Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6640 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 | C5×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10619040 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10619017 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #10619016 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #10618994 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #10618187 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #10618158 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #10618072 | C2 | 1 | 10 | yes | maximal, complemented |
| 9 | #10618020 | C2 | 1 | 10 | yes | maximal, complemented |
| 10 | C5×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#563 | C22 | 1 | 10 | yes | complemented |
| 12 | C5×#562 | C22 | 1 | 5 | yes | complemented |
| 13 | C5×#533 | C22 | 1 | 5 | yes | complemented |
| 14 | C5×#529 | C22 | 1 | 10 | yes | complemented |
| 15 | #66069 | C22 | 1 | 20 | yes | complemented |
| 16 | #66062 | C22 | 1 | 10 | yes | complemented |
| 17 | #66059 | C22 | 1 | 10 | yes | — |
| 18 | #66046 | C22 | 1 | 20 | yes | complemented |
| 19 | #66045 | C22 | 1 | 20 | yes | complemented |
| 20 | #66040 | C22 | 1 | 20 | yes | complemented |
| 21 | #66040 | C22 | 1 | 20 | yes | complemented |
| 22 | #66034 | C22 | 1 | 5 | yes | complemented |
| 23 | #66034 | C22 | 1 | 10 | yes | complemented |
| 24 | #66033 | C22 | 1 | 10 | yes | complemented |
| 25 | #66033 | C22 | 1 | 10 | yes | complemented |
| 26 | #66025 | C22 | 1 | 10 | yes | complemented |
| 27 | #66025 | C22 | 1 | 10 | yes | complemented |
| 28 | #66025 | C22 | 1 | 10 | yes | complemented |
| 29 | #66022 | C22 | 1 | 10 | yes | complemented |
| 30 | C5⋊#564 | C22 | 1 | 5 | yes | complemented |
| 31 | #66018 | C22 | 1 | 10 | yes | complemented |
| 32 | #66017 | C22 | 1 | 10 | yes | complemented |
| 33 | #66014 | C22 | 1 | 10 | yes | complemented |
| 34 | #66002 | C22 | 1 | 10 | yes | — |
| 35 | #66001 | C22 | 1 | 20 | yes | complemented |
| 36 | #66000 | C22 | 1 | 20 | yes | complemented |
| 37 | #65990 | C22 | 1 | 20 | yes | complemented |
| 38 | #65983 | C22 | 1 | 20 | yes | complemented |
| 39 | #65981 | C22 | 1 | 20 | yes | complemented |
| 40 | #65981 | C22 | 1 | 20 | yes | complemented |
| 41 | #65980 | C22 | 1 | 20 | yes | complemented |
| 42 | #65961 | C22 | 1 | 20 | yes | complemented |
| 43 | #65961 | C22 | 1 | 10 | yes | complemented |
| 44 | #65958 | C22 | 1 | 20 | yes | complemented |
| 45 | #65956 | C22 | 1 | 10 | yes | complemented |
| 46 | #65954 | C22 | 1 | 20 | yes | complemented |
| 47 | #65940 | C22 | 1 | 10 | yes | complemented |
| 48 | #65930 | C22 | 1 | 10 | yes | — |
| 49 | #65914 | C22 | 1 | 20 | yes | complemented |
| 50 | #65912 | C22 | 1 | 10 | yes | complemented |
| 51 | C4×#713 | C22 | 1 | 10 | yes | complemented |
| 52 | #65882 | C22 | 1 | 10 | yes | — |
| 53 | #65881 | C22 | 1 | 20 | yes | complemented |
| 54 | C4×#711 | C22 | 1 | 10 | yes | complemented |
| 55 | #65862 | C22 | 1 | 20 | yes | complemented |
| 56 | #65858 | C22 | 1 | 10 | yes | complemented |
| 57 | #65856 | C22 | 1 | 10 | yes | complemented |
| 58 | #65813 | C22 | 1 | 10 | yes | complemented |
| 59 | #65811 | C22 | 1 | 5 | yes | — |
| 60 | C2×C42×D5 | C22 | 1 | 5 | yes | complemented |
| 61 | #62694 | — | 5 | 1 | no | maximal, Sylow |
| 62 | C2×#713 | C23 | 1 | 10 | yes | — |
| 63 | C2×#711 | C23 | 1 | 10 | yes | — |
| 64 | C2×#709 | C23 | 1 | 10 | yes | — |
| 65 | C22×C4×D5 | C23 | 1 | 5 | yes | — |
| 66 | C22×C4×D5 | C23 | 1 | 10 | yes | — |
| 67 | C5×C4⋊Q8 | C23 | 1 | 10 | yes | — |
| 68 | C5×#126 | C23 | 1 | 20 | yes | — |
| 69 | C5×#125 | C23 | 1 | 10 | yes | — |
| 70 | C5×#125 | C23 | 1 | 5 | yes | — |
| 71 | C5×#125 | C23 | 1 | 5 | yes | — |
| 72 | C5×#124 | C23 | 1 | 10 | yes | — |
| 73 | C5×#123 | C23 | 1 | 20 | yes | — |
| 74 | C5×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 75 | C5×C22⋊Q8 | C23 | 1 | 20 | yes | — |
| 76 | C5×#121 | C23 | 1 | 10 | yes | — |
| 77 | C4×C5×Q8 | C23 | 1 | 10 | yes | — |
| 78 | C4×C5×D4 | C23 | 1 | 10 | yes | — |
| 79 | C5×#117 | C23 | 1 | 10 | yes | — |
| 80 | C2×C42×C5 | C23 | 1 | 5 | yes | — |
| 81 | #4093 | C23 | 1 | 20 | yes | — |
| 82 | #4092 | C23 | 1 | 20 | yes | — |
| 83 | #4092 | C23 | 1 | 10 | yes | — |
| 84 | Q8×Dic5 | C23 | 1 | 10 | yes | — |
| 85 | #4090 | C23 | 1 | 10 | yes | — |
| 86 | #4086 | C23 | 1 | 10 | yes | — |
| 87 | #4085 | C23 | 1 | 20 | yes | — |
| 88 | #4084 | C23 | 1 | 10 | yes | — |
| 89 | #4083 | C23 | 1 | 20 | yes | — |
| 90 | D4×Dic5 | C23 | 1 | 10 | yes | — |
| 91 | #4076 | C23 | 1 | 20 | yes | — |
| 92 | #4076 | C23 | 1 | 10 | yes | — |
| 93 | #4075 | C23 | 1 | 20 | yes | — |
| 94 | C4×C22⋊D5 | C23 | 1 | 20 | yes | — |
| 95 | #4070 | C23 | 1 | 10 | yes | — |
| 96 | C2×C4×Dic5 | C23 | 1 | 5 | yes | — |
| 97 | C2×C4×Dic5 | C23 | 1 | 10 | yes | — |
| 98 | #4044 | C23 | 1 | 20 | yes | — |
| 99 | #4044 | C23 | 1 | 20 | yes | — |
| 100 | #4044 | C23 | 1 | 20 | yes | — |
| 101 | #4043 | C23 | 1 | 10 | yes | — |
| 102 | #4043 | C23 | 1 | 10 | yes | — |
| 103 | #4043 | C23 | 1 | 10 | yes | — |
| 104 | #4042 | C23 | 1 | 20 | yes | — |
| 105 | #4042 | C23 | 1 | 20 | yes | — |
| 106 | #4042 | C23 | 1 | 20 | yes | — |
| 107 | #4041 | C23 | 1 | 10 | yes | — |
| 108 | #4041 | C23 | 1 | 10 | yes | — |
| 109 | #4041 | C23 | 1 | 20 | yes | — |
| 110 | #4041 | C23 | 1 | 10 | yes | — |
| 111 | #4040 | C23 | 1 | 20 | yes | — |
| 112 | #4040 | C23 | 1 | 20 | yes | — |
| 113 | #4040 | C23 | 1 | 20 | yes | — |
| 114 | #4040 | C23 | 1 | 20 | yes | — |
| 115 | #4039 | C23 | 1 | 10 | yes | — |
| 116 | #4039 | C23 | 1 | 10 | yes | — |
| 117 | #4039 | C23 | 1 | 20 | yes | — |
| 118 | #4039 | C23 | 1 | 10 | yes | — |
| 119 | #4038 | C23 | 1 | 20 | yes | — |
| 120 | #4038 | C23 | 1 | 10 | yes | — |
| 121 | #4038 | C23 | 1 | 10 | yes | — |
| 122 | #4036 | C23 | 1 | 20 | yes | — |
| 123 | #4035 | C23 | 1 | 20 | yes | — |
| 124 | #4035 | C23 | 1 | 20 | yes | — |
| 125 | #4034 | C23 | 1 | 10 | yes | — |
| 126 | #4034 | C23 | 1 | 10 | yes | — |
| 127 | #4033 | C23 | 1 | 10 | yes | — |
| 128 | #4033 | C23 | 1 | 10 | yes | — |
| 129 | #4033 | C23 | 1 | 10 | yes | — |
| 130 | #4032 | C23 | 1 | 20 | yes | — |
| 131 | #4031 | C23 | 1 | 20 | yes | — |
| 132 | #4031 | C23 | 1 | 20 | yes | — |
| 133 | #4030 | C23 | 1 | 20 | yes | — |
| 134 | #4030 | C23 | 1 | 20 | yes | — |
| 135 | #4030 | C23 | 1 | 20 | yes | — |
| 136 | #4029 | C23 | 1 | 20 | yes | — |
| 137 | #4029 | C23 | 1 | 20 | yes | — |
| 138 | #4028 | C23 | 1 | 20 | yes | — |
| 139 | #4028 | C23 | 1 | 20 | yes | — |
| 140 | #4027 | C23 | 1 | 20 | yes | — |
| 141 | #4027 | C23 | 1 | 20 | yes | — |
| 142 | #4027 | C23 | 1 | 20 | yes | — |
| 143 | #4025 | C23 | 1 | 20 | yes | — |
| 144 | #4024 | C23 | 1 | 20 | yes | — |
| 145 | #4023 | C23 | 1 | 20 | yes | — |
| 146 | #4022 | C23 | 1 | 20 | yes | — |
| 147 | #4021 | C23 | 1 | 10 | yes | — |
| 148 | #4021 | C23 | 1 | 10 | yes | — |
| 149 | #4020 | C23 | 1 | 5 | yes | — |
| 150 | C4×D20 | C23 | 1 | 20 | yes | — |
| 151 | C4×D20 | C23 | 1 | 10 | yes | — |
| 152 | #4018 | C23 | 1 | 20 | yes | — |
| 153 | C42×D5 | C23 | 1 | 10 | yes | — |
| 154 | C42×D5 | C23 | 1 | 10 | yes | — |
| 155 | C42×D5 | C23 | 1 | 10 | yes | — |
| 156 | C42×D5 | C23 | 1 | 10 | yes | — |
| 157 | #4016 | C23 | 1 | 10 | yes | — |
| 158 | #4015 | C23 | 1 | 5 | yes | — |
| 159 | C4×Dic10 | C23 | 1 | 10 | yes | — |
| 160 | #3531 | — | 5 | 2 | no | — |
| 161 | #3531 | — | 5 | 10 | no | — |
| 162 | #3531 | — | 5 | 5 | no | — |
| 163 | #3531 | D5 | 1 | 1 | yes | characteristic, complemented |
| 164 | #3529 | — | 5 | 10 | no | — |
| 165 | #3529 | — | 5 | 10 | no | — |
| 166 | #3529 | — | 5 | 10 | no | — |
| 167 | #3444 | — | 5 | 5 | no | — |
| 168 | #3444 | — | 5 | 10 | no | — |
| 169 | C23×D5 | C24 | 1 | 5 | yes | — |
| 170 | C2×C5×Q8 | C24 | 1 | 10 | yes | — |
| 171 | C2×C5×D4 | C24 | 1 | 10 | yes | — |
| 172 | C22×C4×C5 | C24 | 1 | 5 | yes | — |
| 173 | C22×C4×C5 | C24 | 1 | 10 | yes | — |
| 174 | C2×C22⋊D5 | C24 | 1 | 20 | yes | — |
| 175 | C2×C22⋊D5 | C24 | 1 | 20 | yes | — |
| 176 | C22×Dic5 | C24 | 1 | 10 | yes | — |
| 177 | C22×Dic5 | C24 | 1 | 5 | yes | — |
| 178 | #713 | — | 4 | 20 | no | — |
| 179 | #711 | — | 4 | 20 | no | — |
| 180 | #709 | — | 4 | 20 | no | — |
| 181 | C2×D20 | C24 | 1 | 10 | yes | — |
| 182 | C2×D20 | C24 | 1 | 20 | yes | — |
| 183 | C2×D20 | C24 | 1 | 10 | yes | — |
| 184 | C2×C4×D5 | — | 4 | 20 | no | — |
| 185 | C2×C4×D5 | — | 4 | 10 | no | — |
| 186 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 187 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 188 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 189 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 190 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 191 | C2×C4×D5 | C24 | 1 | 10 | yes | — |
| 192 | C2×Dic10 | C24 | 1 | 10 | yes | — |
| 193 | C2×Dic10 | C24 | 1 | 10 | yes | — |
| 194 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 195 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 196 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 197 | C5×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 198 | C5×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 199 | C5×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 200 | C5×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 201 | C42×C5 | C24 | 1 | 10 | yes | — |
| 202 | C42×C5 | C24 | 1 | 5 | yes | — |
| 203 | C42×C5 | C24 | 1 | 5 | yes | — |
| 204 | C22⋊Dic5 | C24 | 1 | 20 | yes | — |
| 205 | #685 | C24 | 1 | 20 | yes | — |
| 206 | #685 | C24 | 1 | 20 | yes | — |
| 207 | #685 | C24 | 1 | 20 | yes | — |
| 208 | #685 | C24 | 1 | 20 | yes | — |
| 209 | #685 | C24 | 1 | 20 | yes | — |
| 210 | #685 | C24 | 1 | 20 | yes | — |
| 211 | C4⋊Dic5 | C24 | 1 | 10 | yes | — |
| 212 | C4⋊Dic5 | C24 | 1 | 20 | yes | — |
| 213 | C4⋊Dic5 | C24 | 1 | 10 | yes | — |
| 214 | #683 | C24 | 1 | 20 | yes | — |
| 215 | #683 | C24 | 1 | 20 | yes | — |
| 216 | #683 | C24 | 1 | 20 | yes | — |
| 217 | #683 | C24 | 1 | 20 | yes | — |
| 218 | C4×Dic5 | C24 | 1 | 5 | yes | — |
| 219 | C4×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 220 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 221 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 222 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 223 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 224 | C4×Dic5 | C24 | 1 | 10 | yes | — |
| 225 | #564 | — | 5 | 5 | no | — |
| 226 | #564 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 227 | #563 | — | 5 | 20 | no | — |
| 228 | #563 | — | 5 | 20 | no | — |
| 229 | #563 | — | 5 | 10 | no | — |
| 230 | #563 | — | 5 | 10 | no | — |
| 231 | #563 | — | 5 | 20 | no | — |
| 232 | #563 | C2×D5 | 1 | 10 | yes | complemented |
| 233 | #562 | — | 5 | 5 | no | — |
| 234 | #562 | — | 5 | 10 | no | — |
| 235 | #562 | — | 5 | 10 | no | — |
| 236 | #562 | — | 5 | 20 | no | — |
| 237 | #562 | — | 5 | 20 | no | — |
| 238 | #562 | — | 5 | 20 | no | — |
| 239 | #562 | C2×D5 | 1 | 5 | yes | complemented |
| 240 | H(3,𝔽4) | — | 5 | 10 | no | — |
| 241 | #560 | — | 5 | 20 | no | — |
| 242 | #560 | — | 5 | 20 | no | — |
| 243 | #560 | — | 5 | 20 | no | — |
| 244 | #533 | — | 5 | 10 | no | — |
| 245 | #533 | — | 5 | 10 | no | — |
| 246 | #533 | — | 5 | 10 | no | — |
| 247 | #533 | — | 5 | 10 | no | — |
| 248 | #533 | C2×D5 | 1 | 5 | yes | complemented |
| 249 | #532 | — | 5 | 10 | no | — |
| 250 | #532 | — | 5 | 10 | no | — |
| 251 | #532 | — | 5 | 10 | no | — |
| 252 | #532 | — | 5 | 10 | no | — |
| 253 | #532 | — | 5 | 5 | no | — |
| 254 | #529 | — | 5 | 20 | no | — |
| 255 | #529 | — | 5 | 20 | no | — |
| 256 | #529 | — | 5 | 10 | no | — |
| 257 | #529 | — | 5 | 10 | no | — |
| 258 | #529 | — | 5 | 10 | no | — |
| 259 | #529 | — | 5 | 10 | no | — |
| 260 | #529 | — | 5 | 20 | no | — |
| 261 | #529 | — | 5 | 20 | no | — |
| 262 | #529 | — | 5 | 20 | no | — |
| 263 | #529 | — | 5 | 20 | no | — |
| 264 | #529 | — | 5 | 10 | no | — |
| 265 | #529 | C2×D5 | 1 | 10 | yes | complemented |
| 266 | #525 | — | 5 | 20 | no | — |
| 267 | #525 | — | 5 | 20 | no | — |
| 268 | #525 | — | 5 | 10 | no | — |
| 269 | #525 | — | 5 | 10 | no | — |
| 270 | #525 | — | 5 | 20 | no | — |
| 271 | #525 | — | 5 | 10 | no | — |
| 272 | C4×#41 | — | 5 | 10 | no | — |
| 273 | C4×#41 | — | 5 | 10 | no | — |
| 274 | C4×#41 | — | 5 | 10 | no | — |
| 275 | C22×C42 | — | 5 | 5 | no | — |
| 276 | C23×C5 | C25 | 1 | 5 | yes | — |
| 277 | C22×D5 | — | 4 | 10 | no | — |
| 278 | C22×D5 | — | 4 | 5 | no | — |
| 279 | C22×D5 | C25 | 1 | 10 | yes | — |
| 280 | C5×Q8 | — | 4 | 10 | no | — |
| 281 | C5×D4 | — | 4 | 10 | no | — |
| 282 | C2×C4×C5 | — | 2 | 10 | no | — |
| 283 | C2×C4×C5 | — | 4 | 10 | no | — |
| 284 | C2×C4×C5 | C25 | 1 | 10 | yes | — |
| 285 | C2×C4×C5 | C25 | 1 | 5 | yes | — |
| 286 | C2×C4×C5 | C25 | 1 | 10 | yes | — |
| 287 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 288 | C22⋊D5 | — | 4 | 20 | no | — |
| 289 | C22⋊D5 | — | 4 | 20 | no | — |
| 290 | C2×Dic5 | — | 2 | 20 | no | — |
| 291 | C2×Dic5 | — | 4 | 5 | no | — |
| 292 | C2×Dic5 | C25 | 1 | 10 | yes | — |
| 293 | C2×Dic5 | C25 | 1 | 10 | yes | — |
| 294 | C2×Dic5 | C25 | 1 | 2 | yes | — |
| 295 | D20 | — | 4 | 10 | no | — |
| 296 | D20 | — | 4 | 10 | no | — |
| 297 | D20 | — | 4 | 20 | no | — |
| 298 | C4×D5 | — | 2 | 20 | no | — |
| 299 | C4×D5 | — | 2 | 20 | no | — |
| 300 | C4×D5 | — | 2 | 20 | no | — |
| 301 | C4×D5 | — | 4 | 10 | no | — |
| 302 | C4×D5 | — | 4 | 10 | no | — |
| 303 | C4×D5 | — | 4 | 10 | no | — |
| 304 | Dic10 | — | 4 | 10 | no | — |
| 305 | Dic10 | — | 4 | 10 | no | — |
| 306 | C2×#41 | — | 5 | 10 | no | — |
| 307 | C2×#41 | — | 5 | 10 | no | — |
| 308 | C2×#41 | — | 5 | 10 | no | — |
| 309 | C23×C4 | — | 5 | 10 | no | — |
| 310 | C23×C4 | — | 5 | 5 | no | — |
| 311 | C4⋊Q8 | — | 5 | 10 | no | — |
| 312 | C4⋊Q8 | — | 5 | 10 | no | — |
| 313 | C4⋊Q8 | — | 5 | 10 | no | — |
| 314 | C4⋊Q8 | — | 5 | 5 | no | — |
| 315 | C4⋊Q8 | C22×D5 | 1 | 10 | yes | — |
| 316 | #127 | — | 5 | 10 | no | — |
| 317 | #127 | — | 5 | 5 | no | — |
| 318 | #126 | — | 5 | 20 | no | — |
| 319 | #126 | — | 5 | 20 | no | — |
| 320 | #126 | — | 5 | 20 | no | — |
| 321 | #126 | — | 5 | 20 | no | — |
| 322 | #126 | — | 5 | 20 | no | — |
| 323 | #126 | C22×D5 | 1 | 20 | yes | — |
| 324 | #125 | — | 5 | 20 | no | — |
| 325 | #125 | — | 5 | 20 | no | — |
| 326 | #125 | — | 5 | 20 | no | — |
| 327 | #125 | — | 5 | 10 | no | — |
| 328 | #125 | C22×D5 | 1 | 5 | yes | — |
| 329 | #125 | C22×D5 | 1 | 5 | yes | — |
| 330 | #125 | C22×D5 | 1 | 10 | yes | — |
| 331 | #124 | — | 5 | 20 | no | — |
| 332 | #124 | — | 5 | 20 | no | — |
| 333 | #124 | — | 5 | 20 | no | — |
| 334 | #124 | — | 5 | 10 | no | — |
| 335 | #124 | — | 5 | 10 | no | — |
| 336 | #124 | C22×D5 | 1 | 10 | yes | — |
| 337 | #123 | — | 5 | 20 | no | — |
| 338 | #123 | — | 5 | 20 | no | — |
| 339 | #123 | — | 5 | 20 | no | — |
| 340 | #123 | — | 5 | 20 | no | — |
| 341 | #123 | — | 5 | 20 | no | — |
| 342 | #123 | — | 5 | 20 | no | — |
| 343 | #123 | — | 5 | 20 | no | — |
| 344 | #123 | — | 5 | 20 | no | — |
| 345 | #123 | C22×D5 | 1 | 20 | yes | — |
| 346 | C22⋊Q8 | — | 5 | 10 | no | — |
| 347 | C22⋊Q8 | — | 5 | 20 | no | — |
| 348 | C22⋊Q8 | — | 5 | 10 | no | — |
| 349 | C22⋊Q8 | — | 5 | 20 | no | — |
| 350 | C22⋊Q8 | — | 5 | 20 | no | — |
| 351 | C22⋊Q8 | — | 5 | 20 | no | — |
| 352 | C22⋊Q8 | — | 5 | 10 | no | — |
| 353 | C22⋊Q8 | — | 5 | 10 | no | — |
| 354 | C22⋊Q8 | — | 5 | 10 | no | — |
| 355 | C22⋊Q8 | — | 5 | 20 | no | — |
| 356 | C22⋊Q8 | C22×D5 | 1 | 20 | yes | — |
| 357 | C22⋊Q8 | C22×D5 | 1 | 10 | yes | — |
| 358 | #121 | — | 5 | 10 | no | — |
| 359 | #121 | — | 5 | 20 | no | — |
| 360 | #121 | — | 5 | 20 | no | — |
| 361 | #121 | — | 5 | 10 | no | — |
| 362 | #121 | — | 5 | 20 | no | — |
| 363 | #121 | — | 5 | 10 | no | — |
| 364 | #121 | — | 5 | 10 | no | — |
| 365 | #121 | — | 5 | 10 | no | — |
| 366 | #121 | — | 5 | 20 | no | — |
| 367 | #121 | — | 5 | 20 | no | — |
| 368 | #121 | — | 5 | 20 | no | — |
| 369 | #121 | C22×D5 | 1 | 10 | yes | — |
| 370 | #120 | — | 5 | 20 | no | — |
| 371 | #120 | — | 5 | 20 | no | — |
| 372 | #120 | — | 5 | 20 | no | — |
| 373 | C4×Q8 | — | 5 | 10 | no | — |
| 374 | C4×Q8 | — | 5 | 10 | no | — |
| 375 | C4×Q8 | — | 5 | 10 | no | — |
| 376 | C4×Q8 | — | 5 | 10 | no | — |
| 377 | C4×Q8 | — | 5 | 10 | no | — |
| 378 | C4×Q8 | C22×D5 | 1 | 10 | yes | — |
| 379 | C4×D4 | — | 5 | 10 | no | — |
| 380 | C4×D4 | — | 5 | 20 | no | — |
| 381 | C4×D4 | — | 5 | 20 | no | — |
| 382 | C4×D4 | — | 5 | 10 | no | — |
| 383 | C4×D4 | — | 5 | 10 | no | — |
| 384 | C4×D4 | — | 5 | 10 | no | — |
| 385 | C4×D4 | — | 5 | 20 | no | — |
| 386 | C4×D4 | — | 5 | 20 | no | — |
| 387 | C4×D4 | — | 5 | 20 | no | — |
| 388 | C4×D4 | — | 5 | 20 | no | — |
| 389 | C4×D4 | — | 5 | 10 | no | — |
| 390 | C4×D4 | C22×D5 | 1 | 10 | yes | — |
| 391 | #117 | — | 5 | 20 | no | — |
| 392 | #117 | — | 5 | 10 | no | — |
| 393 | #117 | — | 5 | 10 | no | — |
| 394 | #117 | — | 5 | 20 | no | — |
| 395 | #117 | — | 5 | 20 | no | — |
| 396 | #117 | C22×D5 | 1 | 10 | yes | — |
| 397 | C2×C42 | — | 5 | 5 | no | — |
| 398 | C2×C42 | — | 5 | 10 | no | — |
| 399 | C2×C42 | — | 5 | 10 | no | — |
| 400 | C2×C42 | — | 5 | 10 | no | — |
| 401 | C2×C42 | — | 5 | 10 | no | — |
| 402 | C2×C42 | — | 5 | 10 | no | — |
| 403 | C2×C42 | C22×D5 | 1 | 5 | yes | — |
| 404 | C22×C5 | — | 2 | 10 | no | — |
| 405 | C22×C5 | — | 2 | 5 | no | — |
| 406 | C22×C5 | C26 | 1 | 1 | yes | characteristic |
| 407 | C2×D5 | — | 2 | 10 | no | — |
| 408 | C2×D5 | — | 2 | 10 | no | — |
| 409 | C2×D5 | — | 2 | 10 | no | — |
| 410 | C2×D5 | — | 4 | 20 | no | — |
| 411 | C4×C5 | — | 2 | 5 | no | — |
| 412 | C4×C5 | — | 2 | 10 | no | — |
| 413 | C4×C5 | — | 2 | 10 | no | — |
| 414 | C4×C5 | #585 | 1 | 2 | yes | — |
| 415 | Dic5 | — | 2 | 10 | no | — |
| 416 | Dic5 | — | 2 | 10 | no | — |
| 417 | Dic5 | #585 | 1 | 4 | yes | — |
| 418 | C24 | — | 5 | 5 | no | — |
| 419 | #41 | — | 20 | 20 | no | — |
| 420 | #41 | — | 20 | 20 | no | — |
| 421 | #41 | — | 20 | 20 | no | — |
| 422 | C2×Q8 | — | 5 | 10 | no | — |
| 423 | C2×Q8 | — | 5 | 10 | no | — |
| 424 | C2×Q8 | C23×D5 | 1 | 10 | yes | — |
| 425 | C2×D4 | — | 5 | 20 | no | — |
| 426 | C2×D4 | — | 5 | 20 | no | — |
| 427 | C2×D4 | — | 5 | 10 | no | — |
| 428 | C2×D4 | — | 5 | 20 | no | — |
| 429 | C2×D4 | — | 5 | 10 | no | — |
| 430 | C2×D4 | C23×D5 | 1 | 10 | yes | — |
| 431 | C22×C4 | — | 5 | 10 | no | — |
| 432 | C22×C4 | — | 5 | 5 | no | — |
| 433 | C22×C4 | — | 5 | 10 | no | — |
| 434 | C22×C4 | — | 5 | 10 | no | — |
| 435 | C22×C4 | — | 5 | 10 | no | — |
| 436 | C22×C4 | — | 5 | 10 | no | — |
| 437 | C22×C4 | — | 5 | 10 | no | — |
| 438 | C22×C4 | — | 5 | 10 | no | — |
| 439 | C22×C4 | — | 20 | 10 | no | — |
| 440 | C22×C4 | — | 20 | 20 | no | — |
| 441 | C22×C4 | C23×D5 | 1 | 5 | yes | — |
| 442 | C22×C4 | C23×D5 | 1 | 10 | yes | — |
| 443 | C4⋊C4 | — | 5 | 20 | no | — |
| 444 | C4⋊C4 | — | 5 | 20 | no | — |
| 445 | C4⋊C4 | — | 5 | 20 | no | — |
| 446 | C4⋊C4 | — | 5 | 20 | no | — |
| 447 | C4⋊C4 | — | 5 | 10 | no | — |
| 448 | C4⋊C4 | — | 5 | 10 | no | — |
| 449 | C4⋊C4 | — | 5 | 20 | no | — |
| 450 | C4⋊C4 | C23×D5 | 1 | 20 | yes | — |
| 451 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 452 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 453 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 454 | C4⋊C4 | C23×D5 | 1 | 10 | yes | — |
| 455 | C22⋊C4 | — | 5 | 20 | no | — |
| 456 | C22⋊C4 | — | 5 | 20 | no | — |
| 457 | C22⋊C4 | — | 5 | 20 | no | — |
| 458 | C22⋊C4 | — | 5 | 20 | no | — |
| 459 | C22⋊C4 | — | 5 | 20 | no | — |
| 460 | C22⋊C4 | — | 5 | 20 | no | — |
| 461 | C22⋊C4 | — | 5 | 20 | no | — |
| 462 | C22⋊C4 | C23×D5 | 1 | 20 | yes | — |
| 463 | C22⋊C4 | C23×D5 | 1 | 20 | yes | — |
| 464 | C42 | — | 5 | 10 | no | — |
| 465 | C42 | — | 5 | 10 | no | — |
| 466 | C42 | — | 5 | 10 | no | — |
| 467 | C42 | — | 5 | 10 | no | — |
| 468 | C42 | — | 5 | 10 | no | — |
| 469 | C42 | — | 5 | 1 | no | — |
| 470 | C42 | — | 5 | 5 | no | — |
| 471 | C42 | C23×D5 | 1 | 5 | yes | — |
| 472 | C42 | C23×D5 | 1 | 5 | yes | — |
| 473 | C42 | C23×D5 | 1 | 10 | yes | — |
| 474 | C2×C5 | — | 4 | 5 | no | — |
| 475 | C2×C5 | C2×#585 | 1 | 1 | yes | characteristic |
| 476 | C2×C5 | C2×#585 | 1 | 2 | yes | — |
| 477 | D5 | — | 4 | 10 | no | — |
| 478 | C23 | — | 5 | 10 | no | — |
| 479 | C23 | — | 20 | 5 | no | — |
| 480 | C23 | — | 20 | 10 | no | — |
| 481 | C23 | C24×D5 | 1 | 5 | yes | — |
| 482 | Q8 | — | 4 | 10 | no | — |
| 483 | Q8 | — | 20 | 10 | no | — |
| 484 | Q8 | — | 20 | 10 | no | — |
| 485 | D4 | — | 4 | 10 | no | — |
| 486 | D4 | — | 20 | 10 | no | — |
| 487 | D4 | — | 20 | 10 | no | — |
| 488 | D4 | — | 20 | 20 | no | — |
| 489 | D4 | — | 20 | 20 | no | — |
| 490 | D4 | — | 20 | 20 | no | — |
| 491 | C2×C4 | — | 2 | 10 | no | — |
| 492 | C2×C4 | — | 4 | 10 | no | — |
| 493 | C2×C4 | — | 5 | 2 | no | — |
| 494 | C2×C4 | — | 5 | 10 | no | — |
| 495 | C2×C4 | — | 5 | 10 | no | — |
| 496 | C2×C4 | — | 10 | 20 | no | — |
| 497 | C2×C4 | — | 10 | 20 | no | — |
| 498 | C2×C4 | — | 10 | 20 | no | — |
| 499 | C2×C4 | — | 10 | 20 | no | — |
| 500 | C2×C4 | — | 20 | 10 | no | — |
| 501 | C2×C4 | — | 20 | 10 | no | — |
| 502 | C2×C4 | — | 20 | 10 | no | — |
| 503 | C2×C4 | — | 20 | 5 | no | — |
| 504 | C2×C4 | C24×D5 | 1 | 10 | yes | — |
| 505 | C2×C4 | C24×D5 | 1 | 10 | yes | — |
| 506 | C2×C4 | C24×D5 | 1 | 5 | yes | — |
| 507 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 508 | C5 | #62694 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 509 | C22 | — | 2 | 5 | no | — |
| 510 | C22 | — | 2 | 10 | no | — |
| 511 | C22 | — | 10 | 10 | no | — |
| 512 | C22 | — | 10 | 10 | no | — |
| 513 | C22 | — | 10 | 10 | no | — |
| 514 | C22 | — | 20 | 20 | no | — |
| 515 | C22 | C25×D5 | 1 | 1 | yes | characteristic |
| 516 | C4 | — | 2 | 5 | no | — |
| 517 | C4 | — | 2 | 10 | no | — |
| 518 | C4 | — | 2 | 10 | no | — |
| 519 | C4 | — | 5 | 4 | no | — |
| 520 | C4 | — | 10 | 10 | no | — |
| 521 | C4 | — | 10 | 10 | no | — |
| 522 | C4 | #66287 | 1 | 2 | yes | — |
| 523 | C2 | — | 4 | 5 | no | — |
| 524 | C2 | — | 20 | 10 | no | — |
| 525 | C2 | C2×#66287 | 1 | 1 | yes | characteristic |
| 526 | C2 | D5×#585 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C26 |
| Frattini | C22 | C25×D5 |
| Fitting | C5×#3531 | C2 |
| hypercenter | #3531 | D5 |
| hypocenter | C5 | #62694 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3531 | C2 | semidirect |
| 2. #10619040 | C2 | semidirect |
| 3. #10619017 | C2 | semidirect |
| 4. #10619016 | C2 | semidirect |
| 5. #10618994 | C2 | semidirect |
| 6. #10618187 | C2 | semidirect |
| 7. #10618158 | C2 | semidirect |
| 8. #10618072 | C2 | semidirect |
| 9. #10618020 | C2 | semidirect |
| 10. C5×#564 | C22 | semidirect |
| 11. C5×#563 | C22 | semidirect |
| 12. C5×#562 | C22 | semidirect |
| 13. C5×#533 | C22 | semidirect |
| 14. C5×#529 | C22 | semidirect |
| 15. #66069 | C22 | semidirect |
| 16. #66062 | C22 | semidirect |
| 18. #66046 | C22 | semidirect |
| 19. #66045 | C22 | semidirect |
| 20. #66040 | C22 | semidirect |
| 21. #66040 | C22 | semidirect |
| 22. #66034 | C22 | semidirect |
| 23. #66034 | C22 | semidirect |
| 24. #66033 | C22 | semidirect |
| 25. #66033 | C22 | semidirect |
| 26. #66025 | C22 | semidirect |
| 27. #66025 | C22 | semidirect |
| 28. #66025 | C22 | semidirect |
| 29. #66022 | C22 | semidirect |
| 30. C5⋊#564 | C22 | semidirect |
| 31. #66018 | C22 | semidirect |
| 32. #66017 | C22 | semidirect |
| 33. #66014 | C22 | semidirect |
| 35. #66001 | C22 | semidirect |
| 36. #66000 | C22 | semidirect |
| 37. #65990 | C22 | semidirect |
| 38. #65983 | C22 | semidirect |
| 39. #65981 | C22 | semidirect |
| 40. #65981 | C22 | semidirect |
| 41. #65980 | C22 | semidirect |
| 42. #65961 | C22 | semidirect |
| 43. #65961 | C22 | semidirect |
| 44. #65958 | C22 | semidirect |
| 45. #65956 | C22 | semidirect |
| 46. #65954 | C22 | semidirect |
| 47. #65940 | C22 | semidirect |
| 49. #65914 | C22 | semidirect |
| 50. #65912 | C22 | semidirect |
| 51. C4×#713 | C22 | semidirect |
| 53. #65881 | C22 | semidirect |
| 54. C4×#711 | C22 | semidirect |
| 55. #65862 | C22 | semidirect |
| 56. #65858 | C22 | semidirect |
| 57. #65856 | C22 | semidirect |
| 58. #65813 | C22 | semidirect |
| 60. C2×C42×D5 | C22 | semidirect |
| 163. #3531 | D5 | semidirect |
| 226. #564 | C2×D5 | semidirect |
| 232. #563 | C2×D5 | semidirect |
| 239. #562 | C2×D5 | semidirect |
| 248. #533 | C2×D5 | semidirect |
| 265. #529 | C2×D5 | semidirect |
| 508. C5 | #62694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3531 | 2 |
| #10619040 | 2 |
| #10619017 | 2 |
| #10619016 | 2 |
| #10618994 | 2 |
| #10618187 | 2 |
| #10618158 | 2 |
| #10618072 | 2 |
| #10618020 | 2 |
| #62694 | 5 |