Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
684 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #11756863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11754316 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11752414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#65755 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11752008 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11746576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11746575 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10604535 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C3×C4×D5 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6782 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#6762 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#6762 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×#704 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×#704 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91931 | — | 2 | 1 | no | — |
| 16 | #91929 | — | 2 | 2 | no | — |
| 17 | D3×#704 | — | 2 | 1 | no | — |
| 18 | #91927 | — | 2 | 2 | no | — |
| 19 | #91818 | C4 | 1 | 1 | yes | characteristic |
| 20 | C5×#929 | C4 | 1 | 1 | yes | characteristic |
| 21 | #91564 | C4 | 1 | 1 | yes | characteristic |
| 22 | #91563 | C4 | 1 | 1 | yes | characteristic |
| 23 | #91528 | C22 | 1 | 1 | yes | characteristic |
| 24 | #91448 | — | 2 | 1 | no | — |
| 25 | #91444 | — | 2 | 1 | no | — |
| 26 | #91440 | — | 2 | 1 | no | — |
| 27 | #91349 | — | 2 | 1 | no | — |
| 28 | #91232 | — | 2 | 2 | no | — |
| 29 | C3×#4003 | — | 2 | 2 | no | — |
| 30 | #91175 | — | 2 | 1 | no | — |
| 31 | #91174 | — | 2 | 1 | no | — |
| 32 | #69992 | — | 5 | 1 | no | maximal, Hall |
| 33 | #66256 | — | 3 | 1 | no | — |
| 34 | #65990 | — | 3 | 1 | no | — |
| 35 | #65777 | — | 3 | 1 | no | — |
| 36 | #65755 | — | 3 | 1 | no | — |
| 37 | #65755 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #64867 | — | 3 | 1 | no | — |
| 39 | #64867 | — | 3 | 1 | no | — |
| 40 | C23×C3×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C22×C3×C4×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×#1220 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×C5×#67 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C22×C3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×C3×C4×D5 | — | 2 | 1 | no | — |
| 46 | C2×C3×C4×D5 | — | 2 | 1 | no | — |
| 47 | C2×C3×C4×D5 | — | 2 | 1 | no | — |
| 48 | C2×C3×C4×D5 | — | 2 | 1 | no | — |
| 49 | C2×C3×C4×D5 | — | 2 | 1 | no | — |
| 50 | C2×C3×C4×D5 | — | 2 | 1 | no | — |
| 51 | C2×#1204 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×#1203 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×#1202 | — | 2 | 1 | no | — |
| 54 | C2×#1201 | — | 2 | 1 | no | — |
| 55 | C2×#1200 | D4 | 1 | 1 | yes | characteristic |
| 56 | #6782 | — | 2 | 1 | no | — |
| 57 | #6782 | — | 2 | 1 | no | — |
| 58 | #6782 | — | 2 | 1 | no | — |
| 59 | #6782 | — | 2 | 1 | no | — |
| 60 | C2×D3×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 61 | #6762 | — | 2 | 1 | no | — |
| 62 | #6762 | — | 2 | 1 | no | — |
| 63 | #6762 | — | 2 | 1 | no | — |
| 64 | #6762 | — | 2 | 1 | no | — |
| 65 | C2×C3⋊#170 | — | 2 | 1 | no | — |
| 66 | C2×C3⋊#170 | D4 | 1 | 2 | yes | complemented |
| 67 | C3×#704 | — | 2 | 1 | no | — |
| 68 | C3×#704 | — | 2 | 1 | no | — |
| 69 | C3×#704 | — | 2 | 1 | no | — |
| 70 | C3×#704 | — | 2 | 1 | no | — |
| 71 | C2×C3×#170 | — | 2 | 1 | no | — |
| 72 | C2×C3×#170 | D4 | 1 | 2 | yes | complemented |
| 73 | #6740 | — | 2 | 2 | no | — |
| 74 | #6739 | — | 2 | 2 | no | — |
| 75 | #6738 | — | 2 | 2 | no | — |
| 76 | D3×#170 | — | 2 | 2 | no | — |
| 77 | #6719 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #6714 | — | 2 | 1 | no | — |
| 79 | #6712 | — | 2 | 1 | no | — |
| 80 | C5×#217 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 82 | C5×Dic3⋊C4 | — | 2 | 1 | no | — |
| 83 | #6668 | — | 2 | 1 | no | — |
| 84 | #6665 | — | 2 | 1 | no | — |
| 85 | #6665 | — | 2 | 1 | no | — |
| 86 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 87 | #5791 | — | 5 | 1 | no | — |
| 88 | #5745 | — | 5 | 1 | no | — |
| 89 | C3×#407 | — | 5 | 1 | no | — |
| 90 | #5207 | — | 5 | 1 | no | — |
| 91 | #5132 | — | 5 | 1 | no | — |
| 92 | #4559 | — | 5 | 1 | no | — |
| 93 | #4556 | — | 5 | 1 | no | — |
| 94 | C2×#711 | — | 3 | 1 | no | — |
| 95 | C22×C4×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | C2×#704 | — | 3 | 1 | no | — |
| 97 | C2×#704 | — | 3 | 1 | no | — |
| 98 | C2×#704 | — | 6 | 1 | no | — |
| 99 | C2×#704 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | C2×#704 | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | #4131 | — | 6 | 2 | no | — |
| 102 | #4131 | — | 6 | 2 | no | — |
| 103 | D5⋊M16 | — | 6 | 1 | no | — |
| 104 | C5×#123 | — | 3 | 1 | no | — |
| 105 | #4083 | — | 3 | 1 | no | — |
| 106 | #4075 | — | 3 | 1 | no | — |
| 107 | #4042 | — | 6 | 1 | no | — |
| 108 | #4039 | — | 6 | 1 | no | — |
| 109 | #4030 | — | 6 | 1 | no | — |
| 110 | #4028 | — | 3 | 1 | no | — |
| 111 | #4027 | — | 6 | 1 | no | — |
| 112 | #4023 | — | 3 | 1 | no | — |
| 113 | #4013 | — | 6 | 1 | no | — |
| 114 | #4005 | — | 6 | 1 | no | — |
| 115 | #4003 | — | 2 | 2 | no | — |
| 116 | #4003 | — | 6 | 2 | no | — |
| 117 | #1891 | — | 15 | 1 | no | Sylow |
| 118 | C23×C3×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C22×D15 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C22×C5×D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 121 | C22×C3×D5 | — | 2 | 1 | no | — |
| 122 | C22×C3×D5 | — | 2 | 1 | no | — |
| 123 | C22×C3×D5 | — | 2 | 1 | no | — |
| 124 | C22×C3×D5 | — | 4 | 2 | no | — |
| 125 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 126 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 127 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 128 | #1220 | — | 2 | 1 | no | — |
| 129 | #1220 | — | 2 | 1 | no | — |
| 130 | C2×Dic15 | — | 2 | 1 | no | — |
| 131 | C2×Dic15 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 132 | C5×#67 | — | 2 | 1 | no | — |
| 133 | C5×#67 | — | 2 | 1 | no | — |
| 134 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 135 | C2×C5×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×C3×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 141 | C2×C3×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 142 | C3×C4×D5 | — | 4 | 1 | no | — |
| 143 | C3×C4×D5 | — | 4 | 1 | no | — |
| 144 | C3×C4×D5 | — | 4 | 1 | no | — |
| 145 | C3×C4×D5 | — | 4 | 1 | no | — |
| 146 | #1204 | — | 2 | 1 | no | — |
| 147 | #1204 | — | 2 | 1 | no | — |
| 148 | #1203 | — | 2 | 1 | no | — |
| 149 | #1203 | — | 2 | 1 | no | — |
| 150 | #1202 | — | 4 | 2 | no | — |
| 151 | #1201 | — | 4 | 2 | no | — |
| 152 | #1200 | — | 2 | 1 | no | — |
| 153 | #1200 | — | 2 | 1 | no | — |
| 154 | D3×Dic5 | — | 2 | 1 | no | — |
| 155 | D3×Dic5 | — | 2 | 1 | no | — |
| 156 | C3⋊#170 | — | 2 | 2 | no | — |
| 157 | C3⋊#170 | — | 4 | 1 | no | — |
| 158 | C3×#170 | — | 2 | 2 | no | — |
| 159 | C3×#170 | — | 4 | 1 | no | — |
| 160 | C23×C3×C4 | — | 5 | 1 | no | — |
| 161 | C2×#235 | — | 5 | 1 | no | — |
| 162 | C2×C3×M16 | — | 5 | 1 | no | — |
| 163 | C2×C3×M16 | — | 5 | 1 | no | — |
| 164 | #953 | — | 5 | 1 | no | — |
| 165 | #953 | — | 5 | 1 | no | — |
| 166 | #930 | — | 10 | 1 | no | — |
| 167 | #929 | — | 5 | 1 | no | — |
| 168 | #929 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 169 | C4×#67 | — | 10 | 1 | no | — |
| 170 | C4×#67 | — | 10 | 1 | no | — |
| 171 | #926 | — | 5 | 1 | no | — |
| 172 | #924 | — | 10 | 1 | no | — |
| 173 | C2×#208 | — | 5 | 1 | no | — |
| 174 | C2×#208 | — | 5 | 1 | no | — |
| 175 | #907 | — | 10 | 2 | no | — |
| 176 | D3×M16 | — | 10 | 1 | no | — |
| 177 | D3×M16 | — | 10 | 1 | no | — |
| 178 | #901 | — | 10 | 2 | no | — |
| 179 | C3×C22⋊C8 | — | 10 | 2 | no | — |
| 180 | #830 | — | 10 | 2 | no | — |
| 181 | #824 | — | 10 | 1 | no | — |
| 182 | #823 | — | 10 | 1 | no | — |
| 183 | C23×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 184 | C2×C5×D4 | — | 3 | 1 | no | — |
| 185 | C22×C4×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 186 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 187 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 188 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 189 | C22×Dic5 | — | 3 | 1 | no | — |
| 190 | C22×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 191 | #711 | — | 6 | 1 | no | — |
| 192 | #711 | — | 6 | 1 | no | — |
| 193 | #711 | — | 6 | 1 | no | — |
| 194 | #711 | — | 6 | 1 | no | — |
| 195 | C2×D20 | — | 6 | 1 | no | — |
| 196 | C2×C4×D5 | — | 2 | 1 | no | — |
| 197 | C2×C4×D5 | — | 2 | 1 | no | — |
| 198 | C2×C4×D5 | — | 2 | 1 | no | — |
| 199 | C2×C4×D5 | — | 2 | 1 | no | — |
| 200 | C2×C4×D5 | — | 2 | 1 | no | — |
| 201 | C2×C4×D5 | — | 2 | 1 | no | — |
| 202 | C2×C4×D5 | — | 3 | 1 | no | — |
| 203 | C2×Dic10 | — | 3 | 1 | no | — |
| 204 | #704 | — | 2 | 1 | no | — |
| 205 | #704 | — | 2 | 1 | no | — |
| 206 | #704 | — | 2 | 1 | no | — |
| 207 | #704 | — | 2 | 1 | no | — |
| 208 | #704 | — | 6 | 2 | no | — |
| 209 | #704 | — | 6 | 1 | no | — |
| 210 | #704 | — | 6 | 1 | no | — |
| 211 | #704 | — | 6 | 1 | no | — |
| 212 | #704 | — | 6 | 1 | no | — |
| 213 | C2×#170 | — | 2 | 1 | no | — |
| 214 | C2×#170 | — | 3 | 2 | no | — |
| 215 | C2×#170 | — | 6 | 2 | no | — |
| 216 | C2×#170 | — | 6 | 1 | no | — |
| 217 | C2×#170 | #67 | 1 | 2 | yes | complemented |
| 218 | #700 | — | 6 | 2 | no | — |
| 219 | D5⋊C8 | — | 6 | 2 | no | — |
| 220 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 221 | C5×C22⋊C4 | — | 3 | 1 | no | — |
| 222 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 223 | C22⋊Dic5 | — | 3 | 1 | no | — |
| 224 | #685 | — | 6 | 1 | no | — |
| 225 | #685 | — | 6 | 1 | no | — |
| 226 | #685 | — | 6 | 1 | no | — |
| 227 | #683 | — | 6 | 1 | no | — |
| 228 | #683 | — | 6 | 1 | no | — |
| 229 | C4×Dic5 | — | 6 | 1 | no | — |
| 230 | #568 | — | 15 | 1 | no | — |
| 231 | #525 | — | 15 | 1 | no | — |
| 232 | #413 | — | 15 | 1 | no | — |
| 233 | #407 | — | 5 | 1 | no | — |
| 234 | #407 | — | 15 | 1 | no | — |
| 235 | #344 | — | 15 | 1 | no | — |
| 236 | #344 | — | 15 | 1 | no | — |
| 237 | C22×C3×C5 | — | 4 | 1 | no | — |
| 238 | C22×C3×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 239 | C22×C3×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 240 | C22×C3×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×D15 | — | 2 | 1 | no | — |
| 242 | C2×D15 | — | 4 | 1 | no | — |
| 243 | C2×C5×D3 | — | 2 | 1 | no | — |
| 244 | C2×C5×D3 | — | 4 | 1 | no | — |
| 245 | C2×C3×D5 | — | 2 | 2 | no | — |
| 246 | C2×C3×D5 | — | 2 | 2 | no | — |
| 247 | C2×C3×D5 | — | 2 | 2 | no | — |
| 248 | C2×C3×D5 | — | 4 | 1 | no | — |
| 249 | C2×C3×D5 | — | 4 | 1 | no | — |
| 250 | C2×C3×D5 | — | 4 | 1 | no | — |
| 251 | C2×C3×D5 | — | 4 | 1 | no | — |
| 252 | C3×C4×C5 | — | 4 | 1 | no | — |
| 253 | Dic15 | — | 2 | 1 | no | — |
| 254 | Dic15 | — | 4 | 1 | no | — |
| 255 | C3×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 256 | C3×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 257 | C3×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 258 | C3×Dic5 | #123 | 1 | 1 | yes | characteristic |
| 259 | C5×Dic3 | — | 2 | 1 | no | — |
| 260 | C5×Dic3 | — | 4 | 1 | no | — |
| 261 | C24×C3 | — | 5 | 1 | no | — |
| 262 | C22×C3×C4 | — | 5 | 1 | no | — |
| 263 | C22×C3×C4 | — | 10 | 1 | no | — |
| 264 | C22×C3×C4 | — | 10 | 1 | no | — |
| 265 | C22×C3×C4 | — | 10 | 1 | no | — |
| 266 | C22×C3×C4 | — | 10 | 1 | no | — |
| 267 | C22×C3×C4 | — | 10 | 1 | no | — |
| 268 | C22×C3×C4 | — | 10 | 1 | no | — |
| 269 | C22×C3×C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 270 | C2×#67 | — | 5 | 1 | no | — |
| 271 | C2×#67 | — | 10 | 1 | no | — |
| 272 | C2×#67 | — | 10 | 1 | no | — |
| 273 | C2×#67 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 274 | #235 | — | 10 | 1 | no | — |
| 275 | #235 | — | 10 | 1 | no | — |
| 276 | #235 | — | 10 | 1 | no | — |
| 277 | #235 | — | 10 | 1 | no | — |
| 278 | C2×D12 | — | 5 | 1 | no | — |
| 279 | C2×C4×D3 | — | 5 | 1 | no | — |
| 280 | C2×C4×D3 | — | 5 | 1 | no | — |
| 281 | C2×Dic6 | — | 5 | 1 | no | — |
| 282 | C3×M16 | — | 10 | 1 | no | — |
| 283 | C3×M16 | — | 10 | 1 | no | — |
| 284 | C3×M16 | — | 10 | 1 | no | — |
| 285 | C3×M16 | — | 10 | 1 | no | — |
| 286 | C2×C3×C8 | — | 5 | 2 | no | — |
| 287 | C2×C3×C8 | — | 10 | 1 | no | — |
| 288 | #217 | — | 5 | 1 | no | — |
| 289 | #217 | — | 10 | 1 | no | — |
| 290 | #217 | — | 10 | 1 | no | — |
| 291 | #217 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 292 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 293 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 294 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 295 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 296 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 297 | C4×Dic3 | — | 10 | 1 | no | — |
| 298 | #208 | — | 10 | 1 | no | — |
| 299 | #208 | — | 10 | 1 | no | — |
| 300 | #208 | — | 10 | 1 | no | — |
| 301 | #208 | — | 10 | 1 | no | — |
| 302 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 303 | C2×C3⋊C8 | — | 10 | 1 | no | — |
| 304 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 305 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 306 | D3×C8 | — | 10 | 2 | no | — |
| 307 | D3×C8 | — | 10 | 2 | no | — |
| 308 | C23×C5 | — | 3 | 1 | no | — |
| 309 | C23×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 310 | C22×D5 | — | 2 | 1 | no | — |
| 311 | C22×D5 | — | 2 | 1 | no | — |
| 312 | C22×D5 | — | 2 | 1 | no | — |
| 313 | C22×D5 | — | 3 | 1 | no | — |
| 314 | C22×D5 | — | 4 | 2 | no | — |
| 315 | C5×D4 | — | 6 | 1 | no | — |
| 316 | C5×D4 | — | 6 | 1 | no | — |
| 317 | C2×C4×C5 | — | 2 | 1 | no | — |
| 318 | C2×C4×C5 | — | 2 | 1 | no | — |
| 319 | C2×C4×C5 | — | 2 | 1 | no | — |
| 320 | C2×C4×C5 | — | 3 | 1 | no | — |
| 321 | C2×C4×C5 | — | 6 | 1 | no | — |
| 322 | C22⋊D5 | — | 6 | 1 | no | — |
| 323 | C22⋊D5 | — | 6 | 1 | no | — |
| 324 | C22⋊D5 | — | 6 | 1 | no | — |
| 325 | C22⋊D5 | — | 6 | 1 | no | — |
| 326 | C22⋊D5 | — | 12 | 2 | no | — |
| 327 | C2×Dic5 | — | 3 | 1 | no | — |
| 328 | C2×Dic5 | — | 6 | 1 | no | — |
| 329 | C2×Dic5 | — | 6 | 1 | no | — |
| 330 | C2×Dic5 | — | 6 | 1 | no | — |
| 331 | C2×Dic5 | #235 | 1 | 1 | yes | characteristic |
| 332 | C2×Dic5 | D3×D4 | 1 | 1 | yes | characteristic |
| 333 | C2×Dic5 | D3×D4 | 1 | 1 | yes | characteristic |
| 334 | C2×Dic5 | D3×D4 | 1 | 1 | yes | characteristic |
| 335 | C2×Dic5 | #237 | 1 | 1 | yes | characteristic |
| 336 | C2×Dic5 | C2×#67 | 1 | 1 | yes | characteristic |
| 337 | D20 | — | 12 | 2 | no | — |
| 338 | C4×D5 | — | 4 | 1 | no | — |
| 339 | C4×D5 | — | 4 | 1 | no | — |
| 340 | C4×D5 | — | 4 | 1 | no | — |
| 341 | C4×D5 | — | 4 | 1 | no | — |
| 342 | C4×D5 | — | 6 | 1 | no | — |
| 343 | C4×D5 | — | 6 | 1 | no | — |
| 344 | Dic10 | — | 6 | 1 | no | — |
| 345 | Dic10 | — | 6 | 1 | no | — |
| 346 | #170 | — | 2 | 2 | no | — |
| 347 | #170 | — | 4 | 1 | no | — |
| 348 | #170 | — | 6 | 2 | no | — |
| 349 | #170 | — | 12 | 1 | no | — |
| 350 | C2×#41 | — | 15 | 1 | no | — |
| 351 | C23×C4 | — | 5 | 1 | no | — |
| 352 | #131 | — | 30 | 2 | no | — |
| 353 | #131 | — | 30 | 2 | no | — |
| 354 | C2×M16 | — | 5 | 1 | no | — |
| 355 | C2×M16 | — | 5 | 1 | no | — |
| 356 | C2×M16 | — | 15 | 1 | no | — |
| 357 | C2×M16 | — | 15 | 1 | no | — |
| 358 | C2×M16 | — | 30 | 1 | no | — |
| 359 | C2×M16 | — | 30 | 1 | no | — |
| 360 | #123 | — | 3 | 1 | no | — |
| 361 | #123 | — | 15 | 1 | no | — |
| 362 | C22⋊Q8 | — | 30 | 1 | no | — |
| 363 | #121 | — | 30 | 1 | no | — |
| 364 | #120 | — | 15 | 1 | no | — |
| 365 | #120 | — | 15 | 1 | no | — |
| 366 | C4×D4 | — | 30 | 1 | no | — |
| 367 | C4×D4 | — | 30 | 1 | no | — |
| 368 | #117 | — | 15 | 1 | no | — |
| 369 | #101 | — | 30 | 1 | no | — |
| 370 | #100 | — | 30 | 1 | no | — |
| 371 | C22⋊C8 | — | 10 | 2 | no | — |
| 372 | C22⋊C8 | — | 30 | 2 | no | — |
| 373 | C2×C3×C5 | — | 2 | 1 | no | — |
| 374 | C2×C3×C5 | — | 2 | 1 | no | — |
| 375 | C2×C3×C5 | — | 2 | 1 | no | — |
| 376 | C2×C3×C5 | #386 | 1 | 1 | yes | characteristic |
| 377 | D15 | — | 4 | 1 | no | — |
| 378 | C3×D5 | — | 4 | 2 | no | — |
| 379 | C5×D3 | — | 4 | 1 | no | — |
| 380 | C23×C3 | — | 10 | 1 | no | — |
| 381 | C23×C3 | — | 10 | 1 | no | — |
| 382 | C23×C3 | — | 10 | 1 | no | — |
| 383 | C23×C3 | — | 20 | 2 | no | — |
| 384 | C23×C3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 385 | C22×D3 | — | 5 | 1 | no | — |
| 386 | C22×D3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 387 | C2×C3×C4 | — | 2 | 1 | no | — |
| 388 | C2×C3×C4 | — | 2 | 1 | no | — |
| 389 | C2×C3×C4 | — | 2 | 1 | no | — |
| 390 | C2×C3×C4 | — | 5 | 1 | no | — |
| 391 | C2×C3×C4 | — | 5 | 1 | no | — |
| 392 | C2×C3×C4 | — | 5 | 1 | no | — |
| 393 | C2×C3×C4 | — | 5 | 1 | no | — |
| 394 | C2×C3×C4 | — | 5 | 1 | no | — |
| 395 | C2×C3×C4 | — | 5 | 1 | no | — |
| 396 | C2×C3×C4 | — | 20 | 1 | no | — |
| 397 | C2×C3×C4 | — | 20 | 1 | no | — |
| 398 | C2×C3×C4 | — | 20 | 1 | no | — |
| 399 | C2×C3×C4 | — | 20 | 1 | no | — |
| 400 | #67 | — | 2 | 1 | no | — |
| 401 | #67 | — | 2 | 1 | no | — |
| 402 | #67 | — | 10 | 1 | no | — |
| 403 | #67 | — | 10 | 1 | no | — |
| 404 | #67 | — | 20 | 2 | no | — |
| 405 | #67 | — | 20 | 2 | no | — |
| 406 | C2×Dic3 | — | 2 | 1 | no | — |
| 407 | C2×Dic3 | — | 5 | 1 | no | — |
| 408 | C2×Dic3 | — | 10 | 1 | no | — |
| 409 | C2×Dic3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 410 | D12 | — | 10 | 1 | no | — |
| 411 | D12 | — | 10 | 1 | no | — |
| 412 | C4×D3 | — | 10 | 1 | no | — |
| 413 | C4×D3 | — | 10 | 1 | no | — |
| 414 | C4×D3 | — | 10 | 1 | no | — |
| 415 | C4×D3 | — | 10 | 1 | no | — |
| 416 | Dic6 | — | 10 | 1 | no | — |
| 417 | Dic6 | — | 10 | 1 | no | — |
| 418 | C3×C8 | — | 10 | 2 | no | — |
| 419 | C3×C8 | — | 20 | 1 | no | — |
| 420 | C3⋊C8 | — | 10 | 2 | no | — |
| 421 | C3⋊C8 | — | 20 | 1 | no | — |
| 422 | C22×C5 | — | 4 | 1 | no | — |
| 423 | C22×C5 | — | 6 | 1 | no | — |
| 424 | C22×C5 | — | 12 | 1 | no | — |
| 425 | C22×C5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 426 | C22×C5 | #67⋊C4 | 1 | 1 | yes | characteristic |
| 427 | C22×C5 | C4×#67 | 1 | 1 | yes | characteristic |
| 428 | C2×D5 | — | 2 | 2 | no | — |
| 429 | C2×D5 | — | 2 | 2 | no | — |
| 430 | C2×D5 | — | 2 | 2 | no | — |
| 431 | C2×D5 | — | 4 | 1 | no | — |
| 432 | C2×D5 | — | 4 | 1 | no | — |
| 433 | C2×D5 | — | 4 | 1 | no | — |
| 434 | C2×D5 | — | 4 | 1 | no | — |
| 435 | C2×D5 | — | 6 | 1 | no | — |
| 436 | C2×D5 | — | 12 | 1 | no | — |
| 437 | C4×C5 | — | 4 | 1 | no | — |
| 438 | C4×C5 | — | 6 | 1 | no | — |
| 439 | C4×C5 | — | 12 | 1 | no | — |
| 440 | Dic5 | — | 6 | 1 | no | — |
| 441 | Dic5 | — | 12 | 1 | no | — |
| 442 | Dic5 | #883 | 1 | 1 | yes | characteristic |
| 443 | Dic5 | #884 | 1 | 1 | yes | characteristic |
| 444 | Dic5 | #937 | 1 | 1 | yes | characteristic |
| 445 | Dic5 | #938 | 1 | 1 | yes | characteristic |
| 446 | C24 | — | 5 | 1 | no | — |
| 447 | #41 | — | 30 | 1 | no | — |
| 448 | #41 | — | 30 | 1 | no | — |
| 449 | #41 | — | 30 | 1 | no | — |
| 450 | #41 | — | 30 | 1 | no | — |
| 451 | C2×Q8 | — | 15 | 1 | no | — |
| 452 | C2×D4 | — | 3 | 1 | no | — |
| 453 | C2×D4 | — | 15 | 1 | no | — |
| 454 | C2×D4 | — | 15 | 1 | no | — |
| 455 | C2×D4 | — | 30 | 1 | no | — |
| 456 | C2×D4 | — | 30 | 1 | no | — |
| 457 | C22×C4 | — | 5 | 1 | no | — |
| 458 | C22×C4 | — | 10 | 1 | no | — |
| 459 | C22×C4 | — | 10 | 1 | no | — |
| 460 | C22×C4 | — | 10 | 1 | no | — |
| 461 | C22×C4 | — | 10 | 1 | no | — |
| 462 | C22×C4 | — | 10 | 1 | no | — |
| 463 | C22×C4 | — | 10 | 1 | no | — |
| 464 | C22×C4 | — | 15 | 1 | no | — |
| 465 | C22×C4 | — | 15 | 1 | no | — |
| 466 | C22×C4 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 467 | M16 | — | 10 | 1 | no | — |
| 468 | M16 | — | 10 | 1 | no | — |
| 469 | M16 | — | 10 | 1 | no | — |
| 470 | M16 | — | 10 | 1 | no | — |
| 471 | M16 | — | 30 | 2 | no | — |
| 472 | M16 | — | 30 | 2 | no | — |
| 473 | M16 | — | 30 | 1 | no | — |
| 474 | M16 | — | 30 | 1 | no | — |
| 475 | M16 | — | 30 | 1 | no | — |
| 476 | M16 | — | 30 | 1 | no | — |
| 477 | C2×C8 | — | 5 | 2 | no | — |
| 478 | C2×C8 | — | 10 | 1 | no | — |
| 479 | C2×C8 | — | 15 | 2 | no | — |
| 480 | C2×C8 | — | 30 | 2 | no | — |
| 481 | C2×C8 | — | 30 | 2 | no | — |
| 482 | C2×C8 | — | 30 | 1 | no | — |
| 483 | C4⋊C4 | — | 6 | 1 | no | — |
| 484 | C4⋊C4 | — | 30 | 1 | no | — |
| 485 | C4⋊C4 | — | 30 | 1 | no | — |
| 486 | C22⋊C4 | — | 3 | 1 | no | — |
| 487 | C22⋊C4 | — | 6 | 1 | no | — |
| 488 | C22⋊C4 | — | 15 | 1 | no | — |
| 489 | C22⋊C4 | — | 30 | 1 | no | — |
| 490 | C22⋊C4 | — | 30 | 1 | no | — |
| 491 | C22⋊C4 | — | 30 | 1 | no | — |
| 492 | C42 | — | 30 | 1 | no | — |
| 493 | C3×C5 | #1891 | 1 | 1 | yes | characteristic, complemented, Hall |
| 494 | C22×C3 | — | 4 | 1 | no | — |
| 495 | C22×C3 | — | 10 | 2 | no | — |
| 496 | C22×C3 | — | 10 | 2 | no | — |
| 497 | C22×C3 | — | 10 | 2 | no | — |
| 498 | C22×C3 | — | 20 | 1 | no | — |
| 499 | C22×C3 | — | 20 | 1 | no | — |
| 500 | C22×C3 | — | 20 | 1 | no | — |
| 501 | C22×C3 | — | 20 | 1 | no | — |
| 502 | C22×C3 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 503 | C22×C3 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 504 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 505 | C2×D3 | — | 2 | 1 | no | — |
| 506 | C2×D3 | — | 4 | 1 | no | — |
| 507 | C2×D3 | — | 10 | 1 | no | — |
| 508 | C2×D3 | — | 20 | 1 | no | — |
| 509 | C3×C4 | — | 4 | 1 | no | — |
| 510 | C3×C4 | — | 5 | 1 | no | — |
| 511 | C3×C4 | — | 5 | 1 | no | — |
| 512 | C3×C4 | — | 5 | 1 | no | — |
| 513 | C3×C4 | — | 5 | 1 | no | — |
| 514 | Dic3 | — | 2 | 1 | no | — |
| 515 | Dic3 | — | 4 | 1 | no | — |
| 516 | Dic3 | — | 10 | 1 | no | — |
| 517 | Dic3 | — | 20 | 1 | no | — |
| 518 | C2×C5 | — | 2 | 1 | no | — |
| 519 | C2×C5 | — | 2 | 1 | no | — |
| 520 | C2×C5 | — | 2 | 1 | no | — |
| 521 | C2×C5 | — | 12 | 1 | no | — |
| 522 | C2×C5 | #4956 | 1 | 1 | yes | characteristic |
| 523 | D5 | — | 4 | 2 | no | — |
| 524 | D5 | — | 12 | 1 | no | — |
| 525 | C23 | — | 3 | 1 | no | — |
| 526 | C23 | — | 10 | 1 | no | — |
| 527 | C23 | — | 10 | 1 | no | — |
| 528 | C23 | — | 10 | 1 | no | — |
| 529 | C23 | — | 15 | 1 | no | — |
| 530 | C23 | — | 20 | 2 | no | — |
| 531 | C23 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 532 | Q8 | — | 30 | 1 | no | — |
| 533 | Q8 | — | 30 | 1 | no | — |
| 534 | D4 | — | 6 | 1 | no | — |
| 535 | D4 | — | 6 | 1 | no | — |
| 536 | D4 | — | 30 | 1 | no | — |
| 537 | D4 | — | 30 | 1 | no | — |
| 538 | D4 | — | 30 | 1 | no | — |
| 539 | D4 | — | 30 | 1 | no | — |
| 540 | D4 | — | 60 | 2 | no | — |
| 541 | D4 | — | 60 | 2 | no | — |
| 542 | C2×C4 | — | 2 | 1 | no | — |
| 543 | C2×C4 | — | 2 | 1 | no | — |
| 544 | C2×C4 | — | 2 | 1 | no | — |
| 545 | C2×C4 | — | 3 | 1 | no | — |
| 546 | C2×C4 | — | 5 | 1 | no | — |
| 547 | C2×C4 | — | 5 | 1 | no | — |
| 548 | C2×C4 | — | 5 | 1 | no | — |
| 549 | C2×C4 | — | 5 | 1 | no | — |
| 550 | C2×C4 | — | 5 | 1 | no | — |
| 551 | C2×C4 | — | 5 | 1 | no | — |
| 552 | C2×C4 | — | 6 | 1 | no | — |
| 553 | C2×C4 | — | 15 | 1 | no | — |
| 554 | C2×C4 | — | 20 | 1 | no | — |
| 555 | C2×C4 | — | 20 | 1 | no | — |
| 556 | C2×C4 | — | 20 | 1 | no | — |
| 557 | C2×C4 | — | 20 | 1 | no | — |
| 558 | C2×C4 | — | 30 | 1 | no | — |
| 559 | C2×C4 | — | 30 | 1 | no | — |
| 560 | C2×C4 | — | 30 | 1 | no | — |
| 561 | C2×C4 | — | 30 | 1 | no | — |
| 562 | C2×C4 | — | 30 | 1 | no | — |
| 563 | C8 | — | 10 | 2 | no | — |
| 564 | C8 | — | 20 | 1 | no | — |
| 565 | C8 | — | 30 | 2 | no | — |
| 566 | C8 | — | 60 | 1 | no | — |
| 567 | C2×C3 | — | 2 | 1 | no | — |
| 568 | C2×C3 | — | 2 | 1 | no | — |
| 569 | C2×C3 | — | 2 | 1 | no | — |
| 570 | C2×C3 | — | 20 | 2 | no | — |
| 571 | C2×C3 | #65779 | 1 | 1 | yes | characteristic |
| 572 | D3 | — | 4 | 1 | no | — |
| 573 | D3 | — | 20 | 1 | no | — |
| 574 | C5 | #69992 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 575 | C22 | — | 4 | 1 | no | — |
| 576 | C22 | — | 6 | 1 | no | — |
| 577 | C22 | — | 10 | 2 | no | — |
| 578 | C22 | — | 10 | 2 | no | — |
| 579 | C22 | — | 10 | 2 | no | — |
| 580 | C22 | — | 12 | 1 | no | — |
| 581 | C22 | — | 20 | 1 | no | — |
| 582 | C22 | — | 20 | 1 | no | — |
| 583 | C22 | — | 20 | 1 | no | — |
| 584 | C22 | — | 20 | 1 | no | — |
| 585 | C22 | — | 30 | 1 | no | — |
| 586 | C22 | — | 60 | 1 | no | — |
| 587 | C22 | AGL(1,𝔽5)×#67 | 1 | 1 | yes | characteristic |
| 588 | C22 | D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 589 | C22 | #67⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 590 | C4 | — | 4 | 1 | no | — |
| 591 | C4 | — | 5 | 1 | no | — |
| 592 | C4 | — | 5 | 1 | no | — |
| 593 | C4 | — | 5 | 1 | no | — |
| 594 | C4 | — | 5 | 1 | no | — |
| 595 | C4 | — | 6 | 1 | no | — |
| 596 | C4 | — | 12 | 1 | no | — |
| 597 | C4 | — | 30 | 1 | no | — |
| 598 | C4 | — | 60 | 1 | no | — |
| 599 | C3 | #10604535 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 600 | C2 | — | 2 | 1 | no | — |
| 601 | C2 | — | 2 | 1 | no | — |
| 602 | C2 | — | 2 | 1 | no | — |
| 603 | C2 | — | 12 | 1 | no | — |
| 604 | C2 | — | 20 | 2 | no | — |
| 605 | C2 | — | 60 | 1 | no | — |
| 606 | C2 | #11752055 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756863 | C2 | semidirect |
| 3. #11752414 | C2 | semidirect |
| 4. C3×#65755 | C2 | semidirect |
| 5. #11752008 | C2 | semidirect |
| 6. #11746576 | C2 | semidirect |
| 7. #11746575 | C2 | semidirect |
| 37. #65755 | D3 | semidirect |
| 66. C2×C3⋊#170 | D4 | semidirect |
| 72. C2×C3×#170 | D4 | semidirect |
| 217. C2×#170 | #67 | semidirect |
| 493. C3×C5 | #1891 | semidirect |
| 574. C5 | #69992 | semidirect |
| 599. C3 | #10604535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756863 | 2 |
| #11754316 | 2 |
| #11752414 | 2 |
| C3×#65755 | 2 |
| #11752008 | 2 |
| #11746576 | 2 |
| #11746575 | 2 |
| #10604535 | 3 |
| #69992 | 5 |