Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
986 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13107746 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13104918 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13103963 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13101682 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13099902 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×D4×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C22⋊#1044 | — | 2 | 2 | no | — |
| 8 | C2×C4⋊#1044 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C4×#1044 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C22⋊#1043 | — | 2 | 2 | no | — |
| 11 | D4×#1043 | — | 2 | 2 | no | — |
| 12 | D4×#1043 | — | 2 | 2 | no | — |
| 13 | #11717438 | C22 | 1 | 2 | yes | — |
| 14 | #11716936 | C22 | 1 | 2 | yes | — |
| 15 | #11716772 | — | 2 | 2 | no | — |
| 16 | #11716771 | — | 2 | 2 | no | — |
| 17 | C5×#3965 | C4 | 1 | 2 | yes | complemented |
| 18 | #11716600 | C4 | 1 | 2 | yes | complemented |
| 19 | #10603925 | — | 5 | 2 | no | maximal |
| 20 | C23×C5⋊D5 | D4 | 1 | 2 | yes | — |
| 21 | C22×#1044 | — | 2 | 1 | no | — |
| 22 | C22×#1044 | — | 2 | 1 | no | — |
| 23 | C22×#1043 | — | 2 | 2 | no | — |
| 24 | C22×#1043 | — | 2 | 2 | no | — |
| 25 | C2×C52×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C2×C22⋊(C5⋊D5) | Q8 | 1 | 2 | yes | — |
| 27 | D4×C5⋊D5 | — | 2 | 2 | no | — |
| 28 | D4×C5⋊D5 | — | 2 | 2 | no | — |
| 29 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22⋊#1044 | — | 4 | 4 | no | — |
| 32 | C4⋊#1044 | — | 2 | 2 | no | — |
| 33 | C4×#1044 | — | 2 | 2 | no | — |
| 34 | C22⋊#1043 | — | 2 | 4 | no | — |
| 35 | C22⋊#1043 | — | 2 | 2 | no | — |
| 36 | C4⋊#1043 | D4 | 1 | 2 | yes | — |
| 37 | C4⋊#1043 | D4 | 1 | 2 | yes | — |
| 38 | C4×#1043 | — | 2 | 2 | no | — |
| 39 | C5×#681 | C2×C4 | 1 | 4 | yes | complemented |
| 40 | #87769 | — | 2 | 2 | no | — |
| 41 | #87767 | — | 2 | 2 | no | — |
| 42 | #66258 | — | 5 | 2 | no | — |
| 43 | #66258 | — | 10 | 2 | no | — |
| 44 | #65780 | — | 5 | 2 | no | — |
| 45 | #65727 | — | 5 | 4 | no | — |
| 46 | D5×#100 | — | 5 | 2 | no | — |
| 47 | #64900 | — | 5 | 4 | no | — |
| 48 | C23×C52 | C4⋊C4 | 1 | 2 | yes | — |
| 49 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 50 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 51 | C22×C5⋊D5 | — | 4 | 2 | no | — |
| 52 | C22×C5⋊D5 | — | 4 | 2 | no | — |
| 53 | C22×C5⋊D5 | C4⋊C4 | 1 | 2 | yes | — |
| 54 | C22×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 55 | C2×#1044 | — | 2 | 2 | no | — |
| 56 | C2×#1044 | — | 4 | 1 | no | — |
| 57 | C2×#1044 | — | 4 | 1 | no | — |
| 58 | C2×#1044 | — | 4 | 2 | no | — |
| 59 | C2×#1044 | — | 4 | 1 | no | — |
| 60 | C2×#1043 | — | 2 | 2 | no | — |
| 61 | C2×#1043 | — | 2 | 2 | no | — |
| 62 | C2×#1043 | — | 8 | 2 | no | — |
| 63 | C2×#1043 | — | 8 | 2 | no | — |
| 64 | C52×D4 | — | 2 | 2 | no | — |
| 65 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 66 | C22⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 67 | C2×#1039 | C2×Q8 | 1 | 1 | yes | characteristic |
| 68 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 69 | C4×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 70 | C4×C5⋊D5 | #41 | 1 | 2 | yes | — |
| 71 | C5×#168 | — | 2 | 4 | no | — |
| 72 | C2×D4×D5 | — | 5 | 2 | no | — |
| 73 | C2×D4×D5 | — | 10 | 2 | no | — |
| 74 | C2×C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 75 | C2×C22⋊AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 76 | C2×C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 77 | D4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 78 | D4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 79 | D4×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 80 | D4×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 81 | #4130 | — | 5 | 4 | no | — |
| 82 | #4130 | — | 10 | 4 | no | — |
| 83 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 84 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 85 | D5×M16 | — | 5 | 4 | no | — |
| 86 | #3994 | — | 10 | 4 | no | — |
| 87 | #3993 | — | 10 | 4 | no | — |
| 88 | C5×#100 | — | 5 | 2 | no | — |
| 89 | #3965 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 90 | #3955 | — | 5 | 4 | no | — |
| 91 | #1856 | — | 25 | 1 | no | Sylow |
| 92 | C22×C52 | — | 2 | 2 | no | — |
| 93 | C22×C52 | — | 4 | 2 | no | — |
| 94 | C22×C52 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 96 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 97 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 98 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 99 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 100 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 101 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 102 | C2×C5⋊D5 | #120 | 1 | 1 | yes | characteristic |
| 103 | C2×C5⋊D5 | #123 | 1 | 1 | yes | characteristic |
| 104 | #1044 | — | 4 | 2 | no | — |
| 105 | #1044 | — | 8 | 1 | no | — |
| 106 | #1043 | — | 4 | 2 | no | — |
| 107 | #1043 | — | 4 | 2 | no | — |
| 108 | C4×C52 | C4×D4 | 1 | 2 | yes | — |
| 109 | #1039 | C22⋊Q8 | 1 | 2 | yes | — |
| 110 | C23×D5 | — | 5 | 4 | no | — |
| 111 | C23×D5 | — | 10 | 4 | no | — |
| 112 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 113 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 114 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 115 | C22×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 116 | C22×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 117 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 118 | C2×C5×D4 | — | 2 | 2 | no | — |
| 119 | C2×C5×D4 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 120 | C2×C22⋊D5 | — | 5 | 4 | no | — |
| 121 | C2×C22⋊D5 | — | 10 | 4 | no | — |
| 122 | D4×D5 | — | 10 | 4 | no | — |
| 123 | D4×D5 | — | 10 | 4 | no | — |
| 124 | D4×D5 | — | 10 | 8 | no | — |
| 125 | D4×D5 | — | 10 | 8 | no | — |
| 126 | C2×D20 | — | 5 | 2 | no | — |
| 127 | C2×D20 | — | 10 | 2 | no | — |
| 128 | C2×C4×D5 | — | 5 | 2 | no | — |
| 129 | C2×C4×D5 | — | 10 | 2 | no | — |
| 130 | C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 131 | C22⋊AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 132 | C22⋊AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 133 | C22⋊AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 134 | C22⋊AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 135 | C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 136 | C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 137 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 138 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 139 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 140 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 141 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 142 | C4×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 143 | C5×M16 | — | 5 | 4 | no | — |
| 144 | #681 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 145 | #676 | — | 10 | 4 | no | — |
| 146 | C8×D5 | — | 10 | 4 | no | — |
| 147 | #518 | — | 25 | 1 | no | — |
| 148 | #428 | — | 25 | 2 | no | — |
| 149 | C2×#100 | — | 25 | 1 | no | — |
| 150 | #390 | — | 25 | 1 | no | — |
| 151 | #339 | — | 25 | 2 | no | — |
| 152 | C2×C52 | — | 2 | 1 | no | — |
| 153 | C2×C52 | — | 4 | 2 | no | — |
| 154 | C2×C52 | #385 | 1 | 1 | yes | characteristic |
| 155 | C5⋊D5 | — | 2 | 1 | no | — |
| 156 | C5⋊D5 | — | 4 | 2 | no | — |
| 157 | C5⋊D5 | #453 | 1 | 1 | yes | characteristic |
| 158 | C5⋊D5 | #455 | 1 | 1 | yes | characteristic |
| 159 | C23×C5 | — | 2 | 4 | no | — |
| 160 | C23×C5 | C4⋊AGL(1,𝔽5) | 1 | 4 | yes | — |
| 161 | C22×D5 | — | 5 | 2 | no | — |
| 162 | C22×D5 | — | 5 | 4 | no | — |
| 163 | C22×D5 | — | 10 | 2 | no | — |
| 164 | C22×D5 | — | 10 | 4 | no | — |
| 165 | C22×D5 | — | 10 | 4 | no | — |
| 166 | C22×D5 | — | 10 | 4 | no | — |
| 167 | C22×D5 | — | 10 | 8 | no | — |
| 168 | C22×D5 | — | 10 | 8 | no | — |
| 169 | C22×D5 | — | 20 | 4 | no | — |
| 170 | C22×D5 | — | 20 | 4 | no | — |
| 171 | C22×D5 | — | 40 | 4 | no | — |
| 172 | C22×D5 | — | 40 | 4 | no | — |
| 173 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 174 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 175 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 176 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 177 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 178 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 179 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 180 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 181 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 182 | C2×AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 183 | C2×AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 184 | C2×AGL(1,𝔽5) | — | 40 | 8 | no | — |
| 185 | C2×AGL(1,𝔽5) | — | 40 | 8 | no | — |
| 186 | C5×D4 | — | 2 | 8 | no | — |
| 187 | C5×D4 | — | 2 | 4 | no | — |
| 188 | C2×C4×C5 | — | 2 | 2 | no | — |
| 189 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 190 | C22⋊D5 | — | 10 | 8 | no | — |
| 191 | C22⋊D5 | — | 10 | 16 | no | — |
| 192 | C2×Dic5 | — | 5 | 2 | no | — |
| 193 | C2×Dic5 | — | 10 | 2 | no | — |
| 194 | D20 | — | 10 | 8 | no | — |
| 195 | D20 | — | 10 | 4 | no | — |
| 196 | C4×D5 | — | 5 | 4 | no | — |
| 197 | C4×D5 | — | 5 | 4 | no | — |
| 198 | C4×D5 | — | 10 | 4 | no | — |
| 199 | C4×D5 | — | 10 | 4 | no | — |
| 200 | C5×C8 | — | 10 | 4 | no | — |
| 201 | #168 | — | 2 | 4 | no | — |
| 202 | C22×D4 | — | 25 | 1 | no | — |
| 203 | C2×M16 | — | 25 | 2 | no | — |
| 204 | C4×D4 | — | 50 | 2 | no | — |
| 205 | C4×D4 | — | 50 | 2 | no | — |
| 206 | #117 | — | 25 | 2 | no | — |
| 207 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 208 | C2×C22⋊C4 | — | 50 | 2 | no | — |
| 209 | C2×C22⋊C4 | — | 50 | 2 | no | — |
| 210 | C2×C42 | — | 25 | 1 | no | — |
| 211 | #107 | — | 50 | 2 | no | — |
| 212 | #106 | — | 50 | 2 | no | — |
| 213 | #100 | — | 5 | 2 | no | — |
| 214 | #100 | — | 25 | 2 | no | — |
| 215 | C52 | #1856 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 216 | C22×C5 | — | 2 | 8 | no | — |
| 217 | C22×C5 | — | 2 | 4 | no | — |
| 218 | C22×C5 | — | 2 | 2 | no | — |
| 219 | C22×C5 | — | 4 | 4 | no | — |
| 220 | C22×C5 | — | 8 | 4 | no | — |
| 221 | C22×C5 | C2×C4⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 222 | C2×D5 | — | 5 | 2 | no | — |
| 223 | C2×D5 | — | 5 | 2 | no | — |
| 224 | C2×D5 | — | 10 | 2 | no | — |
| 225 | C2×D5 | — | 10 | 2 | no | — |
| 226 | C2×D5 | — | 10 | 2 | no | — |
| 227 | C2×D5 | — | 10 | 2 | no | — |
| 228 | C2×D5 | — | 10 | 8 | no | — |
| 229 | C2×D5 | — | 10 | 4 | no | — |
| 230 | C2×D5 | — | 20 | 2 | no | — |
| 231 | C2×D5 | — | 20 | 2 | no | — |
| 232 | C2×D5 | — | 20 | 4 | no | — |
| 233 | C2×D5 | — | 20 | 4 | no | — |
| 234 | C2×D5 | — | 20 | 8 | no | — |
| 235 | C2×D5 | — | 20 | 8 | no | — |
| 236 | C2×D5 | — | 20 | 4 | no | — |
| 237 | C2×D5 | — | 40 | 4 | no | — |
| 238 | C2×D5 | — | 40 | 4 | no | — |
| 239 | C2×D5 | — | 40 | 8 | no | — |
| 240 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 241 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 242 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 243 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 244 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 245 | AGL(1,𝔽5) | — | 40 | 2 | no | — |
| 246 | C4×C5 | — | 2 | 4 | no | — |
| 247 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 248 | Dic5 | — | 5 | 4 | no | — |
| 249 | Dic5 | — | 10 | 4 | no | — |
| 250 | C24 | — | 25 | 2 | no | — |
| 251 | C2×D4 | — | 25 | 2 | no | — |
| 252 | C2×D4 | — | 25 | 1 | no | — |
| 253 | C2×D4 | — | 50 | 2 | no | — |
| 254 | C2×D4 | — | 50 | 2 | no | — |
| 255 | C2×D4 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 256 | C22×C4 | — | 25 | 1 | no | — |
| 257 | C22×C4 | — | 50 | 1 | no | — |
| 258 | C22×C4 | — | 50 | 2 | no | — |
| 259 | C22×C4 | — | 50 | 2 | no | — |
| 260 | C22×C4 | — | 50 | 1 | no | — |
| 261 | M16 | — | 5 | 4 | no | — |
| 262 | M16 | — | 50 | 2 | no | — |
| 263 | C2×C8 | — | 50 | 2 | no | — |
| 264 | C4⋊C4 | — | 25 | 2 | no | — |
| 265 | C4⋊C4 | — | 25 | 2 | no | — |
| 266 | C4⋊C4 | — | 50 | 2 | no | — |
| 267 | C22⋊C4 | — | 50 | 2 | no | — |
| 268 | C22⋊C4 | — | 50 | 4 | no | — |
| 269 | C22⋊C4 | — | 100 | 4 | no | — |
| 270 | C42 | — | 50 | 2 | no | — |
| 271 | C42 | — | 50 | 2 | no | — |
| 272 | C2×C5 | — | 2 | 2 | no | — |
| 273 | C2×C5 | — | 2 | 2 | no | — |
| 274 | C2×C5 | — | 4 | 2 | no | — |
| 275 | C2×C5 | — | 4 | 8 | no | — |
| 276 | C2×C5 | — | 4 | 4 | no | — |
| 277 | C2×C5 | #65699 | 1 | 2 | yes | — |
| 278 | D5 | — | 5 | 2 | no | — |
| 279 | D5 | — | 5 | 2 | no | — |
| 280 | D5 | — | 10 | 2 | no | — |
| 281 | D5 | — | 10 | 2 | no | — |
| 282 | D5 | — | 10 | 2 | no | — |
| 283 | D5 | — | 20 | 2 | no | — |
| 284 | D5 | — | 20 | 8 | no | — |
| 285 | D5 | — | 20 | 4 | no | — |
| 286 | C23 | — | 25 | 1 | no | — |
| 287 | C23 | — | 25 | 2 | no | — |
| 288 | C23 | — | 50 | 2 | no | — |
| 289 | C23 | — | 50 | 2 | no | — |
| 290 | C23 | — | 100 | 2 | no | — |
| 291 | C23 | — | 100 | 2 | no | — |
| 292 | C23 | #87832 | 1 | 2 | yes | — |
| 293 | D4 | — | 2 | 2 | no | — |
| 294 | D4 | — | 50 | 4 | no | — |
| 295 | D4 | — | 50 | 2 | no | — |
| 296 | C2×C4 | — | 25 | 1 | no | — |
| 297 | C2×C4 | — | 25 | 2 | no | — |
| 298 | C2×C4 | — | 25 | 2 | no | — |
| 299 | C2×C4 | — | 50 | 2 | no | — |
| 300 | C2×C4 | — | 50 | 2 | no | — |
| 301 | C2×C4 | — | 50 | 2 | no | — |
| 302 | C2×C4 | — | 100 | 1 | no | — |
| 303 | C2×C4 | — | 100 | 1 | no | — |
| 304 | C2×C4 | — | 100 | 1 | no | — |
| 305 | C2×C4 | — | 100 | 2 | no | — |
| 306 | C2×C4 | — | 200 | 2 | no | — |
| 307 | C2×C4 | — | 200 | 2 | no | — |
| 308 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 309 | C8 | — | 10 | 4 | no | — |
| 310 | C5 | — | 2 | 2 | no | — |
| 311 | C5 | #10603925 | 1 | 2 | yes | complemented |
| 312 | C22 | — | 2 | 2 | no | — |
| 313 | C22 | — | 4 | 2 | no | — |
| 314 | C22 | — | 25 | 1 | no | — |
| 315 | C22 | — | 25 | 1 | no | — |
| 316 | C22 | — | 50 | 1 | no | — |
| 317 | C22 | — | 50 | 1 | no | — |
| 318 | C22 | — | 50 | 2 | no | — |
| 319 | C22 | — | 100 | 2 | no | — |
| 320 | C22 | — | 100 | 2 | no | — |
| 321 | C22 | — | 100 | 2 | no | — |
| 322 | C22 | — | 200 | 2 | no | — |
| 323 | C22 | C2×#87832 | 1 | 1 | yes | characteristic |
| 324 | C4 | — | 25 | 2 | no | — |
| 325 | C4 | — | 100 | 2 | no | — |
| 326 | C4 | — | 100 | 2 | no | — |
| 327 | C4 | — | 100 | 2 | no | — |
| 328 | C4 | — | 200 | 1 | no | — |
| 329 | C4 | #11717375 | 1 | 2 | yes | — |
| 330 | C2 | — | 2 | 1 | no | — |
| 331 | C2 | — | 4 | 2 | no | — |
| 332 | C2 | — | 25 | 1 | no | — |
| 333 | C2 | — | 25 | 1 | no | — |
| 334 | C2 | — | 50 | 1 | no | — |
| 335 | C2 | — | 100 | 2 | no | — |
| 336 | C2 | #13104120 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13103963 | C2 | semidirect |
| 5. #13099902 | C2 | semidirect |
| 17. C5×#3965 | C4 | semidirect |
| 18. #11716600 | C4 | semidirect |
| 39. C5×#681 | C2×C4 | semidirect |
| 89. #3965 | AGL(1,𝔽5) | semidirect |
| 144. #681 | C2×AGL(1,𝔽5) | semidirect |
| 215. C52 | #1856 | semidirect |
| 311. C5 | #10603925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107746 | 2 |
| #13104918 | 2 |
| #13103963 | 2 |
| #13101682 | 2 |
| #13099902 | 2 |
| #10603925 | 5 |