | — | 5 | 4 | no | — |
| 282 | C22×D4 | — | 5 | 4 | no | — |
| 283 | C22×D4 | C22×D5 | 1 | 4 | yes | — |
| 284 | C22×D4 | C22×D5 | 1 | 4 | yes | — |
| 285 | C22×D4 | C22×D5 | 1 | 2 | yes | — |
| 286 | C23×C4 | — | 5 | 1 | no | — |
| 287 | C23×C4 | — | 5 | 2 | no | — |
| 288 | C23×C4 | — | 5 | 8 | no | — |
| 289 | C23×C4 | — | 5 | 2 | no | — |
| 290 | C23×C4 | — | 5 | 4 | no | — |
| 291 | C23×C4 | — | 5 | 2 | no | — |
| 292 | C23×C4 | — | 20 | 4 | no | — |
| 293 | C23×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 294 | C23×C4 | C22×D5 | 1 | 2 | yes | — |
| 295 | #123 | — | 10 | 16 | no | — |
| 296 | C22⋊Q8 | — | 10 | 8 | no | — |
| 297 | C22⋊Q8 | — | 10 | 8 | no | — |
| 298 | #121 | — | 2 | 8 | no | — |
| 299 | #121 | — | 2 | 16 | no | — |
| 300 | #121 | — | 10 | 8 | no | — |
| 301 | #120 | — | 10 | 16 | no | — |
| 302 | C4×D4 | — | 10 | 16 | no | — |
| 303 | C4×D4 | — | 10 | 16 | no | — |
| 304 | C4×D4 | — | 20 | 8 | no | — |
| 305 | #117 | — | 10 | 8 | no | — |
| 306 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 307 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 308 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 309 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 310 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 311 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 312 | C2×C4⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 313 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 314 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 315 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 316 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 317 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 318 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 319 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 320 | C2×C22⋊C4 | — | 10 | 8 | no | — |
| 321 | C2×C22⋊C4 | C22×D5 | 1 | 4 | yes | — |
| 322 | C2×C22⋊C4 | C22×D5 | 1 | 8 | yes | — |
| 323 | C2×C42 | — | 5 | 4 | no | — |
| 324 | C2×C42 | — | 5 | 4 | no | — |
| 325 | C2×C42 | — | 5 | 4 | no | — |
| 326 | C2×C42 | — | 20 | 4 | no | — |
| 327 | #95 | — | 5 | 4 | no | — |
| 328 | #95 | — | 5 | 8 | no | — |
| 329 | #95 | — | 5 | 8 | no | — |
| 330 | #95 | — | 5 | 8 | no | — |
| 331 | #95 | C22×D5 | 1 | 4 | yes | — |
| 332 | C22×C5 | — | 2 | 2 | no | — |
| 333 | C22×C5 | — | 2 | 2 | no | — |
| 334 | C22×C5 | — | 2 | 4 | no | — |
| 335 | C22×C5 | — | 2 | 4 | no | — |
| 336 | C22×C5 | — | 4 | 4 | no | — |
| 337 | C22×C5 | — | 4 | 4 | no | — |
| 338 | C22×C5 | — | 4 | 4 | no | — |
| 339 | C22×C5 | — | 4 | 8 | no | — |
| 340 | C22×C5 | — | 4 | 8 | no | — |
| 341 | C22×C5 | #532 | 1 | 4 | yes | — |
| 342 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 343 | C22×C5 | C22×#41 | 1 | 2 | yes | — |
| 344 | C22×C5 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 345 | C22×C5 | #585 | 1 | 1 | yes | characteristic |
| 346 | C22×C5 | #585 | 1 | 1 | yes | characteristic |
| 347 | C2×D5 | — | 2 | 4 | no | — |
| 348 | C2×D5 | — | 2 | 4 | no | — |
| 349 | C2×D5 | — | 2 | 4 | no | — |
| 350 | C2×D5 | — | 4 | 16 | no | — |
| 351 | C2×D5 | — | 4 | 4 | no | — |
| 352 | C2×D5 | — | 4 | 4 | no | — |
| 353 | C4×C5 | — | 2 | 4 | no | — |
| 354 | C4×C5 | — | 2 | 8 | no | — |
| 355 | C4×C5 | — | 4 | 4 | no | — |
| 356 | Dic5 | — | 2 | 2 | no | — |
| 357 | Dic5 | — | 4 | 4 | no | — |
| 358 | Dic5 | — | 4 | 4 | no | — |
| 359 | Dic5 | — | 4 | 4 | no | — |
| 360 | Dic5 | #534 | 1 | 4 | yes | — |
| 361 | C24 | — | 5 | 2 | no | — |
| 362 | C24 | — | 5 | 4 | no | — |
| 363 | C24 | — | 10 | 4 | no | — |
| 364 | C24 | — | 20 | 2 | no | — |
| 365 | C24 | — | 20 | 1 | no | — |
| 366 | C24 | — | 20 | 1 | no | — |
| 367 | C24 | C23×D5 | 1 | 4 | yes | — |
| 368 | C24 | C23×D5 | 1 | 1 | yes | characteristic |
| 369 | #41 | — | 20 | 32 | no | — |
| 370 | C2×Q8 | — | 10 | 4 | no | — |
| 371 | C2×Q8 | — | 20 | 4 | no | — |
| 372 | C2×D4 | — | 2 | 8 | no | — |
| 373 | C2×D4 | — | 2 | 16 | no | — |
| 374 | C2×D4 | — | 2 | 4 | no | — |
| 375 | C2×D4 | — | 2 | 8 | no | — |
| 376 | C2×D4 | — | 4 | 4 | no | — |
| 377 | C2×D4 | — | 4 | 4 | no | — |
| 378 | C2×D4 | — | 4 | 4 | no | — |
| 379 | C2×D4 | — | 10 | 8 | no | — |
| 380 | C2×D4 | — | 10 | 8 | no | — |
| 381 | C2×D4 | — | 20 | 8 | no | — |
| 382 | C2×D4 | — | 20 | 4 | no | — |
| 383 | C2×D4 | — | 20 | 4 | no | — |
| 384 | C22×C4 | — | 4 | 2 | no | — |
| 385 | C22×C4 | — | 4 | 2 | no | — |
| 386 | C22×C4 | — | 4 | 2 | no | — |
| 387 | C22×C4 | — | 5 | 1 | no | — |
| 388 | C22×C4 | — | 5 | 4 | no | — |
| 389 | C22×C4 | — | 5 | 1 | no | — |
| 390 | C22×C4 | — | 5 | 8 | no | — |
| 391 | C22×C4 | — | 5 | 8 | no | — |
| 392 | C22×C4 | — | 5 | 4 | no | — |
| 393 | C22×C4 | — | 5 | 4 | no | — |
| 394 | C22×C4 | — | 5 | 4 | no | — |
| 395 | C22×C4 | — | 10 | 8 | no | — |
| 396 | C22×C4 | — | 10 | 4 | no | — |
| 397 | C22×C4 | — | 10 | 8 | no | — |
| 398 | C22×C4 | — | 10 | 16 | no | — |
| 399 | C22×C4 | — | 10 | 4 | no | — |
| 400 | C22×C4 | — | 20 | 4 | no | — |
| 401 | C22×C4 | — | 20 | 16 | no | — |
| 402 | C22×C4 | — | 20 | 2 | no | — |
| 403 | C22×C4 | — | 20 | 2 | no | — |
| 404 | C22×C4 | D4×D5 | 1 | 4 | yes | — |
| 405 | C22×C4 | #711 | 1 | 8 | yes | complemented |
| 406 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 407 | C22×C4 | C23×D5 | 1 | 2 | yes | — |
| 408 | C22×C4 | C23×D5 | 1 | 4 | yes | — |
| 409 | C4⋊C4 | — | 2 | 4 | no | — |
| 410 | C4⋊C4 | — | 2 | 8 | no | — |
| 411 | C4⋊C4 | — | 10 | 8 | no | — |
| 412 | C4⋊C4 | — | 10 | 4 | no | — |
| 413 | C4⋊C4 | — | 10 | 8 | no | — |
| 414 | C4⋊C4 | — | 20 | 4 | no | — |
| 415 | C4⋊C4 | — | 20 | 4 | no | — |
| 416 | C22⋊C4 | — | 2 | 8 | no | — |
| 417 | C22⋊C4 | — | 2 | 16 | no | — |
| 418 | C22⋊C4 | — | 10 | 8 | no | — |
| 419 | C22⋊C4 | — | 10 | 8 | no | — |
| 420 | C22⋊C4 | — | 10 | 8 | no | — |
| 421 | C22⋊C4 | — | 10 | 8 | no | — |
| 422 | C22⋊C4 | — | 10 | 16 | no | — |
| 423 | C22⋊C4 | — | 20 | 8 | no | — |
| 424 | C22⋊C4 | — | 20 | 8 | no | — |
| 425 | C42 | — | 10 | 8 | no | — |
| 426 | C42 | — | 10 | 8 | no | — |
| 427 | C42 | — | 20 | 4 | no | — |
| 428 | C2×C5 | — | 2 | 4 | no | — |
| 429 | C2×C5 | — | 8 | 4 | no | — |
| 430 | C2×C5 | C2×#532 | 1 | 1 | yes | characteristic |
| 431 | C2×C5 | C2×#534 | 1 | 1 | yes | characteristic |
| 432 | C2×C5 | #3449 | 1 | 1 | yes | characteristic |
| 433 | C2×C5 | #3459 | 1 | 2 | yes | — |
| 434 | C2×C5 | #3460 | 1 | 2 | yes | — |
| 435 | D5 | — | 4 | 4 | no | — |
| 436 | C23 | — | 2 | 2 | no | — |
| 437 | C23 | — | 2 | 1 | no | — |
| 438 | C23 | — | 2 | 1 | no | — |
| 439 | C23 | — | 2 | 4 | no | — |
| 440 | C23 | — | 2 | 8 | no | — |
| 441 | C23 | — | 2 | 8 | no | — |
| 442 | C23 | — | 2 | 4 | no | — |
| 443 | C23 | — | 2 | 4 | no | — |
| 444 | C23 | — | 5 | 4 | no | — |
| 445 | C23 | — | 10 | 8 | no | — |
| 446 | C23 | — | 10 | 4 | no | — |
| 447 | C23 | — | 10 | 4 | no | — |
| 448 | C23 | — | 10 | 2 | no | — |
| 449 | C23 | — | 10 | 2 | no | — |
| 450 | C23 | — | 20 | 4 | no | — |
| 451 | C23 | — | 20 | 4 | no | — |
| 452 | C23 | — | 20 | 8 | no | — |
| 453 | C23 | — | 20 | 8 | no | — |
| 454 | C23 | C2×D4×D5 | 1 | 2 | yes | — |
| 455 | C23 | C2×#711 | 1 | 4 | yes | — |
| 456 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 457 | Q8 | — | 20 | 8 | no | — |
| 458 | D4 | — | 4 | 8 | no | — |
| 459 | D4 | — | 4 | 16 | no | — |
| 460 | D4 | — | 4 | 16 | no | — |
| 461 | D4 | — | 20 | 16 | no | — |
| 462 | D4 | — | 20 | 16 | no | — |
| 463 | C2×C4 | — | 2 | 4 | no | — |
| 464 | C2×C4 | — | 2 | 4 | no | — |
| 465 | C2×C4 | — | 2 | 4 | no | — |
| 466 | C2×C4 | — | 2 | 4 | no | — |
| 467 | C2×C4 | — | 2 | 8 | no | — |
| 468 | C2×C4 | — | 4 | 4 | no | — |
| 469 | C2×C4 | — | 4 | 8 | no | — |
| 470 | C2×C4 | — | 5 | 2 | no | — |
| 471 | C2×C4 | — | 5 | 4 | no | — |
| 472 | C2×C4 | — | 5 | 2 | no | — |
| 473 | C2×C4 | — | 10 | 16 | no | — |
| 474 | C2×C4 | — | 10 | 8 | no | — |
| 475 | C2×C4 | — | 10 | 2 | no | — |
| 476 | C2×C4 | — | 10 | 4 | no | — |
| 477 | C2×C4 | — | 10 | 4 | no | — |
| 478 | C2×C4 | — | 10 | 4 | no | — |
| 479 | C2×C4 | — | 10 | 4 | no | — |
| 480 | C2×C4 | — | 10 | 8 | no | — |
| 481 | C2×C4 | — | 10 | 4 | no | — |
| 482 | C2×C4 | — | 10 | 4 | no | — |
| 483 | C2×C4 | — | 10 | 4 | no | — |
| 484 | C2×C4 | — | 20 | 8 | no | — |
| 485 | C2×C4 | — | 20 | 16 | no | — |
| 486 | C2×C4 | — | 20 | 8 | no | — |
| 487 | C2×C4 | C2×D4×D5 | 1 | 4 | yes | — |
| 488 | C2×C4 | C2×#711 | 1 | 8 | yes | — |
| 489 | C5 | #34575 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 490 | C22 | — | 2 | 4 | no | — |
| 491 | C22 | — | 2 | 2 | no | — |
| 492 | C22 | — | 2 | 2 | no | — |
| 493 | C22 | — | 2 | 4 | no | — |
| 494 | C22 | — | 4 | 8 | no | — |
| 495 | C22 | — | 4 | 4 | no | — |
| 496 | C22 | — | 4 | 4 | no | — |
| 497 | C22 | — | 4 | 8 | no | — |
| 498 | C22 | — | 4 | 4 | no | — |
| 499 | C22 | — | 10 | 4 | no | — |
| 500 | C22 | — | 10 | 4 | no | — |
| 501 | C22 | — | 10 | 4 | no | — |
| 502 | C22 | — | 20 | 16 | no | — |
| 503 | C22 | — | 20 | 4 | no | — |
| 504 | C22 | — | 20 | 4 | no | — |
| 505 | C22 | #66050 | 1 | 4 | yes | — |
| 506 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 507 | C22 | C22×#711 | 1 | 2 | yes | — |
| 508 | C22 | D5×H(5,𝔽2) | 1 | 2 | yes | — |
| 509 | C22 | #66285 | 1 | 1 | yes | characteristic |
| 510 | C22 | #66287 | 1 | 1 | yes | characteristic |
| 511 | C4 | — | 2 | 8 | no | — |
| 512 | C4 | — | 2 | 4 | no | — |
| 513 | C4 | — | 4 | 4 | no | — |
| 514 | C4 | — | 5 | 4 | no | — |
| 515 | C4 | — | 10 | 2 | no | — |
| 516 | C4 | — | 20 | 4 | no | — |
| 517 | C4 | — | 20 | 4 | no | — |
| 518 | C4 | — | 20 | 4 | no | — |
| 519 | C2 | — | 2 | 4 | no | — |
| 520 | C2 | — | 8 | 4 | no | — |
| 521 | C2 | — | 20 | 4 | no | — |
| 522 | C2 | C2×#66050 | 1 | 1 | yes | characteristic |
| 523 | C2 | #10618196 | 1 | 2 | yes | — |
| 524 | C2 | D5×#534 | 1 | 1 | yes | characteristic |
| 525 | C2 | #10618264 | 1 | 1 | yes | characteristic |
| 526 | C2 | #10618265 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2656 | C2 |
| hypercenter | #2656 | D5 |
| hypocenter | C5 | #34575 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2656 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#65940 | C2 | semidirect |
| 2. C5×#2656 | C2 | semidirect |
| 3. #10614441 | C2 | semidirect |
| 4. #10614410 | C2 | semidirect |
| 5. Dic5×#121 | C2 | semidirect |
| 6. #10609789 | C2 | semidirect |
| 7. #10609748 | C2 | semidirect |
| 8. #10608439 | C2 | semidirect |
| 9. #10608396 | C2 | semidirect |
| 10. #10605092 | C2 | semidirect |
| 11. C2×#64955 | C2 | semidirect |
| 19. C2×D4×Dic5 | C22 | semidirect |
| 28. C5×#399 | C22 | semidirect |
| 29. C5×#392 | C22 | semidirect |
| 32. #65511 | C22 | semidirect |
| 33. #65510 | C22 | semidirect |
| 38. #65274 | C22 | semidirect |
| 39. #65271 | C22 | semidirect |
| 40. C4⋊C4×Dic5 | C22 | semidirect |
| 43. #65242 | C22 | semidirect |
| 44. #65240 | C22 | semidirect |
| 45. #65236 | C22 | semidirect |
| 46. C22⋊C4×Dic5 | C22 | semidirect |
| 49. #64950 | C22 | semidirect |
| 50. #64945 | C22 | semidirect |
| 66. C22×C4×D5 | D4 | semidirect |
| 111. #2656 | D5 | semidirect |
| 137. C22×C4×C5 | #41 | semidirect |
| 202. #399 | C2×D5 | semidirect |
| 212. #392 | C2×D5 | semidirect |
| 405. C22×C4 | #711 | semidirect |
| 489. C5 | #34575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65940 | 2 |
| C5×#2656 | 2 |
| #10614441 | 2 |
| #10614410 | 2 |
| Dic5×#121 | 2 |
| #10609789 | 2 |
| #10609748 | 2 |
| #10608439 | 2 |
| #10608396 | 2 |
| #10605092 | 2 |
| C2×#64955 | 2 |
| #34575 | 5 |