Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 1594 conjugacy classes of subgroups — too many to draw. Only its 129 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 | D5×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11756786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11756785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D5×#986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D5×#985 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11756772 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11756771 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | D5×#983 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×D5×GL(2,𝔽3) | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | D5×#577 | — | 3 | 1 | no | maximal, Hall |
| 13 | C5×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | D3×D4×D5 | — | 4 | 1 | no | maximal |
| 15 | #4150⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | D5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #4147⋊C3 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×D5×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 19 | #91956 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #91955 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #91953 | C22 | 1 | 2 | yes | complemented |
| 22 | C2×C5⋊GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 23 | C5×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C5×#985 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C5×#983 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×C5×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 27 | D5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | D5×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 29 | D5×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 30 | D5×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 31 | #91897 | C22 | 1 | 2 | yes | complemented |
| 32 | #91896 | C22 | 1 | 2 | yes | complemented |
| 33 | D5×#226 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #91894 | C22 | 1 | 2 | yes | complemented |
| 35 | #91893 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #91892 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×#5926 | — | 5 | 1 | no | maximal, Hall |
| 38 | D5×2−1+4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 39 | D5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 40 | C5×#577 | — | 3 | 1 | no | — |
| 41 | #66171 | — | 3 | 1 | no | — |
| 42 | #66170 | — | 3 | 1 | no | — |
| 43 | #66112 | — | 3 | 1 | no | — |
| 44 | #66112 | — | 3 | 2 | no | — |
| 45 | D5×#137 | — | 3 | 1 | no | — |
| 46 | D5×#137 | — | 3 | 2 | no | — |
| 47 | #66109 | — | 3 | 2 | no | — |
| 48 | #66109 | — | 3 | 1 | no | — |
| 49 | D5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 50 | D5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 51 | #66104 | — | 3 | 2 | no | — |
| 52 | #66104 | — | 3 | 1 | no | — |
| 53 | D5×#135 | — | 3 | 2 | no | — |
| 54 | D5×#135 | — | 3 | 1 | no | — |
| 55 | #66096 | — | 3 | 1 | no | — |
| 56 | #66096 | — | 3 | 2 | no | — |
| 57 | C2×D5×SD16 | — | 3 | 1 | no | — |
| 58 | C2×D5×SD16 | — | 3 | 2 | no | — |
| 59 | #66085 | — | 3 | 1 | no | — |
| 60 | D5×#131 | — | 3 | 1 | no | — |
| 61 | C22×D3×D5 | — | 4 | 2 | no | — |
| 62 | D4×D15 | — | 4 | 1 | no | — |
| 63 | C5×D3×D4 | — | 4 | 1 | no | — |
| 64 | C3×D4×D5 | — | 4 | 1 | no | — |
| 65 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2×C5×SL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 67 | #6790 | — | 4 | 2 | no | — |
| 68 | D3×C22⋊D5 | — | 4 | 2 | no | — |
| 69 | D5×#67 | — | 4 | 2 | no | — |
| 70 | #6777 | — | 4 | 1 | no | — |
| 71 | D3×D20 | — | 4 | 1 | no | — |
| 72 | D5×D12 | — | 4 | 1 | no | — |
| 73 | C4×D3×D5 | — | 4 | 1 | no | — |
| 74 | D5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 75 | D5×SL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 76 | C5⋊(#41⋊C3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 77 | C5⋊GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 78 | C5⋊GL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 79 | C5⋊#226 | C23 | 1 | 1 | yes | characteristic, complemented |
| 80 | C5×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 81 | C5×GL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 82 | C5×#226 | C23 | 1 | 1 | yes | characteristic, complemented |
| 83 | C2×2−1+4⋊C3 | — | 5 | 1 | no | — |
| 84 | #5926 | — | 5 | 1 | no | — |
| 85 | #5926 | — | 5 | 1 | no | — |
| 86 | #5926 | — | 5 | 1 | no | — |
| 87 | #5926 | — | 5 | 2 | no | — |
| 88 | #5926 | — | 5 | 2 | no | — |
| 89 | #5926 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 90 | C2×#986 | — | 5 | 1 | no | — |
| 91 | C2×#985 | — | 5 | 1 | no | — |
| 92 | C2×#983 | — | 5 | 2 | no | — |
| 93 | C22×GL(2,𝔽3) | — | 5 | 2 | no | — |
| 94 | C5×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 96 | #4150 | — | 3 | 1 | no | — |
| 97 | #4150 | — | 3 | 2 | no | — |
| 98 | #4150 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 99 | #4149 | — | 3 | 1 | no | — |
| 100 | #4149 | — | 3 | 2 | no | — |
| 101 | #4149 | — | 3 | 1 | no | — |
| 102 | #4149 | — | 6 | 1 | no | — |
| 103 | D5×#41 | — | 3 | 1 | no | — |
| 104 | D5×#41 | — | 3 | 2 | no | — |
| 105 | D5×#41 | — | 3 | 2 | no | — |
| 106 | D5×#41 | — | 3 | 1 | no | — |
| 107 | D5×#41 | — | 6 | 1 | no | — |
| 108 | D5×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 109 | #4147 | — | 3 | 1 | no | — |
| 110 | #4147 | C2×D3 | 1 | 2 | yes | complemented |
| 111 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 112 | C2×Q8×D5 | C2×D3 | 1 | 2 | yes | complemented |
| 113 | #4144 | — | 3 | 2 | no | — |
| 114 | #4144 | — | 3 | 1 | no | — |
| 115 | #4144 | — | 6 | 1 | no | — |
| 116 | #4144 | — | 6 | 2 | no | — |
| 117 | C2×D4×D5 | — | 3 | 2 | no | — |
| 118 | C2×D4×D5 | — | 3 | 1 | no | — |
| 119 | C2×D4×D5 | — | 6 | 2 | no | — |
| 120 | C2×D4×D5 | — | 6 | 1 | no | — |
| 121 | C5×#137 | — | 3 | 1 | no | — |
| 122 | C5×#137 | — | 3 | 2 | no | — |
| 123 | C5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 124 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 125 | C5×#135 | — | 3 | 2 | no | — |
| 126 | C5×#135 | — | 3 | 1 | no | — |
| 127 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 128 | C2×C5×SD16 | — | 3 | 2 | no | — |
| 129 | C5×#131 | — | 3 | 1 | no | — |
| 130 | #4097 | — | 3 | 1 | no | — |
| 131 | #4097 | — | 3 | 2 | no | — |
| 132 | #4096 | — | 3 | 2 | no | — |
| 133 | #4096 | — | 3 | 1 | no | — |
| 134 | #4096 | — | 3 | 2 | no | — |
| 135 | #4096 | — | 3 | 1 | no | — |
| 136 | #4095 | — | 3 | 2 | no | — |
| 137 | #4095 | — | 3 | 1 | no | — |
| 138 | #4094 | — | 3 | 1 | no | — |
| 139 | #4088 | — | 3 | 1 | no | — |
| 140 | #4088 | — | 3 | 2 | no | — |
| 141 | C2×#688 | — | 3 | 1 | no | — |
| 142 | C2×#688 | — | 3 | 2 | no | — |
| 143 | C2×#687 | — | 3 | 1 | no | — |
| 144 | C2×#687 | — | 3 | 2 | no | — |
| 145 | #4078 | — | 3 | 1 | no | — |
| 146 | #4078 | — | 3 | 2 | no | — |
| 147 | #4065 | — | 3 | 2 | no | — |
| 148 | #4065 | — | 3 | 1 | no | — |
| 149 | #4064 | — | 3 | 2 | no | — |
| 150 | #4064 | — | 3 | 2 | no | — |
| 151 | #4064 | — | 3 | 2 | no | — |
| 152 | D5×Q16 | — | 3 | 2 | no | — |
| 153 | D5×Q16 | — | 3 | 1 | no | — |
| 154 | #4062 | — | 3 | 2 | no | — |
| 155 | #4062 | — | 3 | 1 | no | — |
| 156 | #4062 | — | 3 | 2 | no | — |
| 157 | #4062 | — | 3 | 1 | no | — |
| 158 | #4061 | — | 3 | 2 | no | — |
| 159 | #4061 | — | 3 | 2 | no | — |
| 160 | #4061 | — | 3 | 2 | no | — |
| 161 | #4060 | — | 3 | 2 | no | — |
| 162 | #4060 | — | 3 | 2 | no | — |
| 163 | #4060 | — | 3 | 2 | no | — |
| 164 | D5×SD16 | — | 3 | 2 | no | — |
| 165 | D5×SD16 | — | 3 | 2 | no | — |
| 166 | D5×SD16 | — | 3 | 2 | no | — |
| 167 | D5×SD16 | — | 3 | 2 | no | — |
| 168 | D5×SD16 | — | 3 | 2 | no | — |
| 169 | D5×SD16 | — | 3 | 2 | no | — |
| 170 | D5×SD16 | — | 3 | 2 | no | — |
| 171 | D5×SD16 | — | 3 | 1 | no | — |
| 172 | D5×SD16 | — | 3 | 1 | no | — |
| 173 | D5×SD16 | — | 3 | 2 | no | — |
| 174 | D5×SD16 | — | 3 | 2 | no | — |
| 175 | D5×SD16 | — | 3 | 2 | no | — |
| 176 | #4058 | — | 3 | 1 | no | — |
| 177 | #4058 | — | 3 | 2 | no | — |
| 178 | #4057 | — | 3 | 2 | no | — |
| 179 | #4057 | — | 3 | 2 | no | — |
| 180 | #4057 | — | 3 | 2 | no | — |
| 181 | D5×D8 | — | 3 | 2 | no | — |
| 182 | D5×D8 | — | 3 | 1 | no | — |
| 183 | #4055 | — | 3 | 1 | no | — |
| 184 | #4055 | — | 3 | 2 | no | — |
| 185 | #4054 | — | 3 | 1 | no | — |
| 186 | #4054 | — | 3 | 2 | no | — |
| 187 | #4053 | — | 3 | 2 | no | — |
| 188 | #4053 | — | 3 | 1 | no | — |
| 189 | D5×M16 | — | 3 | 2 | no | — |
| 190 | D5×M16 | — | 3 | 1 | no | — |
| 191 | #4050 | — | 3 | 1 | no | — |
| 192 | #4050 | — | 3 | 2 | no | — |
| 193 | C2×#677 | — | 3 | 1 | no | — |
| 194 | C2×#677 | — | 3 | 2 | no | — |
| 195 | #4047 | — | 3 | 2 | no | — |
| 196 | #4047 | — | 3 | 1 | no | — |
| 197 | C2×C8×D5 | — | 3 | 2 | no | — |
| 198 | C2×C8×D5 | — | 3 | 1 | no | — |
| 199 | C2×#577 | — | 15 | 1 | no | Sylow |
| 200 | C22×D15 | — | 4 | 2 | no | — |
| 201 | C22×C5×D3 | — | 4 | 2 | no | — |
| 202 | C22×C3×D5 | — | 4 | 2 | no | — |
| 203 | C2×D3×D5 | — | 4 | 1 | no | — |
| 204 | C2×D3×D5 | — | 4 | 2 | no | — |
| 205 | C2×D3×D5 | — | 4 | 2 | no | — |
| 206 | C2×D3×D5 | — | 4 | 2 | no | — |
| 207 | C2×D3×D5 | — | 8 | 8 | no | — |
| 208 | C3×C5×D4 | — | 4 | 1 | no | — |
| 209 | #1220 | — | 4 | 2 | no | — |
| 210 | D60 | — | 4 | 1 | no | — |
| 211 | C4×D15 | — | 4 | 1 | no | — |
| 212 | C5×#67 | — | 4 | 2 | no | — |
| 213 | C5×D12 | — | 4 | 1 | no | — |
| 214 | C4×C5×D3 | — | 4 | 1 | no | — |
| 215 | C3×C22⋊D5 | — | 4 | 2 | no | — |
| 216 | C3×D20 | — | 4 | 1 | no | — |
| 217 | C3×C4×D5 | — | 4 | 1 | no | — |
| 218 | C5×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 219 | #1203 | — | 4 | 2 | no | — |
| 220 | #1202 | — | 4 | 2 | no | — |
| 221 | #1201 | — | 4 | 2 | no | — |
| 222 | #1200 | — | 4 | 1 | no | — |
| 223 | D3×Dic5 | — | 4 | 1 | no | — |
| 224 | D5×Dic3 | — | 4 | 1 | no | — |
| 225 | C2×D3×D4 | — | 20 | 1 | no | — |
| 226 | 2−1+4⋊C3 | — | 5 | 1 | no | — |
| 227 | 2−1+4⋊C3 | — | 5 | 2 | no | — |
| 228 | 2−1+4⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 229 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 230 | C22×SL(2,𝔽3) | — | 5 | 2 | no | — |
| 231 | #986 | — | 5 | 1 | no | — |
| 232 | #986 | — | 5 | 2 | no | — |
| 233 | #986 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 234 | #985 | — | 5 | 1 | no | — |
| 235 | #985 | — | 5 | 1 | no | — |
| 236 | #985 | — | 5 | 1 | no | — |
| 237 | #985 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 238 | #983 | — | 5 | 2 | no | — |
| 239 | #983 | — | 5 | 2 | no | — |
| 240 | #983 | — | 5 | 2 | no | — |
| 241 | #983 | C2×D5 | 1 | 2 | yes | complemented |
| 242 | C2×GL(2,𝔽3) | — | 5 | 2 | no | — |
| 243 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 244 | C2×GL(2,𝔽3) | — | 5 | 2 | no | — |
| 245 | C2×GL(2,𝔽3) | — | 5 | 2 | no | — |
| 246 | C2×GL(2,𝔽3) | — | 5 | 2 | no | — |
| 247 | C2×GL(2,𝔽3) | C2×D5 | 1 | 2 | yes | complemented |
| 248 | C2×#226 | — | 5 | 1 | no | — |
| 249 | C23×D5 | — | 6 | 1 | no | — |
| 250 | C23×D5 | — | 6 | 2 | no | — |
| 251 | C5×#41 | — | 3 | 1 | no | — |
| 252 | C5×#41 | — | 3 | 2 | no | — |
| 253 | C5×#41 | — | 3 | 2 | no | — |
| 254 | C5×#41 | — | 3 | 1 | no | — |
| 255 | C5×#41 | — | 6 | 1 | no | — |
| 256 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 257 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 258 | C2×C5×Q8 | C22×D3 | 1 | 2 | yes | complemented |
| 259 | C2×C5×D4 | — | 3 | 2 | no | — |
| 260 | C2×C5×D4 | — | 3 | 1 | no | — |
| 261 | C2×C5×D4 | — | 6 | 2 | no | — |
| 262 | C2×C5×D4 | — | 6 | 1 | no | — |
| 263 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 264 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 265 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 266 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 267 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 268 | #713 | — | 3 | 1 | no | — |
| 269 | #713 | — | 3 | 2 | no | — |
| 270 | #713 | — | 3 | 2 | no | — |
| 271 | #713 | — | 3 | 1 | no | — |
| 272 | #713 | — | 6 | 1 | no | — |
| 273 | #713 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 274 | Q8×D5 | — | 3 | 1 | no | — |
| 275 | Q8×D5 | — | 3 | 2 | no | — |
| 276 | Q8×D5 | — | 3 | 2 | no | — |
| 277 | Q8×D5 | — | 3 | 2 | no | — |
| 278 | Q8×D5 | — | 3 | 1 | no | — |
| 279 | Q8×D5 | — | 6 | 1 | no | — |
| 280 | Q8×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 281 | Q8×D5 | C22×D3 | 1 | 2 | yes | complemented |
| 282 | #711 | — | 3 | 1 | no | — |
| 283 | #711 | — | 3 | 2 | no | — |
| 284 | #711 | — | 3 | 1 | no | — |
| 285 | #711 | — | 3 | 2 | no | — |
| 286 | #711 | — | 3 | 2 | no | — |
| 287 | #711 | — | 3 | 1 | no | — |
| 288 | #711 | — | 6 | 1 | no | — |
| 289 | #711 | — | 6 | 2 | no | — |
| 290 | #711 | — | 6 | 2 | no | — |
| 291 | #711 | — | 6 | 2 | no | — |
| 292 | #711 | — | 6 | 1 | no | — |
| 293 | D4×D5 | — | 3 | 2 | no | — |
| 294 | D4×D5 | — | 3 | 1 | no | — |
| 295 | D4×D5 | — | 3 | 2 | no | — |
| 296 | D4×D5 | — | 3 | 1 | no | — |
| 297 | D4×D5 | — | 3 | 2 | no | — |
| 298 | D4×D5 | — | 3 | 2 | no | — |
| 299 | D4×D5 | — | 3 | 2 | no | — |
| 300 | D4×D5 | — | 6 | 2 | no | — |
| 301 | D4×D5 | — | 6 | 2 | no | — |
| 302 | D4×D5 | — | 6 | 1 | no | — |
| 303 | D4×D5 | — | 6 | 2 | no | — |
| 304 | D4×D5 | — | 6 | 2 | no | — |
| 305 | D4×D5 | — | 6 | 2 | no | — |
| 306 | D4×D5 | — | 6 | 2 | no | — |
| 307 | D4×D5 | — | 6 | 1 | no | — |
| 308 | D4×D5 | — | 6 | 2 | no | — |
| 309 | D4×D5 | — | 6 | 1 | no | — |
| 310 | D4×D5 | — | 6 | 2 | no | — |
| 311 | D4×D5 | — | 6 | 1 | no | — |
| 312 | D4×D5 | — | 6 | 1 | no | — |
| 313 | D4×D5 | S4 | 1 | 1 | yes | characteristic |
| 314 | #709 | — | 3 | 2 | no | — |
| 315 | #709 | — | 3 | 1 | no | — |
| 316 | #709 | — | 3 | 1 | no | — |
| 317 | #709 | — | 3 | 2 | no | — |
| 318 | #709 | — | 3 | 2 | no | — |
| 319 | #709 | — | 3 | 1 | no | — |
| 320 | #709 | — | 6 | 1 | no | — |
| 321 | #709 | — | 6 | 2 | no | — |
| 322 | #709 | — | 6 | 2 | no | — |
| 323 | #709 | — | 6 | 2 | no | — |
| 324 | #709 | — | 6 | 1 | no | — |
| 325 | C2×D20 | — | 3 | 2 | no | — |
| 326 | C2×D20 | — | 3 | 1 | no | — |
| 327 | C2×D20 | — | 6 | 2 | no | — |
| 328 | C2×D20 | — | 6 | 1 | no | — |
| 329 | C2×C4×D5 | — | 3 | 2 | no | — |
| 330 | C2×C4×D5 | — | 3 | 1 | no | — |
| 331 | C2×C4×D5 | — | 6 | 1 | no | — |
| 332 | C2×C4×D5 | — | 6 | 2 | no | — |
| 333 | C2×C4×D5 | — | 6 | 1 | no | — |
| 334 | C2×Dic10 | — | 3 | 1 | no | — |
| 335 | C2×Dic10 | — | 3 | 2 | no | — |
| 336 | C2×Dic10 | — | 6 | 1 | no | — |
| 337 | C5×Q16 | — | 3 | 2 | no | — |
| 338 | C5×Q16 | — | 3 | 1 | no | — |
| 339 | C5×SD16 | — | 3 | 2 | no | — |
| 340 | C5×SD16 | — | 3 | 2 | no | — |
| 341 | C5×SD16 | — | 3 | 2 | no | — |
| 342 | C5×SD16 | — | 3 | 1 | no | — |
| 343 | C5×SD16 | — | 3 | 1 | no | — |
| 344 | C5×SD16 | — | 3 | 2 | no | — |
| 345 | C5×D8 | — | 3 | 2 | no | — |
| 346 | C5×D8 | — | 3 | 1 | no | — |
| 347 | C5×M16 | — | 3 | 2 | no | — |
| 348 | C5×M16 | — | 3 | 1 | no | — |
| 349 | C2×C5×C8 | — | 3 | 2 | no | — |
| 350 | C2×C5×C8 | — | 3 | 1 | no | — |
| 351 | #689 | — | 3 | 1 | no | — |
| 352 | #689 | — | 3 | 2 | no | — |
| 353 | #689 | — | 3 | 2 | no | — |
| 354 | #689 | — | 3 | 1 | no | — |
| 355 | #688 | — | 3 | 1 | no | — |
| 356 | #688 | — | 3 | 2 | no | — |
| 357 | #688 | — | 3 | 2 | no | — |
| 358 | #688 | — | 3 | 2 | no | — |
| 359 | #688 | — | 3 | 1 | no | — |
| 360 | #688 | — | 3 | 2 | no | — |
| 361 | #687 | — | 3 | 1 | no | — |
| 362 | #687 | — | 3 | 1 | no | — |
| 363 | #687 | — | 3 | 2 | no | — |
| 364 | #687 | — | 3 | 2 | no | — |
| 365 | #687 | — | 3 | 2 | no | — |
| 366 | #687 | — | 3 | 2 | no | — |
| 367 | #686 | — | 3 | 2 | no | — |
| 368 | #686 | — | 3 | 1 | no | — |
| 369 | #686 | — | 3 | 1 | no | — |
| 370 | #686 | — | 3 | 2 | no | — |
| 371 | #681 | — | 3 | 2 | no | — |
| 372 | #681 | — | 3 | 1 | no | — |
| 373 | C2×#168 | — | 3 | 2 | no | — |
| 374 | C2×#168 | — | 3 | 1 | no | — |
| 375 | Dic20 | — | 3 | 1 | no | — |
| 376 | Dic20 | — | 3 | 2 | no | — |
| 377 | D40 | — | 3 | 1 | no | — |
| 378 | D40 | — | 3 | 2 | no | — |
| 379 | #677 | — | 3 | 1 | no | — |
| 380 | #677 | — | 3 | 2 | no | — |
| 381 | #677 | — | 3 | 2 | no | — |
| 382 | #677 | — | 3 | 2 | no | — |
| 383 | #677 | — | 3 | 2 | no | — |
| 384 | #677 | — | 3 | 1 | no | — |
| 385 | #676 | — | 3 | 2 | no | — |
| 386 | #676 | — | 3 | 2 | no | — |
| 387 | #676 | — | 3 | 2 | no | — |
| 388 | C8×D5 | — | 3 | 1 | no | — |
| 389 | C8×D5 | — | 3 | 2 | no | — |
| 390 | C8×D5 | — | 3 | 1 | no | — |
| 391 | C8×D5 | — | 3 | 1 | no | — |
| 392 | C8×D5 | — | 3 | 2 | no | — |
| 393 | C8×D5 | — | 3 | 2 | no | — |
| 394 | C8×D5 | — | 3 | 1 | no | — |
| 395 | C2×2−1+4 | — | 5 | 1 | no | — |
| 396 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 397 | #577 | — | 3 | 1 | no | — |
| 398 | #577 | — | 15 | 1 | no | — |
| 399 | #577 | — | 15 | 2 | no | — |
| 400 | #577 | — | 15 | 1 | no | — |
| 401 | #577 | — | 15 | 1 | no | — |
| 402 | #577 | — | 15 | 2 | no | — |
| 403 | #577 | — | 15 | 1 | no | — |
| 404 | #577 | — | 15 | 2 | no | — |
| 405 | #577 | — | 15 | 2 | no | — |
| 406 | #577 | — | 15 | 1 | no | — |
| 407 | #577 | — | 15 | 1 | no | — |
| 408 | #577 | — | 15 | 1 | no | — |
| 409 | C2×#137 | — | 15 | 2 | no | — |
| 410 | C2×#137 | — | 15 | 1 | no | — |
| 411 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 412 | C2×AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 413 | C2×#135 | — | 15 | 1 | no | — |
| 414 | C2×#135 | — | 15 | 2 | no | — |
| 415 | C22×SD16 | — | 15 | 2 | no | — |
| 416 | C22×SD16 | — | 15 | 1 | no | — |
| 417 | C2×#131 | — | 15 | 1 | no | — |
| 418 | C22×C3×C5 | — | 4 | 2 | no | — |
| 419 | C2×D15 | — | 4 | 1 | no | — |
| 420 | C2×D15 | — | 4 | 2 | no | — |
| 421 | C2×D15 | — | 8 | 4 | no | — |
| 422 | C2×C5×D3 | — | 4 | 1 | no | — |
| 423 | C2×C5×D3 | — | 4 | 2 | no | — |
| 424 | C2×C5×D3 | — | 8 | 4 | no | — |
| 425 | C2×C3×D5 | — | 4 | 1 | no | — |
| 426 | C2×C3×D5 | — | 4 | 2 | no | — |
| 427 | C2×C3×D5 | — | 8 | 4 | no | — |
| 428 | D3×D5 | — | 4 | 4 | no | — |
| 429 | D3×D5 | — | 8 | 4 | no | — |
| 430 | D3×D5 | — | 8 | 4 | no | — |
| 431 | D3×D5 | — | 8 | 4 | no | — |
| 432 | C3×C4×C5 | — | 4 | 1 | no | — |
| 433 | Dic15 | — | 4 | 1 | no | — |
| 434 | C3×Dic5 | — | 4 | 1 | no | — |
| 435 | C5×Dic3 | — | 4 | 1 | no | — |
| 436 | C23×D3 | — | 20 | 2 | no | — |
| 437 | C2×C3×D4 | — | 20 | 1 | no | — |
| 438 | C2×#67 | — | 20 | 2 | no | — |
| 439 | D3×D4 | — | 4 | 1 | no | — |
| 440 | D3×D4 | — | 20 | 1 | no | — |
| 441 | D3×D4 | — | 20 | 1 | no | — |
| 442 | D3×D4 | — | 20 | 2 | no | — |
| 443 | D3×D4 | — | 20 | 1 | no | — |
| 444 | D3×D4 | — | 20 | 2 | no | — |
| 445 | C2×D12 | — | 20 | 1 | no | — |
| 446 | C2×C4×D3 | — | 20 | 1 | no | — |
| 447 | #41⋊C3 | — | 5 | 1 | no | — |
| 448 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 449 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 450 | C2×SL(2,𝔽3) | — | 5 | 2 | no | — |
| 451 | C2×SL(2,𝔽3) | C22×D5 | 1 | 2 | yes | complemented |
| 452 | GL(2,𝔽3) | — | 5 | 1 | no | — |
| 453 | GL(2,𝔽3) | — | 5 | 2 | no | — |
| 454 | GL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 455 | GL(2,𝔽3) | C22×D5 | 1 | 2 | yes | complemented |
| 456 | #226 | — | 5 | 1 | no | — |
| 457 | #226 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 458 | C23×C5 | — | 6 | 1 | no | — |
| 459 | C23×C5 | — | 6 | 2 | no | — |
| 460 | C22×D5 | — | 3 | 1 | no | — |
| 461 | C22×D5 | — | 6 | 2 | no | — |
| 462 | C22×D5 | — | 6 | 1 | no | — |
| 463 | C22×D5 | — | 6 | 2 | no | — |
| 464 | C22×D5 | — | 6 | 1 | no | — |
| 465 | C22×D5 | — | 6 | 2 | no | — |
| 466 | C22×D5 | — | 6 | 2 | no | — |
| 467 | C22×D5 | — | 6 | 2 | no | — |
| 468 | C22×D5 | — | 24 | 4 | no | — |
| 469 | C22×D5 | — | 24 | 2 | no | — |
| 470 | C22×D5 | C2×S4 | 1 | 2 | yes | — |
| 471 | C5×Q8 | — | 3 | 2 | no | — |
| 472 | C5×Q8 | — | 3 | 1 | no | — |
| 473 | C5×Q8 | — | 3 | 1 | no | — |
| 474 | C5×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 475 | C5×D4 | — | 3 | 1 | no | — |
| 476 | C5×D4 | — | 3 | 2 | no | — |
| 477 | C5×D4 | — | 3 | 2 | no | — |
| 478 | C5×D4 | — | 3 | 1 | no | — |
| 479 | C5×D4 | — | 6 | 2 | no | — |
| 480 | C5×D4 | — | 6 | 1 | no | — |
| 481 | C5×D4 | — | 6 | 2 | no | — |
| 482 | C5×D4 | — | 6 | 1 | no | — |
| 483 | C5×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 484 | C2×C4×C5 | — | 3 | 2 | no | — |
| 485 | C2×C4×C5 | — | 3 | 1 | no | — |
| 486 | C2×C4×C5 | — | 6 | 1 | no | — |
| 487 | C2×C4×C5 | — | 6 | 2 | no | — |
| 488 | C2×C4×C5 | — | 6 | 1 | no | — |
| 489 | C22⋊D5 | — | 3 | 2 | no | — |
| 490 | C22⋊D5 | — | 3 | 2 | no | — |
| 491 | C22⋊D5 | — | 6 | 1 | no | — |
| 492 | C22⋊D5 | — | 6 | 2 | no | — |
| 493 | C22⋊D5 | — | 6 | 2 | no | — |
| 494 | C22⋊D5 | — | 6 | 1 | no | — |
| 495 | C22⋊D5 | — | 6 | 2 | no | — |
| 496 | C22⋊D5 | — | 6 | 1 | no | — |
| 497 | C22⋊D5 | — | 6 | 1 | no | — |
| 498 | C22⋊D5 | — | 6 | 2 | no | — |
| 499 | C22⋊D5 | — | 6 | 2 | no | — |
| 500 | C22⋊D5 | — | 6 | 2 | no | — |
| 501 | C22⋊D5 | C2×S4 | 1 | 2 | yes | — |
| 502 | C2×Dic5 | — | 3 | 2 | no | — |
| 503 | C2×Dic5 | — | 3 | 1 | no | — |
| 504 | C2×Dic5 | — | 6 | 1 | no | — |
| 505 | C2×Dic5 | — | 6 | 2 | no | — |
| 506 | C2×Dic5 | — | 6 | 1 | no | — |
| 507 | D20 | — | 3 | 1 | no | — |
| 508 | D20 | — | 3 | 2 | no | — |
| 509 | D20 | — | 3 | 2 | no | — |
| 510 | D20 | — | 3 | 1 | no | — |
| 511 | D20 | — | 6 | 2 | no | — |
| 512 | D20 | — | 6 | 1 | no | — |
| 513 | D20 | — | 6 | 2 | no | — |
| 514 | D20 | — | 6 | 1 | no | — |
| 515 | D20 | C2×S4 | 1 | 1 | yes | characteristic |
| 516 | C4×D5 | — | 3 | 1 | no | — |
| 517 | C4×D5 | — | 3 | 2 | no | — |
| 518 | C4×D5 | — | 3 | 2 | no | — |
| 519 | C4×D5 | — | 3 | 2 | no | — |
| 520 | C4×D5 | — | 3 | 1 | no | — |
| 521 | C4×D5 | — | 3 | 1 | no | — |
| 522 | C4×D5 | — | 6 | 2 | no | — |
| 523 | C4×D5 | — | 6 | 2 | no | — |
| 524 | C4×D5 | — | 6 | 2 | no | — |
| 525 | C4×D5 | — | 6 | 1 | no | — |
| 526 | C4×D5 | — | 6 | 1 | no | — |
| 527 | C4×D5 | — | 6 | 1 | no | — |
| 528 | C4×D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 529 | Dic10 | — | 3 | 1 | no | — |
| 530 | Dic10 | — | 3 | 2 | no | — |
| 531 | Dic10 | — | 3 | 1 | no | — |
| 532 | Dic10 | — | 3 | 2 | no | — |
| 533 | Dic10 | — | 3 | 1 | no | — |
| 534 | Dic10 | — | 6 | 2 | no | — |
| 535 | Dic10 | — | 6 | 1 | no | — |
| 536 | C5×C8 | — | 3 | 1 | no | — |
| 537 | C5×C8 | — | 3 | 1 | no | — |
| 538 | C5×C8 | — | 3 | 2 | no | — |
| 539 | #168 | — | 3 | 1 | no | — |
| 540 | #168 | — | 3 | 1 | no | — |
| 541 | #168 | — | 3 | 2 | no | — |
| 542 | 2−1+4 | — | 5 | 1 | no | — |
| 543 | 2−1+4 | — | 5 | 2 | no | — |
| 544 | 2−1+4 | — | 15 | 1 | no | — |
| 545 | 2−1+4 | — | 15 | 1 | no | — |
| 546 | 2−1+4 | — | 15 | 2 | no | — |
| 547 | 2−1+4 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 548 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 549 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 550 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 551 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 552 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 553 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 554 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 555 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 556 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 557 | C2×#41 | — | 5 | 1 | no | — |
| 558 | C2×#41 | — | 15 | 1 | no | — |
| 559 | C2×#41 | — | 15 | 2 | no | — |
| 560 | C2×#41 | — | 15 | 1 | no | — |
| 561 | C2×#41 | — | 15 | 2 | no | — |
| 562 | C2×#41 | — | 30 | 1 | no | — |
| 563 | C22×Q8 | — | 5 | 2 | no | — |
| 564 | C22×Q8 | — | 15 | 1 | no | — |
| 565 | C22×D4 | — | 15 | 1 | no | — |
| 566 | C22×D4 | — | 15 | 2 | no | — |
| 567 | C22×D4 | — | 30 | 1 | no | — |
| 568 | C22×D4 | — | 30 | 2 | no | — |
| 569 | #137 | — | 3 | 1 | no | — |
| 570 | #137 | — | 3 | 2 | no | — |
| 571 | #137 | — | 15 | 2 | no | — |
| 572 | #137 | — | 15 | 1 | no | — |
| 573 | #137 | — | 15 | 2 | no | — |
| 574 | #137 | — | 15 | 2 | no | — |
| 575 | #137 | — | 15 | 2 | no | — |
| 576 | #137 | — | 15 | 2 | no | — |
| 577 | #137 | — | 15 | 2 | no | — |
| 578 | #137 | — | 15 | 2 | no | — |
| 579 | #137 | — | 15 | 1 | no | — |
| 580 | #137 | — | 15 | 2 | no | — |
| 581 | #137 | — | 15 | 1 | no | — |
| 582 | #137 | — | 15 | 2 | no | — |
| 583 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 584 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 585 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 586 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 587 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 588 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 589 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 590 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 591 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 592 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 593 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 594 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 595 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 596 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 597 | #135 | — | 3 | 2 | no | — |
| 598 | #135 | — | 3 | 1 | no | — |
| 599 | #135 | — | 15 | 1 | no | — |
| 600 | #135 | — | 15 | 2 | no | — |
| 601 | #135 | — | 15 | 1 | no | — |
| 602 | #135 | — | 15 | 2 | no | — |
| 603 | #135 | — | 15 | 1 | no | — |
| 604 | #135 | — | 15 | 2 | no | — |
| 605 | #135 | — | 15 | 1 | no | — |
| 606 | #135 | — | 15 | 2 | no | — |
| 607 | #135 | — | 15 | 1 | no | — |
| 608 | #135 | — | 15 | 2 | no | — |
| 609 | #135 | — | 15 | 1 | no | — |
| 610 | #135 | — | 15 | 2 | no | — |
| 611 | #135 | — | 15 | 2 | no | — |
| 612 | #135 | — | 15 | 1 | no | — |
| 613 | C2×Q16 | — | 15 | 1 | no | — |
| 614 | C2×Q16 | — | 15 | 2 | no | — |
| 615 | C2×SD16 | — | 3 | 1 | no | — |
| 616 | C2×SD16 | — | 3 | 2 | no | — |
| 617 | C2×SD16 | — | 15 | 2 | no | — |
| 618 | C2×SD16 | — | 15 | 1 | no | — |
| 619 | C2×SD16 | — | 15 | 1 | no | — |
| 620 | C2×SD16 | — | 15 | 2 | no | — |
| 621 | C2×SD16 | — | 15 | 2 | no | — |
| 622 | C2×SD16 | — | 15 | 2 | no | — |
| 623 | C2×SD16 | — | 15 | 2 | no | — |
| 624 | C2×SD16 | — | 15 | 2 | no | — |
| 625 | C2×SD16 | — | 15 | 2 | no | — |
| 626 | C2×SD16 | — | 15 | 2 | no | — |
| 627 | C2×SD16 | — | 15 | 2 | no | — |
| 628 | C2×SD16 | — | 15 | 2 | no | — |
| 629 | C2×SD16 | — | 15 | 2 | no | — |
| 630 | C2×SD16 | — | 15 | 1 | no | — |
| 631 | C2×SD16 | — | 15 | 2 | no | — |
| 632 | C2×SD16 | — | 15 | 1 | no | — |
| 633 | C2×SD16 | — | 15 | 1 | no | — |
| 634 | C2×SD16 | — | 15 | 2 | no | — |
| 635 | C2×D8 | — | 15 | 1 | no | — |
| 636 | C2×D8 | — | 15 | 2 | no | — |
| 637 | #131 | — | 3 | 1 | no | — |
| 638 | #131 | — | 15 | 2 | no | — |
| 639 | #131 | — | 15 | 1 | no | — |
| 640 | #131 | — | 15 | 1 | no | — |
| 641 | #131 | — | 15 | 2 | no | — |
| 642 | #131 | — | 15 | 1 | no | — |
| 643 | C2×M16 | — | 15 | 1 | no | — |
| 644 | C2×M16 | — | 15 | 2 | no | — |
| 645 | C22×C8 | — | 15 | 1 | no | — |
| 646 | C22×C8 | — | 15 | 2 | no | — |
| 647 | C2×C3×C5 | — | 4 | 1 | no | — |
| 648 | C2×C3×C5 | — | 8 | 2 | no | — |
| 649 | D15 | — | 4 | 2 | no | — |
| 650 | D15 | — | 8 | 2 | no | — |
| 651 | C3×D5 | — | 4 | 2 | no | — |
| 652 | C3×D5 | — | 8 | 2 | no | — |
| 653 | C5×D3 | — | 4 | 2 | no | — |
| 654 | C5×D3 | — | 8 | 2 | no | — |
| 655 | C23×C3 | — | 20 | 2 | no | — |
| 656 | C22×D3 | — | 4 | 2 | no | — |
| 657 | C22×D3 | — | 20 | 1 | no | — |
| 658 | C22×D3 | — | 20 | 2 | no | — |
| 659 | C22×D3 | — | 20 | 2 | no | — |
| 660 | C22×D3 | — | 20 | 2 | no | — |
| 661 | C22×D3 | — | 20 | 2 | no | — |
| 662 | C22×D3 | — | 40 | 8 | no | — |
| 663 | C3×D4 | — | 4 | 1 | no | — |
| 664 | C3×D4 | — | 20 | 1 | no | — |
| 665 | C3×D4 | — | 20 | 2 | no | — |
| 666 | C2×C3×C4 | — | 20 | 1 | no | — |
| 667 | #67 | — | 4 | 2 | no | — |
| 668 | #67 | — | 20 | 2 | no | — |
| 669 | #67 | — | 20 | 2 | no | — |
| 670 | #67 | — | 20 | 2 | no | — |
| 671 | C2×Dic3 | — | 20 | 1 | no | — |
| 672 | D12 | — | 4 | 1 | no | — |
| 673 | D12 | — | 20 | 1 | no | — |
| 674 | D12 | — | 20 | 2 | no | — |
| 675 | C4×D3 | — | 4 | 1 | no | — |
| 676 | C4×D3 | — | 20 | 1 | no | — |
| 677 | C4×D3 | — | 20 | 1 | no | — |
| 678 | C4×D3 | — | 20 | 1 | no | — |
| 679 | SL(2,𝔽3) | C23×D5 | 1 | 1 | yes | characteristic |
| 680 | C22×C5 | — | 3 | 1 | no | — |
| 681 | C22×C5 | — | 6 | 1 | no | — |
| 682 | C22×C5 | — | 6 | 2 | no | — |
| 683 | C22×C5 | — | 24 | 2 | no | — |
| 684 | C22×C5 | — | 24 | 1 | no | — |
| 685 | C22×C5 | C22×S4 | 1 | 2 | yes | — |
| 686 | C2×D5 | — | 2 | 4 | no | — |
| 687 | C2×D5 | — | 3 | 1 | no | — |
| 688 | C2×D5 | — | 6 | 2 | no | — |
| 689 | C2×D5 | — | 6 | 1 | no | — |
| 690 | C2×D5 | — | 6 | 2 | no | — |
| 691 | C2×D5 | — | 12 | 2 | no | — |
| 692 | C2×D5 | — | 12 | 4 | no | — |
| 693 | C2×D5 | — | 24 | 2 | no | — |
| 694 | C2×D5 | — | 24 | 2 | no | — |
| 695 | C2×D5 | — | 24 | 2 | no | — |
| 696 | C2×D5 | — | 24 | 2 | no | — |
| 697 | C2×D5 | — | 24 | 1 | no | — |
| 698 | C2×D5 | C22×S4 | 1 | 2 | yes | — |
| 699 | C2×D5 | C22×S4 | 1 | 1 | yes | characteristic |
| 700 | C4×C5 | — | 3 | 1 | no | — |
| 701 | C4×C5 | — | 3 | 2 | no | — |
| 702 | C4×C5 | — | 6 | 1 | no | — |
| 703 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 704 | Dic5 | — | 3 | 2 | no | — |
| 705 | Dic5 | — | 3 | 1 | no | — |
| 706 | Dic5 | — | 6 | 1 | no | — |
| 707 | Dic5 | C22×S4 | 1 | 1 | yes | characteristic |
| 708 | C24 | — | 30 | 2 | no | — |
| 709 | C24 | — | 30 | 1 | no | — |
| 710 | #41 | — | 3 | 1 | no | — |
| 711 | #41 | — | 3 | 2 | no | — |
| 712 | #41 | — | 3 | 2 | no | — |
| 713 | #41 | — | 3 | 1 | no | — |
| 714 | #41 | — | 5 | 1 | no | — |
| 715 | #41 | — | 6 | 1 | no | — |
| 716 | #41 | — | 15 | 2 | no | — |
| 717 | #41 | — | 15 | 1 | no | — |
| 718 | #41 | — | 15 | 1 | no | — |
| 719 | #41 | — | 15 | 2 | no | — |
| 720 | #41 | — | 15 | 2 | no | — |
| 721 | #41 | — | 15 | 1 | no | — |
| 722 | #41 | — | 15 | 2 | no | — |
| 723 | #41 | — | 15 | 1 | no | — |
| 724 | #41 | — | 15 | 1 | no | — |
| 725 | #41 | — | 15 | 1 | no | — |
| 726 | #41 | — | 15 | 2 | no | — |
| 727 | #41 | — | 15 | 1 | no | — |
| 728 | #41 | — | 15 | 2 | no | — |
| 729 | #41 | — | 15 | 2 | no | — |
| 730 | #41 | — | 15 | 1 | no | — |
| 731 | #41 | — | 15 | 2 | no | — |
| 732 | #41 | — | 30 | 2 | no | — |
| 733 | #41 | — | 30 | 2 | no | — |
| 734 | #41 | — | 30 | 1 | no | — |
| 735 | #41 | — | 30 | 2 | no | — |
| 736 | #41 | — | 30 | 1 | no | — |
| 737 | #41 | — | 30 | 2 | no | — |
| 738 | #41 | — | 30 | 1 | no | — |
| 739 | #41 | — | 30 | 2 | no | — |
| 740 | #41 | — | 30 | 2 | no | — |
| 741 | #41 | — | 30 | 1 | no | — |
| 742 | #41 | — | 30 | 1 | no | — |
| 743 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 744 | C2×Q8 | — | 3 | 1 | no | — |
| 745 | C2×Q8 | — | 5 | 1 | no | — |
| 746 | C2×Q8 | — | 5 | 2 | no | — |
| 747 | C2×Q8 | — | 15 | 2 | no | — |
| 748 | C2×Q8 | — | 15 | 1 | no | — |
| 749 | C2×Q8 | — | 15 | 1 | no | — |
| 750 | C2×Q8 | — | 15 | 2 | no | — |
| 751 | C2×Q8 | — | 15 | 2 | no | — |
| 752 | C2×Q8 | — | 15 | 2 | no | — |
| 753 | C2×Q8 | — | 15 | 1 | no | — |
| 754 | C2×Q8 | — | 30 | 1 | no | — |
| 755 | C2×Q8 | — | 30 | 1 | no | — |
| 756 | C2×Q8 | C2×D3×D5 | 1 | 2 | yes | complemented |
| 757 | C2×D4 | — | 3 | 2 | no | — |
| 758 | C2×D4 | — | 3 | 1 | no | — |
| 759 | C2×D4 | — | 5 | 1 | no | — |
| 760 | C2×D4 | — | 6 | 2 | no | — |
| 761 | C2×D4 | — | 6 | 1 | no | — |
| 762 | C2×D4 | — | 15 | 2 | no | — |
| 763 | C2×D4 | — | 15 | 1 | no | — |
| 764 | C2×D4 | — | 15 | 2 | no | — |
| 765 | C2×D4 | — | 15 | 1 | no | — |
| 766 | C2×D4 | — | 15 | 1 | no | — |
| 767 | C2×D4 | — | 15 | 2 | no | — |
| 768 | C2×D4 | — | 15 | 2 | no | — |
| 769 | C2×D4 | — | 15 | 2 | no | — |
| 770 | C2×D4 | — | 15 | 2 | no | — |
| 771 | C2×D4 | — | 30 | 1 | no | — |
| 772 | C2×D4 | — | 30 | 1 | no | — |
| 773 | C2×D4 | — | 30 | 2 | no | — |
| 774 | C2×D4 | — | 30 | 2 | no | — |
| 775 | C2×D4 | — | 30 | 2 | no | — |
| 776 | C2×D4 | — | 30 | 1 | no | — |
| 777 | C2×D4 | — | 30 | 1 | no | — |
| 778 | C2×D4 | — | 30 | 2 | no | — |
| 779 | C2×D4 | — | 30 | 2 | no | — |
| 780 | C2×D4 | — | 30 | 2 | no | — |
| 781 | C2×D4 | — | 30 | 1 | no | — |
| 782 | C2×D4 | — | 30 | 2 | no | — |
| 783 | C2×D4 | — | 30 | 2 | no | — |
| 784 | C2×D4 | — | 30 | 2 | no | — |
| 785 | C2×D4 | — | 30 | 2 | no | — |
| 786 | C2×D4 | — | 30 | 2 | no | — |
| 787 | C2×D4 | — | 30 | 1 | no | — |
| 788 | C2×D4 | — | 30 | 2 | no | — |
| 789 | C2×D4 | — | 30 | 2 | no | — |
| 790 | C2×D4 | — | 30 | 1 | no | — |
| 791 | C22×C4 | — | 15 | 1 | no | — |
| 792 | C22×C4 | — | 15 | 2 | no | — |
| 793 | C22×C4 | — | 30 | 1 | no | — |
| 794 | C22×C4 | — | 30 | 1 | no | — |
| 795 | C22×C4 | — | 30 | 2 | no | — |
| 796 | Q16 | — | 3 | 2 | no | — |
| 797 | Q16 | — | 3 | 1 | no | — |
| 798 | Q16 | — | 15 | 1 | no | — |
| 799 | Q16 | — | 15 | 2 | no | — |
| 800 | Q16 | — | 15 | 2 | no | — |
| 801 | Q16 | — | 15 | 1 | no | — |
| 802 | Q16 | — | 15 | 2 | no | — |
| 803 | Q16 | — | 15 | 1 | no | — |
| 804 | SD16 | — | 3 | 2 | no | — |
| 805 | SD16 | — | 3 | 2 | no | — |
| 806 | SD16 | — | 3 | 2 | no | — |
| 807 | SD16 | — | 3 | 1 | no | — |
| 808 | SD16 | — | 3 | 1 | no | — |
| 809 | SD16 | — | 3 | 2 | no | — |
| 810 | SD16 | — | 15 | 1 | no | — |
| 811 | SD16 | — | 15 | 2 | no | — |
| 812 | SD16 | — | 15 | 2 | no | — |
| 813 | SD16 | — | 15 | 2 | no | — |
| 814 | SD16 | — | 15 | 2 | no | — |
| 815 | SD16 | — | 15 | 1 | no | — |
| 816 | SD16 | — | 15 | 1 | no | — |
| 817 | SD16 | — | 15 | 2 | no | — |
| 818 | SD16 | — | 15 | 2 | no | — |
| 819 | SD16 | — | 15 | 2 | no | — |
| 820 | SD16 | — | 15 | 2 | no | — |
| 821 | SD16 | — | 15 | 1 | no | — |
| 822 | SD16 | — | 15 | 2 | no | — |
| 823 | SD16 | — | 15 | 2 | no | — |
| 824 | SD16 | — | 15 | 2 | no | — |
| 825 | SD16 | — | 15 | 1 | no | — |
| 826 | SD16 | — | 15 | 1 | no | — |
| 827 | SD16 | — | 15 | 2 | no | — |
| 828 | D8 | — | 3 | 2 | no | — |
| 829 | D8 | — | 3 | 1 | no | — |
| 830 | D8 | — | 15 | 1 | no | — |
| 831 | D8 | — | 15 | 2 | no | — |
| 832 | D8 | — | 15 | 2 | no | — |
| 833 | D8 | — | 15 | 1 | no | — |
| 834 | D8 | — | 15 | 1 | no | — |
| 835 | D8 | — | 15 | 2 | no | — |
| 836 | M16 | — | 3 | 2 | no | — |
| 837 | M16 | — | 3 | 1 | no | — |
| 838 | M16 | — | 15 | 2 | no | — |
| 839 | M16 | — | 15 | 2 | no | — |
| 840 | M16 | — | 15 | 2 | no | — |
| 841 | M16 | — | 15 | 2 | no | — |
| 842 | M16 | — | 15 | 1 | no | — |
| 843 | C2×C8 | — | 3 | 2 | no | — |
| 844 | C2×C8 | — | 3 | 1 | no | — |
| 845 | C2×C8 | — | 15 | 1 | no | — |
| 846 | C2×C8 | — | 15 | 2 | no | — |
| 847 | C2×C8 | — | 15 | 1 | no | — |
| 848 | C2×C8 | — | 15 | 1 | no | — |
| 849 | C2×C8 | — | 15 | 2 | no | — |
| 850 | C2×C8 | — | 15 | 1 | no | — |
| 851 | C2×C8 | — | 15 | 2 | no | — |
| 852 | C2×C8 | — | 15 | 2 | no | — |
| 853 | C2×C8 | — | 15 | 1 | no | — |
| 854 | C3×C5 | — | 4 | 1 | no | Hall |
| 855 | C22×C3 | — | 4 | 2 | no | — |
| 856 | C22×C3 | — | 20 | 1 | no | — |
| 857 | C22×C3 | — | 20 | 2 | no | — |
| 858 | C22×C3 | — | 40 | 4 | no | — |
| 859 | C2×D3 | — | 4 | 1 | no | — |
| 860 | C2×D3 | — | 4 | 2 | no | — |
| 861 | C2×D3 | — | 8 | 4 | no | — |
| 862 | C2×D3 | — | 20 | 1 | no | — |
| 863 | C2×D3 | — | 20 | 2 | no | — |
| 864 | C2×D3 | — | 20 | 4 | no | — |
| 865 | C2×D3 | — | 40 | 4 | no | — |
| 866 | C2×D3 | — | 40 | 4 | no | — |
| 867 | C2×D3 | — | 40 | 4 | no | — |
| 868 | C2×D3 | — | 40 | 4 | no | — |
| 869 | C3×C4 | — | 4 | 1 | no | — |
| 870 | C3×C4 | — | 20 | 1 | no | — |
| 871 | Dic3 | — | 4 | 1 | no | — |
| 872 | Dic3 | — | 20 | 1 | no | — |
| 873 | C2×C5 | — | 2 | 2 | no | — |
| 874 | C2×C5 | — | 6 | 1 | no | — |
| 875 | C2×C5 | — | 12 | 1 | no | — |
| 876 | C2×C5 | — | 12 | 2 | no | — |
| 877 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 878 | D5 | — | 2 | 2 | no | — |
| 879 | D5 | — | 6 | 1 | no | — |
| 880 | D5 | — | 12 | 1 | no | — |
| 881 | D5 | — | 12 | 2 | no | — |
| 882 | D5 | #5926 | 1 | 2 | yes | direct product factor |
| 883 | C23 | — | 5 | 2 | no | — |
| 884 | C23 | — | 6 | 1 | no | — |
| 885 | C23 | — | 6 | 2 | no | — |
| 886 | C23 | — | 15 | 1 | no | — |
| 887 | C23 | — | 30 | 1 | no | — |
| 888 | C23 | — | 30 | 1 | no | — |
| 889 | C23 | — | 30 | 2 | no | — |
| 890 | C23 | — | 30 | 2 | no | — |
| 891 | C23 | — | 30 | 2 | no | — |
| 892 | C23 | — | 30 | 2 | no | — |
| 893 | C23 | — | 30 | 2 | no | — |
| 894 | C23 | — | 120 | 4 | no | — |
| 895 | C23 | — | 120 | 2 | no | — |
| 896 | Q8 | — | 3 | 2 | no | — |
| 897 | Q8 | — | 3 | 1 | no | — |
| 898 | Q8 | — | 3 | 1 | no | — |
| 899 | Q8 | — | 15 | 2 | no | — |
| 900 | Q8 | — | 15 | 1 | no | — |
| 901 | Q8 | — | 15 | 2 | no | — |
| 902 | Q8 | — | 15 | 1 | no | — |
| 903 | Q8 | — | 15 | 1 | no | — |
| 904 | Q8 | — | 30 | 2 | no | — |
| 905 | Q8 | — | 30 | 1 | no | — |
| 906 | Q8 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 907 | D4 | — | 3 | 1 | no | — |
| 908 | D4 | — | 3 | 2 | no | — |
| 909 | D4 | — | 3 | 2 | no | — |
| 910 | D4 | — | 3 | 1 | no | — |
| 911 | D4 | — | 5 | 2 | no | — |
| 912 | D4 | — | 5 | 1 | no | — |
| 913 | D4 | — | 6 | 2 | no | — |
| 914 | D4 | — | 6 | 1 | no | — |
| 915 | D4 | — | 6 | 2 | no | — |
| 916 | D4 | — | 6 | 1 | no | — |
| 917 | D4 | — | 15 | 2 | no | — |
| 918 | D4 | — | 15 | 1 | no | — |
| 919 | D4 | — | 15 | 2 | no | — |
| 920 | D4 | — | 15 | 1 | no | — |
| 921 | D4 | — | 15 | 2 | no | — |
| 922 | D4 | — | 15 | 2 | no | — |
| 923 | D4 | — | 30 | 2 | no | — |
| 924 | D4 | — | 30 | 2 | no | — |
| 925 | D4 | — | 30 | 2 | no | — |
| 926 | D4 | — | 30 | 1 | no | — |
| 927 | D4 | — | 30 | 1 | no | — |
| 928 | D4 | — | 30 | 1 | no | — |
| 929 | D4 | — | 30 | 2 | no | — |
| 930 | D4 | — | 30 | 2 | no | — |
| 931 | D4 | — | 30 | 2 | no | — |
| 932 | D4 | — | 30 | 1 | no | — |
| 933 | D4 | — | 30 | 2 | no | — |
| 934 | D4 | — | 30 | 1 | no | — |
| 935 | D4 | — | 30 | 2 | no | — |
| 936 | D4 | — | 30 | 1 | no | — |
| 937 | D4 | D5×S4 | 1 | 1 | yes | characteristic |
| 938 | C2×C4 | — | 3 | 2 | no | — |
| 939 | C2×C4 | — | 3 | 1 | no | — |
| 940 | C2×C4 | — | 5 | 1 | no | — |
| 941 | C2×C4 | — | 6 | 1 | no | — |
| 942 | C2×C4 | — | 6 | 2 | no | — |
| 943 | C2×C4 | — | 6 | 1 | no | — |
| 944 | C2×C4 | — | 15 | 1 | no | — |
| 945 | C2×C4 | — | 15 | 1 | no | — |
| 946 | C2×C4 | — | 15 | 2 | no | — |
| 947 | C2×C4 | — | 15 | 2 | no | — |
| 948 | C2×C4 | — | 15 | 2 | no | — |
| 949 | C2×C4 | — | 15 | 1 | no | — |
| 950 | C2×C4 | — | 15 | 2 | no | — |
| 951 | C2×C4 | — | 15 | 1 | no | — |
| 952 | C2×C4 | — | 30 | 2 | no | — |
| 953 | C2×C4 | — | 30 | 2 | no | — |
| 954 | C2×C4 | — | 30 | 1 | no | — |
| 955 | C2×C4 | — | 30 | 1 | no | — |
| 956 | C2×C4 | — | 30 | 2 | no | — |
| 957 | C2×C4 | — | 30 | 1 | no | — |
| 958 | C2×C4 | — | 30 | 1 | no | — |
| 959 | C2×C4 | — | 30 | 2 | no | — |
| 960 | C2×C4 | — | 30 | 1 | no | — |
| 961 | C8 | — | 3 | 1 | no | — |
| 962 | C8 | — | 3 | 1 | no | — |
| 963 | C8 | — | 3 | 2 | no | — |
| 964 | C8 | — | 15 | 1 | no | — |
| 965 | C8 | — | 15 | 1 | no | — |
| 966 | C8 | — | 15 | 2 | no | — |
| 967 | C2×C3 | — | 4 | 1 | no | — |
| 968 | C2×C3 | — | 8 | 2 | no | — |
| 969 | C2×C3 | — | 20 | 2 | no | — |
| 970 | C2×C3 | — | 40 | 2 | no | — |
| 971 | D3 | — | 4 | 2 | no | — |
| 972 | D3 | — | 8 | 2 | no | — |
| 973 | D3 | — | 20 | 2 | no | — |
| 974 | D3 | — | 40 | 2 | no | — |
| 975 | C5 | C2×#5926 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 976 | C22 | — | 3 | 1 | no | — |
| 977 | C22 | — | 5 | 1 | no | — |
| 978 | C22 | — | 5 | 2 | no | — |
| 979 | C22 | — | 6 | 1 | no | — |
| 980 | C22 | — | 6 | 2 | no | — |
| 981 | C22 | — | 10 | 4 | no | — |
| 982 | C22 | — | 15 | 1 | no | — |
| 983 | C22 | — | 24 | 2 | no | — |
| 984 | C22 | — | 24 | 1 | no | — |
| 985 | C22 | — | 30 | 2 | no | — |
| 986 | C22 | — | 30 | 1 | no | — |
| 987 | C22 | — | 30 | 2 | no | — |
| 988 | C22 | — | 60 | 2 | no | — |
| 989 | C22 | — | 60 | 4 | no | — |
| 990 | C22 | — | 120 | 2 | no | — |
| 991 | C22 | — | 120 | 1 | no | — |
| 992 | C22 | — | 120 | 2 | no | — |
| 993 | C22 | — | 120 | 2 | no | — |
| 994 | C22 | — | 120 | 2 | no | — |
| 995 | C22 | C2×D5×S4 | 1 | 2 | yes | — |
| 996 | C4 | — | 3 | 1 | no | — |
| 997 | C4 | — | 3 | 2 | no | — |
| 998 | C4 | — | 5 | 1 | no | — |
| 999 | C4 | — | 6 | 1 | no | — |
| 1000 | C4 | — | 15 | 1 | no | — |
| 1001 | C4 | — | 15 | 2 | no | — |
| 1002 | C4 | — | 30 | 1 | no | — |
| 1003 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 1004 | C3 | — | 4 | 1 | no | Sylow |
| 1005 | C2 | — | 2 | 2 | no | — |
| 1006 | C2 | — | 5 | 2 | no | — |
| 1007 | C2 | — | 6 | 1 | no | — |
| 1008 | C2 | — | 10 | 2 | no | — |
| 1009 | C2 | — | 12 | 1 | no | — |
| 1010 | C2 | — | 12 | 2 | no | — |
| 1011 | C2 | — | 30 | 1 | no | — |
| 1012 | C2 | — | 60 | 1 | no | — |
| 1013 | C2 | — | 60 | 2 | no | — |
| 1014 | 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 | C5×2−1+4 | C2×D3 |
| socle | C2×C5 | C23×S4 |
| hypercenter | D4 | D5×S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D5×2−1+4⋊C3 | C2 | semidirect |
| 2. #11756910 | C2 | semidirect |
| 3. C5×#5926 | C2 | semidirect |
| 4. #11756786 | C2 | semidirect |
| 5. #11756785 | C2 | semidirect |
| 6. D5×#986 | C2 | semidirect |
| 7. D5×#985 | C2 | semidirect |
| 8. #11756772 | C2 | semidirect |
| 9. #11756771 | C2 | semidirect |
| 10. D5×#983 | C2 | semidirect |
| 11. C2×D5×GL(2,𝔽3) | C2 | semidirect |
| 13. C5×2−1+4⋊C3 | C22 | semidirect |
| 15. #4150⋊C3 | C22 | semidirect |
| 16. D5×#41⋊C3 | C22 | semidirect |
| 17. #4147⋊C3 | C22 | semidirect |
| 18. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 19. #91956 | C22 | semidirect |
| 20. #91955 | C22 | semidirect |
| 21. #91953 | C22 | semidirect |
| 22. C2×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 23. C5×#986 | C22 | semidirect |
| 24. C5×#985 | C22 | semidirect |
| 25. C5×#983 | C22 | semidirect |
| 26. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 27. D5×GL(2,𝔽3) | C22 | semidirect |
| 28. D5×GL(2,𝔽3) | C22 | semidirect |
| 29. D5×GL(2,𝔽3) | C22 | semidirect |
| 30. D5×GL(2,𝔽3) | C22 | semidirect |
| 31. #91897 | C22 | semidirect |
| 32. #91896 | C22 | semidirect |
| 33. D5×#226 | C22 | semidirect |
| 34. #91894 | C22 | semidirect |
| 35. #91893 | C22 | semidirect |
| 36. #91892 | C22 | semidirect |
| 38. D5×2−1+4 | D3 | semidirect |
| 65. C5×#41⋊C3 | C23 | semidirect |
| 66. C2×C5×SL(2,𝔽3) | C23 | semidirect |
| 75. D5×SL(2,𝔽3) | C23 | semidirect |
| 76. C5⋊(#41⋊C3) | C23 | semidirect |
| 77. C5⋊GL(2,𝔽3) | C23 | semidirect |
| 78. C5⋊GL(2,𝔽3) | C23 | semidirect |
| 79. C5⋊#226 | C23 | semidirect |
| 80. C5×GL(2,𝔽3) | C23 | semidirect |
| 81. C5×GL(2,𝔽3) | C23 | semidirect |
| 82. C5×#226 | C23 | semidirect |
| 89. #5926 | D5 | direct (N × H) |
| 94. C5×2−1+4 | C2×D3 | semidirect |
| 98. #4150 | C2×D3 | semidirect |
| 108. D5×#41 | C2×D3 | semidirect |
| 110. #4147 | C2×D3 | semidirect |
| 112. C2×Q8×D5 | C2×D3 | semidirect |
| 228. 2−1+4⋊C3 | C2×D5 | semidirect |
| 233. #986 | C2×D5 | semidirect |
| 237. #985 | C2×D5 | semidirect |
| 241. #983 | C2×D5 | semidirect |
| 247. C2×GL(2,𝔽3) | C2×D5 | semidirect |
| 256. C5×#41 | C22×D3 | semidirect |
| 258. C2×C5×Q8 | C22×D3 | semidirect |
| 273. #713 | C22×D3 | semidirect |
| 281. Q8×D5 | C22×D3 | semidirect |
| 448. #41⋊C3 | C22×D5 | semidirect |
| 451. C2×SL(2,𝔽3) | C22×D5 | semidirect |
| 454. GL(2,𝔽3) | C22×D5 | semidirect |
| 455. GL(2,𝔽3) | C22×D5 | semidirect |
| 457. #226 | C22×D5 | semidirect |
| 547. 2−1+4 | D3×D5 | semidirect |
| 743. #41 | C2×D3×D5 | semidirect |
| 756. C2×Q8 | C2×D3×D5 | semidirect |
| 882. D5 | #5926 | direct (N × H) |
| 975. C5 | C2×#5926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×2−1+4⋊C3 | 2 |
| #11756910 | 2 |
| C5×#5926 | 2 |
| #11756786 | 2 |
| #11756785 | 2 |
| D5×#986 | 2 |
| D5×#985 | 2 |
| #11756772 | 2 |
| #11756771 | 2 |
| D5×#983 | 2 |
| C2×D5×GL(2,𝔽3) | 2 |
| D5×#577 | 3 |
| D3×D4×D5 | 4 |
| C2×#5926 | 5 |