Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1098 conjugacy classes of subgroups.
The subgroup lattice has 570 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13107772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13107550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13106550 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13104804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13104086 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13104068 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13103965 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13103946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#11716763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #41×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11717471 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11717454 | C22 | 1 | 2 | yes | complemented |
| 13 | #11717452 | — | 2 | 2 | no | — |
| 14 | #11717452 | C22 | 1 | 2 | yes | complemented |
| 15 | #11717448 | — | 2 | 1 | no | — |
| 16 | #11717448 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#87862 | — | 2 | 1 | no | — |
| 18 | C2×#87862 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×#1043 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11717435 | C22 | 1 | 1 | yes | characteristic |
| 21 | #11717373 | — | 2 | 2 | no | — |
| 22 | #11717361 | — | 2 | 1 | no | — |
| 23 | #11717360 | C22 | 1 | 4 | yes | complemented |
| 24 | D5⋊(D5⋊C8) | — | 2 | 1 | no | — |
| 25 | C5×#4096 | C4 | 1 | 2 | yes | complemented |
| 26 | #11717068 | C22 | 1 | 2 | yes | — |
| 27 | #11717062 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #11717058 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #11717054 | C22 | 1 | 2 | yes | — |
| 30 | #11717048 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | #11717044 | C4 | 1 | 1 | yes | characteristic, complemented |
| 32 | #11716947 | C4 | 1 | 2 | yes | complemented |
| 33 | C2×#87767 | C22 | 1 | 1 | yes | characteristic |
| 34 | #11716878 | C22 | 1 | 2 | yes | complemented |
| 35 | #11716876 | C22 | 1 | 2 | yes | complemented |
| 36 | #11716773 | C22 | 1 | 4 | yes | complemented |
| 37 | #11716770 | C22 | 1 | 4 | yes | complemented |
| 38 | #11716763 | C22 | 1 | 4 | yes | complemented |
| 39 | D5⋊#444 | — | 5 | 2 | no | maximal |
| 40 | C22×#1043 | — | 2 | 1 | no | — |
| 41 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #87904 | C23 | 1 | 1 | yes | characteristic |
| 43 | Q8×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #87902 | — | 2 | 1 | no | — |
| 45 | #87902 | C23 | 1 | 1 | yes | characteristic |
| 46 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 47 | D4×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #87900 | — | 2 | 1 | no | — |
| 49 | #87900 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 51 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 52 | C5×#709 | C2×C4 | 1 | 2 | yes | — |
| 53 | #87886 | — | 2 | 1 | no | — |
| 54 | #87880 | — | 2 | 1 | no | — |
| 55 | #87877 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C4×D52 | — | 2 | 1 | no | — |
| 57 | #87873 | — | 2 | 1 | no | — |
| 58 | #87872 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | #87871 | C23 | 1 | 2 | yes | — |
| 60 | #87867 | — | 2 | 1 | no | — |
| 61 | #87867 | — | 2 | 2 | no | — |
| 62 | C2×#6034 | — | 2 | 2 | no | — |
| 63 | C2×#6034 | D4 | 1 | 2 | yes | — |
| 64 | #87863 | — | 2 | 2 | no | — |
| 65 | #87863 | C23 | 1 | 2 | yes | — |
| 66 | #87862 | — | 2 | 1 | no | — |
| 67 | #87862 | — | 2 | 2 | no | — |
| 68 | #87862 | D4 | 1 | 1 | yes | characteristic |
| 69 | #87862 | D4 | 1 | 1 | yes | characteristic |
| 70 | #87862 | C23 | 1 | 2 | yes | — |
| 71 | #87860 | — | 2 | 1 | no | — |
| 72 | C4×#1043 | — | 2 | 1 | no | — |
| 73 | C4×#1043 | C23 | 1 | 2 | yes | — |
| 74 | #87856 | C23 | 1 | 2 | yes | — |
| 75 | #87855 | — | 2 | 1 | no | — |
| 76 | #87834 | — | 2 | 4 | no | — |
| 77 | D5⋊#170 | — | 2 | 4 | no | — |
| 78 | C5×#689 | C2×C4 | 1 | 2 | yes | complemented |
| 79 | C5×#688 | C2×C4 | 1 | 2 | yes | complemented |
| 80 | C5×#687 | C2×C4 | 1 | 2 | yes | complemented |
| 81 | C5×#686 | C2×C4 | 1 | 2 | yes | complemented |
| 82 | C2×C5×#168 | C2×C4 | 1 | 2 | yes | — |
| 83 | #87776 | C2×C4 | 1 | 2 | yes | complemented |
| 84 | #87774 | C2×C4 | 1 | 2 | yes | complemented |
| 85 | #87773 | C2×C4 | 1 | 2 | yes | complemented |
| 86 | #87771 | C2×C4 | 1 | 2 | yes | complemented |
| 87 | #87767 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | #87767 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | #87767 | C23 | 1 | 2 | yes | — |
| 90 | D5⋊#131 | — | 5 | 2 | no | — |
| 91 | D5⋊#131 | — | 5 | 2 | no | — |
| 92 | D5×#135 | — | 5 | 2 | no | — |
| 93 | D5⋊#104 | — | 5 | 2 | no | — |
| 94 | D5⋊#104 | — | 5 | 2 | no | — |
| 95 | D5⋊#104 | — | 10 | 2 | no | — |
| 96 | #65741 | — | 5 | 4 | no | — |
| 97 | #65737 | — | 5 | 4 | no | — |
| 98 | #65737 | — | 5 | 4 | no | — |
| 99 | #65733 | — | 5 | 4 | no | — |
| 100 | D5⋊#108 | — | 5 | 2 | no | — |
| 101 | C2×#3992 | — | 5 | 2 | no | — |
| 102 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 103 | C22×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 104 | C2×D52 | — | 2 | 1 | no | — |
| 105 | C2×#1043 | — | 2 | 2 | no | — |
| 106 | C2×#1043 | — | 4 | 2 | no | — |
| 107 | C52×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 108 | C52×D4 | — | 2 | 1 | no | — |
| 109 | C52×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C52 | — | 2 | 1 | no | — |
| 111 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 113 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 114 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 115 | C2×#1039 | — | 2 | 1 | no | — |
| 116 | C2×#1039 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 118 | C4⋊(C5⋊D5) | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 120 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 121 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 122 | C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C4×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 125 | C4×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 126 | #6045 | — | 2 | 1 | no | — |
| 127 | #6045 | C22×C4 | 1 | 1 | yes | characteristic |
| 128 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 129 | C5×D20 | C22×C4 | 1 | 2 | yes | — |
| 130 | C4×C5×D5 | — | 2 | 2 | no | — |
| 131 | C5×Dic10 | C22×C4 | 1 | 2 | yes | — |
| 132 | #6039 | — | 2 | 1 | no | — |
| 133 | #6038 | — | 2 | 2 | no | — |
| 134 | #6037 | — | 2 | 1 | no | — |
| 135 | #6036 | — | 2 | 1 | no | — |
| 136 | D5×Dic5 | — | 2 | 2 | no | — |
| 137 | #6034 | — | 2 | 2 | no | — |
| 138 | #6034 | C2×D4 | 1 | 2 | yes | — |
| 139 | #6034 | C2×D4 | 1 | 2 | yes | — |
| 140 | #6033 | — | 2 | 2 | no | — |
| 141 | C5×#168 | C22×C4 | 1 | 2 | yes | — |
| 142 | C5×#168 | C22×C4 | 1 | 2 | yes | — |
| 143 | D5×#41 | — | 5 | 2 | no | — |
| 144 | D5×#41 | — | 5 | 2 | no | — |
| 145 | D5×#41 | — | 10 | 2 | no | — |
| 146 | #4133 | — | 5 | 4 | no | — |
| 147 | #4133 | — | 5 | 4 | no | — |
| 148 | #4131 | — | 5 | 4 | no | — |
| 149 | #4131 | — | 5 | 4 | no | — |
| 150 | #4131 | — | 10 | 4 | no | — |
| 151 | #4131 | — | 10 | 4 | no | — |
| 152 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 153 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 154 | D5⋊M16 | — | 5 | 2 | no | — |
| 155 | D5⋊M16 | — | 5 | 2 | no | — |
| 156 | D5⋊M16 | — | 10 | 2 | no | — |
| 157 | D5⋊M16 | — | 10 | 2 | no | — |
| 158 | D5⋊M16 | — | 10 | 2 | no | — |
| 159 | C2×D5⋊C8 | — | 5 | 2 | no | — |
| 160 | C2×D5⋊C8 | — | 10 | 2 | no | — |
| 161 | C2×D5⋊C8 | — | 10 | 2 | no | — |
| 162 | C5×#135 | — | 5 | 2 | no | — |
| 163 | #4096 | — | 5 | 2 | no | — |
| 164 | #4096 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 165 | #4065 | — | 5 | 2 | no | — |
| 166 | D5×Q16 | — | 5 | 2 | no | — |
| 167 | #4062 | — | 5 | 2 | no | — |
| 168 | #4062 | — | 5 | 2 | no | — |
| 169 | D5×SD16 | — | 5 | 2 | no | — |
| 170 | D5×SD16 | — | 5 | 2 | no | — |
| 171 | #4058 | — | 5 | 2 | no | — |
| 172 | D5×D8 | — | 5 | 2 | no | — |
| 173 | #4050 | — | 5 | 2 | no | — |
| 174 | C2×C8×D5 | — | 5 | 2 | no | — |
| 175 | #4010 | — | 5 | 4 | no | — |
| 176 | #4010 | — | 5 | 4 | no | — |
| 177 | #4010 | — | 10 | 4 | no | — |
| 178 | #4008 | — | 5 | 4 | no | — |
| 179 | #4008 | — | 5 | 4 | no | — |
| 180 | #4008 | — | 10 | 4 | no | — |
| 181 | #3996 | — | 5 | 4 | no | — |
| 182 | #3995 | — | 5 | 4 | no | — |
| 183 | #3992 | — | 5 | 4 | no | — |
| 184 | #3992 | — | 5 | 4 | no | — |
| 185 | C2×#444 | — | 25 | 1 | no | Sylow |
| 186 | C22×C52 | — | 2 | 1 | no | — |
| 187 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 189 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 190 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 191 | C2×C5⋊D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×C5⋊D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 193 | C2×C5×D5 | — | 2 | 2 | no | — |
| 194 | D52 | — | 4 | 2 | no | — |
| 195 | #1043 | — | 4 | 2 | no | — |
| 196 | C4×C52 | — | 2 | 1 | no | — |
| 197 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 198 | C4×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 199 | #1039 | — | 2 | 1 | no | — |
| 200 | #1039 | C4×D4 | 1 | 1 | yes | characteristic |
| 201 | #1039 | C22×D4 | 1 | 1 | yes | characteristic |
| 202 | C5×Dic5 | — | 2 | 2 | no | — |
| 203 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 204 | C22×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 205 | C5×#41 | — | 2 | 2 | no | — |
| 206 | C5×#41 | — | 5 | 2 | no | — |
| 207 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 208 | #713 | — | 5 | 2 | no | — |
| 209 | #713 | — | 5 | 2 | no | — |
| 210 | #713 | — | 10 | 2 | no | — |
| 211 | Q8×D5 | — | 5 | 2 | no | — |
| 212 | Q8×D5 | — | 5 | 2 | no | — |
| 213 | Q8×D5 | — | 10 | 2 | no | — |
| 214 | #711 | — | 5 | 2 | no | — |
| 215 | #711 | — | 5 | 2 | no | — |
| 216 | #711 | — | 10 | 2 | no | — |
| 217 | #711 | — | 10 | 2 | no | — |
| 218 | #711 | — | 10 | 2 | no | — |
| 219 | #711 | — | 20 | 2 | no | — |
| 220 | D4×D5 | — | 5 | 2 | no | — |
| 221 | D4×D5 | — | 5 | 2 | no | — |
| 222 | D4×D5 | — | 10 | 2 | no | — |
| 223 | D4×D5 | — | 10 | 2 | no | — |
| 224 | D4×D5 | — | 10 | 2 | no | — |
| 225 | D4×D5 | — | 20 | 2 | no | — |
| 226 | #709 | — | 5 | 2 | no | — |
| 227 | #709 | — | 10 | 2 | no | — |
| 228 | #709 | — | 10 | 2 | no | — |
| 229 | #709 | — | 10 | 2 | no | — |
| 230 | #709 | — | 20 | 2 | no | — |
| 231 | #709 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 232 | C2×C4×D5 | — | 5 | 2 | no | — |
| 233 | C2×C4×D5 | — | 10 | 2 | no | — |
| 234 | C2×C4×D5 | — | 10 | 2 | no | — |
| 235 | C2×C4×D5 | — | 10 | 2 | no | — |
| 236 | C2×C4×D5 | — | 20 | 2 | no | — |
| 237 | #704 | — | 10 | 4 | no | — |
| 238 | #704 | — | 10 | 4 | no | — |
| 239 | #704 | — | 10 | 2 | no | — |
| 240 | #704 | — | 10 | 2 | no | — |
| 241 | #704 | — | 20 | 2 | no | — |
| 242 | C2×#170 | — | 5 | 4 | no | — |
| 243 | C2×#170 | — | 10 | 4 | no | — |
| 244 | C2×#170 | — | 10 | 4 | no | — |
| 245 | C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 246 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 247 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 248 | C4×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 249 | #700 | — | 5 | 4 | no | — |
| 250 | #700 | — | 5 | 4 | no | — |
| 251 | #700 | — | 10 | 4 | no | — |
| 252 | #700 | — | 10 | 4 | no | — |
| 253 | #700 | — | 10 | 4 | no | — |
| 254 | D5⋊C8 | — | 5 | 2 | no | — |
| 255 | D5⋊C8 | — | 5 | 2 | no | — |
| 256 | D5⋊C8 | — | 5 | 4 | no | — |
| 257 | D5⋊C8 | — | 10 | 4 | no | — |
| 258 | D5⋊C8 | — | 10 | 4 | no | — |
| 259 | D5⋊C8 | — | 10 | 2 | no | — |
| 260 | D5⋊C8 | — | 10 | 2 | no | — |
| 261 | D5⋊C8 | — | 20 | 2 | no | — |
| 262 | C5×Q16 | — | 5 | 2 | no | — |
| 263 | C5×SD16 | — | 5 | 2 | no | — |
| 264 | C5×SD16 | — | 5 | 2 | no | — |
| 265 | C5×D8 | — | 5 | 2 | no | — |
| 266 | C2×C5×C8 | — | 5 | 2 | no | — |
| 267 | #689 | — | 5 | 2 | no | — |
| 268 | #689 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 269 | #688 | — | 5 | 2 | no | — |
| 270 | #688 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 271 | #687 | — | 5 | 2 | no | — |
| 272 | #687 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 273 | #686 | — | 5 | 2 | no | — |
| 274 | #686 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 275 | C2×#168 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 276 | Dic20 | — | 5 | 2 | no | — |
| 277 | D40 | — | 5 | 2 | no | — |
| 278 | #677 | — | 5 | 2 | no | — |
| 279 | #677 | — | 5 | 2 | no | — |
| 280 | C8×D5 | — | 5 | 2 | no | — |
| 281 | C8×D5 | — | 5 | 2 | no | — |
| 282 | C8×D5 | — | 5 | 2 | no | — |
| 283 | C8×D5 | — | 5 | 2 | no | — |
| 284 | C2×#135 | — | 25 | 1 | no | — |
| 285 | C2×#131 | — | 25 | 1 | no | — |
| 286 | C2×#131 | — | 25 | 1 | no | — |
| 287 | #444 | — | 25 | 4 | no | — |
| 288 | #444 | — | 25 | 4 | no | — |
| 289 | C2×#108 | — | 25 | 1 | no | — |
| 290 | C2×#104 | — | 25 | 1 | no | — |
| 291 | C2×#104 | — | 25 | 1 | no | — |
| 292 | C2×#97 | — | 25 | 1 | no | — |
| 293 | C2×C52 | — | 2 | 1 | no | — |
| 294 | C2×C52 | — | 4 | 1 | no | — |
| 295 | C2×C52 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 296 | C5⋊D5 | — | 2 | 1 | no | — |
| 297 | C5⋊D5 | — | 4 | 1 | no | — |
| 298 | C5⋊D5 | #444 | 1 | 2 | yes | complemented |
| 299 | C5×D5 | — | 4 | 2 | no | — |
| 300 | C22×D5 | — | 5 | 2 | no | — |
| 301 | C22×D5 | — | 10 | 2 | no | — |
| 302 | C22×D5 | — | 10 | 2 | no | — |
| 303 | C22×D5 | — | 10 | 2 | no | — |
| 304 | C22×D5 | — | 20 | 2 | no | — |
| 305 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 306 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 307 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 308 | C2×AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 309 | C5×Q8 | — | 2 | 2 | no | — |
| 310 | C5×Q8 | — | 5 | 2 | no | — |
| 311 | C5×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 312 | C5×D4 | — | 2 | 2 | no | — |
| 313 | C5×D4 | — | 2 | 2 | no | — |
| 314 | C5×D4 | — | 4 | 2 | no | — |
| 315 | C5×D4 | — | 5 | 2 | no | — |
| 316 | C5×D4 | — | 10 | 2 | no | — |
| 317 | C5×D4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 318 | C2×C4×C5 | — | 2 | 2 | no | — |
| 319 | C2×C4×C5 | — | 2 | 2 | no | — |
| 320 | C2×C4×C5 | — | 4 | 2 | no | — |
| 321 | C2×C4×C5 | — | 10 | 2 | no | — |
| 322 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 323 | C22⋊D5 | — | 2 | 2 | no | — |
| 324 | C22⋊D5 | — | 10 | 2 | no | — |
| 325 | C22⋊D5 | — | 10 | 2 | no | — |
| 326 | C22⋊D5 | — | 10 | 2 | no | — |
| 327 | C22⋊D5 | — | 10 | 2 | no | — |
| 328 | C22⋊D5 | — | 10 | 2 | no | — |
| 329 | C22⋊D5 | — | 20 | 2 | no | — |
| 330 | C22⋊D5 | — | 20 | 2 | no | — |
| 331 | C22⋊D5 | — | 20 | 2 | no | — |
| 332 | C2×Dic5 | — | 5 | 2 | no | — |
| 333 | C2×Dic5 | — | 10 | 2 | no | — |
| 334 | C2×Dic5 | — | 10 | 2 | no | — |
| 335 | C2×Dic5 | — | 10 | 2 | no | — |
| 336 | C2×Dic5 | — | 20 | 2 | no | — |
| 337 | D20 | — | 5 | 2 | no | — |
| 338 | D20 | — | 10 | 2 | no | — |
| 339 | D20 | — | 10 | 2 | no | — |
| 340 | D20 | — | 10 | 2 | no | — |
| 341 | D20 | — | 20 | 2 | no | — |
| 342 | D20 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 343 | C4×D5 | — | 2 | 2 | no | — |
| 344 | C4×D5 | — | 5 | 2 | no | — |
| 345 | C4×D5 | — | 5 | 2 | no | — |
| 346 | C4×D5 | — | 5 | 2 | no | — |
| 347 | C4×D5 | — | 5 | 2 | no | — |
| 348 | C4×D5 | — | 10 | 2 | no | — |
| 349 | C4×D5 | — | 10 | 2 | no | — |
| 350 | C4×D5 | — | 10 | 2 | no | — |
| 351 | C4×D5 | — | 10 | 2 | no | — |
| 352 | C4×D5 | — | 10 | 2 | no | — |
| 353 | C4×D5 | — | 10 | 2 | no | — |
| 354 | C4×D5 | — | 10 | 2 | no | — |
| 355 | C4×D5 | — | 10 | 2 | no | — |
| 356 | C4×D5 | — | 10 | 2 | no | — |
| 357 | C4×D5 | — | 20 | 2 | no | — |
| 358 | C4×D5 | — | 20 | 2 | no | — |
| 359 | C4×D5 | — | 20 | 2 | no | — |
| 360 | Dic10 | — | 5 | 2 | no | — |
| 361 | Dic10 | — | 10 | 2 | no | — |
| 362 | Dic10 | — | 10 | 2 | no | — |
| 363 | Dic10 | — | 10 | 2 | no | — |
| 364 | Dic10 | — | 20 | 2 | no | — |
| 365 | Dic10 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 366 | #170 | — | 5 | 4 | no | — |
| 367 | #170 | — | 5 | 4 | no | — |
| 368 | #170 | — | 10 | 4 | no | — |
| 369 | #170 | — | 10 | 4 | no | — |
| 370 | #170 | — | 20 | 4 | no | — |
| 371 | C5×C8 | — | 5 | 2 | no | — |
| 372 | C5×C8 | — | 5 | 2 | no | — |
| 373 | #168 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 374 | #168 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 375 | C2×#41 | — | 25 | 1 | no | — |
| 376 | C2×#41 | — | 25 | 1 | no | — |
| 377 | #135 | — | 5 | 2 | no | — |
| 378 | #135 | — | 25 | 2 | no | — |
| 379 | #135 | — | 25 | 2 | no | — |
| 380 | #135 | — | 25 | 2 | no | — |
| 381 | C2×Q16 | — | 25 | 1 | no | — |
| 382 | C2×SD16 | — | 25 | 1 | no | — |
| 383 | C2×SD16 | — | 25 | 1 | no | — |
| 384 | C2×D8 | — | 25 | 1 | no | — |
| 385 | #131 | — | 25 | 2 | no | — |
| 386 | #131 | — | 25 | 4 | no | — |
| 387 | #131 | — | 25 | 2 | no | — |
| 388 | #131 | — | 50 | 2 | no | — |
| 389 | #131 | — | 50 | 2 | no | — |
| 390 | C2×M16 | — | 25 | 1 | no | — |
| 391 | C2×M16 | — | 25 | 1 | no | — |
| 392 | C2×M16 | — | 50 | 1 | no | — |
| 393 | C2×M16 | — | 50 | 1 | no | — |
| 394 | C22×C8 | — | 25 | 1 | no | — |
| 395 | C22×C8 | — | 25 | 1 | no | — |
| 396 | C22×C8 | — | 50 | 1 | no | — |
| 397 | C22×C8 | — | 50 | 1 | no | — |
| 398 | C2×C42 | — | 25 | 1 | no | — |
| 399 | #108 | — | 25 | 4 | no | — |
| 400 | #104 | — | 25 | 2 | no | — |
| 401 | #104 | — | 25 | 4 | no | — |
| 402 | #104 | — | 25 | 2 | no | — |
| 403 | #97 | — | 25 | 4 | no | — |
| 404 | C52 | C2×#444 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 405 | C22×C5 | — | 2 | 2 | no | — |
| 406 | C22×C5 | — | 2 | 2 | no | — |
| 407 | C22×C5 | — | 4 | 2 | no | — |
| 408 | C22×C5 | — | 10 | 2 | no | — |
| 409 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 410 | C2×D5 | — | 2 | 2 | no | — |
| 411 | C2×D5 | — | 5 | 2 | no | — |
| 412 | C2×D5 | — | 5 | 2 | no | — |
| 413 | C2×D5 | — | 10 | 2 | no | — |
| 414 | C2×D5 | — | 10 | 2 | no | — |
| 415 | C2×D5 | — | 10 | 4 | no | — |
| 416 | C2×D5 | — | 10 | 2 | no | — |
| 417 | C2×D5 | — | 20 | 4 | no | — |
| 418 | C2×D5 | — | 20 | 2 | no | — |
| 419 | C2×D5 | — | 20 | 4 | no | — |
| 420 | C2×D5 | — | 20 | 4 | no | — |
| 421 | C2×D5 | — | 40 | 4 | no | — |
| 422 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 423 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 424 | C4×C5 | — | 2 | 2 | no | — |
| 425 | C4×C5 | — | 2 | 2 | no | — |
| 426 | C4×C5 | — | 2 | 2 | no | — |
| 427 | C4×C5 | — | 4 | 2 | no | — |
| 428 | C4×C5 | — | 10 | 2 | no | — |
| 429 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 430 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 431 | Dic5 | — | 2 | 2 | no | — |
| 432 | Dic5 | — | 5 | 2 | no | — |
| 433 | Dic5 | — | 5 | 2 | no | — |
| 434 | Dic5 | — | 10 | 2 | no | — |
| 435 | Dic5 | — | 10 | 2 | no | — |
| 436 | Dic5 | — | 10 | 2 | no | — |
| 437 | Dic5 | — | 20 | 2 | no | — |
| 438 | #41 | — | 5 | 2 | no | — |
| 439 | #41 | — | 25 | 2 | no | — |
| 440 | #41 | — | 25 | 1 | no | — |
| 441 | #41 | — | 25 | 1 | no | — |
| 442 | #41 | — | 25 | 1 | no | — |
| 443 | #41 | — | 50 | 1 | no | — |
| 444 | #41 | — | 50 | 1 | no | — |
| 445 | #41 | — | 50 | 1 | no | — |
| 446 | #41 | — | 50 | 1 | no | — |
| 447 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 448 | C2×Q8 | — | 25 | 1 | no | — |
| 449 | C2×Q8 | — | 25 | 1 | no | — |
| 450 | C2×D4 | — | 25 | 1 | no | — |
| 451 | C2×D4 | — | 25 | 1 | no | — |
| 452 | C2×D4 | — | 50 | 1 | no | — |
| 453 | C2×D4 | — | 50 | 1 | no | — |
| 454 | C22×C4 | — | 25 | 1 | no | — |
| 455 | C22×C4 | — | 50 | 1 | no | — |
| 456 | C22×C4 | — | 50 | 1 | no | — |
| 457 | C22×C4 | — | 50 | 1 | no | — |
| 458 | Q16 | — | 5 | 2 | no | — |
| 459 | Q16 | — | 25 | 2 | no | — |
| 460 | SD16 | — | 5 | 2 | no | — |
| 461 | SD16 | — | 5 | 2 | no | — |
| 462 | SD16 | — | 25 | 2 | no | — |
| 463 | SD16 | — | 25 | 2 | no | — |
| 464 | D8 | — | 5 | 2 | no | — |
| 465 | D8 | — | 25 | 2 | no | — |
| 466 | M16 | — | 25 | 2 | no | — |
| 467 | M16 | — | 25 | 2 | no | — |
| 468 | M16 | — | 50 | 2 | no | — |
| 469 | M16 | — | 50 | 4 | no | — |
| 470 | M16 | — | 50 | 2 | no | — |
| 471 | M16 | — | 50 | 1 | no | — |
| 472 | M16 | — | 50 | 1 | no | — |
| 473 | C2×C8 | — | 5 | 2 | no | — |
| 474 | C2×C8 | — | 25 | 2 | no | — |
| 475 | C2×C8 | — | 25 | 1 | no | — |
| 476 | C2×C8 | — | 25 | 1 | no | — |
| 477 | C2×C8 | — | 25 | 2 | no | — |
| 478 | C2×C8 | — | 25 | 1 | no | — |
| 479 | C2×C8 | — | 25 | 1 | no | — |
| 480 | C2×C8 | — | 25 | 2 | no | — |
| 481 | C2×C8 | — | 50 | 2 | no | — |
| 482 | C2×C8 | — | 50 | 4 | no | — |
| 483 | C2×C8 | — | 50 | 2 | no | — |
| 484 | C2×C8 | — | 50 | 1 | no | — |
| 485 | C2×C8 | — | 50 | 1 | no | — |
| 486 | C42 | — | 25 | 2 | no | — |
| 487 | C42 | — | 50 | 1 | no | — |
| 488 | C2×C5 | — | 2 | 2 | no | — |
| 489 | C2×C5 | — | 2 | 2 | no | — |
| 490 | C2×C5 | — | 4 | 2 | no | — |
| 491 | C2×C5 | — | 4 | 2 | no | — |
| 492 | C2×C5 | — | 8 | 2 | no | — |
| 493 | C2×C5 | — | 20 | 2 | no | — |
| 494 | C2×C5 | C2×D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 495 | D5 | — | 4 | 2 | no | — |
| 496 | D5 | — | 5 | 4 | no | — |
| 497 | D5 | — | 10 | 4 | no | — |
| 498 | D5 | — | 10 | 2 | no | — |
| 499 | D5 | — | 20 | 2 | no | — |
| 500 | D5 | — | 20 | 2 | no | — |
| 501 | D5 | — | 40 | 2 | no | — |
| 502 | C23 | — | 25 | 1 | no | — |
| 503 | C23 | — | 50 | 1 | no | — |
| 504 | C23 | — | 50 | 1 | no | — |
| 505 | Q8 | — | 5 | 2 | no | — |
| 506 | Q8 | — | 25 | 1 | no | — |
| 507 | Q8 | — | 50 | 1 | no | — |
| 508 | Q8 | — | 50 | 1 | no | — |
| 509 | Q8 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 510 | D4 | — | 2 | 1 | no | — |
| 511 | D4 | — | 5 | 2 | no | — |
| 512 | D4 | — | 10 | 2 | no | — |
| 513 | D4 | — | 25 | 1 | no | — |
| 514 | D4 | — | 50 | 1 | no | — |
| 515 | D4 | — | 50 | 2 | no | — |
| 516 | D4 | — | 50 | 1 | no | — |
| 517 | D4 | — | 50 | 1 | no | — |
| 518 | D4 | — | 50 | 1 | no | — |
| 519 | D4 | — | 50 | 1 | no | — |
| 520 | D4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 521 | C2×C4 | — | 2 | 1 | no | — |
| 522 | C2×C4 | — | 10 | 2 | no | — |
| 523 | C2×C4 | — | 25 | 1 | no | — |
| 524 | C2×C4 | — | 25 | 1 | no | — |
| 525 | C2×C4 | — | 25 | 1 | no | — |
| 526 | C2×C4 | — | 25 | 1 | no | — |
| 527 | C2×C4 | — | 25 | 1 | no | — |
| 528 | C2×C4 | — | 50 | 1 | no | — |
| 529 | C2×C4 | — | 50 | 1 | no | — |
| 530 | C2×C4 | — | 50 | 1 | no | — |
| 531 | C2×C4 | — | 50 | 2 | no | — |
| 532 | C2×C4 | — | 50 | 1 | no | — |
| 533 | C2×C4 | — | 50 | 1 | no | — |
| 534 | C2×C4 | — | 50 | 2 | no | — |
| 535 | C2×C4 | — | 100 | 2 | no | — |
| 536 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 537 | C8 | — | 5 | 2 | no | — |
| 538 | C8 | — | 5 | 2 | no | — |
| 539 | C8 | — | 25 | 2 | no | — |
| 540 | C8 | — | 25 | 2 | no | — |
| 541 | C8 | — | 50 | 2 | no | — |
| 542 | C8 | — | 50 | 2 | no | — |
| 543 | C5 | — | 2 | 2 | no | — |
| 544 | C5 | D5⋊#444 | 1 | 2 | yes | complemented |
| 545 | C22 | — | 2 | 1 | no | — |
| 546 | C22 | — | 10 | 2 | no | — |
| 547 | C22 | — | 25 | 1 | no | — |
| 548 | C22 | — | 25 | 1 | no | — |
| 549 | C22 | — | 50 | 2 | no | — |
| 550 | C22 | — | 50 | 1 | no | — |
| 551 | C22 | — | 100 | 2 | no | — |
| 552 | C22 | — | 100 | 2 | no | — |
| 553 | C22 | #11717377 | 1 | 1 | yes | characteristic |
| 554 | C4 | — | 2 | 1 | no | — |
| 555 | C4 | — | 10 | 2 | no | — |
| 556 | C4 | — | 25 | 1 | no | — |
| 557 | C4 | — | 25 | 1 | no | — |
| 558 | C4 | — | 50 | 1 | no | — |
| 559 | C4 | — | 100 | 2 | no | — |
| 560 | C4 | #11717377 | 1 | 1 | yes | characteristic |
| 561 | C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 562 | C2 | — | 2 | 1 | no | — |
| 563 | C2 | — | 4 | 1 | no | — |
| 564 | C2 | — | 20 | 2 | no | — |
| 565 | C2 | — | 25 | 2 | no | — |
| 566 | C2 | — | 50 | 1 | no | — |
| 567 | C2 | — | 100 | 1 | no | — |
| 568 | C2 | C2×#11717377 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107772 | C2 | semidirect |
| 2. #13107550 | C2 | semidirect |
| 4. #13104804 | C2 | semidirect |
| 5. #13104086 | C2 | semidirect |
| 6. #13104068 | C2 | semidirect |
| 7. #13103965 | C2 | semidirect |
| 8. #13103946 | C2 | semidirect |
| 9. C2×#11716763 | C2 | semidirect |
| 12. #11717454 | C22 | semidirect |
| 14. #11717452 | C22 | semidirect |
| 23. #11717360 | C22 | semidirect |
| 25. C5×#4096 | C4 | semidirect |
| 27. #11717062 | C4 | semidirect |
| 28. #11717058 | C4 | semidirect |
| 30. #11717048 | C4 | semidirect |
| 31. #11717044 | C4 | semidirect |
| 32. #11716947 | C4 | semidirect |
| 34. #11716878 | C22 | semidirect |
| 35. #11716876 | C22 | semidirect |
| 36. #11716773 | C22 | semidirect |
| 37. #11716770 | C22 | semidirect |
| 38. #11716763 | C22 | semidirect |
| 78. C5×#689 | C2×C4 | semidirect |
| 79. C5×#688 | C2×C4 | semidirect |
| 80. C5×#687 | C2×C4 | semidirect |
| 81. C5×#686 | C2×C4 | semidirect |
| 83. #87776 | C2×C4 | semidirect |
| 84. #87774 | C2×C4 | semidirect |
| 85. #87773 | C2×C4 | semidirect |
| 86. #87771 | C2×C4 | semidirect |
| 164. #4096 | AGL(1,𝔽5) | semidirect |
| 268. #689 | C2×AGL(1,𝔽5) | semidirect |
| 270. #688 | C2×AGL(1,𝔽5) | semidirect |
| 272. #687 | C2×AGL(1,𝔽5) | semidirect |
| 274. #686 | C2×AGL(1,𝔽5) | semidirect |
| 298. C5⋊D5 | #444 | semidirect |
| 404. C52 | C2×#444 | semidirect |
| 544. C5 | D5⋊#444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107772 | 2 |
| #13107550 | 2 |
| #13106550 | 2 |
| #13104804 | 2 |
| #13104086 | 2 |
| #13104068 | 2 |
| #13103965 | 2 |
| #13103946 | 2 |
| C2×#11716763 | 2 |
| D5⋊#444 | 5 |