Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C5×#5945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5927 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C5×#5926 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C5×#5925 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#5924 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#5923 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×C5×#985 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C5×#3584 | — | 3 | 1 | no | maximal, Hall |
| 9 | C5×D3×#41 | — | 4 | 1 | no | maximal |
| 10 | C5×2−1+4⋊C3 | C22 | 1 | 3 | yes | complemented |
| 11 | C5×#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C5×#41⋊C3 | C22 | 1 | 3 | yes | complemented |
| 13 | C5×#986 | C22 | 1 | 3 | yes | complemented |
| 14 | C5×#985 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×#985 | C22 | 1 | 3 | yes | complemented |
| 16 | C5×#985 | C22 | 1 | 3 | yes | complemented |
| 17 | C5×#985 | C22 | 1 | 3 | yes | complemented |
| 18 | C5×#984 | C22 | 1 | 3 | yes | complemented |
| 19 | C5×#983 | C22 | 1 | 6 | yes | complemented |
| 20 | C2×C5×GL(2,𝔽3) | C22 | 1 | 3 | yes | complemented |
| 21 | C2×C5×#226 | C22 | 1 | 3 | yes | complemented |
| 22 | #87497 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 23 | C5×#585 | — | 3 | 1 | no | — |
| 24 | C5×#585 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C5×#578 | — | 3 | 1 | no | — |
| 26 | C5×#578 | — | 3 | 3 | no | — |
| 27 | C5×#577 | — | 3 | 3 | no | — |
| 28 | C5×#577 | — | 3 | 1 | no | — |
| 29 | C5×#577 | — | 3 | 3 | no | — |
| 30 | C5×#577 | — | 3 | 1 | no | — |
| 31 | C5×#576 | — | 3 | 3 | no | — |
| 32 | C5×#576 | — | 3 | 1 | no | — |
| 33 | C5×#575 | — | 3 | 3 | no | — |
| 34 | C5×#575 | — | 3 | 3 | no | — |
| 35 | C2×C5×#135 | — | 3 | 3 | no | — |
| 36 | C2×C5×#135 | — | 3 | 3 | no | — |
| 37 | C2×C5×#131 | — | 3 | 1 | no | — |
| 38 | C3×C5×#41 | — | 4 | 1 | no | — |
| 39 | C5×#239 | — | 4 | 1 | no | — |
| 40 | C5×D3×Q8 | — | 4 | 1 | no | — |
| 41 | C5×#237 | — | 4 | 3 | no | — |
| 42 | C5×D3×D4 | — | 4 | 3 | no | — |
| 43 | C5×#235 | — | 4 | 3 | no | — |
| 44 | C2×C4×C5×D3 | — | 4 | 3 | no | — |
| 45 | C5×#41⋊C3 | C23 | 1 | 3 | yes | — |
| 46 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C5×SL(2,𝔽3) | C23 | 1 | 3 | yes | — |
| 48 | C5×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 49 | C5×GL(2,𝔽3) | C23 | 1 | 3 | yes | — |
| 50 | C5×#226 | C23 | 1 | 1 | yes | characteristic |
| 51 | C5×#226 | C23 | 1 | 3 | yes | — |
| 52 | #5945 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5927 | C2×C5 | 1 | 3 | yes | complemented |
| 54 | #5926 | C2×C5 | 1 | 3 | yes | complemented |
| 55 | #5925 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 56 | #5924 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 57 | #5923 | C2×C5 | 1 | 3 | yes | complemented |
| 58 | C2×#985 | C2×C5 | 1 | 3 | yes | complemented |
| 59 | C5×2−1+4 | — | 3 | 1 | no | — |
| 60 | C5×2−1+4 | — | 3 | 3 | no | — |
| 61 | C5×2−1+4 | — | 3 | 1 | no | — |
| 62 | C5×2−1+4 | — | 6 | 1 | no | — |
| 63 | C5×2−1+4 | C2×D3 | 1 | 3 | yes | complemented |
| 64 | C5×H(5,𝔽2) | — | 3 | 3 | no | — |
| 65 | C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 66 | C5×H(5,𝔽2) | — | 3 | 3 | no | — |
| 67 | C5×H(5,𝔽2) | — | 6 | 3 | no | — |
| 68 | C5×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×C5×#41 | — | 3 | 1 | no | — |
| 70 | C2×C5×#41 | — | 3 | 3 | no | — |
| 71 | C2×C5×#41 | — | 3 | 3 | no | — |
| 72 | C2×C5×#41 | — | 3 | 3 | no | — |
| 73 | C2×C5×#41 | — | 6 | 3 | no | — |
| 74 | C2×C5×#41 | — | 6 | 1 | no | — |
| 75 | C2×C5×#41 | C2×D3 | 1 | 3 | yes | complemented |
| 76 | C5×#137 | — | 3 | 3 | no | — |
| 77 | C5×#137 | — | 3 | 3 | no | — |
| 78 | C5×#137 | — | 3 | 3 | no | — |
| 79 | C5×#137 | — | 3 | 6 | no | — |
| 80 | C5×#137 | — | 3 | 3 | no | — |
| 81 | C5×#137 | — | 3 | 6 | no | — |
| 82 | C5×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 83 | C5×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 84 | C5×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 85 | C5×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 86 | C5×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 87 | C5×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 88 | C5×#135 | — | 3 | 3 | no | — |
| 89 | C5×#135 | — | 3 | 6 | no | — |
| 90 | C5×#135 | — | 3 | 3 | no | — |
| 91 | C5×#135 | — | 3 | 3 | no | — |
| 92 | C5×#135 | — | 3 | 6 | no | — |
| 93 | C5×#135 | — | 3 | 3 | no | — |
| 94 | C5×#135 | — | 3 | 6 | no | — |
| 95 | C5×#135 | — | 3 | 1 | no | — |
| 96 | C5×#135 | — | 3 | 3 | no | — |
| 97 | C5×#135 | — | 3 | 3 | no | — |
| 98 | C5×#135 | — | 3 | 3 | no | — |
| 99 | C2×C5×Q16 | — | 3 | 3 | no | — |
| 100 | C2×C5×Q16 | — | 3 | 3 | no | — |
| 101 | C2×C5×SD16 | — | 3 | 3 | no | — |
| 102 | C2×C5×SD16 | — | 3 | 3 | no | — |
| 103 | C2×C5×SD16 | — | 3 | 3 | no | — |
| 104 | C2×C5×SD16 | — | 3 | 3 | no | — |
| 105 | C2×C5×D8 | — | 3 | 3 | no | — |
| 106 | C2×C5×D8 | — | 3 | 3 | no | — |
| 107 | C5×#131 | — | 3 | 1 | no | — |
| 108 | C5×#131 | — | 3 | 3 | no | — |
| 109 | C5×#131 | — | 3 | 1 | no | — |
| 110 | C5×#131 | — | 3 | 3 | no | — |
| 111 | C2×C5×M16 | — | 3 | 3 | no | — |
| 112 | C22×C5×C8 | — | 3 | 3 | no | — |
| 113 | #3584 | — | 3 | 1 | no | Sylow |
| 114 | C22×C5×D3 | — | 4 | 3 | no | — |
| 115 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 116 | C3×C5×D4 | — | 4 | 3 | no | — |
| 117 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 118 | C5×#67 | — | 4 | 6 | no | — |
| 119 | C2×C5×Dic3 | — | 4 | 3 | no | — |
| 120 | C5×D12 | — | 4 | 3 | no | — |
| 121 | C4×C5×D3 | — | 4 | 1 | no | — |
| 122 | C4×C5×D3 | — | 4 | 3 | no | — |
| 123 | C4×C5×D3 | — | 4 | 3 | no | — |
| 124 | C4×C5×D3 | — | 4 | 3 | no | — |
| 125 | C5×Dic6 | — | 4 | 3 | no | — |
| 126 | C5×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 127 | D3×#41 | — | 4 | 1 | no | — |
| 128 | 2−1+4⋊C3 | C22×C5 | 1 | 3 | yes | complemented |
| 129 | #994 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×#41⋊C3 | C22×C5 | 1 | 3 | yes | complemented |
| 131 | #986 | C22×C5 | 1 | 3 | yes | complemented |
| 132 | #985 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 133 | #985 | C22×C5 | 1 | 3 | yes | complemented |
| 134 | #985 | C22×C5 | 1 | 3 | yes | complemented |
| 135 | #985 | C22×C5 | 1 | 3 | yes | complemented |
| 136 | #984 | C22×C5 | 1 | 3 | yes | complemented |
| 137 | #983 | C22×C5 | 1 | 6 | yes | complemented |
| 138 | C2×GL(2,𝔽3) | C22×C5 | 1 | 3 | yes | complemented |
| 139 | C2×#226 | C22×C5 | 1 | 3 | yes | complemented |
| 140 | C5×#41 | — | 3 | 1 | no | — |
| 141 | C5×#41 | — | 3 | 3 | no | — |
| 142 | C5×#41 | — | 3 | 3 | no | — |
| 143 | C5×#41 | — | 3 | 3 | no | — |
| 144 | C5×#41 | — | 3 | 3 | no | — |
| 145 | C5×#41 | — | 3 | 6 | no | — |
| 146 | C5×#41 | — | 3 | 3 | no | — |
| 147 | C5×#41 | — | 3 | 1 | no | — |
| 148 | C5×#41 | — | 3 | 6 | no | — |
| 149 | C5×#41 | — | 3 | 3 | no | — |
| 150 | C5×#41 | — | 3 | 3 | no | — |
| 151 | C5×#41 | — | 6 | 3 | no | — |
| 152 | C5×#41 | — | 6 | 3 | no | — |
| 153 | C5×#41 | — | 6 | 3 | no | — |
| 154 | C5×#41 | — | 6 | 3 | no | — |
| 155 | C5×#41 | — | 6 | 6 | no | — |
| 156 | C5×#41 | — | 6 | 3 | no | — |
| 157 | C5×#41 | — | 6 | 3 | no | — |
| 158 | C5×#41 | — | 6 | 1 | no | — |
| 159 | C5×#41 | — | 6 | 3 | no | — |
| 160 | C5×#41 | — | 6 | 3 | no | — |
| 161 | C5×#41 | S4 | 1 | 1 | yes | characteristic |
| 162 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 163 | C5×#41 | C22×D3 | 1 | 3 | yes | — |
| 164 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 165 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 166 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 167 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 168 | C2×C5×Q8 | — | 6 | 3 | no | — |
| 169 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 170 | C2×C5×Q8 | C22×D3 | 1 | 3 | yes | — |
| 171 | C2×C5×D4 | — | 3 | 3 | no | — |
| 172 | C2×C5×D4 | — | 3 | 3 | no | — |
| 173 | C2×C5×D4 | — | 3 | 3 | no | — |
| 174 | C2×C5×D4 | — | 3 | 3 | no | — |
| 175 | C2×C5×D4 | — | 3 | 3 | no | — |
| 176 | C2×C5×D4 | — | 6 | 3 | no | — |
| 177 | C2×C5×D4 | — | 6 | 6 | no | — |
| 178 | C2×C5×D4 | — | 6 | 3 | no | — |
| 179 | C2×C5×D4 | — | 6 | 3 | no | — |
| 180 | C2×C5×D4 | — | 6 | 3 | no | — |
| 181 | C2×C5×D4 | — | 6 | 3 | no | — |
| 182 | C22×C4×C5 | — | 3 | 3 | no | — |
| 183 | C22×C4×C5 | — | 6 | 1 | no | — |
| 184 | C22×C4×C5 | — | 6 | 3 | no | — |
| 185 | C22×C4×C5 | — | 6 | 3 | no | — |
| 186 | C5×Q16 | — | 3 | 3 | no | — |
| 187 | C5×Q16 | — | 3 | 6 | no | — |
| 188 | C5×Q16 | — | 3 | 3 | no | — |
| 189 | C5×Q16 | — | 3 | 1 | no | — |
| 190 | C5×Q16 | — | 3 | 3 | no | — |
| 191 | C5×SD16 | — | 3 | 3 | no | — |
| 192 | C5×SD16 | — | 3 | 1 | no | — |
| 193 | C5×SD16 | — | 3 | 3 | no | — |
| 194 | C5×SD16 | — | 3 | 6 | no | — |
| 195 | C5×SD16 | — | 3 | 3 | no | — |
| 196 | C5×SD16 | — | 3 | 3 | no | — |
| 197 | C5×SD16 | — | 3 | 6 | no | — |
| 198 | C5×SD16 | — | 3 | 3 | no | — |
| 199 | C5×SD16 | — | 3 | 1 | no | — |
| 200 | C5×SD16 | — | 3 | 3 | no | — |
| 201 | C5×D8 | — | 3 | 3 | no | — |
| 202 | C5×D8 | — | 3 | 1 | no | — |
| 203 | C5×D8 | — | 3 | 6 | no | — |
| 204 | C5×D8 | — | 3 | 3 | no | — |
| 205 | C5×D8 | — | 3 | 3 | no | — |
| 206 | C5×M16 | — | 3 | 6 | no | — |
| 207 | C5×M16 | — | 3 | 3 | no | — |
| 208 | C5×M16 | — | 3 | 3 | no | — |
| 209 | C2×C5×C8 | — | 3 | 1 | no | — |
| 210 | C2×C5×C8 | — | 3 | 3 | no | — |
| 211 | C2×C5×C8 | — | 3 | 3 | no | — |
| 212 | C2×C5×C8 | — | 3 | 3 | no | — |
| 213 | C2×C5×C8 | — | 3 | 3 | no | — |
| 214 | C2×C5×C8 | — | 3 | 3 | no | — |
| 215 | #585 | — | 3 | 1 | no | — |
| 216 | #585 | C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 217 | #578 | — | 3 | 1 | no | — |
| 218 | #578 | — | 3 | 3 | no | — |
| 219 | #577 | — | 3 | 3 | no | — |
| 220 | #577 | — | 3 | 1 | no | — |
| 221 | #577 | — | 3 | 3 | no | — |
| 222 | #577 | — | 3 | 1 | no | — |
| 223 | #576 | — | 3 | 3 | no | — |
| 224 | #576 | — | 3 | 1 | no | — |
| 225 | #575 | — | 3 | 3 | no | — |
| 226 | #575 | — | 3 | 3 | no | — |
| 227 | C2×#135 | — | 3 | 3 | no | — |
| 228 | C2×#135 | — | 3 | 3 | no | — |
| 229 | C2×#131 | — | 3 | 1 | no | — |
| 230 | C22×C3×C5 | — | 4 | 3 | no | — |
| 231 | C2×C5×D3 | — | 4 | 1 | no | — |
| 232 | C2×C5×D3 | — | 4 | 3 | no | — |
| 233 | C2×C5×D3 | — | 8 | 6 | no | — |
| 234 | C3×C4×C5 | — | 4 | 3 | no | — |
| 235 | C3×C4×C5 | — | 4 | 1 | no | — |
| 236 | C5×Dic3 | — | 4 | 3 | no | — |
| 237 | C5×Dic3 | — | 4 | 1 | no | — |
| 238 | C3×#41 | — | 4 | 1 | no | — |
| 239 | #239 | — | 4 | 1 | no | — |
| 240 | D3×Q8 | — | 4 | 1 | no | — |
| 241 | #237 | — | 4 | 3 | no | — |
| 242 | D3×D4 | — | 4 | 3 | no | — |
| 243 | #235 | — | 4 | 3 | no | — |
| 244 | C2×C4×D3 | — | 4 | 3 | no | — |
| 245 | #41⋊C3 | C23×C5 | 1 | 3 | yes | — |
| 246 | #41⋊C3 | C23×C5 | 1 | 1 | yes | characteristic |
| 247 | C2×SL(2,𝔽3) | C23×C5 | 1 | 3 | yes | — |
| 248 | GL(2,𝔽3) | C23×C5 | 1 | 1 | yes | characteristic |
| 249 | GL(2,𝔽3) | C23×C5 | 1 | 3 | yes | — |
| 250 | #226 | C23×C5 | 1 | 1 | yes | characteristic |
| 251 | #226 | C23×C5 | 1 | 3 | yes | — |
| 252 | C23×C5 | — | 3 | 3 | no | — |
| 253 | C23×C5 | — | 6 | 1 | no | — |
| 254 | C23×C5 | — | 6 | 3 | no | — |
| 255 | C23×C5 | — | 6 | 3 | no | — |
| 256 | C5×Q8 | — | 3 | 3 | no | — |
| 257 | C5×Q8 | — | 3 | 3 | no | — |
| 258 | C5×Q8 | — | 3 | 3 | no | — |
| 259 | C5×Q8 | — | 3 | 1 | no | — |
| 260 | C5×Q8 | — | 6 | 3 | no | — |
| 261 | C5×Q8 | — | 6 | 3 | no | — |
| 262 | C5×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 263 | C5×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 264 | C5×D4 | — | 3 | 1 | no | — |
| 265 | C5×D4 | — | 3 | 3 | no | — |
| 266 | C5×D4 | — | 3 | 6 | no | — |
| 267 | C5×D4 | — | 3 | 3 | no | — |
| 268 | C5×D4 | — | 3 | 1 | no | — |
| 269 | C5×D4 | — | 3 | 3 | no | — |
| 270 | C5×D4 | — | 6 | 3 | no | — |
| 271 | C5×D4 | — | 6 | 3 | no | — |
| 272 | C5×D4 | — | 6 | 3 | no | — |
| 273 | C5×D4 | — | 6 | 1 | no | — |
| 274 | C5×D4 | — | 6 | 3 | no | — |
| 275 | C5×D4 | — | 6 | 3 | no | — |
| 276 | C5×D4 | — | 6 | 6 | no | — |
| 277 | C5×D4 | — | 6 | 3 | no | — |
| 278 | C5×D4 | C2×S4 | 1 | 3 | yes | — |
| 279 | C2×C4×C5 | — | 3 | 3 | no | — |
| 280 | C2×C4×C5 | — | 3 | 3 | no | — |
| 281 | C2×C4×C5 | — | 3 | 3 | no | — |
| 282 | C2×C4×C5 | — | 3 | 1 | no | — |
| 283 | C2×C4×C5 | — | 3 | 3 | no | — |
| 284 | C2×C4×C5 | — | 6 | 3 | no | — |
| 285 | C2×C4×C5 | — | 6 | 6 | no | — |
| 286 | C2×C4×C5 | — | 6 | 3 | no | — |
| 287 | C2×C4×C5 | — | 6 | 3 | no | — |
| 288 | C2×C4×C5 | — | 6 | 3 | no | — |
| 289 | C2×C4×C5 | — | 6 | 3 | no | — |
| 290 | C2×C4×C5 | — | 6 | 1 | no | — |
| 291 | C2×C4×C5 | — | 6 | 3 | no | — |
| 292 | C2×C4×C5 | C2×S4 | 1 | 3 | yes | — |
| 293 | C5×C8 | — | 3 | 1 | no | — |
| 294 | C5×C8 | — | 3 | 1 | no | — |
| 295 | C5×C8 | — | 3 | 3 | no | — |
| 296 | C5×C8 | — | 3 | 3 | no | — |
| 297 | 2−1+4 | — | 3 | 1 | no | — |
| 298 | 2−1+4 | — | 3 | 3 | no | — |
| 299 | 2−1+4 | — | 3 | 1 | no | — |
| 300 | 2−1+4 | — | 6 | 1 | no | — |
| 301 | 2−1+4 | C2×C5×D3 | 1 | 3 | yes | complemented |
| 302 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 303 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 304 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 305 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 306 | H(5,𝔽2) | C2×C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 307 | C2×#41 | — | 3 | 1 | no | — |
| 308 | C2×#41 | — | 3 | 3 | no | — |
| 309 | C2×#41 | — | 3 | 3 | no | — |
| 310 | C2×#41 | — | 3 | 3 | no | — |
| 311 | C2×#41 | — | 6 | 3 | no | — |
| 312 | C2×#41 | — | 6 | 1 | no | — |
| 313 | C2×#41 | C2×C5×D3 | 1 | 3 | yes | complemented |
| 314 | #137 | — | 3 | 3 | no | — |
| 315 | #137 | — | 3 | 3 | no | — |
| 316 | #137 | — | 3 | 3 | no | — |
| 317 | #137 | — | 3 | 6 | no | — |
| 318 | #137 | — | 3 | 3 | no | — |
| 319 | #137 | — | 3 | 6 | no | — |
| 320 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 321 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 322 | AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 323 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 324 | AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 325 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 326 | #135 | — | 3 | 3 | no | — |
| 327 | #135 | — | 3 | 6 | no | — |
| 328 | #135 | — | 3 | 3 | no | — |
| 329 | #135 | — | 3 | 3 | no | — |
| 330 | #135 | — | 3 | 6 | no | — |
| 331 | #135 | — | 3 | 3 | no | — |
| 332 | #135 | — | 3 | 6 | no | — |
| 333 | #135 | — | 3 | 1 | no | — |
| 334 | #135 | — | 3 | 3 | no | — |
| 335 | #135 | — | 3 | 3 | no | — |
| 336 | #135 | — | 3 | 3 | no | — |
| 337 | C2×Q16 | — | 3 | 3 | no | — |
| 338 | C2×Q16 | — | 3 | 3 | no | — |
| 339 | C2×SD16 | — | 3 | 3 | no | — |
| 340 | C2×SD16 | — | 3 | 3 | no | — |
| 341 | C2×SD16 | — | 3 | 3 | no | — |
| 342 | C2×SD16 | — | 3 | 3 | no | — |
| 343 | C2×D8 | — | 3 | 3 | no | — |
| 344 | C2×D8 | — | 3 | 3 | no | — |
| 345 | #131 | — | 3 | 1 | no | — |
| 346 | #131 | — | 3 | 3 | no | — |
| 347 | #131 | — | 3 | 1 | no | — |
| 348 | #131 | — | 3 | 3 | no | — |
| 349 | C2×M16 | — | 3 | 3 | no | — |
| 350 | C22×C8 | — | 3 | 3 | no | — |
| 351 | C2×C3×C5 | — | 4 | 1 | no | — |
| 352 | C2×C3×C5 | — | 8 | 3 | no | — |
| 353 | C5×D3 | — | 4 | 2 | no | — |
| 354 | C5×D3 | — | 8 | 3 | no | — |
| 355 | C22×D3 | — | 4 | 3 | no | — |
| 356 | C3×Q8 | — | 4 | 1 | no | — |
| 357 | C3×D4 | — | 4 | 3 | no | — |
| 358 | C2×C3×C4 | — | 4 | 3 | no | — |
| 359 | #67 | — | 4 | 6 | no | — |
| 360 | C2×Dic3 | — | 4 | 3 | no | — |
| 361 | D12 | — | 4 | 3 | no | — |
| 362 | C4×D3 | — | 4 | 1 | no | — |
| 363 | C4×D3 | — | 4 | 3 | no | — |
| 364 | C4×D3 | — | 4 | 3 | no | — |
| 365 | C4×D3 | — | 4 | 3 | no | — |
| 366 | Dic6 | — | 4 | 3 | no | — |
| 367 | SL(2,𝔽3) | C24×C5 | 1 | 1 | yes | characteristic |
| 368 | C22×C5 | — | 3 | 1 | no | — |
| 369 | C22×C5 | — | 3 | 3 | no | — |
| 370 | C22×C5 | — | 6 | 1 | no | — |
| 371 | C22×C5 | — | 6 | 3 | no | — |
| 372 | C22×C5 | — | 12 | 3 | no | — |
| 373 | C22×C5 | — | 24 | 3 | no | — |
| 374 | C22×C5 | — | 24 | 1 | no | — |
| 375 | C22×C5 | — | 24 | 3 | no | — |
| 376 | C22×C5 | C22×S4 | 1 | 3 | yes | — |
| 377 | C4×C5 | — | 3 | 1 | no | — |
| 378 | C4×C5 | — | 3 | 3 | no | — |
| 379 | C4×C5 | — | 6 | 3 | no | — |
| 380 | C4×C5 | — | 6 | 1 | no | — |
| 381 | C4×C5 | C22×S4 | 1 | 3 | yes | — |
| 382 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 383 | #41 | — | 3 | 1 | no | — |
| 384 | #41 | — | 3 | 3 | no | — |
| 385 | #41 | — | 3 | 3 | no | — |
| 386 | #41 | — | 3 | 3 | no | — |
| 387 | #41 | — | 3 | 3 | no | — |
| 388 | #41 | — | 3 | 6 | no | — |
| 389 | #41 | — | 3 | 3 | no | — |
| 390 | #41 | — | 3 | 1 | no | — |
| 391 | #41 | — | 3 | 6 | no | — |
| 392 | #41 | — | 3 | 3 | no | — |
| 393 | #41 | — | 3 | 3 | no | — |
| 394 | #41 | — | 6 | 3 | no | — |
| 395 | #41 | — | 6 | 3 | no | — |
| 396 | #41 | — | 6 | 3 | no | — |
| 397 | #41 | — | 6 | 3 | no | — |
| 398 | #41 | — | 6 | 6 | no | — |
| 399 | #41 | — | 6 | 3 | no | — |
| 400 | #41 | — | 6 | 3 | no | — |
| 401 | #41 | — | 6 | 1 | no | — |
| 402 | #41 | — | 6 | 3 | no | — |
| 403 | #41 | — | 6 | 3 | no | — |
| 404 | #41 | C5×S4 | 1 | 1 | yes | characteristic |
| 405 | #41 | C22×C5×D3 | 1 | 1 | yes | characteristic |
| 406 | #41 | C22×C5×D3 | 1 | 3 | yes | — |
| 407 | C2×Q8 | — | 3 | 1 | no | — |
| 408 | C2×Q8 | — | 3 | 3 | no | — |
| 409 | C2×Q8 | — | 3 | 3 | no | — |
| 410 | C2×Q8 | — | 3 | 3 | no | — |
| 411 | C2×Q8 | — | 6 | 3 | no | — |
| 412 | C2×Q8 | — | 6 | 1 | no | — |
| 413 | C2×Q8 | C22×C5×D3 | 1 | 3 | yes | — |
| 414 | C2×D4 | — | 3 | 3 | no | — |
| 415 | C2×D4 | — | 3 | 3 | no | — |
| 416 | C2×D4 | — | 3 | 3 | no | — |
| 417 | C2×D4 | — | 3 | 3 | no | — |
| 418 | C2×D4 | — | 3 | 3 | no | — |
| 419 | C2×D4 | — | 6 | 3 | no | — |
| 420 | C2×D4 | — | 6 | 6 | no | — |
| 421 | C2×D4 | — | 6 | 3 | no | — |
| 422 | C2×D4 | — | 6 | 3 | no | — |
| 423 | C2×D4 | — | 6 | 3 | no | — |
| 424 | C2×D4 | — | 6 | 3 | no | — |
| 425 | C22×C4 | — | 3 | 3 | no | — |
| 426 | C22×C4 | — | 6 | 1 | no | — |
| 427 | C22×C4 | — | 6 | 3 | no | — |
| 428 | C22×C4 | — | 6 | 3 | no | — |
| 429 | Q16 | — | 3 | 3 | no | — |
| 430 | Q16 | — | 3 | 6 | no | — |
| 431 | Q16 | — | 3 | 3 | no | — |
| 432 | Q16 | — | 3 | 1 | no | — |
| 433 | Q16 | — | 3 | 3 | no | — |
| 434 | SD16 | — | 3 | 3 | no | — |
| 435 | SD16 | — | 3 | 1 | no | — |
| 436 | SD16 | — | 3 | 3 | no | — |
| 437 | SD16 | — | 3 | 6 | no | — |
| 438 | SD16 | — | 3 | 3 | no | — |
| 439 | SD16 | — | 3 | 3 | no | — |
| 440 | SD16 | — | 3 | 6 | no | — |
| 441 | SD16 | — | 3 | 3 | no | — |
| 442 | SD16 | — | 3 | 1 | no | — |
| 443 | SD16 | — | 3 | 3 | no | — |
| 444 | D8 | — | 3 | 3 | no | — |
| 445 | D8 | — | 3 | 1 | no | — |
| 446 | D8 | — | 3 | 6 | no | — |
| 447 | D8 | — | 3 | 3 | no | — |
| 448 | D8 | — | 3 | 3 | no | — |
| 449 | M16 | — | 3 | 6 | no | — |
| 450 | M16 | — | 3 | 3 | no | — |
| 451 | M16 | — | 3 | 3 | no | — |
| 452 | C2×C8 | — | 3 | 1 | no | — |
| 453 | C2×C8 | — | 3 | 3 | no | — |
| 454 | C2×C8 | — | 3 | 3 | no | — |
| 455 | C2×C8 | — | 3 | 3 | no | — |
| 456 | C2×C8 | — | 3 | 3 | no | — |
| 457 | C2×C8 | — | 3 | 3 | no | — |
| 458 | C3×C5 | — | 4 | 1 | no | Hall |
| 459 | C22×C3 | — | 4 | 3 | no | — |
| 460 | C2×D3 | — | 4 | 1 | no | — |
| 461 | C2×D3 | — | 4 | 3 | no | — |
| 462 | C2×D3 | — | 8 | 6 | no | — |
| 463 | C3×C4 | — | 4 | 3 | no | — |
| 464 | C3×C4 | — | 4 | 1 | no | — |
| 465 | Dic3 | — | 4 | 3 | no | — |
| 466 | Dic3 | — | 4 | 1 | no | — |
| 467 | C2×C5 | — | 2 | 3 | no | — |
| 468 | C2×C5 | — | 6 | 1 | no | — |
| 469 | C2×C5 | — | 6 | 3 | no | — |
| 470 | C2×C5 | — | 12 | 1 | no | — |
| 471 | C2×C5 | — | 12 | 3 | no | — |
| 472 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 473 | C23 | — | 3 | 3 | no | — |
| 474 | C23 | — | 6 | 1 | no | — |
| 475 | C23 | — | 6 | 3 | no | — |
| 476 | C23 | — | 6 | 3 | no | — |
| 477 | Q8 | — | 3 | 3 | no | — |
| 478 | Q8 | — | 3 | 3 | no | — |
| 479 | Q8 | — | 3 | 3 | no | — |
| 480 | Q8 | — | 3 | 1 | no | — |
| 481 | Q8 | — | 6 | 3 | no | — |
| 482 | Q8 | — | 6 | 3 | no | — |
| 483 | Q8 | C2×C5×S4 | 1 | 1 | yes | characteristic |
| 484 | Q8 | C23×C5×D3 | 1 | 1 | yes | characteristic |
| 485 | D4 | — | 3 | 1 | no | — |
| 486 | D4 | — | 3 | 3 | no | — |
| 487 | D4 | — | 3 | 6 | no | — |
| 488 | D4 | — | 3 | 3 | no | — |
| 489 | D4 | — | 3 | 1 | no | — |
| 490 | D4 | — | 3 | 3 | no | — |
| 491 | D4 | — | 6 | 3 | no | — |
| 492 | D4 | — | 6 | 3 | no | — |
| 493 | D4 | — | 6 | 3 | no | — |
| 494 | D4 | — | 6 | 1 | no | — |
| 495 | D4 | — | 6 | 3 | no | — |
| 496 | D4 | — | 6 | 3 | no | — |
| 497 | D4 | — | 6 | 6 | no | — |
| 498 | D4 | — | 6 | 3 | no | — |
| 499 | D4 | C2×C5×S4 | 1 | 3 | yes | — |
| 500 | C2×C4 | — | 3 | 3 | no | — |
| 501 | C2×C4 | — | 3 | 1 | no | — |
| 502 | C2×C4 | — | 3 | 3 | no | — |
| 503 | C2×C4 | — | 3 | 3 | no | — |
| 504 | C2×C4 | — | 3 | 3 | no | — |
| 505 | C2×C4 | — | 6 | 3 | no | — |
| 506 | C2×C4 | — | 6 | 6 | no | — |
| 507 | C2×C4 | — | 6 | 3 | no | — |
| 508 | C2×C4 | — | 6 | 3 | no | — |
| 509 | C2×C4 | — | 6 | 3 | no | — |
| 510 | C2×C4 | — | 6 | 1 | no | — |
| 511 | C2×C4 | — | 6 | 3 | no | — |
| 512 | C2×C4 | — | 6 | 3 | no | — |
| 513 | C2×C4 | C2×C5×S4 | 1 | 3 | yes | — |
| 514 | C8 | — | 3 | 1 | no | — |
| 515 | C8 | — | 3 | 1 | no | — |
| 516 | C8 | — | 3 | 3 | no | — |
| 517 | C8 | — | 3 | 3 | no | — |
| 518 | C2×C3 | — | 4 | 1 | no | — |
| 519 | C2×C3 | — | 8 | 3 | no | — |
| 520 | D3 | — | 4 | 2 | no | — |
| 521 | D3 | — | 8 | 3 | no | — |
| 522 | C5 | #87497 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 523 | C22 | — | 3 | 1 | no | — |
| 524 | C22 | — | 3 | 3 | no | — |
| 525 | C22 | — | 6 | 1 | no | — |
| 526 | C22 | — | 6 | 3 | no | — |
| 527 | C22 | — | 12 | 3 | no | — |
| 528 | C22 | — | 24 | 3 | no | — |
| 529 | C22 | — | 24 | 1 | no | — |
| 530 | C22 | — | 24 | 3 | no | — |
| 531 | C22 | C22×C5×S4 | 1 | 3 | yes | — |
| 532 | C4 | — | 3 | 1 | no | — |
| 533 | C4 | — | 3 | 3 | no | — |
| 534 | C4 | — | 6 | 3 | no | — |
| 535 | C4 | — | 6 | 1 | no | — |
| 536 | C4 | C22×C5×S4 | 1 | 1 | yes | characteristic |
| 537 | C4 | C22×C5×S4 | 1 | 3 | yes | — |
| 538 | C3 | — | 4 | 1 | no | Sylow |
| 539 | C2 | — | 2 | 3 | no | — |
| 540 | C2 | — | 6 | 1 | no | — |
| 541 | C2 | — | 6 | 3 | no | — |
| 542 | C2 | — | 12 | 1 | no | — |
| 543 | C2 | — | 12 | 3 | no | — |
| 544 | C2 | C23×C5×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C24×C5 |
| Frattini | C2 | C23×C5×S4 |
| Fitting | C5×#585 | D3 |
| socle | C2×C5 | C23×S4 |
| hypercenter | C5×#41 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5945 | C2 | semidirect |
| 2. C5×#5927 | C2 | semidirect |
| 3. C5×#5926 | C2 | semidirect |
| 4. C5×#5925 | C2 | semidirect |
| 5. C5×#5924 | C2 | semidirect |
| 6. C5×#5923 | C2 | semidirect |
| 7. C2×C5×#985 | C2 | semidirect |
| 10. C5×2−1+4⋊C3 | C22 | semidirect |
| 11. C5×#994 | C22 | semidirect |
| 12. C2×C5×#41⋊C3 | C22 | semidirect |
| 13. C5×#986 | C22 | semidirect |
| 14. C5×#985 | C22 | semidirect |
| 15. C5×#985 | C22 | semidirect |
| 16. C5×#985 | C22 | semidirect |
| 17. C5×#985 | C22 | semidirect |
| 18. C5×#984 | C22 | semidirect |
| 19. C5×#983 | C22 | semidirect |
| 20. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 21. C2×C5×#226 | C22 | semidirect |
| 22. #87497 | C5 | direct (N × H) |
| 24. C5×#585 | D3 | semidirect |
| 52. #5945 | C2×C5 | semidirect |
| 53. #5927 | C2×C5 | semidirect |
| 54. #5926 | C2×C5 | semidirect |
| 55. #5925 | C2×C5 | semidirect |
| 56. #5924 | C2×C5 | semidirect |
| 57. #5923 | C2×C5 | semidirect |
| 58. C2×#985 | C2×C5 | semidirect |
| 63. C5×2−1+4 | C2×D3 | semidirect |
| 68. C5×H(5,𝔽2) | C2×D3 | semidirect |
| 75. C2×C5×#41 | C2×D3 | semidirect |
| 128. 2−1+4⋊C3 | C22×C5 | semidirect |
| 129. #994 | C22×C5 | semidirect |
| 130. C2×#41⋊C3 | C22×C5 | semidirect |
| 131. #986 | C22×C5 | semidirect |
| 132. #985 | C22×C5 | semidirect |
| 133. #985 | C22×C5 | semidirect |
| 134. #985 | C22×C5 | semidirect |
| 135. #985 | C22×C5 | semidirect |
| 136. #984 | C22×C5 | semidirect |
| 137. #983 | C22×C5 | semidirect |
| 138. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 139. C2×#226 | C22×C5 | semidirect |
| 216. #585 | C5×D3 | semidirect |
| 301. 2−1+4 | C2×C5×D3 | semidirect |
| 306. H(5,𝔽2) | C2×C5×D3 | semidirect |
| 313. C2×#41 | C2×C5×D3 | semidirect |
| 522. C5 | #87497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| C5×#5927 | 2 |
| C5×#5926 | 2 |
| C5×#5925 | 2 |
| C5×#5924 | 2 |
| C5×#5923 | 2 |
| C2×C5×#985 | 2 |
| C5×#3584 | 3 |
| C5×D3×#41 | 4 |
| #87497 | 5 |