Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2598 conjugacy classes of subgroups.
The subgroup lattice has 592 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D5×#578 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C5×#3293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615749 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10613539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D5×#494 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10612678 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | D5×#473 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10612034 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | D5×#456 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10611626 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | D5×#443 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | D5×2−1+4 | C22 | 1 | 4 | yes | — |
| 13 | C5×#578 | C22 | 1 | 4 | yes | complemented |
| 14 | #66172 | C22 | 1 | 8 | yes | complemented |
| 15 | #66113 | — | 2 | 8 | no | — |
| 16 | #66113 | C22 | 1 | 8 | yes | complemented |
| 17 | D5×#137 | — | 2 | 8 | no | — |
| 18 | D5×#137 | C22 | 1 | 8 | yes | — |
| 19 | #66105 | — | 2 | 4 | no | — |
| 20 | #66105 | C22 | 1 | 4 | yes | complemented |
| 21 | D5×#135 | — | 2 | 4 | no | — |
| 22 | D5×#135 | C22 | 1 | 2 | yes | — |
| 23 | #66100 | — | 2 | 4 | no | — |
| 24 | #66100 | C22 | 1 | 4 | yes | complemented |
| 25 | C2×D5×Q16 | — | 2 | 4 | no | — |
| 26 | C2×D5×Q16 | C22 | 1 | 4 | yes | — |
| 27 | #66087 | C22 | 1 | 4 | yes | complemented |
| 28 | D5×#131 | C22 | 1 | 4 | yes | — |
| 29 | D5×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 30 | C5×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C5×#473 | C22 | 1 | 4 | yes | complemented |
| 32 | C5×#456 | C22 | 1 | 4 | yes | complemented |
| 33 | C5×#443 | C22 | 1 | 2 | yes | complemented |
| 34 | #65535 | C22 | 1 | 4 | yes | complemented |
| 35 | #65494 | C22 | 1 | 8 | yes | complemented |
| 36 | #65493 | C22 | 1 | 8 | yes | complemented |
| 37 | #65485 | C22 | 1 | 2 | yes | complemented |
| 38 | #65481 | C22 | 1 | 4 | yes | complemented |
| 39 | #65470 | C22 | 1 | 4 | yes | complemented |
| 40 | #65433 | C22 | 1 | 4 | yes | complemented |
| 41 | #65432 | C22 | 1 | 4 | yes | complemented |
| 42 | #65384 | C22 | 1 | 4 | yes | complemented |
| 43 | #65381 | C22 | 1 | 2 | yes | complemented |
| 44 | #65185 | C22 | 1 | 4 | yes | complemented |
| 45 | #65184 | C22 | 1 | 2 | yes | complemented |
| 46 | D5×#108 | C22 | 1 | 2 | yes | — |
| 47 | #65115 | C22 | 1 | 8 | yes | complemented |
| 48 | #65113 | C22 | 1 | 4 | yes | complemented |
| 49 | D5×#104 | C22 | 1 | 4 | yes | — |
| 50 | #65044 | C22 | 1 | 8 | yes | complemented |
| 51 | #65041 | C22 | 1 | 4 | yes | complemented |
| 52 | D5×#101 | C22 | 1 | 4 | yes | — |
| 53 | #64989 | C22 | 1 | 2 | yes | complemented |
| 54 | #64988 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C4×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#3293 | — | 5 | 1 | no | maximal, Sylow |
| 57 | C5×2−1+4 | C23 | 1 | 4 | yes | — |
| 58 | #4150 | — | 2 | 8 | no | — |
| 59 | #4150 | — | 4 | 4 | no | — |
| 60 | #4150 | C23 | 1 | 8 | yes | — |
| 61 | D5×#41 | — | 2 | 8 | no | — |
| 62 | D5×#41 | — | 4 | 4 | no | — |
| 63 | D5×#41 | C23 | 1 | 4 | yes | — |
| 64 | #4147 | — | 2 | 8 | no | — |
| 65 | #4147 | C23 | 1 | 4 | yes | — |
| 66 | C2×Q8×D5 | — | 2 | 8 | no | — |
| 67 | C2×Q8×D5 | C23 | 1 | 4 | yes | — |
| 68 | C5×#137 | — | 2 | 8 | no | — |
| 69 | C5×#137 | C23 | 1 | 8 | yes | — |
| 70 | C5×#135 | — | 2 | 4 | no | — |
| 71 | C5×#135 | C23 | 1 | 2 | yes | — |
| 72 | C2×C5×Q16 | — | 2 | 4 | no | — |
| 73 | C2×C5×Q16 | C23 | 1 | 4 | yes | — |
| 74 | C5×#131 | C23 | 1 | 4 | yes | — |
| 75 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 76 | #4097 | — | 2 | 8 | no | — |
| 77 | #4097 | C23 | 1 | 8 | yes | — |
| 78 | #4096 | — | 2 | 8 | no | — |
| 79 | #4096 | C23 | 1 | 4 | yes | — |
| 80 | #4094 | C23 | 1 | 4 | yes | — |
| 81 | #4090 | C23 | 1 | 4 | yes | — |
| 82 | C2×#689 | — | 2 | 8 | no | — |
| 83 | C2×#689 | C23 | 1 | 8 | yes | — |
| 84 | #4088 | — | 2 | 8 | no | — |
| 85 | #4088 | C23 | 1 | 8 | yes | — |
| 86 | #4065 | — | 2 | 4 | no | — |
| 87 | #4065 | D4 | 1 | 2 | yes | — |
| 88 | #4064 | — | 2 | 8 | no | — |
| 89 | #4064 | — | 2 | 8 | no | — |
| 90 | #4064 | — | 2 | 8 | no | — |
| 91 | D5×Q16 | — | 2 | 8 | no | — |
| 92 | D5×Q16 | — | 2 | 4 | no | — |
| 93 | D5×Q16 | — | 2 | 8 | no | — |
| 94 | D5×Q16 | — | 2 | 4 | no | — |
| 95 | D5×Q16 | — | 2 | 4 | no | — |
| 96 | D5×Q16 | — | 2 | 4 | no | — |
| 97 | D5×Q16 | — | 2 | 4 | no | — |
| 98 | D5×Q16 | — | 2 | 4 | no | — |
| 99 | D5×Q16 | D4 | 1 | 2 | yes | — |
| 100 | #4062 | — | 2 | 8 | no | — |
| 101 | #4062 | D4 | 1 | 4 | yes | — |
| 102 | #4061 | — | 2 | 8 | no | — |
| 103 | #4061 | — | 2 | 8 | no | — |
| 104 | #4061 | — | 2 | 8 | no | — |
| 105 | D5×SD16 | — | 2 | 8 | no | — |
| 106 | D5×SD16 | D4 | 1 | 4 | yes | — |
| 107 | #4058 | — | 2 | 4 | no | — |
| 108 | #4058 | D4 | 1 | 2 | yes | — |
| 109 | D5×D8 | D4 | 1 | 2 | yes | — |
| 110 | #4055 | — | 2 | 8 | no | — |
| 111 | #4055 | C23 | 1 | 8 | yes | — |
| 112 | #4053 | — | 2 | 4 | no | — |
| 113 | #4053 | C23 | 1 | 4 | yes | — |
| 114 | D5×M16 | — | 2 | 4 | no | — |
| 115 | D5×M16 | C23 | 1 | 4 | yes | — |
| 116 | C2×Dic20 | — | 2 | 4 | no | — |
| 117 | C2×Dic20 | C23 | 1 | 4 | yes | — |
| 118 | #4050 | — | 2 | 4 | no | — |
| 119 | #4050 | C23 | 1 | 2 | yes | — |
| 120 | #4047 | — | 2 | 4 | no | — |
| 121 | #4047 | C23 | 1 | 4 | yes | — |
| 122 | C2×C8×D5 | — | 2 | 4 | no | — |
| 123 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 124 | D5×C4⋊C4 | — | 4 | 2 | no | — |
| 125 | #4034 | — | 4 | 2 | no | — |
| 126 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 127 | #4015 | C23 | 1 | 2 | yes | — |
| 128 | C5×#108 | C23 | 1 | 2 | yes | — |
| 129 | C5×#104 | C23 | 1 | 4 | yes | — |
| 130 | C5×#101 | C23 | 1 | 4 | yes | — |
| 131 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 132 | #3969 | C23 | 1 | 4 | yes | — |
| 133 | #3968 | C23 | 1 | 4 | yes | — |
| 134 | #3957 | C23 | 1 | 4 | yes | — |
| 135 | #3956 | C23 | 1 | 8 | yes | — |
| 136 | #3954 | C23 | 1 | 4 | yes | — |
| 137 | #3951 | C23 | 1 | 2 | yes | — |
| 138 | C8×Dic5 | C23 | 1 | 2 | yes | — |
| 139 | #3937 | C23 | 1 | 4 | yes | — |
| 140 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 141 | C2×#578 | — | 5 | 4 | no | — |
| 142 | #3293 | — | 5 | 1 | no | — |
| 143 | #3293 | — | 5 | 4 | no | — |
| 144 | #3293 | — | 5 | 4 | no | — |
| 145 | #3293 | — | 5 | 2 | no | — |
| 146 | #3293 | — | 5 | 4 | no | — |
| 147 | #3293 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 148 | C2×#494 | — | 5 | 1 | no | — |
| 149 | C2×#473 | — | 5 | 4 | no | — |
| 150 | C2×#456 | — | 5 | 4 | no | — |
| 151 | C2×#443 | — | 5 | 2 | no | — |
| 152 | C5×#41 | — | 2 | 8 | no | — |
| 153 | C5×#41 | — | 4 | 4 | no | — |
| 154 | C5×#41 | C24 | 1 | 4 | yes | — |
| 155 | C2×C5×Q8 | — | 2 | 8 | no | — |
| 156 | C2×C5×Q8 | C24 | 1 | 4 | yes | — |
| 157 | #713 | — | 2 | 8 | no | — |
| 158 | #713 | — | 4 | 4 | no | — |
| 159 | #713 | C2×D4 | 1 | 4 | yes | — |
| 160 | Q8×D5 | — | 2 | 8 | no | — |
| 161 | Q8×D5 | — | 2 | 8 | no | — |
| 162 | Q8×D5 | — | 2 | 8 | no | — |
| 163 | Q8×D5 | — | 2 | 8 | no | — |
| 164 | Q8×D5 | — | 4 | 8 | no | — |
| 165 | Q8×D5 | — | 4 | 4 | no | — |
| 166 | Q8×D5 | C2×D4 | 1 | 4 | yes | — |
| 167 | #711 | — | 2 | 4 | no | — |
| 168 | #711 | — | 2 | 8 | no | — |
| 169 | #711 | — | 4 | 8 | no | — |
| 170 | #711 | — | 4 | 8 | no | — |
| 171 | #711 | — | 4 | 4 | no | — |
| 172 | #711 | C2×D4 | 1 | 4 | yes | — |
| 173 | D4×D5 | — | 2 | 4 | no | — |
| 174 | D4×D5 | — | 4 | 4 | no | — |
| 175 | D4×D5 | C2×D4 | 1 | 4 | yes | — |
| 176 | #709 | — | 2 | 4 | no | — |
| 177 | #709 | — | 2 | 8 | no | — |
| 178 | #709 | — | 4 | 8 | no | — |
| 179 | #709 | — | 4 | 8 | no | — |
| 180 | #709 | — | 4 | 4 | no | — |
| 181 | #709 | C24 | 1 | 4 | yes | — |
| 182 | C2×C4×D5 | — | 2 | 1 | no | — |
| 183 | C2×C4×D5 | — | 2 | 4 | no | — |
| 184 | C2×C4×D5 | — | 2 | 4 | no | — |
| 185 | C2×C4×D5 | — | 4 | 8 | no | — |
| 186 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 187 | C2×Dic10 | — | 2 | 8 | no | — |
| 188 | C2×Dic10 | — | 2 | 4 | no | — |
| 189 | C2×Dic10 | — | 4 | 8 | no | — |
| 190 | C2×Dic10 | C24 | 1 | 4 | yes | — |
| 191 | C5×Q16 | — | 2 | 8 | no | — |
| 192 | C5×Q16 | — | 2 | 4 | no | — |
| 193 | C5×Q16 | — | 2 | 4 | no | — |
| 194 | C5×Q16 | C2×D4 | 1 | 2 | yes | — |
| 195 | C5×SD16 | — | 2 | 8 | no | — |
| 196 | C5×SD16 | C2×D4 | 1 | 4 | yes | — |
| 197 | C5×D8 | C2×D4 | 1 | 2 | yes | — |
| 198 | C5×M16 | — | 2 | 4 | no | — |
| 199 | C5×M16 | C24 | 1 | 4 | yes | — |
| 200 | C2×C5×C8 | — | 2 | 4 | no | — |
| 201 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 202 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 203 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 204 | #689 | — | 2 | 8 | no | — |
| 205 | #689 | — | 2 | 8 | no | — |
| 206 | #689 | — | 2 | 8 | no | — |
| 207 | #689 | — | 2 | 8 | no | — |
| 208 | #689 | C2×D4 | 1 | 4 | yes | — |
| 209 | #688 | — | 2 | 8 | no | — |
| 210 | #688 | C2×D4 | 1 | 4 | yes | — |
| 211 | #687 | — | 2 | 8 | no | — |
| 212 | #687 | C2×D4 | 1 | 4 | yes | — |
| 213 | #686 | C2×D4 | 1 | 4 | yes | — |
| 214 | C4⋊Dic5 | — | 4 | 2 | no | — |
| 215 | #683 | — | 4 | 4 | no | — |
| 216 | C4×Dic5 | — | 2 | 1 | no | — |
| 217 | C4×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 218 | #681 | — | 2 | 4 | no | — |
| 219 | #681 | C24 | 1 | 4 | yes | — |
| 220 | C2×#168 | — | 2 | 4 | no | — |
| 221 | C2×#168 | C24 | 1 | 2 | yes | — |
| 222 | Dic20 | — | 2 | 8 | no | — |
| 223 | Dic20 | — | 2 | 4 | no | — |
| 224 | Dic20 | — | 2 | 4 | no | — |
| 225 | Dic20 | C2×D4 | 1 | 2 | yes | — |
| 226 | D40 | C2×D4 | 1 | 2 | yes | — |
| 227 | #677 | — | 2 | 8 | no | — |
| 228 | #677 | C2×D4 | 1 | 4 | yes | — |
| 229 | #676 | — | 2 | 4 | no | — |
| 230 | #676 | — | 2 | 4 | no | — |
| 231 | #676 | — | 2 | 4 | no | — |
| 232 | C8×D5 | — | 2 | 4 | no | — |
| 233 | C8×D5 | — | 2 | 4 | no | — |
| 234 | C8×D5 | — | 2 | 4 | no | — |
| 235 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 236 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 237 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 238 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 239 | C2×2−1+4 | — | 5 | 4 | no | — |
| 240 | #578 | — | 5 | 8 | no | — |
| 241 | #578 | — | 5 | 8 | no | — |
| 242 | #578 | — | 5 | 4 | no | — |
| 243 | #578 | — | 5 | 4 | no | — |
| 244 | #578 | — | 5 | 4 | no | — |
| 245 | #578 | — | 10 | 4 | no | — |
| 246 | #578 | — | 10 | 4 | no | — |
| 247 | #578 | — | 10 | 8 | no | — |
| 248 | #578 | C2×D5 | 1 | 4 | yes | complemented |
| 249 | C2×#137 | — | 5 | 8 | no | — |
| 250 | C2×#137 | — | 10 | 8 | no | — |
| 251 | C2×#135 | — | 5 | 2 | no | — |
| 252 | C2×#135 | — | 10 | 4 | no | — |
| 253 | C22×Q16 | — | 5 | 4 | no | — |
| 254 | C22×Q16 | — | 10 | 4 | no | — |
| 255 | C2×#131 | — | 5 | 4 | no | — |
| 256 | C2×C4⋊Q8 | — | 5 | 2 | no | — |
| 257 | #494 | — | 5 | 4 | no | — |
| 258 | #494 | — | 5 | 2 | no | — |
| 259 | #494 | — | 5 | 1 | no | — |
| 260 | #494 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 261 | #473 | — | 5 | 8 | no | — |
| 262 | #473 | — | 5 | 4 | no | — |
| 263 | #473 | — | 5 | 4 | no | — |
| 264 | #473 | — | 5 | 4 | no | — |
| 265 | #473 | — | 5 | 8 | no | — |
| 266 | #473 | C2×D5 | 1 | 4 | yes | complemented |
| 267 | #456 | — | 5 | 4 | no | — |
| 268 | #456 | — | 5 | 8 | no | — |
| 269 | #456 | — | 5 | 4 | no | — |
| 270 | #456 | — | 5 | 8 | no | — |
| 271 | #456 | — | 5 | 4 | no | — |
| 272 | #456 | C2×D5 | 1 | 4 | yes | complemented |
| 273 | #443 | — | 5 | 2 | no | — |
| 274 | #443 | — | 5 | 4 | no | — |
| 275 | #443 | — | 5 | 2 | no | — |
| 276 | #443 | — | 5 | 4 | no | — |
| 277 | #443 | — | 5 | 2 | no | — |
| 278 | #443 | C2×D5 | 1 | 2 | yes | complemented |
| 279 | C2×#108 | — | 5 | 2 | no | — |
| 280 | C2×#104 | — | 5 | 4 | no | — |
| 281 | C2×#101 | — | 5 | 4 | no | — |
| 282 | C2×C4×C8 | — | 5 | 1 | no | — |
| 283 | C22×D5 | — | 2 | 4 | no | — |
| 284 | C22×D5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 285 | C5×Q8 | — | 2 | 8 | no | — |
| 286 | C5×Q8 | — | 4 | 4 | no | — |
| 287 | C5×Q8 | C22×D4 | 1 | 4 | yes | — |
| 288 | C5×D4 | — | 2 | 4 | no | — |
| 289 | C5×D4 | — | 4 | 4 | no | — |
| 290 | C5×D4 | C22×D4 | 1 | 4 | yes | — |
| 291 | C2×C4×C5 | — | 2 | 1 | no | — |
| 292 | C2×C4×C5 | — | 2 | 4 | no | — |
| 293 | C2×C4×C5 | — | 2 | 4 | no | — |
| 294 | C2×C4×C5 | — | 4 | 8 | no | — |
| 295 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 296 | C22⋊D5 | — | 2 | 4 | no | — |
| 297 | C22⋊D5 | — | 2 | 4 | no | — |
| 298 | C22⋊D5 | — | 2 | 4 | no | — |
| 299 | C22⋊D5 | — | 4 | 8 | no | — |
| 300 | C2×Dic5 | — | 2 | 1 | no | — |
| 301 | C2×Dic5 | — | 2 | 4 | no | — |
| 302 | C2×Dic5 | — | 2 | 4 | no | — |
| 303 | C2×Dic5 | — | 4 | 8 | no | — |
| 304 | C2×Dic5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 305 | D20 | — | 2 | 4 | no | — |
| 306 | D20 | — | 4 | 4 | no | — |
| 307 | D20 | C22×D4 | 1 | 4 | yes | — |
| 308 | C4×D5 | — | 2 | 4 | no | — |
| 309 | C4×D5 | — | 2 | 4 | no | — |
| 310 | C4×D5 | — | 2 | 4 | no | — |
| 311 | C4×D5 | — | 2 | 4 | no | — |
| 312 | C4×D5 | — | 4 | 8 | no | — |
| 313 | C4×D5 | — | 4 | 8 | no | — |
| 314 | C4×D5 | — | 4 | 4 | no | — |
| 315 | C4×D5 | — | 4 | 4 | no | — |
| 316 | C4×D5 | C22×D4 | 1 | 2 | yes | — |
| 317 | C4×D5 | C22×D4 | 1 | 2 | yes | — |
| 318 | Dic10 | — | 2 | 4 | no | — |
| 319 | Dic10 | — | 2 | 8 | no | — |
| 320 | Dic10 | — | 4 | 4 | no | — |
| 321 | Dic10 | — | 4 | 8 | no | — |
| 322 | Dic10 | — | 4 | 8 | no | — |
| 323 | Dic10 | C22×D4 | 1 | 4 | yes | — |
| 324 | C5×C8 | — | 2 | 4 | no | — |
| 325 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 326 | C5×C8 | C22×D4 | 1 | 2 | yes | — |
| 327 | #168 | — | 2 | 4 | no | — |
| 328 | #168 | C22×D4 | 1 | 2 | yes | — |
| 329 | #168 | C22×D4 | 1 | 2 | yes | — |
| 330 | 2−1+4 | — | 5 | 8 | no | — |
| 331 | 2−1+4 | — | 5 | 4 | no | — |
| 332 | 2−1+4 | — | 10 | 8 | no | — |
| 333 | 2−1+4 | — | 10 | 8 | no | — |
| 334 | 2−1+4 | — | 20 | 4 | no | — |
| 335 | 2−1+4 | C22×D5 | 1 | 4 | yes | — |
| 336 | C2×#41 | — | 5 | 4 | no | — |
| 337 | C2×#41 | — | 10 | 8 | no | — |
| 338 | C2×#41 | — | 20 | 4 | no | — |
| 339 | C22×Q8 | — | 5 | 4 | no | — |
| 340 | C22×Q8 | — | 10 | 8 | no | — |
| 341 | #137 | — | 2 | 8 | no | — |
| 342 | #137 | — | 5 | 8 | no | — |
| 343 | #137 | — | 5 | 8 | no | — |
| 344 | #137 | — | 5 | 8 | no | — |
| 345 | #137 | — | 10 | 8 | no | — |
| 346 | #137 | — | 10 | 8 | no | — |
| 347 | #137 | — | 10 | 8 | no | — |
| 348 | #137 | — | 10 | 8 | no | — |
| 349 | #137 | — | 10 | 8 | no | — |
| 350 | #137 | — | 10 | 8 | no | — |
| 351 | #137 | — | 10 | 8 | no | — |
| 352 | #137 | — | 10 | 8 | no | — |
| 353 | #137 | — | 10 | 8 | no | — |
| 354 | #137 | C22×D5 | 1 | 8 | yes | — |
| 355 | #135 | — | 2 | 4 | no | — |
| 356 | #135 | — | 5 | 4 | no | — |
| 357 | #135 | — | 5 | 2 | no | — |
| 358 | #135 | — | 5 | 4 | no | — |
| 359 | #135 | — | 5 | 2 | no | — |
| 360 | #135 | — | 5 | 2 | no | — |
| 361 | #135 | — | 10 | 4 | no | — |
| 362 | #135 | — | 10 | 8 | no | — |
| 363 | #135 | — | 10 | 4 | no | — |
| 364 | #135 | — | 10 | 8 | no | — |
| 365 | #135 | — | 10 | 4 | no | — |
| 366 | #135 | C22×D5 | 1 | 2 | yes | — |
| 367 | C2×Q16 | — | 2 | 4 | no | — |
| 368 | C2×Q16 | — | 5 | 2 | no | — |
| 369 | C2×Q16 | — | 5 | 8 | no | — |
| 370 | C2×Q16 | — | 5 | 4 | no | — |
| 371 | C2×Q16 | — | 10 | 4 | no | — |
| 372 | C2×Q16 | — | 10 | 4 | no | — |
| 373 | C2×Q16 | — | 10 | 4 | no | — |
| 374 | C2×Q16 | — | 10 | 4 | no | — |
| 375 | C2×Q16 | — | 10 | 4 | no | — |
| 376 | C2×Q16 | — | 10 | 8 | no | — |
| 377 | C2×Q16 | — | 10 | 4 | no | — |
| 378 | C2×Q16 | — | 10 | 8 | no | — |
| 379 | C2×Q16 | — | 10 | 8 | no | — |
| 380 | C2×Q16 | — | 10 | 4 | no | — |
| 381 | C2×Q16 | C22×D5 | 1 | 4 | yes | — |
| 382 | C2×SD16 | — | 5 | 4 | no | — |
| 383 | C2×SD16 | — | 10 | 8 | no | — |
| 384 | C2×D8 | — | 5 | 2 | no | — |
| 385 | #131 | — | 5 | 4 | no | — |
| 386 | #131 | — | 5 | 4 | no | — |
| 387 | #131 | — | 5 | 4 | no | — |
| 388 | #131 | — | 10 | 4 | no | — |
| 389 | #131 | — | 10 | 4 | no | — |
| 390 | #131 | C22×D5 | 1 | 4 | yes | — |
| 391 | C2×M16 | — | 5 | 4 | no | — |
| 392 | C2×M16 | — | 10 | 4 | no | — |
| 393 | C22×C8 | — | 5 | 2 | no | — |
| 394 | C22×C8 | — | 10 | 4 | no | — |
| 395 | C4⋊Q8 | — | 5 | 4 | no | — |
| 396 | C4⋊Q8 | — | 5 | 2 | no | — |
| 397 | C4⋊Q8 | — | 20 | 2 | no | — |
| 398 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 399 | C2×C4⋊C4 | — | 20 | 2 | no | — |
| 400 | C2×C42 | — | 5 | 1 | no | — |
| 401 | #108 | — | 5 | 4 | no | — |
| 402 | #108 | — | 5 | 2 | no | — |
| 403 | #108 | C22×D5 | 1 | 2 | yes | — |
| 404 | #104 | — | 5 | 4 | no | — |
| 405 | #104 | — | 5 | 4 | no | — |
| 406 | #104 | — | 5 | 4 | no | — |
| 407 | #104 | C22×D5 | 1 | 4 | yes | — |
| 408 | #101 | — | 5 | 4 | no | — |
| 409 | #101 | — | 5 | 8 | no | — |
| 410 | #101 | C22×D5 | 1 | 4 | yes | — |
| 411 | C4×C8 | — | 5 | 2 | no | — |
| 412 | C4×C8 | — | 5 | 1 | no | — |
| 413 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 414 | C22×C5 | — | 2 | 4 | no | — |
| 415 | C22×C5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 416 | C2×D5 | — | 2 | 2 | no | — |
| 417 | C2×D5 | — | 2 | 4 | no | — |
| 418 | C2×D5 | — | 4 | 8 | no | — |
| 419 | C2×D5 | D42 | 1 | 1 | yes | characteristic |
| 420 | C2×D5 | D42 | 1 | 1 | yes | characteristic |
| 421 | C4×C5 | — | 2 | 2 | no | — |
| 422 | C4×C5 | — | 2 | 4 | no | — |
| 423 | C4×C5 | — | 4 | 4 | no | — |
| 424 | C4×C5 | C23×D4 | 1 | 2 | yes | — |
| 425 | Dic5 | — | 2 | 2 | no | — |
| 426 | Dic5 | — | 2 | 4 | no | — |
| 427 | Dic5 | — | 4 | 4 | no | — |
| 428 | Dic5 | D42 | 1 | 2 | yes | — |
| 429 | #41 | — | 2 | 8 | no | — |
| 430 | #41 | — | 4 | 4 | no | — |
| 431 | #41 | — | 5 | 4 | no | — |
| 432 | #41 | — | 5 | 4 | no | — |
| 433 | #41 | — | 5 | 4 | no | — |
| 434 | #41 | — | 10 | 4 | no | — |
| 435 | #41 | — | 10 | 8 | no | — |
| 436 | #41 | — | 10 | 4 | no | — |
| 437 | #41 | — | 10 | 8 | no | — |
| 438 | #41 | — | 10 | 8 | no | — |
| 439 | #41 | — | 20 | 4 | no | — |
| 440 | #41 | — | 20 | 8 | no | — |
| 441 | #41 | — | 20 | 8 | no | — |
| 442 | #41 | — | 20 | 8 | no | — |
| 443 | #41 | — | 20 | 8 | no | — |
| 444 | #41 | — | 20 | 4 | no | — |
| 445 | #41 | — | 20 | 4 | no | — |
| 446 | #41 | C23×D5 | 1 | 4 | yes | — |
| 447 | C2×Q8 | — | 2 | 8 | no | — |
| 448 | C2×Q8 | — | 5 | 4 | no | — |
| 449 | C2×Q8 | — | 5 | 4 | no | — |
| 450 | C2×Q8 | — | 10 | 4 | no | — |
| 451 | C2×Q8 | — | 10 | 8 | no | — |
| 452 | C2×Q8 | — | 10 | 8 | no | — |
| 453 | C2×Q8 | — | 10 | 8 | no | — |
| 454 | C2×Q8 | — | 10 | 8 | no | — |
| 455 | C2×Q8 | — | 10 | 8 | no | — |
| 456 | C2×Q8 | — | 20 | 8 | no | — |
| 457 | C2×Q8 | — | 20 | 4 | no | — |
| 458 | C2×Q8 | — | 20 | 8 | no | — |
| 459 | C2×Q8 | C23×D5 | 1 | 4 | yes | — |
| 460 | C2×D4 | — | 5 | 4 | no | — |
| 461 | C2×D4 | — | 10 | 4 | no | — |
| 462 | C2×D4 | — | 20 | 4 | no | — |
| 463 | C22×C4 | — | 5 | 1 | no | — |
| 464 | C22×C4 | — | 10 | 4 | no | — |
| 465 | C22×C4 | — | 10 | 1 | no | — |
| 466 | C22×C4 | — | 10 | 4 | no | — |
| 467 | C22×C4 | — | 20 | 8 | no | — |
| 468 | Q16 | — | 2 | 8 | no | — |
| 469 | Q16 | — | 2 | 4 | no | — |
| 470 | Q16 | — | 2 | 4 | no | — |
| 471 | Q16 | — | 5 | 4 | no | — |
| 472 | Q16 | — | 5 | 2 | no | — |
| 473 | Q16 | — | 10 | 8 | no | — |
| 474 | Q16 | — | 10 | 8 | no | — |
| 475 | Q16 | — | 10 | 8 | no | — |
| 476 | Q16 | — | 10 | 8 | no | — |
| 477 | Q16 | — | 10 | 8 | no | — |
| 478 | Q16 | — | 10 | 4 | no | — |
| 479 | Q16 | — | 10 | 4 | no | — |
| 480 | Q16 | D4×D5 | 1 | 2 | yes | — |
| 481 | SD16 | — | 2 | 8 | no | — |
| 482 | SD16 | — | 5 | 4 | no | — |
| 483 | SD16 | — | 5 | 4 | no | — |
| 484 | SD16 | — | 5 | 4 | no | — |
| 485 | SD16 | — | 10 | 8 | no | — |
| 486 | SD16 | — | 10 | 8 | no | — |
| 487 | SD16 | — | 10 | 8 | no | — |
| 488 | SD16 | D4×D5 | 1 | 4 | yes | — |
| 489 | D8 | — | 5 | 4 | no | — |
| 490 | D8 | — | 5 | 2 | no | — |
| 491 | D8 | D4×D5 | 1 | 2 | yes | — |
| 492 | M16 | — | 2 | 4 | no | — |
| 493 | M16 | — | 5 | 4 | no | — |
| 494 | M16 | — | 10 | 4 | no | — |
| 495 | M16 | — | 10 | 4 | no | — |
| 496 | M16 | — | 10 | 4 | no | — |
| 497 | M16 | — | 10 | 4 | no | — |
| 498 | M16 | C23×D5 | 1 | 4 | yes | — |
| 499 | C2×C8 | — | 2 | 4 | no | — |
| 500 | C2×C8 | — | 5 | 2 | no | — |
| 501 | C2×C8 | — | 5 | 2 | no | — |
| 502 | C2×C8 | — | 5 | 2 | no | — |
| 503 | C2×C8 | — | 5 | 2 | no | — |
| 504 | C2×C8 | — | 5 | 2 | no | — |
| 505 | C2×C8 | — | 10 | 4 | no | — |
| 506 | C2×C8 | — | 10 | 4 | no | — |
| 507 | C2×C8 | — | 10 | 4 | no | — |
| 508 | C2×C8 | — | 10 | 4 | no | — |
| 509 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 510 | C4⋊C4 | — | 4 | 2 | no | — |
| 511 | C4⋊C4 | — | 20 | 4 | no | — |
| 512 | C4⋊C4 | — | 20 | 2 | no | — |
| 513 | C42 | — | 5 | 1 | no | — |
| 514 | C42 | — | 10 | 1 | no | — |
| 515 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 516 | C2×C5 | — | 2 | 1 | no | — |
| 517 | C2×C5 | — | 4 | 4 | no | — |
| 518 | C2×C5 | C2×D42 | 1 | 1 | yes | characteristic |
| 519 | D5 | — | 2 | 1 | no | — |
| 520 | D5 | — | 4 | 4 | no | — |
| 521 | D5 | #3293 | 1 | 2 | yes | direct product factor |
| 522 | C23 | — | 5 | 1 | no | — |
| 523 | C23 | — | 10 | 4 | no | — |
| 524 | Q8 | — | 2 | 8 | no | — |
| 525 | Q8 | — | 4 | 4 | no | — |
| 526 | Q8 | — | 5 | 4 | no | — |
| 527 | Q8 | — | 10 | 4 | no | — |
| 528 | Q8 | — | 10 | 8 | no | — |
| 529 | Q8 | — | 20 | 8 | no | — |
| 530 | Q8 | — | 20 | 8 | no | — |
| 531 | Q8 | — | 20 | 4 | no | — |
| 532 | Q8 | C2×D4×D5 | 1 | 4 | yes | — |
| 533 | D4 | — | 2 | 4 | no | — |
| 534 | D4 | — | 4 | 4 | no | — |
| 535 | D4 | — | 5 | 4 | no | — |
| 536 | D4 | — | 10 | 4 | no | — |
| 537 | D4 | — | 10 | 4 | no | — |
| 538 | D4 | — | 10 | 4 | no | — |
| 539 | D4 | — | 10 | 4 | no | — |
| 540 | D4 | — | 20 | 4 | no | — |
| 541 | D4 | — | 20 | 8 | no | — |
| 542 | D4 | C2×D4×D5 | 1 | 4 | yes | — |
| 543 | C2×C4 | — | 2 | 1 | no | — |
| 544 | C2×C4 | — | 2 | 4 | no | — |
| 545 | C2×C4 | — | 2 | 4 | no | — |
| 546 | C2×C4 | — | 4 | 8 | no | — |
| 547 | C2×C4 | — | 5 | 1 | no | — |
| 548 | C2×C4 | — | 5 | 2 | no | — |
| 549 | C2×C4 | — | 5 | 2 | no | — |
| 550 | C2×C4 | — | 10 | 4 | no | — |
| 551 | C2×C4 | — | 10 | 4 | no | — |
| 552 | C2×C4 | — | 10 | 4 | no | — |
| 553 | C2×C4 | — | 10 | 4 | no | — |
| 554 | C2×C4 | — | 10 | 1 | no | — |
| 555 | C2×C4 | — | 10 | 4 | no | — |
| 556 | C2×C4 | — | 10 | 4 | no | — |
| 557 | C2×C4 | — | 20 | 8 | no | — |
| 558 | C2×C4 | — | 20 | 8 | no | — |
| 559 | C2×C4 | — | 20 | 4 | no | — |
| 560 | C2×C4 | — | 20 | 4 | no | — |
| 561 | C2×C4 | — | 20 | 8 | no | — |
| 562 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 563 | C8 | — | 2 | 4 | no | — |
| 564 | C8 | — | 5 | 2 | no | — |
| 565 | C8 | — | 5 | 2 | no | — |
| 566 | C8 | — | 10 | 4 | no | — |
| 567 | C8 | C2×D4×D5 | 1 | 2 | yes | — |
| 568 | C8 | C2×D4×D5 | 1 | 2 | yes | — |
| 569 | C5 | C2×#3293 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 570 | C22 | — | 2 | 4 | no | — |
| 571 | C22 | — | 5 | 1 | no | — |
| 572 | C22 | — | 5 | 1 | no | — |
| 573 | C22 | — | 10 | 2 | no | — |
| 574 | C22 | — | 10 | 4 | no | — |
| 575 | C22 | — | 20 | 8 | no | — |
| 576 | C22 | D5×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 577 | C4 | — | 2 | 2 | no | — |
| 578 | C4 | — | 2 | 4 | no | — |
| 579 | C4 | — | 4 | 4 | no | — |
| 580 | C4 | — | 5 | 2 | no | — |
| 581 | C4 | — | 10 | 2 | no | — |
| 582 | C4 | — | 10 | 4 | no | — |
| 583 | C4 | — | 20 | 4 | no | — |
| 584 | C4 | C22×D4×D5 | 1 | 2 | yes | — |
| 585 | C2 | — | 2 | 1 | no | — |
| 586 | C2 | — | 4 | 4 | no | — |
| 587 | C2 | — | 5 | 2 | no | — |
| 588 | C2 | — | 10 | 1 | no | — |
| 589 | C2 | — | 20 | 4 | no | — |
| 590 | C2 | D42×D5 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D42×D5 |
| commutator, cosocle | C2×C4×C5 | C25 |
| Frattini | C2×C4 | C24×D5 |
| Fitting | C5×#3293 | C2 |
| socle | C2×C5 | C2×D42 |
| hypercenter | #3293 | D5 |
| hypocenter | C5 | C2×#3293 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #3293 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D5×#578 | C2 | semidirect |
| 2. C5×#3293 | C2 | semidirect |
| 3. #10615749 | C2 | semidirect |
| 4. #10613539 | C2 | semidirect |
| 5. D5×#494 | C2 | semidirect |
| 6. #10612678 | C2 | semidirect |
| 7. D5×#473 | C2 | semidirect |
| 8. #10612034 | C2 | semidirect |
| 9. D5×#456 | C2 | semidirect |
| 10. #10611626 | C2 | semidirect |
| 11. D5×#443 | C2 | semidirect |
| 13. C5×#578 | C22 | semidirect |
| 14. #66172 | C22 | semidirect |
| 16. #66113 | C22 | semidirect |
| 20. #66105 | C22 | semidirect |
| 24. #66100 | C22 | semidirect |
| 27. #66087 | C22 | semidirect |
| 30. C5×#494 | C22 | semidirect |
| 31. C5×#473 | C22 | semidirect |
| 32. C5×#456 | C22 | semidirect |
| 33. C5×#443 | C22 | semidirect |
| 34. #65535 | C22 | semidirect |
| 35. #65494 | C22 | semidirect |
| 36. #65493 | C22 | semidirect |
| 37. #65485 | C22 | semidirect |
| 38. #65481 | C22 | semidirect |
| 39. #65470 | C22 | semidirect |
| 40. #65433 | C22 | semidirect |
| 41. #65432 | C22 | semidirect |
| 42. #65384 | C22 | semidirect |
| 43. #65381 | C22 | semidirect |
| 44. #65185 | C22 | semidirect |
| 45. #65184 | C22 | semidirect |
| 47. #65115 | C22 | semidirect |
| 48. #65113 | C22 | semidirect |
| 50. #65044 | C22 | semidirect |
| 51. #65041 | C22 | semidirect |
| 53. #64989 | C22 | semidirect |
| 54. #64988 | C22 | semidirect |
| 147. #3293 | D5 | direct (N × H) |
| 248. #578 | C2×D5 | semidirect |
| 260. #494 | C2×D5 | semidirect |
| 266. #473 | C2×D5 | semidirect |
| 272. #456 | C2×D5 | semidirect |
| 278. #443 | C2×D5 | semidirect |
| 521. D5 | #3293 | direct (N × H) |
| 569. C5 | C2×#3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#578 | 2 |
| C5×#3293 | 2 |
| #10615749 | 2 |
| #10613539 | 2 |
| D5×#494 | 2 |
| #10612678 | 2 |
| D5×#473 | 2 |
| #10612034 | 2 |
| D5×#456 | 2 |
| #10611626 | 2 |
| D5×#443 | 2 |
| C2×#3293 | 5 |