Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
418 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #65903⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11752110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5394 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic5×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11751608 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751600 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11751598 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10611491 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 10 | C4×C5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | #91417 | — | 4 | 1 | no | maximal |
| 12 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 13 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 14 | #91184 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91184 | C22 | 1 | 1 | yes | characteristic |
| 16 | C5×#859 | C22 | 1 | 1 | yes | characteristic |
| 17 | #85424 | — | 5 | 1 | no | maximal, Hall |
| 18 | #65903 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | D4×Dic10 | — | 3 | 1 | no | — |
| 20 | C5×#440 | — | 3 | 1 | no | — |
| 21 | #65453 | — | 3 | 1 | no | — |
| 22 | SD16×Dic5 | — | 3 | 1 | no | — |
| 23 | #65310 | — | 3 | 1 | no | — |
| 24 | #65298 | — | 3 | 1 | no | — |
| 25 | #65165 | — | 3 | 1 | no | — |
| 26 | #65163 | — | 3 | 1 | no | — |
| 27 | #65083 | — | 3 | 1 | no | — |
| 28 | #65080 | — | 3 | 1 | no | — |
| 29 | #65052 | — | 3 | 1 | no | — |
| 30 | #65048 | — | 3 | 1 | no | — |
| 31 | #64991 | — | 3 | 1 | no | — |
| 32 | #64990 | — | 3 | 1 | no | — |
| 33 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×#1204 | — | 4 | 1 | no | — |
| 35 | C2×D3×Dic5 | — | 4 | 1 | no | — |
| 36 | C5×GL(2,𝔽3) | Q8 | 1 | 2 | yes | complemented |
| 37 | C4⋊Dic15 | — | 4 | 1 | no | — |
| 38 | C5×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 39 | C3×#683 | — | 4 | 1 | no | — |
| 40 | #6668 | — | 4 | 1 | no | — |
| 41 | (C2×D3)⋊Dic5 | — | 4 | 1 | no | — |
| 42 | #557⋊C3 | — | 5 | 1 | no | — |
| 43 | #5394 | — | 5 | 1 | no | — |
| 44 | #5394 | D5 | 1 | 1 | yes | characteristic |
| 45 | C4×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 46 | #5391 | — | 5 | 1 | no | — |
| 47 | #5391 | — | 5 | 1 | no | — |
| 48 | #5386 | — | 5 | 1 | no | — |
| 49 | C22×Dic10 | — | 6 | 1 | no | — |
| 50 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 51 | C4×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 52 | C4×C5×D4 | — | 3 | 1 | no | — |
| 53 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | D4×Dic5 | — | 3 | 1 | no | — |
| 56 | D4×Dic5 | — | 3 | 1 | no | — |
| 57 | #4070 | — | 6 | 1 | no | — |
| 58 | #4036 | — | 3 | 1 | no | — |
| 59 | #4034 | — | 3 | 1 | no | — |
| 60 | #4034 | — | 3 | 1 | no | — |
| 61 | #4034 | — | 3 | 1 | no | — |
| 62 | #4024 | — | 6 | 1 | no | — |
| 63 | #4024 | — | 6 | 1 | no | — |
| 64 | #4016 | — | 3 | 1 | no | — |
| 65 | #4015 | — | 3 | 1 | no | — |
| 66 | C4×Dic10 | — | 3 | 1 | no | — |
| 67 | C5×#107 | — | 3 | 1 | no | — |
| 68 | C5×#103 | — | 3 | 1 | no | — |
| 69 | C5×#102 | — | 3 | 1 | no | — |
| 70 | C5×#97 | — | 3 | 1 | no | — |
| 71 | #3967 | — | 3 | 1 | no | — |
| 72 | #3967 | — | 3 | 1 | no | — |
| 73 | #3964 | — | 3 | 1 | no | — |
| 74 | #3964 | — | 3 | 1 | no | — |
| 75 | #3950 | — | 3 | 1 | no | — |
| 76 | #3950 | — | 3 | 1 | no | — |
| 77 | #3949 | — | 3 | 1 | no | — |
| 78 | #3949 | — | 3 | 1 | no | — |
| 79 | #3947 | — | 3 | 1 | no | — |
| 80 | #3946 | — | 3 | 1 | no | — |
| 81 | #3946 | — | 3 | 1 | no | — |
| 82 | C8×Dic5 | — | 3 | 1 | no | — |
| 83 | #3940 | — | 3 | 1 | no | — |
| 84 | #3939 | — | 3 | 1 | no | — |
| 85 | #3939 | — | 3 | 1 | no | — |
| 86 | #3939 | — | 3 | 1 | no | — |
| 87 | C4⋊#168 | — | 3 | 1 | no | — |
| 88 | #3386 | — | 15 | 1 | no | Sylow |
| 89 | C22×C5×D3 | — | 4 | 1 | no | — |
| 90 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 91 | C2×Dic15 | — | 4 | 1 | no | — |
| 92 | C2×Dic15 | — | 4 | 1 | no | — |
| 93 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 94 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 95 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 96 | C5×SL(2,𝔽3) | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 97 | #1204 | — | 8 | 2 | no | — |
| 98 | D3×Dic5 | — | 8 | 2 | no | — |
| 99 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 100 | #897 | — | 20 | 1 | no | — |
| 101 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 102 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 103 | C4×SL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 104 | #859 | — | 5 | 1 | no | — |
| 105 | #859 | — | 5 | 1 | no | — |
| 106 | #859 | C2×D5 | 1 | 1 | yes | characteristic |
| 107 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 108 | C2×C5×D4 | — | 3 | 1 | no | — |
| 109 | C22×C4×C5 | — | 6 | 1 | no | — |
| 110 | C22×Dic5 | — | 6 | 1 | no | — |
| 111 | C22×Dic5 | — | 6 | 1 | no | — |
| 112 | C2×Dic10 | — | 3 | 1 | no | — |
| 113 | C2×Dic10 | — | 6 | 1 | no | — |
| 114 | C2×Dic10 | — | 6 | 1 | no | — |
| 115 | C2×Dic10 | — | 6 | 1 | no | — |
| 116 | C2×Dic10 | — | 12 | 4 | no | — |
| 117 | C5×SD16 | — | 3 | 2 | no | — |
| 118 | C5×SD16 | — | 3 | 2 | no | — |
| 119 | C2×C5×C8 | — | 3 | 1 | no | — |
| 120 | C2×C5×C8 | — | 3 | 1 | no | — |
| 121 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 122 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 123 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 124 | C42×C5 | — | 3 | 1 | no | — |
| 125 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 126 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 127 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 128 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 129 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 130 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 131 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 132 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 133 | #683 | — | 3 | 1 | no | — |
| 134 | #683 | — | 6 | 1 | no | — |
| 135 | #683 | — | 6 | 1 | no | — |
| 136 | #683 | — | 6 | 1 | no | — |
| 137 | #683 | S4 | 1 | 1 | yes | characteristic |
| 138 | C4×Dic5 | — | 3 | 1 | no | — |
| 139 | C4×Dic5 | — | 3 | 1 | no | — |
| 140 | C2×#168 | — | 3 | 1 | no | — |
| 141 | C2×#168 | — | 3 | 1 | no | — |
| 142 | #557 | — | 5 | 1 | no | — |
| 143 | D4×Q8 | — | 15 | 1 | no | — |
| 144 | #501 | — | 15 | 1 | no | — |
| 145 | #501 | — | 15 | 1 | no | — |
| 146 | #500 | — | 15 | 1 | no | — |
| 147 | #478 | — | 15 | 1 | no | — |
| 148 | #478 | — | 15 | 1 | no | — |
| 149 | #477 | — | 15 | 1 | no | — |
| 150 | #477 | — | 15 | 1 | no | — |
| 151 | #475 | — | 15 | 1 | no | — |
| 152 | #474 | — | 15 | 1 | no | — |
| 153 | #446 | — | 15 | 1 | no | — |
| 154 | #440 | — | 3 | 1 | no | — |
| 155 | #440 | — | 15 | 1 | no | — |
| 156 | C4×SD16 | — | 15 | 1 | no | — |
| 157 | C22×C3×C5 | — | 4 | 1 | no | — |
| 158 | C2×C5×D3 | — | 4 | 2 | no | — |
| 159 | C2×C5×D3 | — | 8 | 1 | no | — |
| 160 | C2×C5×D3 | — | 8 | 1 | no | — |
| 161 | C3×C4×C5 | — | 8 | 1 | no | — |
| 162 | Dic15 | — | 8 | 1 | no | — |
| 163 | Dic15 | — | 8 | 1 | no | — |
| 164 | C3×Dic5 | — | 4 | 2 | no | — |
| 165 | C3×Dic5 | — | 8 | 1 | no | — |
| 166 | C5×Dic3 | — | 8 | 1 | no | — |
| 167 | C2×C4×D3 | — | 20 | 1 | no | — |
| 168 | C2×Dic6 | — | 20 | 1 | no | — |
| 169 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 170 | GL(2,𝔽3) | Dic10 | 1 | 2 | yes | complemented |
| 171 | C3×C4⋊C4 | — | 20 | 1 | no | — |
| 172 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 173 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 174 | C4⋊Dic3 | — | 20 | 1 | no | — |
| 175 | C4⋊Dic3 | — | 20 | 1 | no | — |
| 176 | C23×C5 | — | 6 | 1 | no | — |
| 177 | C5×Q8 | — | 3 | 1 | no | — |
| 178 | C5×Q8 | D3×Q8 | 1 | 1 | yes | characteristic |
| 179 | C5×D4 | — | 3 | 2 | no | — |
| 180 | C5×D4 | — | 6 | 1 | no | — |
| 181 | C2×C4×C5 | — | 3 | 1 | no | — |
| 182 | C2×C4×C5 | — | 3 | 1 | no | — |
| 183 | C2×C4×C5 | — | 6 | 1 | no | — |
| 184 | C2×C4×C5 | — | 12 | 2 | no | — |
| 185 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic5 | — | 3 | 1 | no | — |
| 187 | C2×Dic5 | — | 3 | 1 | no | — |
| 188 | C2×Dic5 | — | 6 | 1 | no | — |
| 189 | C2×Dic5 | — | 6 | 1 | no | — |
| 190 | C2×Dic5 | — | 12 | 2 | no | — |
| 191 | C2×Dic5 | — | 12 | 2 | no | — |
| 192 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 193 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 194 | Dic10 | — | 6 | 2 | no | — |
| 195 | Dic10 | — | 12 | 2 | no | — |
| 196 | Dic10 | — | 12 | 2 | no | — |
| 197 | Dic10 | — | 12 | 2 | no | — |
| 198 | C5×C8 | — | 3 | 2 | no | — |
| 199 | C5×C8 | — | 6 | 1 | no | — |
| 200 | #168 | — | 6 | 1 | no | — |
| 201 | #168 | — | 6 | 1 | no | — |
| 202 | C22×Q8 | — | 30 | 1 | no | — |
| 203 | C2×SD16 | — | 3 | 1 | no | — |
| 204 | C4⋊Q8 | — | 15 | 1 | no | — |
| 205 | C4⋊Q8 | — | 15 | 1 | no | — |
| 206 | C4⋊Q8 | — | 15 | 1 | no | — |
| 207 | C4⋊Q8 | — | 15 | 1 | no | — |
| 208 | #125 | — | 15 | 1 | no | — |
| 209 | #125 | — | 15 | 1 | no | — |
| 210 | C22⋊Q8 | — | 30 | 1 | no | — |
| 211 | C22⋊Q8 | — | 30 | 1 | no | — |
| 212 | C22⋊Q8 | — | 30 | 1 | no | — |
| 213 | C4×Q8 | — | 5 | 1 | no | — |
| 214 | C4×Q8 | — | 5 | 1 | no | — |
| 215 | C4×Q8 | — | 15 | 1 | no | — |
| 216 | C4×Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 217 | C4×D4 | — | 3 | 1 | no | — |
| 218 | C4×D4 | — | 15 | 1 | no | — |
| 219 | C4×D4 | — | 15 | 1 | no | — |
| 220 | #107 | — | 3 | 1 | no | — |
| 221 | #107 | — | 15 | 1 | no | — |
| 222 | #107 | — | 15 | 1 | no | — |
| 223 | #107 | — | 15 | 1 | no | — |
| 224 | #107 | — | 15 | 1 | no | — |
| 225 | #107 | — | 15 | 1 | no | — |
| 226 | #106 | — | 15 | 1 | no | — |
| 227 | #106 | — | 15 | 1 | no | — |
| 228 | #106 | — | 15 | 1 | no | — |
| 229 | C4⋊C8 | — | 15 | 1 | no | — |
| 230 | C4⋊C8 | — | 15 | 1 | no | — |
| 231 | C4⋊C8 | — | 15 | 1 | no | — |
| 232 | #103 | — | 3 | 1 | no | — |
| 233 | #103 | — | 15 | 1 | no | — |
| 234 | #103 | — | 15 | 1 | no | — |
| 235 | #102 | — | 3 | 1 | no | — |
| 236 | #102 | — | 15 | 1 | no | — |
| 237 | #102 | — | 15 | 1 | no | — |
| 238 | #97 | — | 3 | 1 | no | — |
| 239 | #97 | — | 15 | 1 | no | — |
| 240 | C4×C8 | — | 15 | 1 | no | — |
| 241 | C2×C3×C5 | — | 4 | 1 | no | — |
| 242 | C2×C3×C5 | — | 4 | 1 | no | — |
| 243 | C2×C3×C5 | — | 4 | 1 | no | — |
| 244 | C5×D3 | — | 8 | 2 | no | — |
| 245 | C22×D3 | — | 4 | 1 | no | — |
| 246 | C2×C3×C4 | — | 4 | 1 | no | — |
| 247 | C2×C3×C4 | — | 20 | 1 | no | — |
| 248 | C2×C3×C4 | — | 20 | 1 | no | — |
| 249 | C2×Dic3 | — | 4 | 1 | no | — |
| 250 | C2×Dic3 | — | 20 | 1 | no | — |
| 251 | C2×Dic3 | — | 20 | 1 | no | — |
| 252 | C4×D3 | — | 40 | 2 | no | — |
| 253 | Dic6 | — | 40 | 2 | no | — |
| 254 | SL(2,𝔽3) | C2×Dic10 | 1 | 1 | yes | characteristic, complemented |
| 255 | C22×C5 | — | 6 | 2 | no | — |
| 256 | C22×C5 | — | 12 | 1 | no | — |
| 257 | C22×C5 | — | 12 | 1 | no | — |
| 258 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 259 | C4×C5 | — | 2 | 1 | no | — |
| 260 | C4×C5 | — | 3 | 1 | no | — |
| 261 | C4×C5 | — | 3 | 1 | no | — |
| 262 | C4×C5 | — | 6 | 1 | no | — |
| 263 | C4×C5 | — | 12 | 1 | no | — |
| 264 | Dic5 | — | 2 | 1 | no | — |
| 265 | Dic5 | — | 6 | 1 | no | — |
| 266 | Dic5 | — | 6 | 1 | no | — |
| 267 | Dic5 | — | 12 | 1 | no | — |
| 268 | Dic5 | — | 12 | 1 | no | — |
| 269 | Dic5 | #986 | 1 | 2 | yes | — |
| 270 | C2×Q8 | — | 15 | 1 | no | — |
| 271 | C2×Q8 | — | 30 | 1 | no | — |
| 272 | C2×Q8 | — | 30 | 1 | no | — |
| 273 | C2×Q8 | — | 30 | 1 | no | — |
| 274 | C2×Q8 | — | 60 | 4 | no | — |
| 275 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 276 | C2×D4 | — | 3 | 1 | no | — |
| 277 | C22×C4 | — | 6 | 1 | no | — |
| 278 | C22×C4 | — | 30 | 1 | no | — |
| 279 | C22×C4 | — | 30 | 1 | no | — |
| 280 | SD16 | — | 3 | 2 | no | — |
| 281 | SD16 | — | 3 | 2 | no | — |
| 282 | C2×C8 | — | 3 | 1 | no | — |
| 283 | C2×C8 | — | 3 | 1 | no | — |
| 284 | C2×C8 | — | 15 | 1 | no | — |
| 285 | C2×C8 | — | 15 | 1 | no | — |
| 286 | C4⋊C4 | — | 3 | 1 | no | — |
| 287 | C4⋊C4 | — | 3 | 1 | no | — |
| 288 | C4⋊C4 | — | 5 | 1 | no | — |
| 289 | C4⋊C4 | — | 15 | 1 | no | — |
| 290 | C4⋊C4 | — | 15 | 1 | no | — |
| 291 | C4⋊C4 | — | 15 | 1 | no | — |
| 292 | C4⋊C4 | — | 15 | 1 | no | — |
| 293 | C4⋊C4 | — | 15 | 1 | no | — |
| 294 | C4⋊C4 | — | 15 | 1 | no | — |
| 295 | C4⋊C4 | — | 30 | 1 | no | — |
| 296 | C4⋊C4 | — | 30 | 1 | no | — |
| 297 | C4⋊C4 | — | 30 | 1 | no | — |
| 298 | C4⋊C4 | — | 30 | 1 | no | — |
| 299 | C22⋊C4 | — | 6 | 1 | no | — |
| 300 | C22⋊C4 | — | 30 | 1 | no | — |
| 301 | C22⋊C4 | — | 30 | 1 | no | — |
| 302 | C42 | — | 3 | 1 | no | — |
| 303 | C42 | — | 15 | 1 | no | — |
| 304 | C42 | — | 15 | 1 | no | — |
| 305 | C3×C5 | — | 4 | 1 | no | Hall |
| 306 | C22×C3 | — | 4 | 1 | no | — |
| 307 | C2×D3 | — | 4 | 2 | no | — |
| 308 | C2×D3 | — | 8 | 1 | no | — |
| 309 | C2×D3 | — | 8 | 1 | no | — |
| 310 | C3×C4 | — | 8 | 1 | no | — |
| 311 | C3×C4 | — | 20 | 2 | no | — |
| 312 | C3×C4 | — | 40 | 1 | no | — |
| 313 | Dic3 | — | 8 | 1 | no | — |
| 314 | Dic3 | — | 40 | 1 | no | — |
| 315 | Dic3 | — | 40 | 1 | no | — |
| 316 | C2×C5 | — | 12 | 2 | no | — |
| 317 | C2×C5 | Q8×S4 | 1 | 1 | yes | characteristic |
| 318 | C2×C5 | C2×#986 | 1 | 1 | yes | characteristic |
| 319 | C2×C5 | #5927 | 1 | 1 | yes | characteristic |
| 320 | C23 | — | 6 | 1 | no | — |
| 321 | Q8 | — | 3 | 1 | no | — |
| 322 | Q8 | — | 30 | 2 | no | — |
| 323 | Q8 | — | 60 | 2 | no | — |
| 324 | Q8 | — | 60 | 2 | no | — |
| 325 | Q8 | — | 60 | 2 | no | — |
| 326 | Q8 | D3×Dic10 | 1 | 1 | yes | characteristic |
| 327 | D4 | — | 3 | 2 | no | — |
| 328 | D4 | — | 6 | 1 | no | — |
| 329 | C2×C4 | — | 3 | 1 | no | — |
| 330 | C2×C4 | — | 3 | 1 | no | — |
| 331 | C2×C4 | — | 5 | 1 | no | — |
| 332 | C2×C4 | — | 5 | 1 | no | — |
| 333 | C2×C4 | — | 6 | 1 | no | — |
| 334 | C2×C4 | — | 12 | 2 | no | — |
| 335 | C2×C4 | — | 15 | 1 | no | — |
| 336 | C2×C4 | — | 15 | 1 | no | — |
| 337 | C2×C4 | — | 30 | 1 | no | — |
| 338 | C2×C4 | — | 30 | 1 | no | — |
| 339 | C2×C4 | — | 60 | 2 | no | — |
| 340 | C2×C4 | — | 60 | 2 | no | — |
| 341 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 342 | C8 | — | 3 | 2 | no | — |
| 343 | C8 | — | 6 | 1 | no | — |
| 344 | C8 | — | 30 | 1 | no | — |
| 345 | C8 | — | 30 | 1 | no | — |
| 346 | C2×C3 | — | 4 | 1 | no | — |
| 347 | C2×C3 | — | 4 | 1 | no | — |
| 348 | C2×C3 | — | 4 | 1 | no | — |
| 349 | D3 | — | 8 | 2 | no | — |
| 350 | C5 | #85424 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 351 | C22 | — | 6 | 2 | no | — |
| 352 | C22 | — | 12 | 1 | no | — |
| 353 | C22 | — | 12 | 1 | no | — |
| 354 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 355 | C4 | — | 2 | 1 | no | — |
| 356 | C4 | — | 3 | 1 | no | — |
| 357 | C4 | — | 3 | 1 | no | — |
| 358 | C4 | — | 5 | 2 | no | — |
| 359 | C4 | — | 6 | 1 | no | — |
| 360 | C4 | — | 10 | 1 | no | — |
| 361 | C4 | — | 12 | 1 | no | — |
| 362 | C4 | — | 30 | 1 | no | — |
| 363 | C4 | — | 30 | 1 | no | — |
| 364 | C4 | — | 60 | 1 | no | — |
| 365 | C4 | — | 60 | 1 | no | — |
| 366 | C3 | — | 4 | 1 | no | Sylow |
| 367 | C2 | — | 12 | 2 | no | — |
| 368 | C2 | S4×Dic10 | 1 | 1 | yes | characteristic |
| 369 | C2 | #11756766 | 1 | 1 | yes | characteristic |
| 370 | C2 | D5×#986 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #65903⋊C3 | C2 | semidirect |
| 2. #11752110 | C2 | semidirect |
| 5. #11751608 | C2 | semidirect |
| 7. #11751598 | C2 | semidirect |
| 18. #65903 | D3 | semidirect |
| 36. C5×GL(2,𝔽3) | Q8 | semidirect |
| 96. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 170. GL(2,𝔽3) | Dic10 | semidirect |
| 254. SL(2,𝔽3) | C2×Dic10 | semidirect |
| 350. C5 | #85424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65903⋊C3 | 2 |
| #11752110 | 2 |
| C5×#5394 | 2 |
| Dic5×GL(2,𝔽3) | 2 |
| #11751608 | 2 |
| #11751600 | 2 |
| #11751598 | 2 |
| #10611491 | 3 |
| #91417 | 4 |
| #85424 | 5 |