Finite Group DatabasebetaFinite Group DatabasebetaOrder 5760.
1368 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 52 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×C3⋊#5935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×C5×#5935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×D3×#997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C5×#5935 | — | 3 | 1 | no | maximal |
| 5 | C5×D3×#453 | — | 3 | 1 | no | maximal |
| 6 | C2×C5×D3×S4 | — | 4 | 1 | no | maximal |
| 7 | C3×C5×#997 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | C5×D3×GL(2,𝔽3) | — | 4 | 2 | no | maximal |
| 9 | D3×#5935 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 10 | C5×D3×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×C5×#997 | — | 3 | 1 | no | — |
| 12 | C5×#5935 | — | 3 | 1 | no | — |
| 13 | C5×#5935 | — | 6 | 1 | no | — |
| 14 | C5×#5935 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 15 | C5×D3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 16 | C5×D3×#127 | — | 3 | 1 | no | — |
| 17 | C3×C5×#453 | — | 3 | 1 | no | — |
| 18 | C5×#5241 | — | 3 | 1 | no | — |
| 19 | C5×#5198 | — | 3 | 2 | no | — |
| 20 | C5×#5077 | — | 3 | 1 | no | — |
| 21 | C5×#4822 | — | 3 | 2 | no | — |
| 22 | C5×D3×#104 | — | 3 | 2 | no | — |
| 23 | C5×#4747 | — | 3 | 1 | no | — |
| 24 | C5×D3×#100 | — | 3 | 1 | no | — |
| 25 | C2×C5×D3×A4 | — | 4 | 1 | no | — |
| 26 | C2×C5×D3×A4 | — | 8 | 1 | no | — |
| 27 | C2×C5×C3⋊S4 | — | 4 | 1 | no | — |
| 28 | C2×C3×C5×S4 | — | 4 | 1 | no | — |
| 29 | C5×D3×S4 | — | 4 | 4 | no | — |
| 30 | C5×D3×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 31 | C5×C3⋊GL(2,𝔽3) | — | 4 | 2 | no | — |
| 32 | C3×C5×GL(2,𝔽3) | — | 4 | 2 | no | — |
| 33 | C2×C5×#453 | — | 9 | 1 | no | Hall |
| 34 | D3×#997 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 35 | C3⋊#5935 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×#5935 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 37 | C22×C5×S4 | — | 12 | 1 | no | — |
| 38 | C3×C5×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 39 | C5×#1009 | — | 3 | 2 | no | — |
| 40 | C5×D3×#41 | — | 3 | 2 | no | — |
| 41 | C5×#1004 | — | 3 | 1 | no | — |
| 42 | C5×#1004 | — | 6 | 1 | no | — |
| 43 | C2×C5×D3×D4 | — | 3 | 1 | no | — |
| 44 | C2×C5×D3×D4 | — | 3 | 1 | no | — |
| 45 | C2×C5×D3×D4 | — | 6 | 1 | no | — |
| 46 | C2×C5×D3×D4 | — | 6 | 1 | no | — |
| 47 | C2×C5×D3×D4 | — | 6 | 1 | no | — |
| 48 | C5×#997 | — | 2 | 1 | no | — |
| 49 | C5×#997 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C2×C5×GL(2,𝔽3) | — | 12 | 2 | no | — |
| 51 | C3×C5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 52 | C3×C5×#127 | — | 3 | 1 | no | — |
| 53 | C5×#949 | — | 3 | 2 | no | — |
| 54 | C5×#940 | — | 3 | 1 | no | — |
| 55 | C5×#940 | — | 3 | 1 | no | — |
| 56 | C5×#940 | — | 6 | 1 | no | — |
| 57 | C5×#940 | — | 6 | 1 | no | — |
| 58 | C5×#932 | — | 3 | 2 | no | — |
| 59 | C5×#914 | — | 6 | 2 | no | — |
| 60 | C5×D3×SD16 | — | 6 | 2 | no | — |
| 61 | C5×#911 | — | 6 | 2 | no | — |
| 62 | C5×D3×D8 | — | 6 | 2 | no | — |
| 63 | C5×#908 | — | 3 | 2 | no | — |
| 64 | C5×D3×M16 | — | 3 | 2 | no | — |
| 65 | C5×#874 | — | 3 | 1 | no | — |
| 66 | C42×C5×D3 | — | 3 | 1 | no | — |
| 67 | C3×C5×#104 | — | 3 | 2 | no | — |
| 68 | C3×C5×#100 | — | 3 | 1 | no | — |
| 69 | C5×#837 | — | 3 | 2 | no | — |
| 70 | C5×#833 | — | 3 | 1 | no | — |
| 71 | C5×#825 | — | 3 | 2 | no | — |
| 72 | C5×#823 | — | 3 | 2 | no | — |
| 73 | C5×#805 | — | 3 | 2 | no | — |
| 74 | C2×#5935 | — | 3 | 1 | no | — |
| 75 | D3×#453 | — | 3 | 1 | no | — |
| 76 | C2×C3×C5×A4 | — | 4 | 1 | no | — |
| 77 | C2×C3×C5×A4 | — | 8 | 1 | no | — |
| 78 | C2×C5×D32 | — | 16 | 1 | no | — |
| 79 | C5×D3×A4 | — | 4 | 2 | no | — |
| 80 | C5×D3×A4 | — | 8 | 2 | no | — |
| 81 | C5×C3⋊S4 | — | 4 | 2 | no | — |
| 82 | C3×C5×S4 | — | 4 | 2 | no | — |
| 83 | C3×C5×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 84 | C2×C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 85 | C2×C5×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 86 | C2×C5×#127 | — | 9 | 1 | no | — |
| 87 | C5×#453 | — | 3 | 1 | no | — |
| 88 | C5×#453 | — | 9 | 1 | no | — |
| 89 | C5×#453 | — | 9 | 2 | no | — |
| 90 | C5×#453 | — | 9 | 1 | no | — |
| 91 | C5×#453 | — | 9 | 2 | no | — |
| 92 | C5×#453 | — | 9 | 1 | no | — |
| 93 | C2×C5×#104 | — | 9 | 2 | no | — |
| 94 | C2×C5×#100 | — | 9 | 1 | no | — |
| 95 | C2×D3×S4 | — | 4 | 1 | no | — |
| 96 | C3×#997 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 97 | D3×GL(2,𝔽3) | — | 4 | 2 | no | — |
| 98 | C23×C5×D3 | — | 2 | 1 | no | — |
| 99 | C23×C5×D3 | — | 3 | 1 | no | — |
| 100 | C23×C5×D3 | — | 6 | 1 | no | — |
| 101 | C23×C5×D3 | S4 | 1 | 1 | yes | characteristic |
| 102 | C22×C5×A4 | — | 12 | 1 | no | — |
| 103 | C22×C5×A4 | — | 24 | 1 | no | — |
| 104 | C2×C5×S4 | — | 4 | 1 | no | — |
| 105 | C2×C5×S4 | — | 12 | 4 | no | — |
| 106 | C2×C5×S4 | — | 12 | 1 | no | — |
| 107 | C2×C5×S4 | — | 24 | 1 | no | — |
| 108 | C3×C5×#41 | — | 3 | 2 | no | — |
| 109 | C2×C3×C5×D4 | — | 3 | 1 | no | — |
| 110 | C2×C3×C5×D4 | — | 3 | 1 | no | — |
| 111 | C2×C3×C5×D4 | — | 6 | 1 | no | — |
| 112 | C2×C3×C5×D4 | — | 6 | 1 | no | — |
| 113 | C2×C3×C5×D4 | — | 6 | 1 | no | — |
| 114 | C2×C5×#67 | — | 3 | 1 | no | — |
| 115 | C2×C5×#67 | — | 3 | 1 | no | — |
| 116 | C2×C5×#67 | — | 6 | 1 | no | — |
| 117 | C2×C5×#67 | — | 6 | 1 | no | — |
| 118 | C2×C5×#67 | — | 6 | 1 | no | — |
| 119 | C2×C5×#67 | — | 6 | 1 | no | — |
| 120 | C2×C5×#67 | — | 6 | 1 | no | — |
| 121 | C2×C5×#67 | — | 6 | 1 | no | — |
| 122 | C2×C5×#67 | — | 6 | 1 | no | — |
| 123 | C5×#239 | — | 3 | 2 | no | — |
| 124 | C5×D3×Q8 | S4 | 1 | 2 | yes | complemented |
| 125 | C5×#237 | — | 3 | 2 | no | — |
| 126 | C5×#237 | — | 6 | 2 | no | — |
| 127 | C5×D3×D4 | — | 3 | 2 | no | — |
| 128 | C5×D3×D4 | — | 6 | 2 | no | — |
| 129 | C5×D3×D4 | — | 6 | 2 | no | — |
| 130 | C5×D3×D4 | — | 6 | 2 | no | — |
| 131 | C5×D3×D4 | — | 6 | 2 | no | — |
| 132 | C5×D3×D4 | — | 6 | 2 | no | — |
| 133 | C5×D3×D4 | — | 6 | 2 | no | — |
| 134 | C5×D3×D4 | — | 12 | 4 | no | — |
| 135 | C5×D3×D4 | — | 12 | 4 | no | — |
| 136 | C5×#235 | — | 3 | 2 | no | — |
| 137 | C5×#235 | — | 6 | 2 | no | — |
| 138 | C2×C5×D12 | — | 3 | 1 | no | — |
| 139 | C2×C5×D12 | — | 3 | 1 | no | — |
| 140 | C2×C5×D12 | — | 6 | 1 | no | — |
| 141 | C2×C5×D12 | — | 6 | 1 | no | — |
| 142 | C2×C5×D12 | — | 6 | 1 | no | — |
| 143 | C2×C4×C5×D3 | — | 3 | 1 | no | — |
| 144 | C2×C4×C5×D3 | — | 6 | 1 | no | — |
| 145 | C2×C4×C5×D3 | — | 6 | 1 | no | — |
| 146 | C2×C5×SL(2,𝔽3) | — | 12 | 2 | no | — |
| 147 | C5×GL(2,𝔽3) | — | 4 | 2 | no | — |
| 148 | C5×GL(2,𝔽3) | — | 12 | 2 | no | — |
| 149 | C5×GL(2,𝔽3) | — | 24 | 2 | no | — |
| 150 | C3×C5×SD16 | — | 6 | 2 | no | — |
| 151 | C3×C5×D8 | — | 6 | 2 | no | — |
| 152 | C3×C5×M16 | — | 3 | 2 | no | — |
| 153 | C3×C42×C5 | — | 3 | 1 | no | — |
| 154 | C5×#215 | — | 6 | 2 | no | — |
| 155 | C5×#214 | — | 6 | 2 | no | — |
| 156 | C5×#213 | — | 6 | 2 | no | — |
| 157 | C5×#213 | — | 6 | 2 | no | — |
| 158 | C4×C5×Dic3 | — | 3 | 1 | no | — |
| 159 | C4×C5×Dic3 | — | 6 | 1 | no | — |
| 160 | C5×#208 | — | 3 | 2 | no | — |
| 161 | C5×D24 | — | 6 | 2 | no | — |
| 162 | C5×#204 | — | 6 | 2 | no | — |
| 163 | C5×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 164 | C5×D3×C8 | — | 6 | 2 | no | — |
| 165 | D3×H(5,𝔽2) | C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 166 | C2×#997 | — | 3 | 1 | no | — |
| 167 | #5935 | — | 3 | 1 | no | — |
| 168 | #5935 | — | 6 | 1 | no | — |
| 169 | #5935 | C5×D3 | 1 | 1 | yes | characteristic, direct product factor |
| 170 | D3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 171 | D3×#127 | — | 3 | 1 | no | — |
| 172 | C3×#453 | — | 3 | 1 | no | — |
| 173 | #5241 | — | 3 | 1 | no | — |
| 174 | #5198 | — | 3 | 2 | no | — |
| 175 | #5077 | — | 3 | 1 | no | — |
| 176 | #4822 | — | 3 | 2 | no | — |
| 177 | D3×#104 | — | 3 | 2 | no | — |
| 178 | #4747 | — | 3 | 1 | no | — |
| 179 | D3×#100 | — | 3 | 1 | no | — |
| 180 | C2×C5×C3⋊D3 | — | 16 | 1 | no | — |
| 181 | C2×C3×C5×D3 | — | 16 | 1 | no | — |
| 182 | C2×C3×C5×D3 | — | 16 | 1 | no | — |
| 183 | C3×C5×A4 | — | 4 | 1 | no | — |
| 184 | C3×C5×A4 | — | 8 | 1 | no | — |
| 185 | C5×D32 | — | 16 | 4 | no | — |
| 186 | C5×H(5,𝔽2) | — | 9 | 1 | no | — |
| 187 | C5×H(5,𝔽2) | — | 9 | 2 | no | — |
| 188 | C5×H(5,𝔽2) | — | 18 | 1 | no | — |
| 189 | C5×H(5,𝔽2) | D32 | 1 | 1 | yes | characteristic, complemented |
| 190 | C2×C5×#41 | — | 9 | 2 | no | — |
| 191 | C22×C5×D4 | — | 9 | 1 | no | — |
| 192 | C22×C5×D4 | — | 9 | 1 | no | — |
| 193 | C22×C5×D4 | — | 18 | 1 | no | — |
| 194 | C22×C5×D4 | — | 18 | 1 | no | — |
| 195 | C22×C5×D4 | — | 18 | 1 | no | — |
| 196 | C5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 197 | C5×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 198 | C5×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 199 | C5×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 200 | C5×AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 201 | C5×AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 202 | C2×C5×SD16 | — | 18 | 2 | no | — |
| 203 | C2×C5×D8 | — | 18 | 2 | no | — |
| 204 | C2×C5×M16 | — | 9 | 2 | no | — |
| 205 | C5×#127 | — | 3 | 1 | no | — |
| 206 | C5×#127 | — | 9 | 1 | no | — |
| 207 | C5×#127 | — | 9 | 1 | no | — |
| 208 | C5×#127 | — | 9 | 1 | no | — |
| 209 | C5×#127 | — | 18 | 1 | no | — |
| 210 | C5×#127 | — | 18 | 1 | no | — |
| 211 | C2×C42×C5 | — | 9 | 1 | no | — |
| 212 | C5×#104 | — | 3 | 2 | no | — |
| 213 | C5×#104 | — | 9 | 2 | no | — |
| 214 | C5×#104 | — | 9 | 2 | no | — |
| 215 | C5×#104 | — | 9 | 2 | no | — |
| 216 | C5×#100 | — | 3 | 1 | no | — |
| 217 | C5×#100 | — | 9 | 2 | no | — |
| 218 | C5×#100 | — | 9 | 1 | no | — |
| 219 | C2×D3×A4 | — | 4 | 1 | no | — |
| 220 | C2×D3×A4 | — | 8 | 1 | no | — |
| 221 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 222 | C2×C3×S4 | — | 4 | 1 | no | — |
| 223 | D3×S4 | — | 4 | 4 | no | — |
| 224 | D3×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 225 | C3⋊GL(2,𝔽3) | — | 4 | 2 | no | — |
| 226 | C3×GL(2,𝔽3) | — | 4 | 2 | no | — |
| 227 | C2×#453 | — | 9 | 1 | no | Sylow |
| 228 | C23×C3×C5 | — | 2 | 1 | no | — |
| 229 | C23×C3×C5 | — | 3 | 1 | no | — |
| 230 | C23×C3×C5 | — | 6 | 1 | no | — |
| 231 | C23×C3×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 232 | C22×C5×D3 | — | 3 | 1 | no | — |
| 233 | C22×C5×D3 | — | 3 | 1 | no | — |
| 234 | C22×C5×D3 | — | 3 | 1 | no | — |
| 235 | C22×C5×D3 | — | 4 | 2 | no | — |
| 236 | C22×C5×D3 | — | 6 | 1 | no | — |
| 237 | C22×C5×D3 | — | 6 | 1 | no | — |
| 238 | C22×C5×D3 | — | 6 | 1 | no | — |
| 239 | C22×C5×D3 | — | 6 | 1 | no | — |
| 240 | C22×C5×D3 | — | 8 | 2 | no | — |
| 241 | C22×C5×D3 | — | 12 | 1 | no | — |
| 242 | C22×C5×D3 | — | 12 | 2 | no | — |
| 243 | C22×C5×D3 | — | 12 | 2 | no | — |
| 244 | C22×C5×D3 | — | 12 | 2 | no | — |
| 245 | C22×C5×D3 | — | 12 | 1 | no | — |
| 246 | C22×C5×D3 | — | 48 | 1 | no | — |
| 247 | C2×C5×A4 | — | 4 | 1 | no | — |
| 248 | C2×C5×A4 | — | 8 | 1 | no | — |
| 249 | C2×C5×A4 | — | 8 | 1 | no | — |
| 250 | C2×C5×A4 | — | 12 | 2 | no | — |
| 251 | C2×C5×A4 | — | 16 | 1 | no | — |
| 252 | C2×C5×A4 | — | 24 | 2 | no | — |
| 253 | C5×S4 | — | 4 | 2 | no | — |
| 254 | C5×S4 | — | 12 | 2 | no | — |
| 255 | C5×S4 | — | 24 | 2 | no | — |
| 256 | C3×C5×Q8 | C2×S4 | 1 | 2 | yes | complemented |
| 257 | C3×C5×D4 | — | 3 | 2 | no | — |
| 258 | C3×C5×D4 | — | 6 | 2 | no | — |
| 259 | C3×C5×D4 | — | 6 | 2 | no | — |
| 260 | C3×C5×D4 | — | 12 | 2 | no | — |
| 261 | C3×C5×D4 | — | 12 | 2 | no | — |
| 262 | C2×C3×C4×C5 | — | 3 | 1 | no | — |
| 263 | C2×C3×C4×C5 | — | 6 | 1 | no | — |
| 264 | C2×C3×C4×C5 | — | 6 | 1 | no | — |
| 265 | C5×#67 | — | 6 | 2 | no | — |
| 266 | C5×#67 | — | 6 | 2 | no | — |
| 267 | C5×#67 | — | 6 | 2 | no | — |
| 268 | C5×#67 | — | 12 | 2 | no | — |
| 269 | C5×#67 | — | 12 | 2 | no | — |
| 270 | C5×#67 | — | 12 | 2 | no | — |
| 271 | C5×#67 | — | 12 | 2 | no | — |
| 272 | C5×#67 | — | 12 | 2 | no | — |
| 273 | C2×C5×Dic3 | — | 3 | 1 | no | — |
| 274 | C2×C5×Dic3 | — | 6 | 1 | no | — |
| 275 | C2×C5×Dic3 | — | 6 | 1 | no | — |
| 276 | C5×D12 | — | 3 | 2 | no | — |
| 277 | C5×D12 | — | 6 | 2 | no | — |
| 278 | C5×D12 | — | 6 | 2 | no | — |
| 279 | C5×D12 | — | 12 | 2 | no | — |
| 280 | C5×D12 | — | 12 | 2 | no | — |
| 281 | C4×C5×D3 | — | 3 | 2 | no | — |
| 282 | C4×C5×D3 | — | 3 | 2 | no | — |
| 283 | C4×C5×D3 | — | 6 | 2 | no | — |
| 284 | C4×C5×D3 | — | 6 | 4 | no | — |
| 285 | C5×Dic6 | — | 3 | 2 | no | — |
| 286 | C5×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 287 | C5×SL(2,𝔽3) | — | 8 | 2 | no | — |
| 288 | C3×C5×C8 | — | 6 | 2 | no | — |
| 289 | C5×C3⋊C8 | — | 6 | 2 | no | — |
| 290 | C22×S4 | — | 12 | 1 | no | — |
| 291 | C3×H(5,𝔽2) | C2×C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 292 | #1009 | — | 3 | 2 | no | — |
| 293 | D3×#41 | — | 3 | 2 | no | — |
| 294 | #1004 | — | 3 | 1 | no | — |
| 295 | #1004 | — | 6 | 1 | no | — |
| 296 | C2×D3×D4 | — | 3 | 1 | no | — |
| 297 | C2×D3×D4 | — | 3 | 1 | no | — |
| 298 | C2×D3×D4 | — | 6 | 1 | no | — |
| 299 | C2×D3×D4 | — | 6 | 1 | no | — |
| 300 | C2×D3×D4 | — | 6 | 1 | no | — |
| 301 | #997 | — | 2 | 1 | no | — |
| 302 | #997 | C2×C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 303 | C2×GL(2,𝔽3) | — | 12 | 2 | no | — |
| 304 | C3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 305 | C3×#127 | — | 3 | 1 | no | — |
| 306 | #949 | — | 3 | 2 | no | — |
| 307 | #940 | — | 3 | 1 | no | — |
| 308 | #940 | — | 3 | 1 | no | — |
| 309 | #940 | — | 6 | 1 | no | — |
| 310 | #940 | — | 6 | 1 | no | — |
| 311 | #932 | — | 3 | 2 | no | — |
| 312 | #914 | — | 6 | 2 | no | — |
| 313 | D3×SD16 | — | 6 | 2 | no | — |
| 314 | #911 | — | 6 | 2 | no | — |
| 315 | D3×D8 | — | 6 | 2 | no | — |
| 316 | #908 | — | 3 | 2 | no | — |
| 317 | D3×M16 | — | 3 | 2 | no | — |
| 318 | #874 | — | 3 | 1 | no | — |
| 319 | C42×D3 | — | 3 | 1 | no | — |
| 320 | C3×#104 | — | 3 | 2 | no | — |
| 321 | C3×#100 | — | 3 | 1 | no | — |
| 322 | #837 | — | 3 | 2 | no | — |
| 323 | #833 | — | 3 | 1 | no | — |
| 324 | #825 | — | 3 | 2 | no | — |
| 325 | #823 | — | 3 | 2 | no | — |
| 326 | #805 | — | 3 | 2 | no | — |
| 327 | C2×C32×C5 | — | 16 | 1 | no | — |
| 328 | C5×C3⋊D3 | — | 16 | 2 | no | — |
| 329 | C3×C5×D3 | — | 16 | 2 | no | — |
| 330 | C3×C5×D3 | — | 16 | 2 | no | — |
| 331 | C24×C5 | — | 3 | 1 | no | — |
| 332 | C24×C5 | — | 6 | 1 | no | — |
| 333 | C24×C5 | — | 9 | 1 | no | — |
| 334 | C24×C5 | — | 18 | 1 | no | — |
| 335 | C5×#41 | — | 3 | 2 | no | — |
| 336 | C5×#41 | — | 9 | 2 | no | — |
| 337 | C5×#41 | — | 9 | 2 | no | — |
| 338 | C5×#41 | — | 9 | 2 | no | — |
| 339 | C5×#41 | — | 18 | 2 | no | — |
| 340 | C5×#41 | — | 18 | 2 | no | — |
| 341 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 342 | C2×C5×D4 | — | 3 | 1 | no | — |
| 343 | C2×C5×D4 | — | 3 | 1 | no | — |
| 344 | C2×C5×D4 | — | 6 | 1 | no | — |
| 345 | C2×C5×D4 | — | 6 | 1 | no | — |
| 346 | C2×C5×D4 | — | 6 | 1 | no | — |
| 347 | C2×C5×D4 | — | 9 | 1 | no | — |
| 348 | C2×C5×D4 | — | 9 | 1 | no | — |
| 349 | C2×C5×D4 | — | 9 | 2 | no | — |
| 350 | C2×C5×D4 | — | 9 | 1 | no | — |
| 351 | C2×C5×D4 | — | 9 | 1 | no | — |
| 352 | C2×C5×D4 | — | 18 | 1 | no | — |
| 353 | C2×C5×D4 | — | 18 | 1 | no | — |
| 354 | C2×C5×D4 | — | 18 | 1 | no | — |
| 355 | C2×C5×D4 | — | 18 | 2 | no | — |
| 356 | C2×C5×D4 | — | 18 | 2 | no | — |
| 357 | C2×C5×D4 | — | 18 | 2 | no | — |
| 358 | C2×C5×D4 | — | 18 | 2 | no | — |
| 359 | C2×C5×D4 | — | 18 | 1 | no | — |
| 360 | C2×C5×D4 | — | 18 | 2 | no | — |
| 361 | C2×C5×D4 | — | 18 | 2 | no | — |
| 362 | C2×C5×D4 | — | 18 | 1 | no | — |
| 363 | C2×C5×D4 | — | 18 | 1 | no | — |
| 364 | C2×C5×D4 | — | 18 | 1 | no | — |
| 365 | C2×C5×D4 | — | 18 | 1 | no | — |
| 366 | C2×C5×D4 | — | 18 | 1 | no | — |
| 367 | C2×C5×D4 | — | 18 | 1 | no | — |
| 368 | C2×C5×D4 | — | 36 | 4 | no | — |
| 369 | C2×C5×D4 | — | 36 | 4 | no | — |
| 370 | C22×C4×C5 | — | 9 | 1 | no | — |
| 371 | C22×C4×C5 | — | 18 | 1 | no | — |
| 372 | C22×C4×C5 | — | 18 | 1 | no | — |
| 373 | C5×SD16 | — | 6 | 2 | no | — |
| 374 | C5×SD16 | — | 18 | 2 | no | — |
| 375 | C5×SD16 | — | 18 | 2 | no | — |
| 376 | C5×SD16 | — | 18 | 2 | no | — |
| 377 | C5×D8 | — | 6 | 2 | no | — |
| 378 | C5×D8 | — | 18 | 2 | no | — |
| 379 | C5×D8 | — | 18 | 2 | no | — |
| 380 | C5×D8 | — | 18 | 2 | no | — |
| 381 | C5×M16 | — | 3 | 2 | no | — |
| 382 | C5×M16 | — | 9 | 2 | no | — |
| 383 | C5×M16 | — | 18 | 2 | no | — |
| 384 | C2×C5×C8 | — | 18 | 2 | no | — |
| 385 | C42×C5 | — | 3 | 1 | no | — |
| 386 | C42×C5 | — | 9 | 1 | no | — |
| 387 | C42×C5 | — | 18 | 1 | no | — |
| 388 | C2×C3×A4 | — | 4 | 1 | no | — |
| 389 | C2×C3×A4 | — | 8 | 1 | no | — |
| 390 | C2×D32 | — | 16 | 1 | no | — |
| 391 | D3×A4 | — | 4 | 2 | no | — |
| 392 | D3×A4 | — | 8 | 2 | no | — |
| 393 | C3⋊S4 | — | 4 | 2 | no | — |
| 394 | C3×S4 | — | 4 | 2 | no | — |
| 395 | C3×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 396 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 397 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 398 | C2×#127 | — | 9 | 1 | no | — |
| 399 | #453 | — | 3 | 1 | no | — |
| 400 | #453 | — | 9 | 1 | no | — |
| 401 | #453 | — | 9 | 2 | no | — |
| 402 | #453 | — | 9 | 1 | no | — |
| 403 | #453 | — | 9 | 2 | no | — |
| 404 | #453 | — | 9 | 1 | no | — |
| 405 | C2×#104 | — | 9 | 2 | no | — |
| 406 | C2×#100 | — | 9 | 1 | no | — |
| 407 | C22×C3×C5 | — | 3 | 1 | no | — |
| 408 | C22×C3×C5 | — | 4 | 1 | no | — |
| 409 | C22×C3×C5 | — | 6 | 1 | no | — |
| 410 | C22×C3×C5 | — | 8 | 1 | no | — |
| 411 | C22×C3×C5 | — | 12 | 1 | no | — |
| 412 | C22×C3×C5 | — | 12 | 1 | no | — |
| 413 | C22×C3×C5 | — | 12 | 1 | no | — |
| 414 | C22×C3×C5 | — | 12 | 1 | no | — |
| 415 | C22×C3×C5 | — | 48 | 1 | no | — |
| 416 | C2×C5×D3 | — | 3 | 1 | no | — |
| 417 | C2×C5×D3 | — | 6 | 2 | no | — |
| 418 | C2×C5×D3 | — | 6 | 1 | no | — |
| 419 | C2×C5×D3 | — | 12 | 1 | no | — |
| 420 | C2×C5×D3 | — | 12 | 2 | no | — |
| 421 | C2×C5×D3 | — | 12 | 1 | no | — |
| 422 | C2×C5×D3 | — | 12 | 1 | no | — |
| 423 | C2×C5×D3 | — | 12 | 1 | no | — |
| 424 | C2×C5×D3 | — | 12 | 1 | no | — |
| 425 | C2×C5×D3 | — | 16 | 1 | no | — |
| 426 | C2×C5×D3 | — | 24 | 1 | no | — |
| 427 | C2×C5×D3 | — | 24 | 2 | no | — |
| 428 | C2×C5×D3 | — | 24 | 1 | no | — |
| 429 | C2×C5×D3 | — | 24 | 2 | no | — |
| 430 | C2×C5×D3 | — | 48 | 1 | no | — |
| 431 | C2×C5×D3 | — | 48 | 4 | no | — |
| 432 | C2×C5×D3 | — | 96 | 1 | no | — |
| 433 | C2×C5×D3 | #1020 | 1 | 1 | yes | characteristic |
| 434 | C5×A4 | — | 4 | 1 | no | — |
| 435 | C5×A4 | — | 8 | 1 | no | — |
| 436 | C5×A4 | — | 8 | 1 | no | — |
| 437 | C5×A4 | — | 16 | 1 | no | — |
| 438 | C3×C4×C5 | — | 3 | 2 | no | — |
| 439 | C3×C4×C5 | — | 6 | 2 | no | — |
| 440 | C5×Dic3 | — | 3 | 2 | no | — |
| 441 | C5×Dic3 | — | 6 | 2 | no | — |
| 442 | C23×D3 | — | 2 | 1 | no | — |
| 443 | C23×D3 | — | 3 | 1 | no | — |
| 444 | C23×D3 | — | 6 | 1 | no | — |
| 445 | C23×D3 | C5×S4 | 1 | 1 | yes | characteristic |
| 446 | C22×A4 | — | 12 | 1 | no | — |
| 447 | C22×A4 | — | 24 | 1 | no | — |
| 448 | C2×S4 | — | 4 | 1 | no | — |
| 449 | C2×S4 | — | 12 | 1 | no | — |
| 450 | C2×S4 | — | 12 | 4 | no | — |
| 451 | C2×S4 | — | 24 | 1 | no | — |
| 452 | C3×#41 | — | 3 | 2 | no | — |
| 453 | C2×C3×D4 | — | 3 | 1 | no | — |
| 454 | C2×C3×D4 | — | 3 | 1 | no | — |
| 455 | C2×C3×D4 | — | 6 | 1 | no | — |
| 456 | C2×C3×D4 | — | 6 | 1 | no | — |
| 457 | C2×C3×D4 | — | 6 | 1 | no | — |
| 458 | C2×#67 | — | 3 | 1 | no | — |
| 459 | C2×#67 | — | 3 | 1 | no | — |
| 460 | C2×#67 | — | 6 | 1 | no | — |
| 461 | C2×#67 | — | 6 | 1 | no | — |
| 462 | C2×#67 | — | 6 | 1 | no | — |
| 463 | C2×#67 | — | 6 | 1 | no | — |
| 464 | C2×#67 | — | 6 | 1 | no | — |
| 465 | C2×#67 | — | 6 | 1 | no | — |
| 466 | C2×#67 | — | 6 | 1 | no | — |
| 467 | #239 | — | 3 | 2 | no | — |
| 468 | D3×Q8 | C5×S4 | 1 | 2 | yes | complemented |
| 469 | #237 | — | 3 | 2 | no | — |
| 470 | #237 | — | 6 | 2 | no | — |
| 471 | D3×D4 | — | 3 | 2 | no | — |
| 472 | D3×D4 | — | 6 | 2 | no | — |
| 473 | D3×D4 | — | 6 | 2 | no | — |
| 474 | D3×D4 | — | 6 | 2 | no | — |
| 475 | D3×D4 | — | 6 | 2 | no | — |
| 476 | D3×D4 | — | 6 | 2 | no | — |
| 477 | D3×D4 | — | 6 | 2 | no | — |
| 478 | D3×D4 | — | 12 | 4 | no | — |
| 479 | D3×D4 | — | 12 | 4 | no | — |
| 480 | #235 | — | 3 | 2 | no | — |
| 481 | #235 | — | 6 | 2 | no | — |
| 482 | C2×D12 | — | 3 | 1 | no | — |
| 483 | C2×D12 | — | 3 | 1 | no | — |
| 484 | C2×D12 | — | 6 | 1 | no | — |
| 485 | C2×D12 | — | 6 | 1 | no | — |
| 486 | C2×D12 | — | 6 | 1 | no | — |
| 487 | C2×C4×D3 | — | 3 | 1 | no | — |
| 488 | C2×C4×D3 | — | 6 | 1 | no | — |
| 489 | C2×C4×D3 | — | 6 | 1 | no | — |
| 490 | C2×SL(2,𝔽3) | — | 12 | 2 | no | — |
| 491 | GL(2,𝔽3) | — | 4 | 2 | no | — |
| 492 | GL(2,𝔽3) | — | 12 | 2 | no | — |
| 493 | GL(2,𝔽3) | — | 24 | 2 | no | — |
| 494 | C3×SD16 | — | 6 | 2 | no | — |
| 495 | C3×D8 | — | 6 | 2 | no | — |
| 496 | C3×M16 | — | 3 | 2 | no | — |
| 497 | C3×C42 | — | 3 | 1 | no | — |
| 498 | #215 | — | 6 | 2 | no | — |
| 499 | #214 | — | 6 | 2 | no | — |
| 500 | #213 | — | 6 | 2 | no | — |
| 501 | #213 | — | 6 | 2 | no | — |
| 502 | C4×Dic3 | — | 3 | 1 | no | — |
| 503 | C4×Dic3 | — | 6 | 1 | no | — |
| 504 | #208 | — | 3 | 2 | no | — |
| 505 | D24 | — | 6 | 2 | no | — |
| 506 | #204 | — | 6 | 2 | no | — |
| 507 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 508 | D3×C8 | — | 6 | 2 | no | — |
| 509 | C32×C5 | — | 16 | 1 | no | Hall |
| 510 | C23×C5 | — | 2 | 1 | no | — |
| 511 | C23×C5 | — | 3 | 1 | no | — |
| 512 | C23×C5 | — | 6 | 1 | no | — |
| 513 | C23×C5 | — | 9 | 1 | no | — |
| 514 | C23×C5 | — | 9 | 1 | no | — |
| 515 | C23×C5 | — | 9 | 1 | no | — |
| 516 | C23×C5 | — | 12 | 2 | no | — |
| 517 | C23×C5 | — | 18 | 1 | no | — |
| 518 | C23×C5 | — | 18 | 1 | no | — |
| 519 | C23×C5 | — | 18 | 1 | no | — |
| 520 | C23×C5 | — | 18 | 1 | no | — |
| 521 | C23×C5 | — | 24 | 2 | no | — |
| 522 | C23×C5 | — | 36 | 1 | no | — |
| 523 | C23×C5 | — | 36 | 1 | no | — |
| 524 | C23×C5 | — | 36 | 2 | no | — |
| 525 | C23×C5 | — | 36 | 2 | no | — |
| 526 | C23×C5 | — | 36 | 2 | no | — |
| 527 | C23×C5 | D3×S4 | 1 | 1 | yes | characteristic |
| 528 | C5×Q8 | — | 9 | 2 | no | — |
| 529 | C5×Q8 | D3×S4 | 1 | 2 | yes | complemented |
| 530 | C5×D4 | — | 3 | 2 | no | — |
| 531 | C5×D4 | — | 6 | 2 | no | — |
| 532 | C5×D4 | — | 6 | 2 | no | — |
| 533 | C5×D4 | — | 9 | 2 | no | — |
| 534 | C5×D4 | — | 12 | 2 | no | — |
| 535 | C5×D4 | — | 12 | 2 | no | — |
| 536 | C5×D4 | — | 18 | 2 | no | — |
| 537 | C5×D4 | — | 18 | 2 | no | — |
| 538 | C5×D4 | — | 18 | 2 | no | — |
| 539 | C5×D4 | — | 18 | 2 | no | — |
| 540 | C5×D4 | — | 18 | 2 | no | — |
| 541 | C5×D4 | — | 36 | 2 | no | — |
| 542 | C5×D4 | — | 36 | 2 | no | — |
| 543 | C5×D4 | — | 36 | 2 | no | — |
| 544 | C5×D4 | — | 36 | 2 | no | — |
| 545 | C5×D4 | — | 36 | 2 | no | — |
| 546 | C5×D4 | — | 36 | 2 | no | — |
| 547 | C5×D4 | — | 36 | 2 | no | — |
| 548 | C2×C4×C5 | — | 3 | 1 | no | — |
| 549 | C2×C4×C5 | — | 6 | 1 | no | — |
| 550 | C2×C4×C5 | — | 6 | 1 | no | — |
| 551 | C2×C4×C5 | — | 9 | 2 | no | — |
| 552 | C2×C4×C5 | — | 9 | 2 | no | — |
| 553 | C2×C4×C5 | — | 9 | 1 | no | — |
| 554 | C2×C4×C5 | — | 18 | 2 | no | — |
| 555 | C2×C4×C5 | — | 18 | 4 | no | — |
| 556 | C2×C4×C5 | — | 18 | 1 | no | — |
| 557 | C2×C4×C5 | — | 18 | 1 | no | — |
| 558 | C5×C8 | — | 6 | 2 | no | — |
| 559 | C5×C8 | — | 18 | 2 | no | — |
| 560 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 561 | C2×C3×D3 | — | 16 | 1 | no | — |
| 562 | C2×C3×D3 | — | 16 | 1 | no | — |
| 563 | C3×A4 | — | 4 | 1 | no | — |
| 564 | C3×A4 | — | 8 | 1 | no | — |
| 565 | D32 | — | 16 | 4 | no | — |
| 566 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 567 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 568 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 569 | H(5,𝔽2) | C5×D32 | 1 | 1 | yes | characteristic, complemented |
| 570 | C2×#41 | — | 9 | 2 | no | — |
| 571 | C22×D4 | — | 9 | 1 | no | — |
| 572 | C22×D4 | — | 9 | 1 | no | — |
| 573 | C22×D4 | — | 18 | 1 | no | — |
| 574 | C22×D4 | — | 18 | 1 | no | — |
| 575 | C22×D4 | — | 18 | 1 | no | — |
| 576 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 577 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 578 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 579 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 580 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 581 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 582 | C2×SD16 | — | 18 | 2 | no | — |
| 583 | C2×D8 | — | 18 | 2 | no | — |
| 584 | C2×M16 | — | 9 | 2 | no | — |
| 585 | #127 | — | 3 | 1 | no | — |
| 586 | #127 | — | 9 | 1 | no | — |
| 587 | #127 | — | 9 | 1 | no | — |
| 588 | #127 | — | 9 | 1 | no | — |
| 589 | #127 | — | 18 | 1 | no | — |
| 590 | #127 | — | 18 | 1 | no | — |
| 591 | C2×C42 | — | 9 | 1 | no | — |
| 592 | #104 | — | 3 | 2 | no | — |
| 593 | #104 | — | 9 | 2 | no | — |
| 594 | #104 | — | 9 | 2 | no | — |
| 595 | #104 | — | 9 | 2 | no | — |
| 596 | #100 | — | 3 | 1 | no | — |
| 597 | #100 | — | 9 | 2 | no | — |
| 598 | #100 | — | 9 | 1 | no | — |
| 599 | C2×C3×C5 | — | 6 | 1 | no | — |
| 600 | C2×C3×C5 | — | 12 | 1 | no | — |
| 601 | C2×C3×C5 | — | 16 | 1 | no | — |
| 602 | C2×C3×C5 | — | 24 | 1 | no | — |
| 603 | C2×C3×C5 | — | 32 | 1 | no | — |
| 604 | C2×C3×C5 | — | 48 | 2 | no | — |
| 605 | C2×C3×C5 | C2×#1020 | 1 | 1 | yes | characteristic |
| 606 | C5×D3 | — | 6 | 1 | no | — |
| 607 | C5×D3 | — | 12 | 1 | no | — |
| 608 | C5×D3 | — | 16 | 2 | no | — |
| 609 | C5×D3 | — | 24 | 1 | no | — |
| 610 | C5×D3 | — | 48 | 2 | no | — |
| 611 | C5×D3 | — | 96 | 2 | no | — |
| 612 | C5×D3 | #5935 | 1 | 2 | yes | direct product factor |
| 613 | C23×C3 | — | 2 | 1 | no | — |
| 614 | C23×C3 | — | 3 | 1 | no | — |
| 615 | C23×C3 | — | 6 | 1 | no | — |
| 616 | C23×C3 | C2×C5×S4 | 1 | 1 | yes | characteristic |
| 617 | C22×D3 | — | 3 | 1 | no | — |
| 618 | C22×D3 | — | 3 | 1 | no | — |
| 619 | C22×D3 | — | 3 | 1 | no | — |
| 620 | C22×D3 | — | 4 | 2 | no | — |
| 621 | C22×D3 | — | 6 | 1 | no | — |
| 622 | C22×D3 | — | 6 | 1 | no | — |
| 623 | C22×D3 | — | 6 | 1 | no | — |
| 624 | C22×D3 | — | 6 | 1 | no | — |
| 625 | C22×D3 | — | 8 | 2 | no | — |
| 626 | C22×D3 | — | 12 | 1 | no | — |
| 627 | C22×D3 | — | 12 | 2 | no | — |
| 628 | C22×D3 | — | 12 | 2 | no | — |
| 629 | C22×D3 | — | 12 | 2 | no | — |
| 630 | C22×D3 | — | 12 | 1 | no | — |
| 631 | C22×D3 | — | 48 | 1 | no | — |
| 632 | C2×A4 | — | 4 | 1 | no | — |
| 633 | C2×A4 | — | 8 | 1 | no | — |
| 634 | C2×A4 | — | 8 | 1 | no | — |
| 635 | C2×A4 | — | 12 | 2 | no | — |
| 636 | C2×A4 | — | 16 | 1 | no | — |
| 637 | C2×A4 | — | 24 | 2 | no | — |
| 638 | S4 | — | 4 | 2 | no | — |
| 639 | S4 | — | 12 | 2 | no | — |
| 640 | S4 | — | 24 | 2 | no | — |
| 641 | C3×Q8 | C2×C5×S4 | 1 | 2 | yes | complemented |
| 642 | C3×D4 | — | 3 | 2 | no | — |
| 643 | C3×D4 | — | 6 | 2 | no | — |
| 644 | C3×D4 | — | 6 | 2 | no | — |
| 645 | C3×D4 | — | 12 | 2 | no | — |
| 646 | C3×D4 | — | 12 | 2 | no | — |
| 647 | C2×C3×C4 | — | 3 | 1 | no | — |
| 648 | C2×C3×C4 | — | 6 | 1 | no | — |
| 649 | C2×C3×C4 | — | 6 | 1 | no | — |
| 650 | #67 | — | 6 | 2 | no | — |
| 651 | #67 | — | 6 | 2 | no | — |
| 652 | #67 | — | 6 | 2 | no | — |
| 653 | #67 | — | 12 | 2 | no | — |
| 654 | #67 | — | 12 | 2 | no | — |
| 655 | #67 | — | 12 | 2 | no | — |
| 656 | #67 | — | 12 | 2 | no | — |
| 657 | #67 | — | 12 | 2 | no | — |
| 658 | C2×Dic3 | — | 3 | 1 | no | — |
| 659 | C2×Dic3 | — | 6 | 1 | no | — |
| 660 | C2×Dic3 | — | 6 | 1 | no | — |
| 661 | D12 | — | 3 | 2 | no | — |
| 662 | D12 | — | 6 | 2 | no | — |
| 663 | D12 | — | 6 | 2 | no | — |
| 664 | D12 | — | 12 | 2 | no | — |
| 665 | D12 | — | 12 | 2 | no | — |
| 666 | C4×D3 | — | 3 | 2 | no | — |
| 667 | C4×D3 | — | 3 | 2 | no | — |
| 668 | C4×D3 | — | 6 | 2 | no | — |
| 669 | C4×D3 | — | 6 | 4 | no | — |
| 670 | Dic6 | — | 3 | 2 | no | — |
| 671 | SL(2,𝔽3) | — | 4 | 2 | no | — |
| 672 | SL(2,𝔽3) | — | 8 | 2 | no | — |
| 673 | C3×C8 | — | 6 | 2 | no | — |
| 674 | C3⋊C8 | — | 6 | 2 | no | — |
| 675 | C22×C5 | — | 3 | 1 | no | — |
| 676 | C22×C5 | — | 3 | 1 | no | — |
| 677 | C22×C5 | — | 4 | 1 | no | — |
| 678 | C22×C5 | — | 6 | 1 | no | — |
| 679 | C22×C5 | — | 8 | 1 | no | — |
| 680 | C22×C5 | — | 9 | 1 | no | — |
| 681 | C22×C5 | — | 12 | 1 | no | — |
| 682 | C22×C5 | — | 12 | 1 | no | — |
| 683 | C22×C5 | — | 12 | 1 | no | — |
| 684 | C22×C5 | — | 12 | 1 | no | — |
| 685 | C22×C5 | — | 18 | 2 | no | — |
| 686 | C22×C5 | — | 18 | 1 | no | — |
| 687 | C22×C5 | — | 36 | 2 | no | — |
| 688 | C22×C5 | — | 36 | 1 | no | — |
| 689 | C22×C5 | — | 36 | 1 | no | — |
| 690 | C22×C5 | — | 36 | 1 | no | — |
| 691 | C22×C5 | — | 36 | 1 | no | — |
| 692 | C22×C5 | — | 36 | 1 | no | — |
| 693 | C22×C5 | — | 72 | 2 | no | — |
| 694 | C22×C5 | — | 72 | 1 | no | — |
| 695 | C22×C5 | — | 72 | 1 | no | — |
| 696 | C22×C5 | — | 72 | 2 | no | — |
| 697 | C4×C5 | — | 3 | 2 | no | — |
| 698 | C4×C5 | — | 6 | 2 | no | — |
| 699 | C4×C5 | — | 9 | 2 | no | — |
| 700 | C4×C5 | — | 18 | 2 | no | — |
| 701 | C2×C32 | — | 16 | 1 | no | — |
| 702 | C3⋊D3 | — | 16 | 2 | no | — |
| 703 | C3×D3 | — | 16 | 2 | no | — |
| 704 | C3×D3 | — | 16 | 2 | no | — |
| 705 | C24 | — | 3 | 1 | no | — |
| 706 | C24 | — | 6 | 1 | no | — |
| 707 | C24 | — | 9 | 1 | no | — |
| 708 | C24 | — | 18 | 1 | no | — |
| 709 | #41 | — | 3 | 2 | no | — |
| 710 | #41 | — | 9 | 2 | no | — |
| 711 | #41 | — | 9 | 2 | no | — |
| 712 | #41 | — | 9 | 2 | no | — |
| 713 | #41 | — | 18 | 2 | no | — |
| 714 | #41 | — | 18 | 2 | no | — |
| 715 | C2×Q8 | — | 3 | 2 | no | — |
| 716 | C2×D4 | — | 3 | 1 | no | — |
| 717 | C2×D4 | — | 3 | 1 | no | — |
| 718 | C2×D4 | — | 6 | 1 | no | — |
| 719 | C2×D4 | — | 6 | 1 | no | — |
| 720 | C2×D4 | — | 6 | 1 | no | — |
| 721 | C2×D4 | — | 9 | 1 | no | — |
| 722 | C2×D4 | — | 9 | 1 | no | — |
| 723 | C2×D4 | — | 9 | 2 | no | — |
| 724 | C2×D4 | — | 9 | 1 | no | — |
| 725 | C2×D4 | — | 9 | 1 | no | — |
| 726 | C2×D4 | — | 18 | 1 | no | — |
| 727 | C2×D4 | — | 18 | 1 | no | — |
| 728 | C2×D4 | — | 18 | 1 | no | — |
| 729 | C2×D4 | — | 18 | 2 | no | — |
| 730 | C2×D4 | — | 18 | 2 | no | — |
| 731 | C2×D4 | — | 18 | 2 | no | — |
| 732 | C2×D4 | — | 18 | 2 | no | — |
| 733 | C2×D4 | — | 18 | 1 | no | — |
| 734 | C2×D4 | — | 18 | 2 | no | — |
| 735 | C2×D4 | — | 18 | 2 | no | — |
| 736 | C2×D4 | — | 18 | 1 | no | — |
| 737 | C2×D4 | — | 18 | 1 | no | — |
| 738 | C2×D4 | — | 18 | 1 | no | — |
| 739 | C2×D4 | — | 18 | 1 | no | — |
| 740 | C2×D4 | — | 18 | 1 | no | — |
| 741 | C2×D4 | — | 18 | 1 | no | — |
| 742 | C2×D4 | — | 36 | 4 | no | — |
| 743 | C2×D4 | — | 36 | 4 | no | — |
| 744 | C22×C4 | — | 9 | 1 | no | — |
| 745 | C22×C4 | — | 18 | 1 | no | — |
| 746 | C22×C4 | — | 18 | 1 | no | — |
| 747 | SD16 | — | 6 | 2 | no | — |
| 748 | SD16 | — | 18 | 2 | no | — |
| 749 | SD16 | — | 18 | 2 | no | — |
| 750 | SD16 | — | 18 | 2 | no | — |
| 751 | D8 | — | 6 | 2 | no | — |
| 752 | D8 | — | 18 | 2 | no | — |
| 753 | D8 | — | 18 | 2 | no | — |
| 754 | D8 | — | 18 | 2 | no | — |
| 755 | M16 | — | 3 | 2 | no | — |
| 756 | M16 | — | 9 | 2 | no | — |
| 757 | M16 | — | 18 | 2 | no | — |
| 758 | C2×C8 | — | 18 | 2 | no | — |
| 759 | C42 | — | 3 | 1 | no | — |
| 760 | C42 | — | 9 | 1 | no | — |
| 761 | C42 | — | 18 | 1 | no | — |
| 762 | C3×C5 | — | 16 | 1 | no | — |
| 763 | C3×C5 | — | 32 | 1 | no | — |
| 764 | C3×C5 | C2×#5935 | 1 | 1 | yes | characteristic, complemented |
| 765 | C22×C3 | — | 3 | 1 | no | — |
| 766 | C22×C3 | — | 4 | 1 | no | — |
| 767 | C22×C3 | — | 6 | 1 | no | — |
| 768 | C22×C3 | — | 8 | 1 | no | — |
| 769 | C22×C3 | — | 12 | 1 | no | — |
| 770 | C22×C3 | — | 12 | 1 | no | — |
| 771 | C22×C3 | — | 12 | 1 | no | — |
| 772 | C22×C3 | — | 12 | 1 | no | — |
| 773 | C22×C3 | — | 48 | 1 | no | — |
| 774 | C2×D3 | — | 3 | 1 | no | — |
| 775 | C2×D3 | — | 6 | 2 | no | — |
| 776 | C2×D3 | — | 6 | 1 | no | — |
| 777 | C2×D3 | — | 12 | 1 | no | — |
| 778 | C2×D3 | — | 12 | 2 | no | — |
| 779 | C2×D3 | — | 12 | 1 | no | — |
| 780 | C2×D3 | — | 12 | 1 | no | — |
| 781 | C2×D3 | — | 12 | 1 | no | — |
| 782 | C2×D3 | — | 12 | 1 | no | — |
| 783 | C2×D3 | — | 16 | 1 | no | — |
| 784 | C2×D3 | — | 24 | 1 | no | — |
| 785 | C2×D3 | — | 24 | 2 | no | — |
| 786 | C2×D3 | — | 24 | 1 | no | — |
| 787 | C2×D3 | — | 24 | 2 | no | — |
| 788 | C2×D3 | — | 48 | 1 | no | — |
| 789 | C2×D3 | — | 48 | 4 | no | — |
| 790 | C2×D3 | — | 96 | 1 | no | — |
| 791 | C2×D3 | C5×#1020 | 1 | 1 | yes | characteristic |
| 792 | A4 | — | 4 | 1 | no | — |
| 793 | A4 | — | 8 | 1 | no | — |
| 794 | A4 | — | 8 | 1 | no | — |
| 795 | A4 | — | 16 | 1 | no | — |
| 796 | C3×C4 | — | 3 | 2 | no | — |
| 797 | C3×C4 | — | 6 | 2 | no | — |
| 798 | Dic3 | — | 3 | 2 | no | — |
| 799 | Dic3 | — | 6 | 2 | no | — |
| 800 | C2×C5 | — | 3 | 2 | no | — |
| 801 | C2×C5 | — | 6 | 1 | no | — |
| 802 | C2×C5 | — | 12 | 1 | no | — |
| 803 | C2×C5 | — | 18 | 1 | no | — |
| 804 | C2×C5 | — | 24 | 1 | no | — |
| 805 | C2×C5 | — | 36 | 1 | no | — |
| 806 | C2×C5 | — | 72 | 1 | no | — |
| 807 | C2×C5 | D3×#1020 | 1 | 1 | yes | characteristic |
| 808 | C32 | — | 16 | 1 | no | Sylow |
| 809 | C23 | — | 2 | 1 | no | — |
| 810 | C23 | — | 3 | 1 | no | — |
| 811 | C23 | — | 6 | 1 | no | — |
| 812 | C23 | — | 9 | 1 | no | — |
| 813 | C23 | — | 9 | 1 | no | — |
| 814 | C23 | — | 9 | 1 | no | — |
| 815 | C23 | — | 12 | 2 | no | — |
| 816 | C23 | — | 18 | 1 | no | — |
| 817 | C23 | — | 18 | 1 | no | — |
| 818 | C23 | — | 18 | 1 | no | — |
| 819 | C23 | — | 18 | 1 | no | — |
| 820 | C23 | — | 24 | 2 | no | — |
| 821 | C23 | — | 36 | 1 | no | — |
| 822 | C23 | — | 36 | 1 | no | — |
| 823 | C23 | — | 36 | 2 | no | — |
| 824 | C23 | — | 36 | 2 | no | — |
| 825 | C23 | — | 36 | 2 | no | — |
| 826 | C23 | C5×D3×S4 | 1 | 1 | yes | characteristic |
| 827 | Q8 | — | 9 | 2 | no | — |
| 828 | Q8 | C5×D3×S4 | 1 | 2 | yes | complemented |
| 829 | D4 | — | 3 | 2 | no | — |
| 830 | D4 | — | 6 | 2 | no | — |
| 831 | D4 | — | 6 | 2 | no | — |
| 832 | D4 | — | 9 | 2 | no | — |
| 833 | D4 | — | 12 | 2 | no | — |
| 834 | D4 | — | 12 | 2 | no | — |
| 835 | D4 | — | 18 | 2 | no | — |
| 836 | D4 | — | 18 | 2 | no | — |
| 837 | D4 | — | 18 | 2 | no | — |
| 838 | D4 | — | 18 | 2 | no | — |
| 839 | D4 | — | 18 | 2 | no | — |
| 840 | D4 | — | 36 | 2 | no | — |
| 841 | D4 | — | 36 | 2 | no | — |
| 842 | D4 | — | 36 | 2 | no | — |
| 843 | D4 | — | 36 | 2 | no | — |
| 844 | D4 | — | 36 | 2 | no | — |
| 845 | D4 | — | 36 | 2 | no | — |
| 846 | D4 | — | 36 | 2 | no | — |
| 847 | C2×C4 | — | 3 | 1 | no | — |
| 848 | C2×C4 | — | 6 | 1 | no | — |
| 849 | C2×C4 | — | 6 | 1 | no | — |
| 850 | C2×C4 | — | 9 | 2 | no | — |
| 851 | C2×C4 | — | 9 | 2 | no | — |
| 852 | C2×C4 | — | 9 | 1 | no | — |
| 853 | C2×C4 | — | 18 | 2 | no | — |
| 854 | C2×C4 | — | 18 | 4 | no | — |
| 855 | C2×C4 | — | 18 | 1 | no | — |
| 856 | C2×C4 | — | 18 | 1 | no | — |
| 857 | C8 | — | 6 | 2 | no | — |
| 858 | C8 | — | 18 | 2 | no | — |
| 859 | C2×C3 | — | 6 | 1 | no | — |
| 860 | C2×C3 | — | 12 | 1 | no | — |
| 861 | C2×C3 | — | 16 | 1 | no | — |
| 862 | C2×C3 | — | 24 | 1 | no | — |
| 863 | C2×C3 | — | 32 | 1 | no | — |
| 864 | C2×C3 | — | 48 | 2 | no | — |
| 865 | C2×C3 | C2×C5×#1020 | 1 | 1 | yes | characteristic |
| 866 | D3 | — | 6 | 1 | no | — |
| 867 | D3 | — | 12 | 1 | no | — |
| 868 | D3 | — | 16 | 2 | no | — |
| 869 | D3 | — | 24 | 1 | no | — |
| 870 | D3 | — | 48 | 2 | no | — |
| 871 | D3 | — | 96 | 2 | no | — |
| 872 | D3 | C5×#5935 | 1 | 2 | yes | direct product factor |
| 873 | C5 | D3×#5935 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 874 | C22 | — | 3 | 1 | no | — |
| 875 | C22 | — | 3 | 1 | no | — |
| 876 | C22 | — | 4 | 1 | no | — |
| 877 | C22 | — | 6 | 1 | no | — |
| 878 | C22 | — | 8 | 1 | no | — |
| 879 | C22 | — | 9 | 1 | no | — |
| 880 | C22 | — | 12 | 1 | no | — |
| 881 | C22 | — | 12 | 1 | no | — |
| 882 | C22 | — | 12 | 1 | no | — |
| 883 | C22 | — | 12 | 1 | no | — |
| 884 | C22 | — | 18 | 2 | no | — |
| 885 | C22 | — | 18 | 1 | no | — |
| 886 | C22 | — | 36 | 2 | no | — |
| 887 | C22 | — | 36 | 1 | no | — |
| 888 | C22 | — | 36 | 1 | no | — |
| 889 | C22 | — | 36 | 1 | no | — |
| 890 | C22 | — | 36 | 1 | no | — |
| 891 | C22 | — | 36 | 1 | no | — |
| 892 | C22 | — | 72 | 2 | no | — |
| 893 | C22 | — | 72 | 1 | no | — |
| 894 | C22 | — | 72 | 1 | no | — |
| 895 | C22 | — | 72 | 2 | no | — |
| 896 | C4 | — | 3 | 2 | no | — |
| 897 | C4 | — | 6 | 2 | no | — |
| 898 | C4 | — | 9 | 2 | no | — |
| 899 | C4 | — | 18 | 2 | no | — |
| 900 | C3 | — | 16 | 1 | no | — |
| 901 | C3 | — | 32 | 1 | no | — |
| 902 | C3 | C2×C5×#5935 | 1 | 1 | yes | characteristic, complemented |
| 903 | C2 | — | 3 | 2 | no | — |
| 904 | C2 | — | 6 | 1 | no | — |
| 905 | C2 | — | 12 | 1 | no | — |
| 906 | C2 | — | 18 | 1 | no | — |
| 907 | C2 | — | 24 | 1 | no | — |
| 908 | C2 | — | 36 | 1 | no | — |
| 909 | C2 | — | 72 | 1 | no | — |
| 910 | C2 | C5×D3×#1020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×#1020 |
| commutator, cosocle, hypocenter | C3×#997 | C22×C5 |
| Frattini | C2 | C5×D3×#1020 |
| Fitting | C3×C5×H(5,𝔽2) | C2×D3 |
| socle | C2×C3×C5 | C2×#1020 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C3⋊#5935 | C2 | semidirect |
| 2. C3×C5×#5935 | C2 | semidirect |
| 3. C5×D3×#997 | C2 | semidirect |
| 7. C3×C5×#997 | C22 | semidirect |
| 9. D3×#5935 | C5 | direct (N × H) |
| 10. C5×D3×H(5,𝔽2) | D3 | semidirect |
| 14. C5×#5935 | D3 | direct (N × H) |
| 34. D3×#997 | C2×C5 | semidirect |
| 35. C3⋊#5935 | C2×C5 | semidirect |
| 36. C3×#5935 | C2×C5 | semidirect |
| 38. C3×C5×H(5,𝔽2) | C2×D3 | semidirect |
| 49. C5×#997 | C2×D3 | semidirect |
| 96. C3×#997 | C22×C5 | semidirect |
| 124. C5×D3×Q8 | S4 | semidirect |
| 165. D3×H(5,𝔽2) | C5×D3 | semidirect |
| 169. #5935 | C5×D3 | direct (N × H) |
| 189. C5×H(5,𝔽2) | D32 | semidirect |
| 256. C3×C5×Q8 | C2×S4 | semidirect |
| 291. C3×H(5,𝔽2) | C2×C5×D3 | semidirect |
| 302. #997 | C2×C5×D3 | semidirect |
| 468. D3×Q8 | C5×S4 | semidirect |
| 529. C5×Q8 | D3×S4 | semidirect |
| 569. H(5,𝔽2) | C5×D32 | semidirect |
| 612. C5×D3 | #5935 | direct (N × H) |
| 641. C3×Q8 | C2×C5×S4 | semidirect |
| 764. C3×C5 | C2×#5935 | semidirect |
| 828. Q8 | C5×D3×S4 | semidirect |
| 872. D3 | C5×#5935 | direct (N × H) |
| 873. C5 | D3×#5935 | direct (N × H) |
| 902. C3 | C2×C5×#5935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C3⋊#5935 | 2 |
| C3×C5×#5935 | 2 |
| C5×D3×#997 | 2 |
| C2×C5×#5935 | 3 |
| C5×D3×#453 | 3 |
| C2×C5×D3×S4 | 4 |
| C5×D3×GL(2,𝔽3) | 4 |
| D3×#5935 | 5 |