Finite Group DatabasebetaFinite Group DatabasebetaOrder 6720.
852 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 66 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 | #72218791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D7×C5⋊GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | GL(2,𝔽3)×D35 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×D7×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D5×C7⋊GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D5×D7×SD16 | — | 3 | 1 | no | maximal, Hall |
| 7 | C7×D5×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D5×D7×SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×D3×D5×D7 | — | 4 | 1 | no | maximal |
| 10 | SL(2,𝔽3)×D35 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C7×D5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C5×D7×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C5⋊(C7⋊GL(2,𝔽3)) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C7×C5⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×C7⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C5×C7×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×D7×GL(2,𝔽3) | — | 5 | 1 | no | maximal, Hall |
| 18 | Q8×D5×D7 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | D4×D5×D7 | — | 3 | 1 | no | — |
| 20 | SD16×D35 | — | 3 | 1 | no | — |
| 21 | C7×D5×SD16 | — | 3 | 1 | no | — |
| 22 | C5×D7×SD16 | — | 3 | 1 | no | — |
| 23 | #11764953 | — | 3 | 1 | no | — |
| 24 | D5×#1143 | — | 3 | 1 | no | — |
| 25 | D7×#688 | — | 3 | 1 | no | — |
| 26 | #11764935 | — | 3 | 1 | no | — |
| 27 | D5×#1142 | — | 3 | 1 | no | — |
| 28 | D7×#687 | — | 3 | 1 | no | — |
| 29 | #11764703 | — | 3 | 1 | no | — |
| 30 | D5×#1132 | — | 3 | 1 | no | — |
| 31 | D7×#677 | — | 3 | 1 | no | — |
| 32 | C8×D5×D7 | — | 3 | 1 | no | — |
| 33 | C2×D5×GL(2,𝔽3) | — | 7 | 1 | no | maximal, Hall |
| 34 | C2×D15⋊D7 | — | 4 | 1 | no | — |
| 35 | C2×D3×D35 | — | 4 | 1 | no | — |
| 36 | C2×D5×D21 | — | 4 | 1 | no | — |
| 37 | C2×D3×C7×D5 | — | 4 | 1 | no | — |
| 38 | C2×D7×D15 | — | 4 | 1 | no | — |
| 39 | C2×C5×D3×D7 | — | 4 | 1 | no | — |
| 40 | C2×C3×D5×D7 | — | 4 | 1 | no | — |
| 41 | D3×D5×D7 | — | 4 | 8 | no | — |
| 42 | C5×C7×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×D7×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 44 | C2×C7⋊GL(2,𝔽3) | — | 5 | 1 | no | — |
| 45 | C2×C7×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 46 | D7×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 47 | D7×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 48 | D7×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 49 | D7×GL(2,𝔽3) | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 50 | C22×D5×D7 | — | 6 | 1 | no | — |
| 51 | Q8×D35 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | D4×D35 | — | 3 | 1 | no | — |
| 53 | C7×Q8×D5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C7×D4×D5 | — | 3 | 1 | no | — |
| 55 | C5×Q8×D7 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | C5×D4×D7 | — | 3 | 1 | no | — |
| 57 | #10587963 | — | 6 | 1 | no | — |
| 58 | D5×C22⋊D7 | — | 6 | 1 | no | — |
| 59 | D7×C22⋊D5 | — | 6 | 1 | no | — |
| 60 | #10587950 | — | 3 | 1 | no | — |
| 61 | D5×D28 | — | 3 | 1 | no | — |
| 62 | D7×D20 | — | 3 | 1 | no | — |
| 63 | C4×D5×D7 | — | 3 | 1 | no | — |
| 64 | D35⋊Q8 | — | 3 | 1 | no | — |
| 65 | D5×Dic14 | — | 3 | 1 | no | — |
| 66 | D7×Dic10 | — | 3 | 1 | no | — |
| 67 | C5×C7×SD16 | — | 3 | 1 | no | — |
| 68 | #10587905 | — | 3 | 1 | no | — |
| 69 | #10587904 | — | 3 | 1 | no | — |
| 70 | #10587894 | — | 3 | 1 | no | — |
| 71 | C8×D35 | — | 3 | 1 | no | — |
| 72 | C7×#688 | — | 3 | 1 | no | — |
| 73 | C7×#687 | — | 3 | 1 | no | — |
| 74 | C7×#677 | — | 3 | 1 | no | — |
| 75 | C7×C8×D5 | — | 3 | 1 | no | — |
| 76 | C5×#1143 | — | 3 | 1 | no | — |
| 77 | C5×#1142 | — | 3 | 1 | no | — |
| 78 | C5×#1132 | — | 3 | 1 | no | — |
| 79 | C5×C8×D7 | — | 3 | 1 | no | — |
| 80 | #10587849 | — | 3 | 1 | no | — |
| 81 | #10587848 | — | 3 | 1 | no | — |
| 82 | #10587847 | — | 3 | 1 | no | — |
| 83 | #10587846 | — | 3 | 1 | no | — |
| 84 | #10587845 | — | 3 | 1 | no | — |
| 85 | #10587844 | — | 3 | 1 | no | — |
| 86 | #10587837 | — | 3 | 1 | no | — |
| 87 | D5×C7⋊C8 | — | 3 | 1 | no | — |
| 88 | D7×#168 | — | 3 | 1 | no | — |
| 89 | C2×D5×SL(2,𝔽3) | — | 7 | 1 | no | — |
| 90 | C2×C5⋊GL(2,𝔽3) | — | 7 | 1 | no | — |
| 91 | C2×C5×GL(2,𝔽3) | — | 7 | 1 | no | — |
| 92 | D5×GL(2,𝔽3) | — | 7 | 1 | no | — |
| 93 | D5×GL(2,𝔽3) | — | 7 | 1 | no | — |
| 94 | D5×GL(2,𝔽3) | — | 7 | 1 | no | — |
| 95 | D5×GL(2,𝔽3) | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 96 | C2×D7×SD16 | — | 15 | 1 | no | Hall |
| 97 | C2×D105 | — | 4 | 1 | no | — |
| 98 | C2×C7×D15 | — | 4 | 1 | no | — |
| 99 | C2×C5×D21 | — | 4 | 1 | no | — |
| 100 | C2×C5×D3×C7 | — | 4 | 1 | no | — |
| 101 | C2×C3×D35 | — | 4 | 1 | no | — |
| 102 | C2×C3×C7×D5 | — | 4 | 1 | no | — |
| 103 | C2×C3×C5×D7 | — | 4 | 1 | no | — |
| 104 | D15⋊D7 | — | 4 | 4 | no | — |
| 105 | D3×D35 | — | 4 | 4 | no | — |
| 106 | D5×D21 | — | 4 | 4 | no | — |
| 107 | D3×C7×D5 | — | 4 | 4 | no | — |
| 108 | D7×D15 | — | 4 | 4 | no | — |
| 109 | C5×D3×D7 | — | 4 | 4 | no | — |
| 110 | C3×D5×D7 | — | 4 | 4 | no | — |
| 111 | C22×D3×D7 | — | 20 | 1 | no | — |
| 112 | C2×C7×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 113 | D7×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 114 | D7×SL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 115 | C7⋊GL(2,𝔽3) | — | 5 | 1 | no | — |
| 116 | C7⋊GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 117 | C7×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 118 | C7×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 119 | C2×D5×SD16 | — | 21 | 1 | no | Hall |
| 120 | C22×D35 | — | 6 | 1 | no | — |
| 121 | C22×C7×D5 | — | 6 | 1 | no | — |
| 122 | C22×C5×D7 | — | 6 | 1 | no | — |
| 123 | C2×D5×D7 | — | 6 | 1 | no | — |
| 124 | C2×D5×D7 | — | 6 | 1 | no | — |
| 125 | C2×D5×D7 | — | 6 | 1 | no | — |
| 126 | C2×D5×D7 | — | 12 | 4 | no | — |
| 127 | C2×D5×D7 | S4 | 1 | 1 | yes | characteristic |
| 128 | C5×C7×Q8 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 129 | C5×C7×D4 | — | 3 | 1 | no | — |
| 130 | C22⋊D35 | — | 6 | 1 | no | — |
| 131 | D140 | — | 3 | 1 | no | — |
| 132 | C4×D35 | — | 3 | 1 | no | — |
| 133 | Dic70 | — | 3 | 1 | no | — |
| 134 | C7×C22⋊D5 | — | 6 | 1 | no | — |
| 135 | C7×D20 | — | 3 | 1 | no | — |
| 136 | C4×C7×D5 | — | 3 | 1 | no | — |
| 137 | C7×Dic10 | — | 3 | 1 | no | — |
| 138 | C5×C22⋊D7 | — | 6 | 1 | no | — |
| 139 | C5×D28 | — | 3 | 1 | no | — |
| 140 | C4×C5×D7 | — | 3 | 1 | no | — |
| 141 | C5×Dic14 | — | 3 | 1 | no | — |
| 142 | #63308 | — | 6 | 1 | no | — |
| 143 | #63307 | — | 6 | 1 | no | — |
| 144 | #63306 | — | 6 | 1 | no | — |
| 145 | #63305 | — | 6 | 1 | no | — |
| 146 | #63304 | — | 3 | 1 | no | — |
| 147 | D5×Dic7 | — | 3 | 1 | no | — |
| 148 | D7×Dic5 | — | 3 | 1 | no | — |
| 149 | C5×C7×C8 | — | 3 | 1 | no | — |
| 150 | C7⋊#168 | — | 3 | 1 | no | — |
| 151 | C5×C7⋊C8 | — | 3 | 1 | no | — |
| 152 | C7×#168 | — | 3 | 1 | no | — |
| 153 | C22×D3×D5 | — | 28 | 1 | no | — |
| 154 | C2×C5×SL(2,𝔽3) | — | 7 | 1 | no | — |
| 155 | D5×SL(2,𝔽3) | — | 7 | 1 | no | — |
| 156 | D5×SL(2,𝔽3) | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 157 | C5⋊GL(2,𝔽3) | — | 7 | 1 | no | — |
| 158 | C5⋊GL(2,𝔽3) | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 159 | C5×GL(2,𝔽3) | — | 7 | 1 | no | — |
| 160 | C5×GL(2,𝔽3) | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 161 | C2×Q8×D7 | — | 5 | 1 | no | — |
| 162 | C2×D4×D7 | — | 15 | 1 | no | — |
| 163 | C2×C7×SD16 | — | 15 | 1 | no | — |
| 164 | C2×#1143 | — | 15 | 1 | no | — |
| 165 | C2×#1142 | — | 15 | 1 | no | — |
| 166 | D7×SD16 | — | 3 | 1 | no | — |
| 167 | D7×SD16 | — | 15 | 1 | no | — |
| 168 | D7×SD16 | — | 15 | 1 | no | — |
| 169 | D7×SD16 | — | 15 | 1 | no | — |
| 170 | D7×SD16 | — | 15 | 1 | no | — |
| 171 | D7×SD16 | — | 15 | 1 | no | — |
| 172 | D7×SD16 | — | 15 | 1 | no | — |
| 173 | D7×SD16 | — | 15 | 1 | no | — |
| 174 | C2×#1132 | — | 15 | 1 | no | — |
| 175 | C2×C8×D7 | — | 15 | 1 | no | — |
| 176 | C2×C3×C5×C7 | — | 4 | 1 | no | — |
| 177 | D105 | — | 4 | 2 | no | — |
| 178 | C7×D15 | — | 4 | 2 | no | — |
| 179 | C5×D21 | — | 4 | 2 | no | — |
| 180 | C5×D3×C7 | — | 4 | 2 | no | — |
| 181 | C3×D35 | — | 4 | 2 | no | — |
| 182 | C3×C7×D5 | — | 4 | 2 | no | — |
| 183 | C3×C5×D7 | — | 4 | 2 | no | — |
| 184 | C22×GL(2,𝔽3) | — | 35 | 1 | no | Hall |
| 185 | C22×D21 | — | 20 | 1 | no | — |
| 186 | C22×D3×C7 | — | 20 | 1 | no | — |
| 187 | C22×C3×D7 | — | 20 | 1 | no | — |
| 188 | C2×D3×D7 | — | 4 | 1 | no | — |
| 189 | C2×D3×D7 | — | 20 | 1 | no | — |
| 190 | C2×D3×D7 | — | 20 | 1 | no | — |
| 191 | C2×D3×D7 | — | 20 | 1 | no | — |
| 192 | C2×D3×D7 | — | 20 | 8 | no | — |
| 193 | C7×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 194 | C2×Q8×D5 | — | 7 | 1 | no | — |
| 195 | C2×D4×D5 | — | 21 | 1 | no | — |
| 196 | C2×C5×SD16 | — | 21 | 1 | no | — |
| 197 | C2×#688 | — | 21 | 1 | no | — |
| 198 | C2×#687 | — | 21 | 1 | no | — |
| 199 | D5×SD16 | — | 3 | 1 | no | — |
| 200 | D5×SD16 | — | 21 | 1 | no | — |
| 201 | D5×SD16 | — | 21 | 1 | no | — |
| 202 | D5×SD16 | — | 21 | 1 | no | — |
| 203 | D5×SD16 | — | 21 | 1 | no | — |
| 204 | D5×SD16 | — | 21 | 1 | no | — |
| 205 | D5×SD16 | — | 21 | 1 | no | — |
| 206 | D5×SD16 | — | 21 | 1 | no | — |
| 207 | C2×#677 | — | 21 | 1 | no | — |
| 208 | C2×C8×D5 | — | 21 | 1 | no | — |
| 209 | C22×C5×C7 | — | 6 | 1 | no | — |
| 210 | C2×D35 | — | 6 | 1 | no | — |
| 211 | C2×D35 | — | 12 | 2 | no | — |
| 212 | C2×D35 | C2×S4 | 1 | 1 | yes | characteristic |
| 213 | C2×C7×D5 | — | 6 | 1 | no | — |
| 214 | C2×C7×D5 | — | 12 | 2 | no | — |
| 215 | C2×C7×D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 216 | C2×C5×D7 | — | 6 | 1 | no | — |
| 217 | C2×C5×D7 | — | 12 | 2 | no | — |
| 218 | C2×C5×D7 | C2×S4 | 1 | 1 | yes | characteristic |
| 219 | D5×D7 | — | 12 | 2 | no | — |
| 220 | D5×D7 | — | 12 | 2 | no | — |
| 221 | D5×D7 | — | 12 | 2 | no | — |
| 222 | D5×D7 | GL(2,𝔽3) | 1 | 4 | yes | direct product factor |
| 223 | C4×C5×C7 | — | 3 | 1 | no | — |
| 224 | Dic35 | — | 3 | 1 | no | — |
| 225 | C5×Dic7 | — | 3 | 1 | no | — |
| 226 | C7×Dic5 | — | 3 | 1 | no | — |
| 227 | C22×D15 | — | 28 | 1 | no | — |
| 228 | C22×C5×D3 | — | 28 | 1 | no | — |
| 229 | C22×C3×D5 | — | 28 | 1 | no | — |
| 230 | C2×D3×D5 | — | 4 | 1 | no | — |
| 231 | C2×D3×D5 | — | 28 | 8 | no | — |
| 232 | C2×D3×D5 | — | 28 | 1 | no | — |
| 233 | C2×D3×D5 | — | 28 | 1 | no | — |
| 234 | C2×D3×D5 | — | 28 | 1 | no | — |
| 235 | C5×SL(2,𝔽3) | C22×D7 | 1 | 1 | yes | characteristic, complemented |
| 236 | C23×D7 | — | 30 | 1 | no | — |
| 237 | C2×C7×Q8 | — | 5 | 1 | no | — |
| 238 | C2×C7×D4 | — | 15 | 1 | no | — |
| 239 | C2×C22⋊D7 | — | 30 | 1 | no | — |
| 240 | Q8×D7 | — | 5 | 1 | no | — |
| 241 | Q8×D7 | — | 15 | 1 | no | — |
| 242 | Q8×D7 | — | 15 | 1 | no | — |
| 243 | Q8×D7 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 244 | D4×D7 | — | 3 | 1 | no | — |
| 245 | D4×D7 | — | 15 | 1 | no | — |
| 246 | D4×D7 | — | 15 | 1 | no | — |
| 247 | D4×D7 | — | 15 | 1 | no | — |
| 248 | D4×D7 | — | 30 | 1 | no | — |
| 249 | D4×D7 | — | 30 | 1 | no | — |
| 250 | C2×D28 | — | 15 | 1 | no | — |
| 251 | C2×C4×D7 | — | 15 | 1 | no | — |
| 252 | C2×Dic14 | — | 15 | 1 | no | — |
| 253 | C7×SD16 | — | 3 | 1 | no | — |
| 254 | C7×SD16 | — | 15 | 1 | no | — |
| 255 | C7×SD16 | — | 15 | 1 | no | — |
| 256 | C7×SD16 | — | 15 | 1 | no | — |
| 257 | C2×C7×C8 | — | 15 | 1 | no | — |
| 258 | #1143 | — | 3 | 1 | no | — |
| 259 | #1143 | — | 15 | 1 | no | — |
| 260 | #1143 | — | 15 | 1 | no | — |
| 261 | #1143 | — | 15 | 1 | no | — |
| 262 | #1142 | — | 3 | 1 | no | — |
| 263 | #1142 | — | 15 | 1 | no | — |
| 264 | #1142 | — | 15 | 1 | no | — |
| 265 | #1142 | — | 15 | 1 | no | — |
| 266 | C2×C7⋊C8 | — | 15 | 1 | no | — |
| 267 | #1132 | — | 3 | 1 | no | — |
| 268 | #1132 | — | 15 | 1 | no | — |
| 269 | #1132 | — | 15 | 1 | no | — |
| 270 | #1132 | — | 15 | 1 | no | — |
| 271 | C8×D7 | — | 3 | 1 | no | — |
| 272 | C8×D7 | — | 15 | 1 | no | — |
| 273 | C8×D7 | — | 15 | 1 | no | — |
| 274 | C8×D7 | — | 15 | 1 | no | — |
| 275 | C3×C5×C7 | — | 4 | 1 | no | Hall |
| 276 | C22×SL(2,𝔽3) | — | 35 | 1 | no | — |
| 277 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 278 | C2×GL(2,𝔽3) | — | 7 | 1 | no | — |
| 279 | C2×GL(2,𝔽3) | — | 35 | 1 | no | — |
| 280 | C2×GL(2,𝔽3) | — | 35 | 1 | no | — |
| 281 | C2×GL(2,𝔽3) | — | 35 | 1 | no | — |
| 282 | C2×GL(2,𝔽3) | — | 35 | 1 | no | — |
| 283 | C22×C3×C7 | — | 20 | 1 | no | — |
| 284 | C2×D21 | — | 4 | 1 | no | — |
| 285 | C2×D21 | — | 20 | 1 | no | — |
| 286 | C2×D21 | — | 20 | 4 | no | — |
| 287 | C2×D3×C7 | — | 4 | 1 | no | — |
| 288 | C2×D3×C7 | — | 20 | 1 | no | — |
| 289 | C2×D3×C7 | — | 20 | 4 | no | — |
| 290 | C2×C3×D7 | — | 4 | 1 | no | — |
| 291 | C2×C3×D7 | — | 20 | 4 | no | — |
| 292 | C2×C3×D7 | — | 20 | 1 | no | — |
| 293 | D3×D7 | — | 4 | 4 | no | — |
| 294 | D3×D7 | — | 20 | 4 | no | — |
| 295 | D3×D7 | — | 20 | 4 | no | — |
| 296 | D3×D7 | — | 20 | 4 | no | — |
| 297 | C23×D5 | — | 42 | 1 | no | — |
| 298 | C2×C5×Q8 | — | 7 | 1 | no | — |
| 299 | C2×C5×D4 | — | 21 | 1 | no | — |
| 300 | C2×C22⋊D5 | — | 42 | 1 | no | — |
| 301 | Q8×D5 | — | 7 | 1 | no | — |
| 302 | Q8×D5 | — | 21 | 1 | no | — |
| 303 | Q8×D5 | — | 21 | 1 | no | — |
| 304 | Q8×D5 | D3×D7 | 1 | 1 | yes | characteristic, complemented |
| 305 | D4×D5 | — | 3 | 1 | no | — |
| 306 | D4×D5 | — | 21 | 1 | no | — |
| 307 | D4×D5 | — | 21 | 1 | no | — |
| 308 | D4×D5 | — | 21 | 1 | no | — |
| 309 | D4×D5 | — | 42 | 1 | no | — |
| 310 | D4×D5 | — | 42 | 1 | no | — |
| 311 | C2×D20 | — | 21 | 1 | no | — |
| 312 | C2×C4×D5 | — | 21 | 1 | no | — |
| 313 | C2×Dic10 | — | 21 | 1 | no | — |
| 314 | C5×SD16 | — | 3 | 1 | no | — |
| 315 | C5×SD16 | — | 21 | 1 | no | — |
| 316 | C5×SD16 | — | 21 | 1 | no | — |
| 317 | C5×SD16 | — | 21 | 1 | no | — |
| 318 | C2×C5×C8 | — | 21 | 1 | no | — |
| 319 | #688 | — | 3 | 1 | no | — |
| 320 | #688 | — | 21 | 1 | no | — |
| 321 | #688 | — | 21 | 1 | no | — |
| 322 | #688 | — | 21 | 1 | no | — |
| 323 | #687 | — | 3 | 1 | no | — |
| 324 | #687 | — | 21 | 1 | no | — |
| 325 | #687 | — | 21 | 1 | no | — |
| 326 | #687 | — | 21 | 1 | no | — |
| 327 | C2×#168 | — | 21 | 1 | no | — |
| 328 | #677 | — | 3 | 1 | no | — |
| 329 | #677 | — | 21 | 1 | no | — |
| 330 | #677 | — | 21 | 1 | no | — |
| 331 | #677 | — | 21 | 1 | no | — |
| 332 | C8×D5 | — | 3 | 1 | no | — |
| 333 | C8×D5 | — | 21 | 1 | no | — |
| 334 | C8×D5 | — | 21 | 1 | no | — |
| 335 | C8×D5 | — | 21 | 1 | no | — |
| 336 | C2×C5×C7 | — | 12 | 1 | no | — |
| 337 | C2×C5×C7 | C22×S4 | 1 | 1 | yes | characteristic |
| 338 | D35 | — | 12 | 1 | no | — |
| 339 | D35 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 340 | C5×D7 | — | 12 | 1 | no | — |
| 341 | C5×D7 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 342 | C7×D5 | — | 12 | 1 | no | — |
| 343 | C7×D5 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 344 | C22×SD16 | — | 105 | 1 | no | Sylow |
| 345 | C22×C3×C5 | — | 28 | 1 | no | — |
| 346 | C2×D15 | — | 4 | 1 | no | — |
| 347 | C2×D15 | — | 28 | 1 | no | — |
| 348 | C2×D15 | — | 28 | 4 | no | — |
| 349 | C2×C5×D3 | — | 4 | 1 | no | — |
| 350 | C2×C5×D3 | — | 28 | 1 | no | — |
| 351 | C2×C5×D3 | — | 28 | 4 | no | — |
| 352 | C2×C3×D5 | — | 4 | 1 | no | — |
| 353 | C2×C3×D5 | — | 28 | 4 | no | — |
| 354 | C2×C3×D5 | — | 28 | 1 | no | — |
| 355 | D3×D5 | — | 4 | 4 | no | — |
| 356 | D3×D5 | — | 28 | 4 | no | — |
| 357 | D3×D5 | — | 28 | 4 | no | — |
| 358 | D3×D5 | — | 28 | 4 | no | — |
| 359 | C23×C7 | — | 30 | 1 | no | — |
| 360 | C22×D7 | — | 5 | 1 | no | — |
| 361 | C22×D7 | — | 6 | 1 | no | — |
| 362 | C22×D7 | — | 30 | 1 | no | — |
| 363 | C22×D7 | — | 30 | 1 | no | — |
| 364 | C22×D7 | — | 30 | 1 | no | — |
| 365 | C22×D7 | — | 30 | 1 | no | — |
| 366 | C22×D7 | — | 60 | 4 | no | — |
| 367 | C7×Q8 | — | 15 | 1 | no | — |
| 368 | C7×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 369 | C7×D4 | — | 3 | 1 | no | — |
| 370 | C7×D4 | — | 15 | 1 | no | — |
| 371 | C7×D4 | — | 30 | 1 | no | — |
| 372 | C2×C4×C7 | — | 15 | 1 | no | — |
| 373 | C22⋊D7 | — | 6 | 1 | no | — |
| 374 | C22⋊D7 | — | 30 | 1 | no | — |
| 375 | C22⋊D7 | — | 30 | 1 | no | — |
| 376 | C22⋊D7 | — | 30 | 1 | no | — |
| 377 | C2×Dic7 | — | 15 | 1 | no | — |
| 378 | D28 | — | 3 | 1 | no | — |
| 379 | D28 | — | 15 | 1 | no | — |
| 380 | D28 | — | 30 | 1 | no | — |
| 381 | C4×D7 | — | 3 | 1 | no | — |
| 382 | C4×D7 | — | 15 | 1 | no | — |
| 383 | C4×D7 | — | 15 | 1 | no | — |
| 384 | C4×D7 | — | 15 | 1 | no | — |
| 385 | Dic14 | — | 3 | 1 | no | — |
| 386 | Dic14 | — | 15 | 1 | no | — |
| 387 | Dic14 | — | 30 | 1 | no | — |
| 388 | C7×C8 | — | 3 | 1 | no | — |
| 389 | C7×C8 | — | 15 | 1 | no | — |
| 390 | C7⋊C8 | — | 3 | 1 | no | — |
| 391 | C7⋊C8 | — | 15 | 1 | no | — |
| 392 | C23×D3 | — | 140 | 1 | no | — |
| 393 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 394 | C2×SL(2,𝔽3) | — | 7 | 1 | no | — |
| 395 | C2×SL(2,𝔽3) | — | 35 | 1 | no | — |
| 396 | GL(2,𝔽3) | — | 5 | 1 | no | — |
| 397 | GL(2,𝔽3) | — | 7 | 1 | no | — |
| 398 | GL(2,𝔽3) | — | 35 | 1 | no | — |
| 399 | GL(2,𝔽3) | D5×D7 | 1 | 1 | yes | characteristic, direct product factor |
| 400 | C2×C3×C7 | — | 4 | 1 | no | — |
| 401 | C2×C3×C7 | — | 20 | 2 | no | — |
| 402 | D21 | — | 4 | 2 | no | — |
| 403 | D21 | — | 20 | 2 | no | — |
| 404 | C3×D7 | — | 4 | 2 | no | — |
| 405 | C3×D7 | — | 20 | 2 | no | — |
| 406 | D3×C7 | — | 4 | 2 | no | — |
| 407 | D3×C7 | — | 20 | 2 | no | — |
| 408 | C23×C5 | — | 42 | 1 | no | — |
| 409 | C22×D5 | — | 6 | 1 | no | — |
| 410 | C22×D5 | — | 7 | 1 | no | — |
| 411 | C22×D5 | — | 42 | 1 | no | — |
| 412 | C22×D5 | — | 42 | 1 | no | — |
| 413 | C22×D5 | — | 42 | 1 | no | — |
| 414 | C22×D5 | — | 42 | 1 | no | — |
| 415 | C22×D5 | — | 84 | 4 | no | — |
| 416 | C5×Q8 | — | 21 | 1 | no | — |
| 417 | C5×Q8 | C2×D3×D7 | 1 | 1 | yes | characteristic, complemented |
| 418 | C5×D4 | — | 3 | 1 | no | — |
| 419 | C5×D4 | — | 21 | 1 | no | — |
| 420 | C5×D4 | — | 42 | 1 | no | — |
| 421 | C2×C4×C5 | — | 21 | 1 | no | — |
| 422 | C22⋊D5 | — | 6 | 1 | no | — |
| 423 | C22⋊D5 | — | 42 | 1 | no | — |
| 424 | C22⋊D5 | — | 42 | 1 | no | — |
| 425 | C22⋊D5 | — | 42 | 1 | no | — |
| 426 | C2×Dic5 | — | 21 | 1 | no | — |
| 427 | D20 | — | 3 | 1 | no | — |
| 428 | D20 | — | 21 | 1 | no | — |
| 429 | D20 | — | 42 | 1 | no | — |
| 430 | C4×D5 | — | 3 | 1 | no | — |
| 431 | C4×D5 | — | 21 | 1 | no | — |
| 432 | C4×D5 | — | 21 | 1 | no | — |
| 433 | C4×D5 | — | 21 | 1 | no | — |
| 434 | Dic10 | — | 3 | 1 | no | — |
| 435 | Dic10 | — | 21 | 1 | no | — |
| 436 | Dic10 | — | 42 | 1 | no | — |
| 437 | C5×C8 | — | 3 | 1 | no | — |
| 438 | C5×C8 | — | 21 | 1 | no | — |
| 439 | #168 | — | 3 | 1 | no | — |
| 440 | #168 | — | 21 | 1 | no | — |
| 441 | C5×C7 | C22×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented, Hall |
| 442 | C22×Q8 | — | 35 | 1 | no | — |
| 443 | C22×D4 | — | 105 | 1 | no | — |
| 444 | C2×SD16 | — | 15 | 1 | no | — |
| 445 | C2×SD16 | — | 21 | 1 | no | — |
| 446 | C2×SD16 | — | 105 | 1 | no | — |
| 447 | C2×SD16 | — | 105 | 1 | no | — |
| 448 | C2×SD16 | — | 105 | 1 | no | — |
| 449 | C2×SD16 | — | 105 | 1 | no | — |
| 450 | C2×SD16 | — | 105 | 1 | no | — |
| 451 | C2×SD16 | — | 105 | 1 | no | — |
| 452 | C2×SD16 | — | 105 | 1 | no | — |
| 453 | C2×SD16 | — | 105 | 1 | no | — |
| 454 | C2×SD16 | — | 105 | 1 | no | — |
| 455 | C2×SD16 | — | 105 | 1 | no | — |
| 456 | C22×C8 | — | 105 | 1 | no | — |
| 457 | C2×C3×C5 | — | 4 | 1 | no | — |
| 458 | C2×C3×C5 | — | 28 | 2 | no | — |
| 459 | D15 | — | 4 | 2 | no | — |
| 460 | D15 | — | 28 | 2 | no | — |
| 461 | C3×D5 | — | 4 | 2 | no | — |
| 462 | C3×D5 | — | 28 | 2 | no | — |
| 463 | C5×D3 | — | 4 | 2 | no | — |
| 464 | C5×D3 | — | 28 | 2 | no | — |
| 465 | C22×C7 | — | 5 | 1 | no | — |
| 466 | C22×C7 | — | 6 | 1 | no | — |
| 467 | C22×C7 | — | 30 | 1 | no | — |
| 468 | C22×C7 | — | 60 | 2 | no | — |
| 469 | C2×D7 | — | 5 | 1 | no | — |
| 470 | C2×D7 | — | 5 | 4 | no | — |
| 471 | C2×D7 | — | 6 | 1 | no | — |
| 472 | C2×D7 | — | 12 | 2 | no | — |
| 473 | C2×D7 | — | 30 | 1 | no | — |
| 474 | C2×D7 | — | 60 | 2 | no | — |
| 475 | C2×D7 | — | 60 | 2 | no | — |
| 476 | C2×D7 | — | 60 | 2 | no | — |
| 477 | C2×D7 | — | 60 | 2 | no | — |
| 478 | C2×D7 | D5×S4 | 1 | 1 | yes | characteristic |
| 479 | C4×C7 | — | 3 | 1 | no | — |
| 480 | C4×C7 | — | 15 | 1 | no | — |
| 481 | Dic7 | — | 3 | 1 | no | — |
| 482 | Dic7 | — | 15 | 1 | no | — |
| 483 | C23×C3 | — | 140 | 1 | no | — |
| 484 | C22×D3 | — | 20 | 1 | no | — |
| 485 | C22×D3 | — | 28 | 1 | no | — |
| 486 | C22×D3 | — | 140 | 8 | no | — |
| 487 | C22×D3 | — | 140 | 1 | no | — |
| 488 | C22×D3 | — | 140 | 1 | no | — |
| 489 | C22×D3 | — | 140 | 1 | no | — |
| 490 | C22×D3 | — | 140 | 1 | no | — |
| 491 | SL(2,𝔽3) | C2×D5×D7 | 1 | 1 | yes | characteristic, complemented |
| 492 | C3×C7 | — | 4 | 1 | no | Hall |
| 493 | C22×C5 | — | 6 | 1 | no | — |
| 494 | C22×C5 | — | 7 | 1 | no | — |
| 495 | C22×C5 | — | 42 | 1 | no | — |
| 496 | C22×C5 | — | 84 | 2 | no | — |
| 497 | C2×D5 | — | 6 | 1 | no | — |
| 498 | C2×D5 | — | 7 | 1 | no | — |
| 499 | C2×D5 | — | 7 | 4 | no | — |
| 500 | C2×D5 | — | 12 | 2 | no | — |
| 501 | C2×D5 | — | 42 | 1 | no | — |
| 502 | C2×D5 | — | 84 | 2 | no | — |
| 503 | C2×D5 | — | 84 | 2 | no | — |
| 504 | C2×D5 | — | 84 | 2 | no | — |
| 505 | C2×D5 | — | 84 | 2 | no | — |
| 506 | C2×D5 | D7×S4 | 1 | 1 | yes | characteristic |
| 507 | C4×C5 | — | 3 | 1 | no | — |
| 508 | C4×C5 | — | 21 | 1 | no | — |
| 509 | Dic5 | — | 3 | 1 | no | — |
| 510 | Dic5 | — | 21 | 1 | no | — |
| 511 | C24 | — | 210 | 1 | no | — |
| 512 | C2×Q8 | — | 5 | 1 | no | — |
| 513 | C2×Q8 | — | 7 | 1 | no | — |
| 514 | C2×Q8 | — | 35 | 1 | no | — |
| 515 | C2×Q8 | — | 105 | 1 | no | — |
| 516 | C2×Q8 | — | 105 | 1 | no | — |
| 517 | C2×Q8 | — | 105 | 1 | no | — |
| 518 | C2×D4 | — | 15 | 1 | no | — |
| 519 | C2×D4 | — | 21 | 1 | no | — |
| 520 | C2×D4 | — | 105 | 1 | no | — |
| 521 | C2×D4 | — | 105 | 1 | no | — |
| 522 | C2×D4 | — | 105 | 1 | no | — |
| 523 | C2×D4 | — | 105 | 1 | no | — |
| 524 | C2×D4 | — | 210 | 1 | no | — |
| 525 | C2×D4 | — | 210 | 1 | no | — |
| 526 | C2×D4 | — | 210 | 1 | no | — |
| 527 | C22×C4 | — | 105 | 1 | no | — |
| 528 | SD16 | — | 3 | 1 | no | — |
| 529 | SD16 | — | 15 | 1 | no | — |
| 530 | SD16 | — | 15 | 1 | no | — |
| 531 | SD16 | — | 15 | 1 | no | — |
| 532 | SD16 | — | 21 | 1 | no | — |
| 533 | SD16 | — | 21 | 1 | no | — |
| 534 | SD16 | — | 21 | 1 | no | — |
| 535 | SD16 | — | 105 | 1 | no | — |
| 536 | SD16 | — | 105 | 1 | no | — |
| 537 | SD16 | — | 105 | 1 | no | — |
| 538 | SD16 | — | 105 | 1 | no | — |
| 539 | SD16 | — | 105 | 1 | no | — |
| 540 | SD16 | — | 105 | 1 | no | — |
| 541 | SD16 | — | 105 | 1 | no | — |
| 542 | SD16 | — | 105 | 1 | no | — |
| 543 | SD16 | — | 105 | 1 | no | — |
| 544 | C2×C8 | — | 15 | 1 | no | — |
| 545 | C2×C8 | — | 21 | 1 | no | — |
| 546 | C2×C8 | — | 105 | 1 | no | — |
| 547 | C2×C8 | — | 105 | 1 | no | — |
| 548 | C2×C8 | — | 105 | 1 | no | — |
| 549 | C2×C8 | — | 105 | 1 | no | — |
| 550 | C3×C5 | — | 4 | 1 | no | Hall |
| 551 | C2×C7 | — | 5 | 2 | no | — |
| 552 | C2×C7 | — | 12 | 1 | no | — |
| 553 | C2×C7 | — | 60 | 1 | no | — |
| 554 | C2×C7 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 555 | D7 | — | 5 | 2 | no | — |
| 556 | D7 | — | 12 | 1 | no | — |
| 557 | D7 | — | 60 | 1 | no | — |
| 558 | D7 | D5×GL(2,𝔽3) | 1 | 2 | yes | direct product factor |
| 559 | C22×C3 | — | 20 | 1 | no | — |
| 560 | C22×C3 | — | 28 | 1 | no | — |
| 561 | C22×C3 | — | 140 | 1 | no | — |
| 562 | C22×C3 | — | 140 | 4 | no | — |
| 563 | C2×D3 | — | 4 | 1 | no | — |
| 564 | C2×D3 | — | 20 | 1 | no | — |
| 565 | C2×D3 | — | 20 | 4 | no | — |
| 566 | C2×D3 | — | 28 | 1 | no | — |
| 567 | C2×D3 | — | 28 | 4 | no | — |
| 568 | C2×D3 | — | 140 | 4 | no | — |
| 569 | C2×D3 | — | 140 | 4 | no | — |
| 570 | C2×D3 | — | 140 | 4 | no | — |
| 571 | C2×D3 | — | 140 | 4 | no | — |
| 572 | C2×D3 | — | 140 | 1 | no | — |
| 573 | C2×C5 | — | 7 | 2 | no | — |
| 574 | C2×C5 | — | 12 | 1 | no | — |
| 575 | C2×C5 | — | 84 | 1 | no | — |
| 576 | C2×C5 | C2×D7×S4 | 1 | 1 | yes | characteristic |
| 577 | D5 | — | 7 | 2 | no | — |
| 578 | D5 | — | 12 | 1 | no | — |
| 579 | D5 | — | 84 | 1 | no | — |
| 580 | D5 | D7×GL(2,𝔽3) | 1 | 2 | yes | direct product factor |
| 581 | C23 | — | 30 | 1 | no | — |
| 582 | C23 | — | 35 | 1 | no | — |
| 583 | C23 | — | 42 | 1 | no | — |
| 584 | C23 | — | 420 | 4 | no | — |
| 585 | C23 | — | 210 | 1 | no | — |
| 586 | C23 | — | 210 | 1 | no | — |
| 587 | C23 | — | 210 | 1 | no | — |
| 588 | C23 | — | 210 | 1 | no | — |
| 589 | Q8 | — | 15 | 1 | no | — |
| 590 | Q8 | — | 21 | 1 | no | — |
| 591 | Q8 | — | 105 | 1 | no | — |
| 592 | Q8 | — | 210 | 1 | no | — |
| 593 | Q8 | D3×D5×D7 | 1 | 1 | yes | characteristic, complemented |
| 594 | D4 | — | 3 | 1 | no | — |
| 595 | D4 | — | 15 | 1 | no | — |
| 596 | D4 | — | 21 | 1 | no | — |
| 597 | D4 | — | 30 | 1 | no | — |
| 598 | D4 | — | 42 | 1 | no | — |
| 599 | D4 | — | 105 | 1 | no | — |
| 600 | D4 | — | 210 | 1 | no | — |
| 601 | D4 | — | 210 | 1 | no | — |
| 602 | D4 | — | 210 | 1 | no | — |
| 603 | D4 | — | 210 | 1 | no | — |
| 604 | C2×C4 | — | 15 | 1 | no | — |
| 605 | C2×C4 | — | 21 | 1 | no | — |
| 606 | C2×C4 | — | 105 | 1 | no | — |
| 607 | C2×C4 | — | 105 | 1 | no | — |
| 608 | C2×C4 | — | 105 | 1 | no | — |
| 609 | C2×C4 | — | 105 | 1 | no | — |
| 610 | C8 | — | 3 | 1 | no | — |
| 611 | C8 | — | 15 | 1 | no | — |
| 612 | C8 | — | 21 | 1 | no | — |
| 613 | C8 | — | 105 | 1 | no | — |
| 614 | C7 | C2×D5×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 615 | C2×C3 | — | 4 | 1 | no | — |
| 616 | C2×C3 | — | 20 | 2 | no | — |
| 617 | C2×C3 | — | 28 | 2 | no | — |
| 618 | C2×C3 | — | 140 | 2 | no | — |
| 619 | D3 | — | 4 | 2 | no | — |
| 620 | D3 | — | 20 | 2 | no | — |
| 621 | D3 | — | 28 | 2 | no | — |
| 622 | D3 | — | 140 | 2 | no | — |
| 623 | C5 | C2×D7×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 624 | C22 | — | 5 | 1 | no | — |
| 625 | C22 | — | 6 | 1 | no | — |
| 626 | C22 | — | 7 | 1 | no | — |
| 627 | C22 | — | 30 | 1 | no | — |
| 628 | C22 | — | 35 | 4 | no | — |
| 629 | C22 | — | 35 | 1 | no | — |
| 630 | C22 | — | 42 | 1 | no | — |
| 631 | C22 | — | 60 | 2 | no | — |
| 632 | C22 | — | 84 | 2 | no | — |
| 633 | C22 | — | 420 | 2 | no | — |
| 634 | C22 | — | 420 | 2 | no | — |
| 635 | C22 | — | 420 | 2 | no | — |
| 636 | C22 | — | 420 | 2 | no | — |
| 637 | C22 | — | 210 | 1 | no | — |
| 638 | C4 | — | 3 | 1 | no | — |
| 639 | C4 | — | 15 | 1 | no | — |
| 640 | C4 | — | 21 | 1 | no | — |
| 641 | C4 | — | 105 | 1 | no | — |
| 642 | C3 | — | 4 | 1 | no | Sylow |
| 643 | C2 | — | 5 | 2 | no | — |
| 644 | C2 | — | 7 | 2 | no | — |
| 645 | C2 | — | 12 | 1 | no | — |
| 646 | C2 | — | 35 | 2 | no | — |
| 647 | C2 | — | 60 | 1 | no | — |
| 648 | C2 | — | 84 | 1 | no | — |
| 649 | C2 | — | 420 | 1 | no | — |
| 650 | C2 | D5×D7×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D7×S4 |
| commutator, cosocle, hypocenter | C5×C7×SL(2,𝔽3) | C23 |
| Fitting | C5×C7×Q8 | C22×D3 |
| socle | C2×C5×C7 | C22×S4 |
| LCS | G ▷ C5×C7×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72218791 | C2 | semidirect |
| 2. D7×C5⋊GL(2,𝔽3) | C2 | semidirect |
| 3. GL(2,𝔽3)×D35 | C2 | semidirect |
| 4. C5×D7×GL(2,𝔽3) | C2 | semidirect |
| 5. D5×C7⋊GL(2,𝔽3) | C2 | semidirect |
| 7. C7×D5×GL(2,𝔽3) | C2 | semidirect |
| 8. D5×D7×SL(2,𝔽3) | C2 | semidirect |
| 10. SL(2,𝔽3)×D35 | C22 | semidirect |
| 11. C7×D5×SL(2,𝔽3) | C22 | semidirect |
| 12. C5×D7×SL(2,𝔽3) | C22 | semidirect |
| 13. C5⋊(C7⋊GL(2,𝔽3)) | C22 | semidirect |
| 14. C7×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 15. C5×C7⋊GL(2,𝔽3) | C22 | semidirect |
| 16. C5×C7×GL(2,𝔽3) | C22 | semidirect |
| 18. Q8×D5×D7 | D3 | semidirect |
| 42. C5×C7×SL(2,𝔽3) | C23 | semidirect |
| 49. D7×GL(2,𝔽3) | D5 | direct (N × H) |
| 51. Q8×D35 | C2×D3 | semidirect |
| 53. C7×Q8×D5 | C2×D3 | semidirect |
| 55. C5×Q8×D7 | C2×D3 | semidirect |
| 95. D5×GL(2,𝔽3) | D7 | direct (N × H) |
| 114. D7×SL(2,𝔽3) | C2×D5 | semidirect |
| 116. C7⋊GL(2,𝔽3) | C2×D5 | semidirect |
| 118. C7×GL(2,𝔽3) | C2×D5 | semidirect |
| 128. C5×C7×Q8 | C22×D3 | semidirect |
| 156. D5×SL(2,𝔽3) | C2×D7 | semidirect |
| 158. C5⋊GL(2,𝔽3) | C2×D7 | semidirect |
| 160. C5×GL(2,𝔽3) | C2×D7 | semidirect |
| 193. C7×SL(2,𝔽3) | C22×D5 | semidirect |
| 222. D5×D7 | GL(2,𝔽3) | direct (N × H) |
| 235. C5×SL(2,𝔽3) | C22×D7 | semidirect |
| 243. Q8×D7 | D3×D5 | semidirect |
| 304. Q8×D5 | D3×D7 | semidirect |
| 339. D35 | C2×GL(2,𝔽3) | semidirect |
| 341. C5×D7 | C2×GL(2,𝔽3) | semidirect |
| 343. C7×D5 | C2×GL(2,𝔽3) | semidirect |
| 368. C7×Q8 | C2×D3×D5 | semidirect |
| 399. GL(2,𝔽3) | D5×D7 | direct (N × H) |
| 417. C5×Q8 | C2×D3×D7 | semidirect |
| 441. C5×C7 | C22×GL(2,𝔽3) | semidirect |
| 491. SL(2,𝔽3) | C2×D5×D7 | semidirect |
| 558. D7 | D5×GL(2,𝔽3) | direct (N × H) |
| 580. D5 | D7×GL(2,𝔽3) | direct (N × H) |
| 593. Q8 | D3×D5×D7 | semidirect |
| 614. C7 | C2×D5×GL(2,𝔽3) | semidirect |
| 623. C5 | C2×D7×GL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72218791 | 2 |
| D7×C5⋊GL(2,𝔽3) | 2 |
| GL(2,𝔽3)×D35 | 2 |
| C5×D7×GL(2,𝔽3) | 2 |
| D5×C7⋊GL(2,𝔽3) | 2 |
| D5×D7×SD16 | 3 |
| C7×D5×GL(2,𝔽3) | 2 |
| D5×D7×SL(2,𝔽3) | 2 |
| C2×D3×D5×D7 | 4 |
| C2×D7×GL(2,𝔽3) | 5 |
| C2×D5×GL(2,𝔽3) | 7 |