Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1476 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 127 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 | C2×#4150⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756907 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11756786 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11756785 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11756779 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11756778 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | D5×#983 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10619102 | — | 3 | 1 | no | maximal, Hall |
| 10 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #92017 | — | 4 | 1 | no | maximal |
| 12 | #4150⋊C3 | C22 | 1 | 2 | yes | complemented |
| 13 | #4150⋊C3 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×D5×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 15 | #91956 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #91955 | C22 | 1 | 2 | yes | complemented |
| 17 | #91954 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #91953 | C22 | 1 | 2 | yes | complemented |
| 19 | C5×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C5×#985 | C22 | 1 | 2 | yes | complemented |
| 21 | C5×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C5×#983 | C22 | 1 | 2 | yes | complemented |
| 23 | D5×GL(2,𝔽3) | C22 | 1 | 4 | yes | complemented |
| 24 | #91897 | C22 | 1 | 4 | yes | complemented |
| 25 | #91896 | C22 | 1 | 4 | yes | complemented |
| 26 | D5×#226 | C22 | 1 | 4 | yes | complemented |
| 27 | #87496 | — | 5 | 1 | no | maximal, Hall |
| 28 | #66283 | — | 3 | 1 | no | — |
| 29 | C2×#4150 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C5×#575 | — | 3 | 1 | no | — |
| 31 | C2×#4097 | — | 3 | 1 | no | — |
| 32 | #66156 | — | 3 | 1 | no | — |
| 33 | #66113 | — | 3 | 2 | no | — |
| 34 | #66113 | — | 3 | 2 | no | — |
| 35 | D5×#137 | — | 3 | 4 | no | — |
| 36 | #66109 | — | 3 | 2 | no | — |
| 37 | #66109 | — | 3 | 2 | no | — |
| 38 | #66107 | — | 3 | 4 | no | — |
| 39 | #66105 | — | 3 | 2 | no | — |
| 40 | #66105 | — | 3 | 2 | no | — |
| 41 | #66104 | — | 3 | 2 | no | — |
| 42 | #66104 | — | 3 | 2 | no | — |
| 43 | C2×#4055 | — | 3 | 1 | no | — |
| 44 | #66079 | — | 3 | 1 | no | — |
| 45 | #6817 | — | 4 | 1 | no | — |
| 46 | C5×#235 | — | 4 | 1 | no | — |
| 47 | C2×C3×D20 | — | 4 | 1 | no | — |
| 48 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 49 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 51 | D5×#67 | — | 4 | 4 | no | — |
| 52 | #6777 | — | 4 | 2 | no | — |
| 53 | D3×D20 | — | 4 | 2 | no | — |
| 54 | #6766 | — | 4 | 2 | no | — |
| 55 | #6765 | — | 4 | 2 | no | — |
| 56 | D5×SL(2,𝔽3) | C23 | 1 | 4 | yes | — |
| 57 | C5⋊GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 58 | C5⋊#226 | C23 | 1 | 2 | yes | — |
| 59 | C5×GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 60 | C5×#226 | C23 | 1 | 2 | yes | — |
| 61 | C2×2−1+4⋊C3 | — | 5 | 1 | no | — |
| 62 | #5927 | — | 5 | 2 | no | — |
| 63 | #5927 | — | 5 | 2 | no | — |
| 64 | #5926 | — | 5 | 2 | no | — |
| 65 | #5926 | — | 5 | 2 | no | — |
| 66 | #5923 | — | 5 | 1 | no | — |
| 67 | #5923 | D5 | 1 | 1 | yes | characteristic, complemented |
| 68 | C2×#983 | — | 5 | 4 | no | — |
| 69 | C2×C5×#41 | — | 3 | 1 | no | — |
| 70 | C2×C5×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | #4150 | — | 3 | 2 | no | — |
| 72 | #4150 | — | 3 | 2 | no | — |
| 73 | #4150 | — | 3 | 2 | no | — |
| 74 | #4150 | — | 6 | 1 | no | — |
| 75 | #4150 | C2×D3 | 1 | 2 | yes | complemented |
| 76 | #4150 | C2×D3 | 1 | 2 | yes | complemented |
| 77 | #4149 | — | 3 | 2 | no | — |
| 78 | #4149 | — | 6 | 1 | no | — |
| 79 | D5×#41 | — | 3 | 4 | no | — |
| 80 | D5×#41 | — | 6 | 2 | no | — |
| 81 | #4147 | — | 3 | 2 | no | — |
| 82 | C2×Q8×D5 | C2×D3 | 1 | 2 | yes | complemented |
| 83 | #4144 | — | 3 | 2 | no | — |
| 84 | #4144 | — | 6 | 2 | no | — |
| 85 | C2×#711 | — | 3 | 2 | no | — |
| 86 | C2×#709 | — | 3 | 1 | no | — |
| 87 | C2×#709 | — | 3 | 1 | no | — |
| 88 | C2×#709 | — | 6 | 2 | no | — |
| 89 | C22×Dic10 | — | 3 | 1 | no | — |
| 90 | C5×#137 | — | 3 | 1 | no | — |
| 91 | C5×#137 | — | 3 | 1 | no | — |
| 92 | C5×#137 | — | 3 | 2 | no | — |
| 93 | C5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 94 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 95 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 96 | C5×#135 | — | 3 | 2 | no | — |
| 97 | C5×#135 | — | 3 | 2 | no | — |
| 98 | C2×C5×M16 | — | 3 | 1 | no | — |
| 99 | #4097 | — | 3 | 2 | no | — |
| 100 | #4097 | — | 3 | 2 | no | — |
| 101 | #4097 | — | 3 | 1 | no | — |
| 102 | #4097 | — | 3 | 4 | no | — |
| 103 | #4097 | — | 3 | 1 | no | — |
| 104 | #4096 | — | 3 | 2 | no | — |
| 105 | #4096 | — | 3 | 2 | no | — |
| 106 | #4095 | — | 3 | 1 | no | — |
| 107 | #4095 | — | 3 | 1 | no | — |
| 108 | C2×#689 | — | 3 | 2 | no | — |
| 109 | #4088 | — | 3 | 2 | no | — |
| 110 | C2×#687 | — | 3 | 2 | no | — |
| 111 | #4078 | — | 3 | 2 | no | — |
| 112 | C2×#681 | — | 3 | 1 | no | — |
| 113 | #4064 | — | 3 | 4 | no | — |
| 114 | #4064 | — | 3 | 4 | no | — |
| 115 | D5×Q16 | — | 3 | 4 | no | — |
| 116 | D5×Q16 | — | 3 | 4 | no | — |
| 117 | #4062 | — | 3 | 4 | no | — |
| 118 | #4062 | — | 3 | 4 | no | — |
| 119 | #4061 | — | 3 | 4 | no | — |
| 120 | #4061 | — | 3 | 4 | no | — |
| 121 | #4061 | — | 3 | 4 | no | — |
| 122 | #4061 | — | 3 | 4 | no | — |
| 123 | D5×SD16 | — | 3 | 4 | no | — |
| 124 | D5×SD16 | — | 3 | 4 | no | — |
| 125 | #4058 | — | 3 | 4 | no | — |
| 126 | #4058 | — | 3 | 4 | no | — |
| 127 | #4057 | — | 3 | 4 | no | — |
| 128 | #4057 | — | 3 | 4 | no | — |
| 129 | #4055 | — | 3 | 4 | no | — |
| 130 | #4055 | — | 3 | 2 | no | — |
| 131 | #4055 | — | 3 | 2 | no | — |
| 132 | #4053 | — | 3 | 2 | no | — |
| 133 | #4053 | — | 3 | 2 | no | — |
| 134 | D5×M16 | — | 3 | 4 | no | — |
| 135 | C2×Dic20 | — | 3 | 2 | no | — |
| 136 | C2×#677 | — | 3 | 2 | no | — |
| 137 | #4047 | — | 3 | 2 | no | — |
| 138 | #4047 | — | 3 | 2 | no | — |
| 139 | #3586 | — | 15 | 1 | no | Sylow |
| 140 | C22×C3×D5 | — | 4 | 2 | no | — |
| 141 | C2×D3×D5 | — | 4 | 4 | no | — |
| 142 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 143 | #1220 | — | 4 | 2 | no | — |
| 144 | D60 | — | 4 | 1 | no | — |
| 145 | C4×D15 | — | 4 | 2 | no | — |
| 146 | Dic30 | — | 4 | 1 | no | — |
| 147 | C5×#67 | — | 4 | 2 | no | — |
| 148 | C5×D12 | — | 4 | 1 | no | — |
| 149 | C4×C5×D3 | — | 4 | 2 | no | — |
| 150 | C5×Dic6 | — | 4 | 1 | no | — |
| 151 | C3×D20 | — | 4 | 2 | no | — |
| 152 | C3×D20 | — | 4 | 2 | no | — |
| 153 | C5×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 154 | #1202 | — | 4 | 4 | no | — |
| 155 | #1201 | — | 4 | 4 | no | — |
| 156 | D5×Dic3 | — | 4 | 4 | no | — |
| 157 | #1004 | — | 20 | 1 | no | — |
| 158 | 2−1+4⋊C3 | — | 5 | 2 | no | — |
| 159 | 2−1+4⋊C3 | — | 5 | 2 | no | — |
| 160 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 161 | C22×SL(2,𝔽3) | — | 5 | 2 | no | — |
| 162 | #986 | — | 5 | 1 | no | — |
| 163 | #986 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 164 | #985 | — | 5 | 2 | no | — |
| 165 | #985 | C2×D5 | 1 | 2 | yes | complemented |
| 166 | #984 | — | 5 | 1 | no | — |
| 167 | #984 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 168 | #983 | — | 5 | 2 | no | — |
| 169 | #983 | — | 5 | 4 | no | — |
| 170 | #983 | — | 5 | 4 | no | — |
| 171 | #983 | C2×D5 | 1 | 2 | yes | complemented |
| 172 | C2×GL(2,𝔽3) | — | 5 | 4 | no | — |
| 173 | C2×#226 | — | 5 | 4 | no | — |
| 174 | C5×#41 | — | 3 | 1 | no | — |
| 175 | C5×#41 | — | 3 | 1 | no | — |
| 176 | C5×#41 | — | 3 | 2 | no | — |
| 177 | C5×#41 | — | 3 | 2 | no | — |
| 178 | C5×#41 | — | 6 | 1 | no | — |
| 179 | C5×#41 | — | 6 | 1 | no | — |
| 180 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 181 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 182 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 183 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 184 | C2×C5×D4 | — | 3 | 1 | no | — |
| 185 | C2×C5×D4 | — | 3 | 1 | no | — |
| 186 | C2×C5×D4 | — | 6 | 1 | no | — |
| 187 | C22×C4×C5 | — | 3 | 1 | no | — |
| 188 | C22×C4×C5 | — | 6 | 1 | no | — |
| 189 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 190 | C2×C22⋊D5 | — | 6 | 4 | no | — |
| 191 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 192 | C22×Dic5 | — | 6 | 1 | no | — |
| 193 | #713 | — | 3 | 4 | no | — |
| 194 | #713 | — | 6 | 2 | no | — |
| 195 | Q8×D5 | — | 3 | 4 | no | — |
| 196 | Q8×D5 | — | 3 | 4 | no | — |
| 197 | Q8×D5 | — | 6 | 2 | no | — |
| 198 | Q8×D5 | C22×D3 | 1 | 4 | yes | — |
| 199 | #711 | — | 3 | 4 | no | — |
| 200 | #711 | — | 3 | 4 | no | — |
| 201 | #711 | — | 3 | 4 | no | — |
| 202 | #711 | — | 6 | 2 | no | — |
| 203 | #711 | — | 6 | 4 | no | — |
| 204 | #711 | — | 6 | 4 | no | — |
| 205 | #711 | — | 6 | 4 | no | — |
| 206 | D4×D5 | — | 3 | 4 | no | — |
| 207 | D4×D5 | — | 6 | 4 | no | — |
| 208 | D4×D5 | — | 6 | 4 | no | — |
| 209 | D4×D5 | — | 6 | 2 | no | — |
| 210 | #709 | — | 3 | 2 | no | — |
| 211 | #709 | — | 3 | 2 | no | — |
| 212 | #709 | — | 3 | 2 | no | — |
| 213 | #709 | — | 3 | 2 | no | — |
| 214 | #709 | — | 3 | 2 | no | — |
| 215 | #709 | — | 3 | 2 | no | — |
| 216 | #709 | — | 6 | 2 | no | — |
| 217 | #709 | — | 6 | 4 | no | — |
| 218 | #709 | — | 6 | 4 | no | — |
| 219 | #709 | — | 6 | 1 | no | — |
| 220 | #709 | — | 6 | 1 | no | — |
| 221 | #709 | — | 6 | 2 | no | — |
| 222 | C2×D20 | — | 3 | 1 | no | — |
| 223 | C2×D20 | — | 6 | 2 | no | — |
| 224 | C2×D20 | S4 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×D5 | — | 3 | 2 | no | — |
| 226 | C2×C4×D5 | — | 6 | 4 | no | — |
| 227 | C2×C4×D5 | — | 6 | 1 | no | — |
| 228 | C2×Dic10 | — | 3 | 1 | no | — |
| 229 | C2×Dic10 | — | 3 | 2 | no | — |
| 230 | C2×Dic10 | — | 3 | 2 | no | — |
| 231 | C2×Dic10 | — | 3 | 2 | no | — |
| 232 | C2×Dic10 | — | 3 | 1 | no | — |
| 233 | C2×Dic10 | — | 6 | 1 | no | — |
| 234 | C2×Dic10 | — | 6 | 1 | no | — |
| 235 | C2×Dic10 | — | 6 | 2 | no | — |
| 236 | C5×Q16 | — | 3 | 2 | no | — |
| 237 | C5×Q16 | — | 3 | 2 | no | — |
| 238 | C5×SD16 | — | 3 | 2 | no | — |
| 239 | C5×SD16 | — | 3 | 2 | no | — |
| 240 | C5×SD16 | — | 3 | 2 | no | — |
| 241 | C5×SD16 | — | 3 | 2 | no | — |
| 242 | C5×D8 | — | 3 | 2 | no | — |
| 243 | C5×D8 | — | 3 | 2 | no | — |
| 244 | C5×M16 | — | 3 | 2 | no | — |
| 245 | C5×M16 | — | 3 | 1 | no | — |
| 246 | C5×M16 | — | 3 | 1 | no | — |
| 247 | C2×C5×C8 | — | 3 | 2 | no | — |
| 248 | #689 | — | 3 | 2 | no | — |
| 249 | #689 | — | 3 | 4 | no | — |
| 250 | #689 | — | 3 | 4 | no | — |
| 251 | #689 | — | 3 | 2 | no | — |
| 252 | #688 | — | 3 | 2 | no | — |
| 253 | #688 | — | 3 | 2 | no | — |
| 254 | #687 | — | 3 | 2 | no | — |
| 255 | #687 | — | 3 | 2 | no | — |
| 256 | #687 | — | 3 | 4 | no | — |
| 257 | #687 | — | 3 | 4 | no | — |
| 258 | #686 | — | 3 | 2 | no | — |
| 259 | #686 | — | 3 | 2 | no | — |
| 260 | #681 | — | 3 | 1 | no | — |
| 261 | #681 | — | 3 | 1 | no | — |
| 262 | #681 | — | 3 | 2 | no | — |
| 263 | C2×#168 | — | 3 | 2 | no | — |
| 264 | Dic20 | — | 3 | 4 | no | — |
| 265 | Dic20 | — | 3 | 4 | no | — |
| 266 | #677 | — | 3 | 4 | no | — |
| 267 | #677 | — | 3 | 4 | no | — |
| 268 | #676 | — | 3 | 4 | no | — |
| 269 | #676 | — | 3 | 4 | no | — |
| 270 | C8×D5 | — | 3 | 4 | no | — |
| 271 | C8×D5 | — | 3 | 4 | no | — |
| 272 | #585 | — | 15 | 1 | no | — |
| 273 | C2×2−1+4 | — | 5 | 1 | no | — |
| 274 | #578 | — | 15 | 2 | no | — |
| 275 | #578 | — | 15 | 2 | no | — |
| 276 | #578 | — | 15 | 2 | no | — |
| 277 | #578 | — | 15 | 2 | no | — |
| 278 | #577 | — | 15 | 2 | no | — |
| 279 | #577 | — | 15 | 2 | no | — |
| 280 | #577 | — | 15 | 2 | no | — |
| 281 | #577 | — | 15 | 2 | no | — |
| 282 | #575 | — | 3 | 1 | no | — |
| 283 | #575 | — | 15 | 4 | no | — |
| 284 | #575 | — | 15 | 1 | no | — |
| 285 | C2×#137 | — | 15 | 1 | no | — |
| 286 | C2×#137 | — | 15 | 4 | no | — |
| 287 | C2×#137 | — | 15 | 1 | no | — |
| 288 | #568 | — | 15 | 1 | no | — |
| 289 | C22×C3×C5 | — | 4 | 1 | no | — |
| 290 | C2×D15 | — | 4 | 2 | no | — |
| 291 | C2×C5×D3 | — | 4 | 2 | no | — |
| 292 | C2×C3×D5 | — | 4 | 4 | no | — |
| 293 | C2×C3×D5 | — | 16 | 2 | no | — |
| 294 | D3×D5 | — | 16 | 4 | no | — |
| 295 | C3×C4×C5 | — | 4 | 1 | no | — |
| 296 | C3×C4×C5 | — | 4 | 1 | no | — |
| 297 | Dic15 | — | 4 | 2 | no | — |
| 298 | C5×Dic3 | — | 4 | 2 | no | — |
| 299 | C2×C3×D4 | — | 20 | 1 | no | — |
| 300 | C2×#67 | — | 20 | 4 | no | — |
| 301 | #237 | — | 20 | 2 | no | — |
| 302 | #237 | — | 20 | 2 | no | — |
| 303 | D3×D4 | — | 20 | 2 | no | — |
| 304 | D3×D4 | — | 20 | 2 | no | — |
| 305 | #235 | — | 4 | 1 | no | — |
| 306 | #235 | — | 20 | 1 | no | — |
| 307 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 308 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 309 | C2×SL(2,𝔽3) | — | 5 | 4 | no | — |
| 310 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 311 | GL(2,𝔽3) | — | 5 | 2 | no | — |
| 312 | GL(2,𝔽3) | C22×D5 | 1 | 2 | yes | — |
| 313 | #226 | — | 5 | 2 | no | — |
| 314 | #226 | C22×D5 | 1 | 2 | yes | — |
| 315 | C23×C5 | — | 3 | 1 | no | — |
| 316 | C23×C5 | — | 6 | 1 | no | — |
| 317 | C22×D5 | — | 6 | 1 | no | — |
| 318 | C22×D5 | — | 6 | 4 | no | — |
| 319 | C22×D5 | C2×S4 | 1 | 2 | yes | — |
| 320 | C5×Q8 | — | 3 | 1 | no | — |
| 321 | C5×Q8 | — | 3 | 2 | no | — |
| 322 | C5×Q8 | — | 6 | 1 | no | — |
| 323 | C5×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 324 | C5×D4 | — | 3 | 1 | no | — |
| 325 | C5×D4 | — | 3 | 1 | no | — |
| 326 | C5×D4 | — | 3 | 2 | no | — |
| 327 | C5×D4 | — | 6 | 1 | no | — |
| 328 | C5×D4 | — | 6 | 2 | no | — |
| 329 | C5×D4 | — | 6 | 2 | no | — |
| 330 | C5×D4 | — | 6 | 1 | no | — |
| 331 | C2×C4×C5 | — | 3 | 1 | no | — |
| 332 | C2×C4×C5 | — | 3 | 1 | no | — |
| 333 | C2×C4×C5 | — | 3 | 1 | no | — |
| 334 | C2×C4×C5 | — | 3 | 1 | no | — |
| 335 | C2×C4×C5 | — | 3 | 1 | no | — |
| 336 | C2×C4×C5 | — | 6 | 2 | no | — |
| 337 | C2×C4×C5 | — | 6 | 1 | no | — |
| 338 | C2×C4×C5 | — | 6 | 2 | no | — |
| 339 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 340 | C22⋊D5 | — | 3 | 4 | no | — |
| 341 | C22⋊D5 | — | 3 | 4 | no | — |
| 342 | C22⋊D5 | — | 6 | 4 | no | — |
| 343 | C22⋊D5 | — | 6 | 2 | no | — |
| 344 | C22⋊D5 | — | 6 | 2 | no | — |
| 345 | C22⋊D5 | — | 6 | 4 | no | — |
| 346 | C2×Dic5 | — | 3 | 2 | no | — |
| 347 | C2×Dic5 | — | 6 | 2 | no | — |
| 348 | C2×Dic5 | — | 6 | 2 | no | — |
| 349 | C2×Dic5 | — | 6 | 4 | no | — |
| 350 | C2×Dic5 | — | 6 | 1 | no | — |
| 351 | D20 | — | 3 | 2 | no | — |
| 352 | D20 | — | 6 | 4 | no | — |
| 353 | D20 | — | 6 | 1 | no | — |
| 354 | D20 | C2×S4 | 1 | 2 | yes | — |
| 355 | D20 | C2×S4 | 1 | 2 | yes | — |
| 356 | C4×D5 | — | 3 | 4 | no | — |
| 357 | C4×D5 | — | 3 | 4 | no | — |
| 358 | C4×D5 | — | 6 | 4 | no | — |
| 359 | C4×D5 | — | 6 | 2 | no | — |
| 360 | C4×D5 | — | 6 | 4 | no | — |
| 361 | C4×D5 | — | 6 | 2 | no | — |
| 362 | Dic10 | — | 3 | 2 | no | — |
| 363 | Dic10 | — | 3 | 2 | no | — |
| 364 | Dic10 | — | 3 | 4 | no | — |
| 365 | Dic10 | — | 3 | 2 | no | — |
| 366 | Dic10 | — | 6 | 2 | no | — |
| 367 | Dic10 | — | 6 | 4 | no | — |
| 368 | Dic10 | — | 6 | 1 | no | — |
| 369 | C5×C8 | — | 3 | 2 | no | — |
| 370 | C5×C8 | — | 3 | 2 | no | — |
| 371 | #168 | — | 3 | 2 | no | — |
| 372 | #168 | — | 3 | 2 | no | — |
| 373 | 2−1+4 | — | 5 | 2 | no | — |
| 374 | 2−1+4 | — | 5 | 2 | no | — |
| 375 | 2−1+4 | — | 15 | 2 | no | — |
| 376 | 2−1+4 | — | 15 | 2 | no | — |
| 377 | 2−1+4 | — | 15 | 2 | no | — |
| 378 | 2−1+4 | — | 15 | 2 | no | — |
| 379 | 2−1+4 | — | 30 | 1 | no | — |
| 380 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 381 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 382 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 383 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 384 | C2×#41 | — | 3 | 1 | no | — |
| 385 | C2×#41 | — | 15 | 1 | no | — |
| 386 | C2×#41 | — | 15 | 1 | no | — |
| 387 | C2×#41 | — | 15 | 2 | no | — |
| 388 | C2×#41 | — | 15 | 4 | no | — |
| 389 | C2×#41 | — | 30 | 2 | no | — |
| 390 | C2×#41 | — | 30 | 2 | no | — |
| 391 | C2×#41 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 392 | C22×Q8 | — | 5 | 2 | no | — |
| 393 | C22×Q8 | — | 15 | 1 | no | — |
| 394 | #137 | — | 3 | 1 | no | — |
| 395 | #137 | — | 3 | 1 | no | — |
| 396 | #137 | — | 3 | 2 | no | — |
| 397 | #137 | — | 15 | 4 | no | — |
| 398 | #137 | — | 15 | 2 | no | — |
| 399 | #137 | — | 15 | 2 | no | — |
| 400 | #137 | — | 15 | 4 | no | — |
| 401 | #137 | — | 15 | 4 | no | — |
| 402 | #137 | — | 15 | 4 | no | — |
| 403 | #137 | — | 15 | 4 | no | — |
| 404 | #137 | — | 15 | 4 | no | — |
| 405 | #137 | — | 15 | 4 | no | — |
| 406 | #137 | — | 15 | 4 | no | — |
| 407 | #137 | — | 15 | 2 | no | — |
| 408 | #137 | — | 15 | 2 | no | — |
| 409 | #137 | — | 15 | 1 | no | — |
| 410 | #137 | — | 15 | 1 | no | — |
| 411 | #137 | — | 15 | 2 | no | — |
| 412 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 413 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 414 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 415 | AGL(1,ℤ/8) | — | 15 | 4 | no | — |
| 416 | AGL(1,ℤ/8) | — | 15 | 4 | no | — |
| 417 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 418 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 419 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 420 | #135 | — | 3 | 2 | no | — |
| 421 | #135 | — | 3 | 2 | no | — |
| 422 | #135 | — | 15 | 4 | no | — |
| 423 | #135 | — | 15 | 4 | no | — |
| 424 | #135 | — | 15 | 4 | no | — |
| 425 | #135 | — | 15 | 4 | no | — |
| 426 | #135 | — | 15 | 2 | no | — |
| 427 | #135 | — | 15 | 2 | no | — |
| 428 | C2×Q16 | — | 15 | 2 | no | — |
| 429 | C2×Q16 | — | 15 | 4 | no | — |
| 430 | C2×Q16 | — | 15 | 4 | no | — |
| 431 | C2×Q16 | — | 15 | 2 | no | — |
| 432 | C2×SD16 | — | 15 | 2 | no | — |
| 433 | C2×SD16 | — | 15 | 4 | no | — |
| 434 | C2×SD16 | — | 15 | 4 | no | — |
| 435 | C2×SD16 | — | 15 | 2 | no | — |
| 436 | #131 | — | 15 | 2 | no | — |
| 437 | #131 | — | 15 | 2 | no | — |
| 438 | #131 | — | 15 | 2 | no | — |
| 439 | #131 | — | 15 | 2 | no | — |
| 440 | C2×M16 | — | 3 | 1 | no | — |
| 441 | C2×M16 | — | 15 | 4 | no | — |
| 442 | C2×M16 | — | 15 | 1 | no | — |
| 443 | C2×C3×C5 | — | 4 | 1 | no | — |
| 444 | C2×C3×C5 | — | 8 | 1 | no | — |
| 445 | D15 | — | 8 | 2 | no | — |
| 446 | C3×D5 | — | 8 | 4 | no | — |
| 447 | C5×D3 | — | 8 | 2 | no | — |
| 448 | C23×C3 | — | 20 | 2 | no | — |
| 449 | C22×D3 | — | 20 | 4 | no | — |
| 450 | C3×D4 | — | 20 | 2 | no | — |
| 451 | C3×D4 | — | 20 | 2 | no | — |
| 452 | C2×C3×C4 | — | 4 | 1 | no | — |
| 453 | #67 | — | 4 | 2 | no | — |
| 454 | #67 | — | 20 | 4 | no | — |
| 455 | #67 | — | 20 | 4 | no | — |
| 456 | #67 | — | 20 | 2 | no | — |
| 457 | C2×Dic3 | — | 20 | 4 | no | — |
| 458 | D12 | — | 4 | 1 | no | — |
| 459 | D12 | — | 20 | 1 | no | — |
| 460 | C4×D3 | — | 4 | 2 | no | — |
| 461 | C4×D3 | — | 20 | 2 | no | — |
| 462 | Dic6 | — | 4 | 1 | no | — |
| 463 | Dic6 | — | 20 | 1 | no | — |
| 464 | SL(2,𝔽3) | C23×D5 | 1 | 1 | yes | characteristic |
| 465 | C22×C5 | — | 3 | 1 | no | — |
| 466 | C22×C5 | — | 3 | 1 | no | — |
| 467 | C22×C5 | — | 6 | 2 | no | — |
| 468 | C22×C5 | — | 12 | 1 | no | — |
| 469 | C22×C5 | — | 24 | 1 | no | — |
| 470 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 471 | C2×D5 | — | 4 | 2 | no | — |
| 472 | C2×D5 | — | 6 | 2 | no | — |
| 473 | C2×D5 | — | 24 | 4 | no | — |
| 474 | C2×D5 | — | 24 | 1 | no | — |
| 475 | C2×D5 | C22×S4 | 1 | 4 | yes | — |
| 476 | C4×C5 | — | 3 | 1 | no | — |
| 477 | C4×C5 | — | 3 | 1 | no | — |
| 478 | C4×C5 | — | 6 | 2 | no | — |
| 479 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 480 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 481 | Dic5 | — | 3 | 4 | no | — |
| 482 | Dic5 | — | 6 | 2 | no | — |
| 483 | #41 | — | 3 | 1 | no | — |
| 484 | #41 | — | 3 | 1 | no | — |
| 485 | #41 | — | 3 | 2 | no | — |
| 486 | #41 | — | 3 | 2 | no | — |
| 487 | #41 | — | 6 | 1 | no | — |
| 488 | #41 | — | 6 | 1 | no | — |
| 489 | #41 | — | 15 | 2 | no | — |
| 490 | #41 | — | 15 | 2 | no | — |
| 491 | #41 | — | 15 | 2 | no | — |
| 492 | #41 | — | 15 | 2 | no | — |
| 493 | #41 | — | 15 | 2 | no | — |
| 494 | #41 | — | 15 | 2 | no | — |
| 495 | #41 | — | 15 | 4 | no | — |
| 496 | #41 | — | 15 | 4 | no | — |
| 497 | #41 | — | 15 | 4 | no | — |
| 498 | #41 | — | 15 | 4 | no | — |
| 499 | #41 | — | 30 | 1 | no | — |
| 500 | #41 | — | 30 | 4 | no | — |
| 501 | #41 | — | 30 | 2 | no | — |
| 502 | #41 | — | 30 | 4 | no | — |
| 503 | #41 | — | 30 | 2 | no | — |
| 504 | #41 | — | 30 | 4 | no | — |
| 505 | #41 | — | 30 | 4 | no | — |
| 506 | #41 | — | 30 | 2 | no | — |
| 507 | #41 | — | 30 | 4 | no | — |
| 508 | #41 | — | 30 | 2 | no | — |
| 509 | #41 | — | 30 | 1 | no | — |
| 510 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 511 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 512 | C2×Q8 | — | 3 | 1 | no | — |
| 513 | C2×Q8 | — | 5 | 4 | no | — |
| 514 | C2×Q8 | — | 15 | 2 | no | — |
| 515 | C2×Q8 | — | 15 | 2 | no | — |
| 516 | C2×Q8 | — | 15 | 2 | no | — |
| 517 | C2×Q8 | — | 15 | 1 | no | — |
| 518 | C2×Q8 | — | 15 | 1 | no | — |
| 519 | C2×Q8 | — | 15 | 4 | no | — |
| 520 | C2×Q8 | — | 15 | 4 | no | — |
| 521 | C2×Q8 | — | 30 | 1 | no | — |
| 522 | C2×Q8 | — | 30 | 1 | no | — |
| 523 | C2×Q8 | — | 30 | 2 | no | — |
| 524 | C2×Q8 | — | 30 | 2 | no | — |
| 525 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 526 | C2×D4 | — | 3 | 1 | no | — |
| 527 | C2×D4 | — | 3 | 1 | no | — |
| 528 | C2×D4 | — | 5 | 1 | no | — |
| 529 | C2×D4 | — | 6 | 1 | no | — |
| 530 | C2×D4 | — | 15 | 1 | no | — |
| 531 | C2×D4 | — | 15 | 4 | no | — |
| 532 | C2×D4 | — | 15 | 2 | no | — |
| 533 | C2×D4 | — | 30 | 2 | no | — |
| 534 | C2×D4 | — | 30 | 2 | no | — |
| 535 | C2×D4 | — | 30 | 4 | no | — |
| 536 | C2×D4 | — | 30 | 4 | no | — |
| 537 | C2×D4 | — | 30 | 4 | no | — |
| 538 | C2×D4 | — | 30 | 1 | no | — |
| 539 | C22×C4 | — | 3 | 1 | no | — |
| 540 | C22×C4 | — | 6 | 1 | no | — |
| 541 | C22×C4 | — | 15 | 2 | no | — |
| 542 | C22×C4 | — | 30 | 1 | no | — |
| 543 | C22×C4 | — | 30 | 4 | no | — |
| 544 | C22×C4 | — | 30 | 1 | no | — |
| 545 | Q16 | — | 3 | 2 | no | — |
| 546 | Q16 | — | 3 | 2 | no | — |
| 547 | Q16 | — | 15 | 4 | no | — |
| 548 | Q16 | — | 15 | 4 | no | — |
| 549 | Q16 | — | 15 | 2 | no | — |
| 550 | Q16 | — | 15 | 4 | no | — |
| 551 | Q16 | — | 15 | 4 | no | — |
| 552 | Q16 | — | 15 | 2 | no | — |
| 553 | SD16 | — | 3 | 2 | no | — |
| 554 | SD16 | — | 3 | 2 | no | — |
| 555 | SD16 | — | 3 | 2 | no | — |
| 556 | SD16 | — | 3 | 2 | no | — |
| 557 | SD16 | — | 15 | 4 | no | — |
| 558 | SD16 | — | 15 | 4 | no | — |
| 559 | SD16 | — | 15 | 4 | no | — |
| 560 | SD16 | — | 15 | 4 | no | — |
| 561 | SD16 | — | 15 | 2 | no | — |
| 562 | SD16 | — | 15 | 2 | no | — |
| 563 | SD16 | — | 15 | 2 | no | — |
| 564 | SD16 | — | 15 | 2 | no | — |
| 565 | D8 | — | 3 | 2 | no | — |
| 566 | D8 | — | 3 | 2 | no | — |
| 567 | D8 | — | 15 | 2 | no | — |
| 568 | D8 | — | 15 | 2 | no | — |
| 569 | M16 | — | 3 | 2 | no | — |
| 570 | M16 | — | 3 | 1 | no | — |
| 571 | M16 | — | 3 | 1 | no | — |
| 572 | M16 | — | 15 | 4 | no | — |
| 573 | M16 | — | 15 | 4 | no | — |
| 574 | M16 | — | 15 | 2 | no | — |
| 575 | M16 | — | 15 | 1 | no | — |
| 576 | M16 | — | 15 | 1 | no | — |
| 577 | C2×C8 | — | 3 | 2 | no | — |
| 578 | C2×C8 | — | 15 | 4 | no | — |
| 579 | C2×C8 | — | 15 | 4 | no | — |
| 580 | C2×C8 | — | 15 | 2 | no | — |
| 581 | C3×C5 | — | 4 | 1 | no | Hall |
| 582 | C22×C3 | — | 4 | 1 | no | — |
| 583 | C22×C3 | — | 20 | 4 | no | — |
| 584 | C22×C3 | — | 80 | 2 | no | — |
| 585 | C2×D3 | — | 4 | 2 | no | — |
| 586 | C2×D3 | — | 20 | 2 | no | — |
| 587 | C2×D3 | — | 80 | 4 | no | — |
| 588 | C3×C4 | — | 4 | 1 | no | — |
| 589 | C3×C4 | — | 4 | 1 | no | — |
| 590 | Dic3 | — | 4 | 2 | no | — |
| 591 | Dic3 | — | 20 | 2 | no | — |
| 592 | C2×C5 | — | 2 | 1 | no | — |
| 593 | C2×C5 | — | 6 | 1 | no | — |
| 594 | C2×C5 | — | 6 | 1 | no | — |
| 595 | C2×C5 | — | 12 | 2 | no | — |
| 596 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 597 | D5 | — | 2 | 4 | no | — |
| 598 | D5 | — | 12 | 2 | no | — |
| 599 | C23 | — | 3 | 1 | no | — |
| 600 | C23 | — | 5 | 2 | no | — |
| 601 | C23 | — | 6 | 1 | no | — |
| 602 | C23 | — | 30 | 1 | no | — |
| 603 | C23 | — | 30 | 4 | no | — |
| 604 | Q8 | — | 3 | 1 | no | — |
| 605 | Q8 | — | 3 | 2 | no | — |
| 606 | Q8 | — | 6 | 1 | no | — |
| 607 | Q8 | — | 15 | 4 | no | — |
| 608 | Q8 | — | 15 | 2 | no | — |
| 609 | Q8 | — | 15 | 2 | no | — |
| 610 | Q8 | — | 15 | 2 | no | — |
| 611 | Q8 | — | 30 | 2 | no | — |
| 612 | Q8 | — | 30 | 4 | no | — |
| 613 | Q8 | — | 30 | 1 | no | — |
| 614 | Q8 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 615 | D4 | — | 3 | 1 | no | — |
| 616 | D4 | — | 3 | 1 | no | — |
| 617 | D4 | — | 3 | 2 | no | — |
| 618 | D4 | — | 5 | 2 | no | — |
| 619 | D4 | — | 5 | 2 | no | — |
| 620 | D4 | — | 6 | 1 | no | — |
| 621 | D4 | — | 6 | 2 | no | — |
| 622 | D4 | — | 6 | 2 | no | — |
| 623 | D4 | — | 6 | 1 | no | — |
| 624 | D4 | — | 15 | 2 | no | — |
| 625 | D4 | — | 15 | 4 | no | — |
| 626 | D4 | — | 15 | 4 | no | — |
| 627 | D4 | — | 30 | 4 | no | — |
| 628 | D4 | — | 30 | 4 | no | — |
| 629 | D4 | — | 30 | 2 | no | — |
| 630 | D4 | — | 30 | 4 | no | — |
| 631 | D4 | — | 30 | 2 | no | — |
| 632 | D4 | — | 30 | 1 | no | — |
| 633 | C2×C4 | — | 3 | 1 | no | — |
| 634 | C2×C4 | — | 3 | 1 | no | — |
| 635 | C2×C4 | — | 3 | 1 | no | — |
| 636 | C2×C4 | — | 3 | 1 | no | — |
| 637 | C2×C4 | — | 3 | 1 | no | — |
| 638 | C2×C4 | — | 6 | 2 | no | — |
| 639 | C2×C4 | — | 6 | 1 | no | — |
| 640 | C2×C4 | — | 6 | 2 | no | — |
| 641 | C2×C4 | — | 15 | 4 | no | — |
| 642 | C2×C4 | — | 15 | 4 | no | — |
| 643 | C2×C4 | — | 15 | 2 | no | — |
| 644 | C2×C4 | — | 30 | 2 | no | — |
| 645 | C2×C4 | — | 30 | 4 | no | — |
| 646 | C2×C4 | — | 30 | 4 | no | — |
| 647 | C2×C4 | — | 30 | 2 | no | — |
| 648 | C2×C4 | — | 30 | 2 | no | — |
| 649 | C2×C4 | — | 30 | 4 | no | — |
| 650 | C2×C4 | — | 30 | 1 | no | — |
| 651 | C2×C4 | — | 30 | 2 | no | — |
| 652 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 653 | C8 | — | 3 | 2 | no | — |
| 654 | C8 | — | 3 | 2 | no | — |
| 655 | C8 | — | 15 | 2 | no | — |
| 656 | C8 | — | 15 | 2 | no | — |
| 657 | C2×C3 | — | 4 | 1 | no | — |
| 658 | C2×C3 | — | 8 | 1 | no | — |
| 659 | C2×C3 | — | 40 | 4 | no | — |
| 660 | D3 | — | 8 | 2 | no | — |
| 661 | D3 | — | 40 | 2 | no | — |
| 662 | C5 | #87496 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 663 | C22 | — | 3 | 1 | no | — |
| 664 | C22 | — | 3 | 1 | no | — |
| 665 | C22 | — | 5 | 4 | no | — |
| 666 | C22 | — | 6 | 2 | no | — |
| 667 | C22 | — | 12 | 1 | no | — |
| 668 | C22 | — | 20 | 2 | no | — |
| 669 | C22 | — | 24 | 1 | no | — |
| 670 | C22 | — | 30 | 2 | no | — |
| 671 | C22 | — | 120 | 1 | no | — |
| 672 | C22 | — | 120 | 4 | no | — |
| 673 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 674 | C4 | — | 3 | 1 | no | — |
| 675 | C4 | — | 3 | 1 | no | — |
| 676 | C4 | — | 6 | 2 | no | — |
| 677 | C4 | — | 15 | 4 | no | — |
| 678 | C4 | — | 30 | 2 | no | — |
| 679 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 680 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 681 | C3 | — | 4 | 1 | no | Sylow |
| 682 | C2 | — | 2 | 1 | no | — |
| 683 | C2 | — | 6 | 1 | no | — |
| 684 | C2 | — | 6 | 1 | no | — |
| 685 | C2 | — | 10 | 4 | no | — |
| 686 | C2 | — | 12 | 2 | no | — |
| 687 | C2 | — | 60 | 2 | no | — |
| 688 | C2 | C22×D5×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C24 |
| Fitting | C2×C5×#41 | C2×D3 |
| socle | C2×C5 | C23×S4 |
| hypercenter | C2×C4 | D5×S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4150⋊C3 | C2 | semidirect |
| 2. #11756907 | C2 | semidirect |
| 3. C5×#5923 | C2 | semidirect |
| 4. #11756786 | C2 | semidirect |
| 5. #11756785 | C2 | semidirect |
| 6. #11756779 | C2 | semidirect |
| 7. #11756778 | C2 | semidirect |
| 8. D5×#983 | C2 | semidirect |
| 10. C2×C5×#41⋊C3 | C22 | semidirect |
| 12. #4150⋊C3 | C22 | semidirect |
| 13. #4150⋊C3 | C22 | semidirect |
| 14. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 15. #91956 | C22 | semidirect |
| 16. #91955 | C22 | semidirect |
| 17. #91954 | C22 | semidirect |
| 18. #91953 | C22 | semidirect |
| 19. C5×#986 | C22 | semidirect |
| 20. C5×#985 | C22 | semidirect |
| 21. C5×#984 | C22 | semidirect |
| 22. C5×#983 | C22 | semidirect |
| 23. D5×GL(2,𝔽3) | C22 | semidirect |
| 24. #91897 | C22 | semidirect |
| 25. #91896 | C22 | semidirect |
| 26. D5×#226 | C22 | semidirect |
| 29. C2×#4150 | D3 | semidirect |
| 67. #5923 | D5 | semidirect |
| 70. C2×C5×#41 | C2×D3 | semidirect |
| 75. #4150 | C2×D3 | semidirect |
| 76. #4150 | C2×D3 | semidirect |
| 82. C2×Q8×D5 | C2×D3 | semidirect |
| 160. C2×#41⋊C3 | C2×D5 | semidirect |
| 163. #986 | C2×D5 | semidirect |
| 165. #985 | C2×D5 | semidirect |
| 167. #984 | C2×D5 | semidirect |
| 171. #983 | C2×D5 | semidirect |
| 391. C2×#41 | D3×D5 | semidirect |
| 662. C5 | #87496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4150⋊C3 | 2 |
| #11756907 | 2 |
| C5×#5923 | 2 |
| #11756786 | 2 |
| #11756785 | 2 |
| #11756779 | 2 |
| #11756778 | 2 |
| D5×#983 | 2 |
| #10619102 | 3 |
| #92017 | 4 |
| #87496 | 5 |