Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1096 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 1096 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #11757034 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11752436 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#65775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11752008 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11751999 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10605018 | — | 3 | 1 | no | maximal, Hall |
| 7 | #92095 | C4 | 1 | 1 | yes | characteristic |
| 8 | C5×#1004 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×C3×#711 | C22 | 1 | 1 | yes | characteristic |
| 10 | #92049 | — | 2 | 1 | no | — |
| 11 | #92049 | C4 | 1 | 2 | yes | — |
| 12 | C2×#6782 | — | 2 | 1 | no | — |
| 13 | C2×#6782 | C22 | 1 | 2 | yes | — |
| 14 | #92027 | — | 2 | 2 | no | — |
| 15 | #92024 | — | 2 | 2 | no | — |
| 16 | D3×#711 | — | 2 | 2 | no | — |
| 17 | #92020 | — | 2 | 2 | no | — |
| 18 | D5×#235 | — | 2 | 1 | no | — |
| 19 | #92004 | — | 2 | 1 | no | — |
| 20 | C2×#6762 | C22 | 1 | 2 | yes | complemented |
| 21 | C2×C3×#704 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22×C3×#170 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #91242 | — | 2 | 1 | no | — |
| 24 | #91234 | — | 2 | 1 | no | — |
| 25 | C3×C22⋊#170 | — | 2 | 1 | no | — |
| 26 | C3×#4003 | — | 2 | 1 | no | — |
| 27 | #91175 | — | 2 | 2 | no | — |
| 28 | #91174 | — | 2 | 2 | no | — |
| 29 | #91171 | — | 2 | 2 | no | — |
| 30 | (C2×D3)⋊#170 | — | 2 | 2 | no | — |
| 31 | #70009 | — | 5 | 1 | no | maximal, Hall |
| 32 | #66285 | — | 3 | 1 | no | — |
| 33 | #65777 | — | 3 | 1 | no | — |
| 34 | #65777 | — | 3 | 2 | no | — |
| 35 | #65775 | — | 3 | 2 | no | — |
| 36 | #65775 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×C3×C5×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×#1220 | — | 2 | 1 | no | — |
| 39 | C2×#1220 | C2×C4 | 1 | 2 | yes | — |
| 40 | #6819 | — | 2 | 2 | no | — |
| 41 | D4×D15 | — | 2 | 2 | no | — |
| 42 | #6817 | — | 2 | 1 | no | — |
| 43 | C2×C5×#67 | — | 2 | 1 | no | — |
| 44 | C2×C5×#67 | C2×C4 | 1 | 2 | yes | — |
| 45 | C5×#237 | — | 2 | 2 | no | — |
| 46 | C5×D3×D4 | — | 2 | 2 | no | — |
| 47 | C5×#235 | — | 2 | 1 | no | — |
| 48 | C2×C3×C22⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×C22⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 50 | C22×C3×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 51 | C22×C3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 52 | C3×#711 | — | 2 | 2 | no | — |
| 53 | C3×#711 | — | 2 | 2 | no | — |
| 54 | C2×C3×C4×D5 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×C3×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 56 | #6790 | — | 2 | 2 | no | — |
| 57 | #6790 | — | 2 | 2 | no | — |
| 58 | D3×C22⋊D5 | — | 2 | 2 | no | — |
| 59 | D3×C22⋊D5 | — | 2 | 2 | no | — |
| 60 | D5×#67 | — | 2 | 2 | no | — |
| 61 | C2×#1204 | — | 2 | 1 | no | — |
| 62 | C2×#1204 | D4 | 1 | 2 | yes | — |
| 63 | C2×#1203 | — | 2 | 1 | no | — |
| 64 | C2×#1203 | D4 | 1 | 2 | yes | — |
| 65 | C2×#1200 | — | 2 | 1 | no | — |
| 66 | C2×#1200 | D4 | 1 | 2 | yes | — |
| 67 | #6782 | — | 2 | 2 | no | — |
| 68 | #6782 | — | 2 | 2 | no | — |
| 69 | #6782 | — | 2 | 2 | no | — |
| 70 | #6782 | — | 2 | 2 | no | — |
| 71 | #6782 | — | 2 | 2 | no | — |
| 72 | #6782 | — | 2 | 2 | no | — |
| 73 | #6782 | — | 2 | 2 | no | — |
| 74 | C2×D3×Dic5 | — | 2 | 1 | no | — |
| 75 | C2×D3×Dic5 | D4 | 1 | 2 | yes | — |
| 76 | #6780 | — | 2 | 2 | no | — |
| 77 | #6780 | — | 2 | 2 | no | — |
| 78 | #6779 | — | 2 | 2 | no | — |
| 79 | #6779 | — | 2 | 2 | no | — |
| 80 | D5×D12 | — | 2 | 1 | no | — |
| 81 | C4×D3×D5 | — | 2 | 2 | no | — |
| 82 | #6773 | — | 2 | 1 | no | — |
| 83 | #6772 | — | 2 | 1 | no | — |
| 84 | #6771 | — | 2 | 2 | no | — |
| 85 | D15⋊Q8 | — | 2 | 2 | no | — |
| 86 | #6769 | — | 2 | 2 | no | — |
| 87 | #6768 | — | 2 | 2 | no | — |
| 88 | D3×Dic10 | — | 2 | 2 | no | — |
| 89 | D5×Dic6 | — | 2 | 1 | no | — |
| 90 | #6762 | — | 2 | 2 | no | — |
| 91 | #6762 | — | 2 | 2 | no | — |
| 92 | C2×C3⋊#170 | — | 2 | 2 | no | — |
| 93 | C3×#704 | — | 2 | 2 | no | — |
| 94 | C2×C3×#170 | — | 2 | 2 | no | — |
| 95 | C2×C3×#170 | — | 2 | 1 | no | — |
| 96 | C2×C3×#170 | — | 2 | 1 | no | — |
| 97 | #5964 | — | 5 | 1 | no | — |
| 98 | C3×#408 | — | 5 | 1 | no | — |
| 99 | #5237 | — | 5 | 1 | no | — |
| 100 | #5132 | — | 5 | 2 | no | — |
| 101 | #5110 | — | 5 | 2 | no | — |
| 102 | C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 103 | #4150 | — | 6 | 2 | no | — |
| 104 | #4150 | — | 6 | 1 | no | — |
| 105 | D5×#41 | — | 6 | 2 | no | — |
| 106 | D5×#41 | — | 6 | 1 | no | — |
| 107 | #4144 | — | 3 | 1 | no | — |
| 108 | #4144 | — | 3 | 2 | no | — |
| 109 | #4144 | — | 6 | 2 | no | — |
| 110 | #4144 | — | 6 | 1 | no | — |
| 111 | C2×#711 | — | 3 | 2 | no | — |
| 112 | C2×#711 | — | 6 | 2 | no | — |
| 113 | C2×#711 | — | 6 | 1 | no | — |
| 114 | C2×#711 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | C2×#704 | — | 3 | 2 | no | — |
| 116 | C2×#704 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 117 | C22×#170 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 118 | #4013 | — | 6 | 2 | no | — |
| 119 | #4013 | — | 6 | 1 | no | — |
| 120 | C22⋊#170 | — | 2 | 1 | no | — |
| 121 | C22⋊#170 | — | 6 | 2 | no | — |
| 122 | #4005 | — | 6 | 2 | no | — |
| 123 | #4005 | — | 6 | 1 | no | — |
| 124 | #4003 | — | 2 | 1 | no | — |
| 125 | #4003 | — | 6 | 2 | no | — |
| 126 | #1791 | — | 15 | 1 | no | Sylow |
| 127 | C23×C3×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C23×C3×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C22×D15 | — | 2 | 1 | no | — |
| 130 | C22×D15 | C22⋊C4 | 1 | 2 | yes | — |
| 131 | C22×C5×D3 | — | 2 | 1 | no | — |
| 132 | C22×C5×D3 | C22⋊C4 | 1 | 2 | yes | — |
| 133 | C22×C3×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 134 | C2×D3×D5 | — | 2 | 2 | no | — |
| 135 | C3×C5×D4 | — | 2 | 2 | no | — |
| 136 | C2×C3×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 137 | #1220 | — | 2 | 2 | no | — |
| 138 | #1220 | — | 2 | 2 | no | — |
| 139 | #1220 | — | 2 | 2 | no | — |
| 140 | C2×Dic15 | — | 2 | 1 | no | — |
| 141 | C2×Dic15 | C22⋊C4 | 1 | 2 | yes | — |
| 142 | D60 | — | 2 | 1 | no | — |
| 143 | C4×D15 | — | 2 | 2 | no | — |
| 144 | Dic30 | — | 2 | 1 | no | — |
| 145 | C5×#67 | — | 2 | 2 | no | — |
| 146 | C5×#67 | — | 2 | 2 | no | — |
| 147 | C5×#67 | — | 2 | 2 | no | — |
| 148 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 149 | C2×C5×Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 150 | C5×D12 | — | 2 | 1 | no | — |
| 151 | C4×C5×D3 | — | 2 | 2 | no | — |
| 152 | C5×Dic6 | — | 2 | 1 | no | — |
| 153 | C3×C22⋊D5 | — | 2 | 2 | no | — |
| 154 | C3×C22⋊D5 | — | 2 | 2 | no | — |
| 155 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 156 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 157 | C2×C3×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C3×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 160 | C2×C3×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C3×C4×D5 | — | 2 | 1 | no | — |
| 163 | C3×C4×D5 | — | 2 | 1 | no | — |
| 164 | C3×Dic10 | — | 2 | 2 | no | — |
| 165 | #1204 | — | 2 | 2 | no | — |
| 166 | #1204 | — | 2 | 2 | no | — |
| 167 | #1204 | — | 2 | 2 | no | — |
| 168 | #1203 | — | 2 | 2 | no | — |
| 169 | #1203 | — | 2 | 2 | no | — |
| 170 | #1203 | — | 2 | 2 | no | — |
| 171 | #1202 | — | 2 | 2 | no | — |
| 172 | #1201 | — | 2 | 2 | no | — |
| 173 | #1200 | — | 2 | 2 | no | — |
| 174 | #1200 | — | 2 | 2 | no | — |
| 175 | #1200 | — | 2 | 2 | no | — |
| 176 | D3×Dic5 | — | 2 | 2 | no | — |
| 177 | D3×Dic5 | — | 2 | 2 | no | — |
| 178 | D3×Dic5 | — | 2 | 2 | no | — |
| 179 | D5×Dic3 | — | 2 | 2 | no | — |
| 180 | C3⋊#170 | — | 4 | 2 | no | — |
| 181 | C3×#170 | — | 4 | 1 | no | — |
| 182 | C3×#170 | — | 4 | 1 | no | — |
| 183 | C2×C3×#41 | — | 5 | 1 | no | — |
| 184 | #1010 | — | 10 | 2 | no | — |
| 185 | #1009 | — | 10 | 2 | no | — |
| 186 | D3×#41 | — | 10 | 2 | no | — |
| 187 | D3×#41 | — | 10 | 2 | no | — |
| 188 | #1007 | — | 10 | 1 | no | — |
| 189 | #1004 | — | 5 | 1 | no | — |
| 190 | #1004 | — | 5 | 2 | no | — |
| 191 | #1004 | — | 10 | 1 | no | — |
| 192 | #1004 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 193 | C2×#235 | — | 5 | 2 | no | — |
| 194 | C2×#235 | — | 10 | 1 | no | — |
| 195 | C2×#235 | — | 10 | 1 | no | — |
| 196 | C2×C3×M16 | — | 5 | 1 | no | — |
| 197 | C22×C3×C8 | — | 5 | 1 | no | — |
| 198 | C2×#208 | — | 5 | 2 | no | — |
| 199 | C3×C22⋊C8 | — | 10 | 1 | no | — |
| 200 | C3×C22⋊C8 | — | 10 | 1 | no | — |
| 201 | #836 | — | 10 | 1 | no | — |
| 202 | #833 | — | 10 | 1 | no | — |
| 203 | #824 | — | 10 | 2 | no | — |
| 204 | #823 | — | 10 | 2 | no | — |
| 205 | (C2×D3)⋊C8 | — | 10 | 2 | no | — |
| 206 | (C2×D3)⋊C8 | — | 10 | 2 | no | — |
| 207 | C5×#41 | — | 6 | 2 | no | — |
| 208 | C5×#41 | — | 6 | 1 | no | — |
| 209 | C2×C5×D4 | — | 3 | 2 | no | — |
| 210 | C2×C5×D4 | — | 6 | 2 | no | — |
| 211 | C2×C5×D4 | — | 6 | 1 | no | — |
| 212 | C2×C5×D4 | C4×D3 | 1 | 1 | yes | characteristic |
| 213 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 214 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 215 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 216 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 217 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 218 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 219 | C2×C22⋊D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 220 | C2×C22⋊D5 | D12 | 1 | 1 | yes | characteristic |
| 221 | C22×Dic5 | — | 3 | 2 | no | — |
| 222 | C22×Dic5 | — | 6 | 1 | no | — |
| 223 | C22×Dic5 | #67 | 1 | 1 | yes | characteristic |
| 224 | C22×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 225 | #713 | — | 6 | 1 | no | — |
| 226 | Q8×D5 | — | 6 | 2 | no | — |
| 227 | Q8×D5 | — | 6 | 1 | no | — |
| 228 | #711 | — | 2 | 2 | no | — |
| 229 | #711 | — | 2 | 2 | no | — |
| 230 | #711 | — | 6 | 2 | no | — |
| 231 | #711 | — | 6 | 1 | no | — |
| 232 | #711 | — | 6 | 2 | no | — |
| 233 | #711 | — | 6 | 2 | no | — |
| 234 | #711 | — | 6 | 2 | no | — |
| 235 | #711 | — | 6 | 2 | no | — |
| 236 | #711 | — | 6 | 2 | no | — |
| 237 | #711 | — | 6 | 2 | no | — |
| 238 | #711 | — | 6 | 2 | no | — |
| 239 | #711 | — | 6 | 2 | no | — |
| 240 | #711 | — | 6 | 2 | no | — |
| 241 | #711 | — | 6 | 2 | no | — |
| 242 | D4×D5 | — | 6 | 1 | no | — |
| 243 | D4×D5 | — | 6 | 2 | no | — |
| 244 | D4×D5 | — | 6 | 2 | no | — |
| 245 | D4×D5 | — | 6 | 2 | no | — |
| 246 | D4×D5 | — | 6 | 2 | no | — |
| 247 | #709 | — | 6 | 2 | no | — |
| 248 | #709 | — | 6 | 2 | no | — |
| 249 | #709 | — | 6 | 2 | no | — |
| 250 | #709 | — | 6 | 2 | no | — |
| 251 | #709 | — | 6 | 1 | no | — |
| 252 | C2×C4×D5 | — | 3 | 2 | no | — |
| 253 | C2×C4×D5 | — | 6 | 2 | no | — |
| 254 | C2×C4×D5 | — | 6 | 1 | no | — |
| 255 | C2×C4×D5 | #67 | 1 | 1 | yes | characteristic |
| 256 | C2×Dic10 | — | 3 | 2 | no | — |
| 257 | C2×Dic10 | — | 6 | 2 | no | — |
| 258 | C2×Dic10 | — | 6 | 1 | no | — |
| 259 | C2×Dic10 | D12 | 1 | 1 | yes | characteristic |
| 260 | #704 | — | 2 | 2 | no | — |
| 261 | #704 | — | 6 | 2 | no | — |
| 262 | #704 | — | 6 | 2 | no | — |
| 263 | C2×#170 | — | 2 | 2 | no | — |
| 264 | C2×#170 | — | 2 | 1 | no | — |
| 265 | C2×#170 | — | 2 | 1 | no | — |
| 266 | C2×#170 | — | 6 | 2 | no | — |
| 267 | #585 | — | 15 | 1 | no | — |
| 268 | #413 | — | 15 | 2 | no | — |
| 269 | #413 | — | 15 | 1 | no | — |
| 270 | #408 | — | 5 | 1 | no | — |
| 271 | #408 | — | 15 | 2 | no | — |
| 272 | C22×C3×C5 | — | 2 | 1 | no | — |
| 273 | C22×C3×C5 | — | 4 | 1 | no | — |
| 274 | C22×C3×C5 | — | 4 | 1 | no | — |
| 275 | C22×C3×C5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 276 | C22×C3×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 277 | C2×D15 | — | 2 | 2 | no | — |
| 278 | C2×D15 | — | 4 | 2 | no | — |
| 279 | C2×D15 | — | 8 | 1 | no | — |
| 280 | C2×C5×D3 | — | 2 | 2 | no | — |
| 281 | C2×C5×D3 | — | 4 | 2 | no | — |
| 282 | C2×C5×D3 | — | 8 | 1 | no | — |
| 283 | C2×C3×D5 | — | 2 | 1 | no | — |
| 284 | C2×C3×D5 | — | 4 | 1 | no | — |
| 285 | D3×D5 | — | 8 | 2 | no | — |
| 286 | C3×C4×C5 | — | 2 | 1 | no | — |
| 287 | Dic15 | — | 2 | 2 | no | — |
| 288 | C3×Dic5 | — | 2 | 1 | no | — |
| 289 | C3×Dic5 | #120 | 1 | 2 | yes | — |
| 290 | C3×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 291 | C3×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 292 | C5×Dic3 | — | 2 | 2 | no | — |
| 293 | C3×#41 | — | 10 | 2 | no | — |
| 294 | C3×#41 | — | 10 | 2 | no | — |
| 295 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 296 | C2×C3×D4 | — | 5 | 1 | no | — |
| 297 | C2×C3×D4 | — | 5 | 1 | no | — |
| 298 | C2×C3×D4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 299 | C22×C3×C4 | — | 5 | 1 | no | — |
| 300 | C22×C3×C4 | — | 5 | 1 | no | — |
| 301 | C22×C3×C4 | — | 5 | 1 | no | — |
| 302 | C2×#67 | — | 2 | 1 | no | — |
| 303 | C2×#67 | — | 5 | 2 | no | — |
| 304 | C2×#67 | — | 10 | 2 | no | — |
| 305 | C2×#67 | — | 10 | 1 | no | — |
| 306 | C2×#67 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 307 | #239 | — | 10 | 2 | no | — |
| 308 | #239 | — | 10 | 2 | no | — |
| 309 | D3×Q8 | — | 10 | 2 | no | — |
| 310 | D3×Q8 | — | 10 | 2 | no | — |
| 311 | #237 | — | 2 | 2 | no | — |
| 312 | #237 | — | 10 | 2 | no | — |
| 313 | #237 | — | 10 | 2 | no | — |
| 314 | #237 | — | 10 | 2 | no | — |
| 315 | #237 | — | 10 | 2 | no | — |
| 316 | #237 | — | 10 | 2 | no | — |
| 317 | D3×D4 | — | 2 | 2 | no | — |
| 318 | D3×D4 | — | 10 | 2 | no | — |
| 319 | D3×D4 | — | 10 | 2 | no | — |
| 320 | D3×D4 | — | 10 | 2 | no | — |
| 321 | D3×D4 | — | 10 | 2 | no | — |
| 322 | D3×D4 | — | 10 | 2 | no | — |
| 323 | #235 | — | 2 | 1 | no | — |
| 324 | #235 | — | 10 | 1 | no | — |
| 325 | #235 | — | 10 | 2 | no | — |
| 326 | #235 | — | 10 | 1 | no | — |
| 327 | #235 | — | 10 | 2 | no | — |
| 328 | #235 | — | 10 | 2 | no | — |
| 329 | #235 | — | 10 | 2 | no | — |
| 330 | #235 | — | 10 | 2 | no | — |
| 331 | #235 | — | 10 | 2 | no | — |
| 332 | #235 | — | 10 | 2 | no | — |
| 333 | #235 | — | 10 | 2 | no | — |
| 334 | #235 | — | 10 | 1 | no | — |
| 335 | C2×D12 | — | 5 | 2 | no | — |
| 336 | C2×D12 | — | 10 | 1 | no | — |
| 337 | C2×D12 | — | 10 | 1 | no | — |
| 338 | C2×C4×D3 | — | 5 | 2 | no | — |
| 339 | C2×C4×D3 | — | 5 | 2 | no | — |
| 340 | C2×C4×D3 | — | 10 | 2 | no | — |
| 341 | C2×C4×D3 | — | 10 | 1 | no | — |
| 342 | C2×C4×D3 | — | 10 | 1 | no | — |
| 343 | C2×Dic6 | — | 5 | 2 | no | — |
| 344 | C2×Dic6 | — | 10 | 1 | no | — |
| 345 | C2×Dic6 | — | 10 | 1 | no | — |
| 346 | C3×M16 | — | 10 | 2 | no | — |
| 347 | C2×C3×C8 | — | 10 | 2 | no | — |
| 348 | C2×C3×C8 | — | 10 | 1 | no | — |
| 349 | C2×C3×C8 | — | 10 | 1 | no | — |
| 350 | #208 | — | 10 | 2 | no | — |
| 351 | #208 | — | 10 | 2 | no | — |
| 352 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 353 | C23×C5 | — | 3 | 2 | no | — |
| 354 | C23×C5 | — | 6 | 1 | no | — |
| 355 | C23×C5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 356 | C23×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 357 | C22×D5 | — | 3 | 2 | no | — |
| 358 | C22×D5 | — | 6 | 2 | no | — |
| 359 | C22×D5 | — | 6 | 1 | no | — |
| 360 | C22×D5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 361 | C5×Q8 | — | 6 | 1 | no | — |
| 362 | C5×D4 | — | 2 | 2 | no | — |
| 363 | C5×D4 | — | 6 | 1 | no | — |
| 364 | C5×D4 | — | 6 | 2 | no | — |
| 365 | C5×D4 | — | 6 | 2 | no | — |
| 366 | C5×D4 | — | 6 | 2 | no | — |
| 367 | C2×C4×C5 | — | 3 | 2 | no | — |
| 368 | C2×C4×C5 | — | 6 | 2 | no | — |
| 369 | C2×C4×C5 | — | 6 | 1 | no | — |
| 370 | C2×C4×C5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 371 | C22⋊D5 | — | 2 | 2 | no | — |
| 372 | C22⋊D5 | — | 2 | 2 | no | — |
| 373 | C22⋊D5 | — | 6 | 2 | no | — |
| 374 | C22⋊D5 | — | 6 | 2 | no | — |
| 375 | C22⋊D5 | — | 6 | 2 | no | — |
| 376 | C22⋊D5 | — | 6 | 2 | no | — |
| 377 | C22⋊D5 | — | 6 | 2 | no | — |
| 378 | C22⋊D5 | — | 6 | 2 | no | — |
| 379 | C22⋊D5 | — | 6 | 2 | no | — |
| 380 | C2×Dic5 | — | 2 | 1 | no | — |
| 381 | C2×Dic5 | — | 2 | 1 | no | — |
| 382 | C2×Dic5 | — | 3 | 2 | no | — |
| 383 | C2×Dic5 | — | 6 | 2 | no | — |
| 384 | C2×Dic5 | — | 6 | 1 | no | — |
| 385 | C2×Dic5 | — | 6 | 2 | no | — |
| 386 | C2×Dic5 | — | 6 | 2 | no | — |
| 387 | C2×Dic5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 388 | C2×Dic5 | C2×D12 | 1 | 1 | yes | characteristic |
| 389 | C2×Dic5 | D3×D4 | 1 | 2 | yes | — |
| 390 | C2×Dic5 | D3×D4 | 1 | 2 | yes | — |
| 391 | C2×Dic5 | C2×#67 | 1 | 1 | yes | characteristic |
| 392 | D20 | — | 6 | 1 | no | — |
| 393 | D20 | — | 6 | 2 | no | — |
| 394 | C4×D5 | — | 2 | 1 | no | — |
| 395 | C4×D5 | — | 2 | 1 | no | — |
| 396 | C4×D5 | — | 6 | 2 | no | — |
| 397 | C4×D5 | — | 6 | 2 | no | — |
| 398 | C4×D5 | — | 6 | 2 | no | — |
| 399 | C4×D5 | — | 6 | 2 | no | — |
| 400 | C4×D5 | — | 6 | 2 | no | — |
| 401 | Dic10 | — | 2 | 2 | no | — |
| 402 | Dic10 | — | 6 | 2 | no | — |
| 403 | Dic10 | — | 6 | 1 | no | — |
| 404 | Dic10 | — | 6 | 2 | no | — |
| 405 | Dic10 | — | 6 | 2 | no | — |
| 406 | #170 | — | 4 | 1 | no | — |
| 407 | #170 | — | 4 | 1 | no | — |
| 408 | #170 | — | 12 | 2 | no | — |
| 409 | 2−1+4 | — | 30 | 1 | no | — |
| 410 | 2−1+4 | — | 30 | 2 | no | — |
| 411 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 412 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 413 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 414 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 415 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 416 | C2×#41 | — | 5 | 1 | no | — |
| 417 | C2×#41 | — | 15 | 2 | no | — |
| 418 | C2×#41 | — | 30 | 1 | no | — |
| 419 | C2×#41 | — | 30 | 1 | no | — |
| 420 | C2×#41 | — | 30 | 2 | no | — |
| 421 | C2×#41 | — | 30 | 2 | no | — |
| 422 | C2×M16 | — | 5 | 1 | no | — |
| 423 | C2×M16 | — | 15 | 2 | no | — |
| 424 | C22×C8 | — | 5 | 1 | no | — |
| 425 | #101 | — | 30 | 2 | no | — |
| 426 | #101 | — | 30 | 1 | no | — |
| 427 | #100 | — | 30 | 2 | no | — |
| 428 | #100 | — | 30 | 1 | no | — |
| 429 | C22⋊C8 | — | 10 | 1 | no | — |
| 430 | C22⋊C8 | — | 10 | 1 | no | — |
| 431 | C22⋊C8 | — | 30 | 2 | no | — |
| 432 | C22⋊C8 | — | 30 | 2 | no | — |
| 433 | C2×C3×C5 | — | 2 | 1 | no | — |
| 434 | C2×C3×C5 | — | 2 | 2 | no | — |
| 435 | C2×C3×C5 | — | 4 | 1 | no | — |
| 436 | C2×C3×C5 | #379 | 1 | 1 | yes | characteristic |
| 437 | D15 | — | 4 | 2 | no | — |
| 438 | C3×D5 | — | 4 | 1 | no | — |
| 439 | C5×D3 | — | 4 | 2 | no | — |
| 440 | C23×C3 | — | 5 | 1 | no | — |
| 441 | C23×C3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 442 | C23×C3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 443 | C22×D3 | — | 2 | 1 | no | — |
| 444 | C22×D3 | — | 5 | 2 | no | — |
| 445 | C22×D3 | — | 10 | 2 | no | — |
| 446 | C22×D3 | — | 10 | 1 | no | — |
| 447 | C22×D3 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 448 | C3×Q8 | — | 10 | 2 | no | — |
| 449 | C3×D4 | — | 2 | 2 | no | — |
| 450 | C3×D4 | — | 10 | 2 | no | — |
| 451 | C3×D4 | — | 10 | 2 | no | — |
| 452 | C2×C3×C4 | — | 5 | 2 | no | — |
| 453 | C2×C3×C4 | — | 5 | 1 | no | — |
| 454 | C2×C3×C4 | — | 5 | 2 | no | — |
| 455 | C2×C3×C4 | — | 5 | 1 | no | — |
| 456 | C2×C3×C4 | — | 5 | 1 | no | — |
| 457 | C2×C3×C4 | — | 10 | 1 | no | — |
| 458 | C2×C3×C4 | — | 10 | 1 | no | — |
| 459 | C2×C3×C4 | — | 10 | 1 | no | — |
| 460 | C2×C3×C4 | — | 10 | 1 | no | — |
| 461 | C2×C3×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 462 | #67 | — | 2 | 2 | no | — |
| 463 | #67 | — | 2 | 2 | no | — |
| 464 | #67 | — | 2 | 2 | no | — |
| 465 | #67 | — | 10 | 2 | no | — |
| 466 | #67 | — | 10 | 2 | no | — |
| 467 | #67 | — | 10 | 2 | no | — |
| 468 | #67 | — | 10 | 2 | no | — |
| 469 | #67 | — | 10 | 2 | no | — |
| 470 | C2×Dic3 | — | 2 | 1 | no | — |
| 471 | C2×Dic3 | — | 5 | 2 | no | — |
| 472 | C2×Dic3 | — | 10 | 2 | no | — |
| 473 | C2×Dic3 | — | 10 | 1 | no | — |
| 474 | C2×Dic3 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 475 | D12 | — | 2 | 1 | no | — |
| 476 | D12 | — | 10 | 1 | no | — |
| 477 | D12 | — | 10 | 2 | no | — |
| 478 | D12 | — | 10 | 2 | no | — |
| 479 | D12 | — | 10 | 2 | no | — |
| 480 | C4×D3 | — | 2 | 2 | no | — |
| 481 | C4×D3 | — | 10 | 2 | no | — |
| 482 | C4×D3 | — | 10 | 2 | no | — |
| 483 | C4×D3 | — | 10 | 2 | no | — |
| 484 | C4×D3 | — | 10 | 2 | no | — |
| 485 | C4×D3 | — | 10 | 2 | no | — |
| 486 | C4×D3 | — | 10 | 2 | no | — |
| 487 | C4×D3 | — | 10 | 2 | no | — |
| 488 | Dic6 | — | 2 | 1 | no | — |
| 489 | Dic6 | — | 10 | 2 | no | — |
| 490 | Dic6 | — | 10 | 2 | no | — |
| 491 | Dic6 | — | 10 | 2 | no | — |
| 492 | Dic6 | — | 10 | 1 | no | — |
| 493 | C3×C8 | — | 20 | 1 | no | — |
| 494 | C3×C8 | — | 20 | 1 | no | — |
| 495 | C3⋊C8 | — | 20 | 2 | no | — |
| 496 | C22×C5 | — | 2 | 1 | no | — |
| 497 | C22×C5 | — | 4 | 1 | no | — |
| 498 | C22×C5 | — | 4 | 1 | no | — |
| 499 | C22×C5 | — | 6 | 2 | no | — |
| 500 | C22×C5 | — | 12 | 2 | no | — |
| 501 | C22×C5 | — | 24 | 1 | no | — |
| 502 | C22×C5 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 503 | C22×C5 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 504 | C2×D5 | — | 2 | 1 | no | — |
| 505 | C2×D5 | — | 4 | 1 | no | — |
| 506 | C2×D5 | — | 6 | 2 | no | — |
| 507 | C2×D5 | — | 12 | 2 | no | — |
| 508 | C2×D5 | — | 24 | 2 | no | — |
| 509 | C2×D5 | — | 24 | 1 | no | — |
| 510 | C4×C5 | — | 2 | 1 | no | — |
| 511 | C4×C5 | — | 6 | 2 | no | — |
| 512 | Dic5 | — | 2 | 1 | no | — |
| 513 | Dic5 | — | 6 | 2 | no | — |
| 514 | Dic5 | #882 | 1 | 2 | yes | — |
| 515 | Dic5 | #937 | 1 | 1 | yes | characteristic |
| 516 | Dic5 | #937 | 1 | 1 | yes | characteristic |
| 517 | #41 | — | 6 | 2 | no | — |
| 518 | #41 | — | 6 | 1 | no | — |
| 519 | #41 | — | 10 | 2 | no | — |
| 520 | #41 | — | 10 | 2 | no | — |
| 521 | #41 | — | 30 | 2 | no | — |
| 522 | #41 | — | 30 | 2 | no | — |
| 523 | #41 | — | 30 | 2 | no | — |
| 524 | #41 | — | 30 | 2 | no | — |
| 525 | #41 | — | 30 | 2 | no | — |
| 526 | #41 | — | 30 | 2 | no | — |
| 527 | #41 | — | 30 | 2 | no | — |
| 528 | #41 | — | 30 | 2 | no | — |
| 529 | #41 | — | 30 | 2 | no | — |
| 530 | #41 | — | 30 | 1 | no | — |
| 531 | #41 | — | 30 | 2 | no | — |
| 532 | #41 | — | 30 | 2 | no | — |
| 533 | #41 | — | 30 | 1 | no | — |
| 534 | #41 | — | 30 | 2 | no | — |
| 535 | #41 | — | 30 | 2 | no | — |
| 536 | #41 | — | 30 | 2 | no | — |
| 537 | #41 | — | 30 | 2 | no | — |
| 538 | #41 | — | 30 | 1 | no | — |
| 539 | C2×Q8 | — | 5 | 1 | no | — |
| 540 | C2×Q8 | — | 15 | 2 | no | — |
| 541 | C2×Q8 | — | 30 | 1 | no | — |
| 542 | C2×Q8 | — | 30 | 2 | no | — |
| 543 | C2×Q8 | — | 30 | 1 | no | — |
| 544 | C2×Q8 | — | 30 | 2 | no | — |
| 545 | C2×D4 | — | 3 | 2 | no | — |
| 546 | C2×D4 | — | 5 | 1 | no | — |
| 547 | C2×D4 | — | 5 | 1 | no | — |
| 548 | C2×D4 | — | 6 | 2 | no | — |
| 549 | C2×D4 | — | 6 | 1 | no | — |
| 550 | C2×D4 | — | 15 | 2 | no | — |
| 551 | C2×D4 | — | 15 | 2 | no | — |
| 552 | C2×D4 | — | 30 | 1 | no | — |
| 553 | C2×D4 | — | 30 | 1 | no | — |
| 554 | C2×D4 | — | 30 | 2 | no | — |
| 555 | C2×D4 | — | 30 | 2 | no | — |
| 556 | C2×D4 | — | 30 | 2 | no | — |
| 557 | C2×D4 | — | 30 | 2 | no | — |
| 558 | C2×D4 | — | 30 | 2 | no | — |
| 559 | C2×D4 | — | 30 | 2 | no | — |
| 560 | C2×D4 | — | 30 | 1 | no | — |
| 561 | C2×D4 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 562 | C22×C4 | — | 5 | 1 | no | — |
| 563 | C22×C4 | — | 5 | 1 | no | — |
| 564 | C22×C4 | — | 5 | 1 | no | — |
| 565 | C22×C4 | — | 15 | 2 | no | — |
| 566 | C22×C4 | — | 15 | 2 | no | — |
| 567 | C22×C4 | — | 30 | 2 | no | — |
| 568 | C22×C4 | — | 30 | 1 | no | — |
| 569 | C22×C4 | — | 30 | 1 | no | — |
| 570 | M16 | — | 10 | 2 | no | — |
| 571 | M16 | — | 30 | 2 | no | — |
| 572 | M16 | — | 30 | 2 | no | — |
| 573 | C2×C8 | — | 10 | 1 | no | — |
| 574 | C2×C8 | — | 10 | 1 | no | — |
| 575 | C2×C8 | — | 10 | 2 | no | — |
| 576 | C2×C8 | — | 30 | 2 | no | — |
| 577 | C3×C5 | #1791 | 1 | 1 | yes | characteristic, complemented, Hall |
| 578 | C22×C3 | — | 2 | 1 | no | — |
| 579 | C22×C3 | — | 4 | 1 | no | — |
| 580 | C22×C3 | — | 4 | 1 | no | — |
| 581 | C22×C3 | — | 10 | 1 | no | — |
| 582 | C22×C3 | — | 20 | 1 | no | — |
| 583 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 584 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 585 | C2×D3 | — | 2 | 2 | no | — |
| 586 | C2×D3 | — | 4 | 2 | no | — |
| 587 | C2×D3 | — | 8 | 1 | no | — |
| 588 | C2×D3 | — | 10 | 2 | no | — |
| 589 | C2×D3 | — | 20 | 2 | no | — |
| 590 | C2×D3 | — | 40 | 2 | no | — |
| 591 | C2×D3 | — | 40 | 1 | no | — |
| 592 | C3×C4 | — | 2 | 1 | no | — |
| 593 | C3×C4 | — | 5 | 2 | no | — |
| 594 | C3×C4 | — | 5 | 1 | no | — |
| 595 | C3×C4 | — | 5 | 1 | no | — |
| 596 | C3×C4 | — | 10 | 1 | no | — |
| 597 | Dic3 | — | 2 | 2 | no | — |
| 598 | Dic3 | — | 10 | 2 | no | — |
| 599 | C2×C5 | — | 2 | 1 | no | — |
| 600 | C2×C5 | — | 2 | 2 | no | — |
| 601 | C2×C5 | — | 4 | 1 | no | — |
| 602 | C2×C5 | — | 12 | 2 | no | — |
| 603 | C2×C5 | #4955 | 1 | 1 | yes | characteristic |
| 604 | D5 | — | 4 | 1 | no | — |
| 605 | D5 | — | 12 | 2 | no | — |
| 606 | C23 | — | 3 | 2 | no | — |
| 607 | C23 | — | 5 | 1 | no | — |
| 608 | C23 | — | 6 | 1 | no | — |
| 609 | C23 | — | 15 | 2 | no | — |
| 610 | C23 | — | 30 | 1 | no | — |
| 611 | C23 | — | 30 | 2 | no | — |
| 612 | C23 | (C2×D3)⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 613 | C23 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 614 | Q8 | — | 6 | 1 | no | — |
| 615 | Q8 | — | 10 | 2 | no | — |
| 616 | Q8 | — | 30 | 1 | no | — |
| 617 | Q8 | — | 30 | 2 | no | — |
| 618 | Q8 | — | 30 | 2 | no | — |
| 619 | Q8 | — | 30 | 2 | no | — |
| 620 | D4 | — | 2 | 2 | no | — |
| 621 | D4 | — | 6 | 1 | no | — |
| 622 | D4 | — | 6 | 2 | no | — |
| 623 | D4 | — | 6 | 2 | no | — |
| 624 | D4 | — | 6 | 2 | no | — |
| 625 | D4 | — | 10 | 2 | no | — |
| 626 | D4 | — | 10 | 2 | no | — |
| 627 | D4 | — | 30 | 1 | no | — |
| 628 | D4 | — | 30 | 2 | no | — |
| 629 | D4 | — | 30 | 2 | no | — |
| 630 | D4 | — | 30 | 2 | no | — |
| 631 | D4 | — | 30 | 2 | no | — |
| 632 | D4 | — | 30 | 2 | no | — |
| 633 | D4 | — | 30 | 2 | no | — |
| 634 | D4 | — | 30 | 2 | no | — |
| 635 | D4 | — | 30 | 2 | no | — |
| 636 | C2×C4 | — | 3 | 2 | no | — |
| 637 | C2×C4 | — | 5 | 1 | no | — |
| 638 | C2×C4 | — | 5 | 1 | no | — |
| 639 | C2×C4 | — | 5 | 2 | no | — |
| 640 | C2×C4 | — | 5 | 2 | no | — |
| 641 | C2×C4 | — | 5 | 1 | no | — |
| 642 | C2×C4 | — | 6 | 2 | no | — |
| 643 | C2×C4 | — | 6 | 1 | no | — |
| 644 | C2×C4 | — | 10 | 1 | no | — |
| 645 | C2×C4 | — | 10 | 1 | no | — |
| 646 | C2×C4 | — | 10 | 1 | no | — |
| 647 | C2×C4 | — | 10 | 1 | no | — |
| 648 | C2×C4 | — | 15 | 2 | no | — |
| 649 | C2×C4 | — | 30 | 2 | no | — |
| 650 | C2×C4 | — | 30 | 2 | no | — |
| 651 | C2×C4 | — | 30 | 2 | no | — |
| 652 | C2×C4 | — | 30 | 2 | no | — |
| 653 | C2×C4 | — | 30 | 2 | no | — |
| 654 | C2×C4 | — | 30 | 2 | no | — |
| 655 | C2×C4 | — | 30 | 2 | no | — |
| 656 | C2×C4 | — | 30 | 2 | no | — |
| 657 | C2×C4 | — | 30 | 1 | no | — |
| 658 | C2×C4 | (C2×D3)⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 659 | C8 | — | 20 | 1 | no | — |
| 660 | C8 | — | 20 | 1 | no | — |
| 661 | C8 | — | 60 | 2 | no | — |
| 662 | C2×C3 | — | 2 | 2 | no | — |
| 663 | C2×C3 | — | 2 | 1 | no | — |
| 664 | C2×C3 | — | 4 | 1 | no | — |
| 665 | C2×C3 | — | 20 | 1 | no | — |
| 666 | C2×C3 | #65800 | 1 | 1 | yes | characteristic |
| 667 | D3 | — | 4 | 2 | no | — |
| 668 | D3 | — | 20 | 2 | no | — |
| 669 | C5 | #70009 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 670 | C22 | — | 2 | 1 | no | — |
| 671 | C22 | — | 4 | 1 | no | — |
| 672 | C22 | — | 4 | 1 | no | — |
| 673 | C22 | — | 6 | 2 | no | — |
| 674 | C22 | — | 10 | 1 | no | — |
| 675 | C22 | — | 12 | 2 | no | — |
| 676 | C22 | — | 20 | 1 | no | — |
| 677 | C22 | — | 24 | 1 | no | — |
| 678 | C22 | — | 30 | 2 | no | — |
| 679 | C22 | — | 60 | 2 | no | — |
| 680 | C22 | — | 120 | 1 | no | — |
| 681 | C22 | — | 120 | 2 | no | — |
| 682 | C22 | C2×(C2×D3)⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 683 | C22 | D3×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 684 | C4 | — | 2 | 1 | no | — |
| 685 | C4 | — | 5 | 1 | no | — |
| 686 | C4 | — | 5 | 1 | no | — |
| 687 | C4 | — | 5 | 2 | no | — |
| 688 | C4 | — | 6 | 2 | no | — |
| 689 | C4 | — | 10 | 1 | no | — |
| 690 | C4 | — | 30 | 2 | no | — |
| 691 | C3 | #10605018 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 692 | C2 | — | 2 | 1 | no | — |
| 693 | C2 | — | 2 | 2 | no | — |
| 694 | C2 | — | 4 | 1 | no | — |
| 695 | C2 | — | 12 | 2 | no | — |
| 696 | C2 | — | 20 | 1 | no | — |
| 697 | C2 | — | 60 | 2 | no | — |
| 698 | C2 | #11752025 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11752436 | C2 | semidirect |
| 3. C3×#65775 | C2 | semidirect |
| 4. #11752008 | C2 | semidirect |
| 5. #11751999 | C2 | semidirect |
| 20. C2×#6762 | C22 | semidirect |
| 21. C2×C3×#704 | C22 | semidirect |
| 22. C22×C3×#170 | C22 | semidirect |
| 36. #65775 | D3 | semidirect |
| 116. C2×#704 | C2×D3 | semidirect |
| 117. C22×#170 | C2×D3 | semidirect |
| 577. C3×C5 | #1791 | semidirect |
| 669. C5 | #70009 | semidirect |
| 691. C3 | #10605018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757034 | 2 |
| #11752436 | 2 |
| C3×#65775 | 2 |
| #11752008 | 2 |
| #11751999 | 2 |
| #10605018 | 3 |
| #70009 | 5 |