Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
398 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 49 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 | C4×C5⋊#226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5395 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic5×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11751601 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11751597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | Dic5×#226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10612311 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C5⋊#226 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C5×#226 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4×C5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 13 | #91400 | — | 4 | 1 | no | maximal |
| 14 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 16 | #91184 | C22 | 1 | 1 | yes | characteristic |
| 17 | #85419 | — | 5 | 1 | no | maximal, Hall |
| 18 | #66005 | — | 3 | 1 | no | — |
| 19 | #65903 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C5×#464 | — | 3 | 1 | no | — |
| 21 | Q16×Dic5 | — | 3 | 1 | no | — |
| 22 | #65471 | — | 3 | 1 | no | — |
| 23 | #65455 | — | 3 | 1 | no | — |
| 24 | SD16×Dic5 | — | 3 | 1 | no | — |
| 25 | #65345 | — | 3 | 1 | no | — |
| 26 | C4×#689 | — | 3 | 1 | no | — |
| 27 | #65119 | — | 3 | 1 | no | — |
| 28 | #65118 | — | 3 | 1 | no | — |
| 29 | #65088 | — | 3 | 1 | no | — |
| 30 | #65081 | — | 3 | 1 | no | — |
| 31 | #65057 | — | 3 | 1 | no | — |
| 32 | #65048 | — | 3 | 1 | no | — |
| 33 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×D3×Dic5 | — | 4 | 1 | no | — |
| 35 | C5⋊#226 | — | 2 | 1 | no | — |
| 36 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 37 | C5×#226 | — | 2 | 1 | no | — |
| 38 | C4×Dic15 | — | 4 | 1 | no | — |
| 39 | C5×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 40 | C3×#683 | — | 4 | 1 | no | — |
| 41 | #6668 | — | 4 | 1 | no | — |
| 42 | (C2×D3)⋊Dic5 | — | 4 | 1 | no | — |
| 43 | Dic3×Dic5 | — | 4 | 1 | no | — |
| 44 | #557⋊C3 | — | 5 | 1 | no | — |
| 45 | #5395 | — | 5 | 1 | no | — |
| 46 | #5395 | D5 | 1 | 1 | yes | characteristic |
| 47 | C4×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 48 | C4⋊#226 | — | 5 | 1 | no | — |
| 49 | C4×#226 | — | 5 | 1 | no | — |
| 50 | C4×#226 | — | 5 | 1 | no | — |
| 51 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 52 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 53 | C5×#124 | — | 3 | 1 | no | — |
| 54 | C4×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | Q8×Dic5 | — | 3 | 1 | no | — |
| 56 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 58 | #4090 | — | 3 | 1 | no | — |
| 59 | C2×#689 | — | 3 | 1 | no | — |
| 60 | #4082 | — | 3 | 1 | no | — |
| 61 | D4×Dic5 | — | 3 | 1 | no | — |
| 62 | #4036 | — | 3 | 1 | no | — |
| 63 | #4034 | — | 3 | 1 | no | — |
| 64 | #4025 | — | 6 | 1 | no | — |
| 65 | #4025 | — | 6 | 1 | no | — |
| 66 | #4024 | — | 6 | 1 | no | — |
| 67 | #4023 | — | 6 | 1 | no | — |
| 68 | #4016 | — | 3 | 1 | no | — |
| 69 | C4×Dic10 | — | 3 | 1 | no | — |
| 70 | C4×Dic10 | — | 3 | 1 | no | — |
| 71 | C5×C4⋊C8 | — | 3 | 1 | no | — |
| 72 | C5×#103 | — | 3 | 1 | no | — |
| 73 | C5×#102 | — | 3 | 1 | no | — |
| 74 | #3967 | — | 3 | 1 | no | — |
| 75 | #3967 | — | 3 | 1 | no | — |
| 76 | #3967 | — | 3 | 1 | no | — |
| 77 | #3964 | — | 3 | 1 | no | — |
| 78 | #3964 | — | 3 | 1 | no | — |
| 79 | #3950 | — | 3 | 1 | no | — |
| 80 | #3949 | — | 3 | 1 | no | — |
| 81 | #3948 | — | 3 | 1 | no | — |
| 82 | #3948 | — | 3 | 1 | no | — |
| 83 | #3946 | — | 3 | 1 | no | — |
| 84 | #3946 | — | 3 | 1 | no | — |
| 85 | C8×Dic5 | — | 3 | 1 | no | — |
| 86 | C8×Dic5 | — | 3 | 1 | no | — |
| 87 | #3942 | — | 3 | 1 | no | — |
| 88 | #3939 | — | 3 | 1 | no | — |
| 89 | C4×#168 | — | 3 | 1 | no | — |
| 90 | #3364 | — | 15 | 1 | no | Sylow |
| 91 | C22×C5×D3 | — | 4 | 1 | no | — |
| 92 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 93 | C2×Dic15 | — | 4 | 1 | no | — |
| 94 | C2×Dic15 | — | 4 | 1 | no | — |
| 95 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 96 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 97 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 98 | C5×SL(2,𝔽3) | #41 | 1 | 1 | yes | characteristic |
| 99 | D3×Dic5 | — | 4 | 4 | no | — |
| 100 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 101 | C2×#226 | — | 5 | 1 | no | — |
| 102 | C2×#226 | C2×D5 | 1 | 1 | yes | characteristic |
| 103 | #892 | — | 20 | 1 | no | — |
| 104 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 105 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 106 | C4×SL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 107 | #859 | — | 5 | 1 | no | — |
| 108 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 109 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 110 | C2×C5×D4 | — | 3 | 1 | no | — |
| 111 | C22×Dic5 | — | 6 | 1 | no | — |
| 112 | C2×Dic10 | — | 3 | 1 | no | — |
| 113 | C2×Dic10 | — | 3 | 1 | no | — |
| 114 | C5×Q16 | — | 6 | 1 | no | — |
| 115 | C5×Q16 | — | 6 | 1 | no | — |
| 116 | C5×SD16 | — | 6 | 1 | no | — |
| 117 | C5×SD16 | — | 6 | 1 | no | — |
| 118 | C2×C5×C8 | — | 3 | 1 | no | — |
| 119 | C2×C5×C8 | — | 3 | 1 | no | — |
| 120 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 121 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 122 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 123 | C42×C5 | — | 3 | 1 | no | — |
| 124 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 125 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 126 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 127 | #689 | — | 6 | 1 | no | — |
| 128 | #689 | — | 6 | 1 | no | — |
| 129 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 130 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 131 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 132 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 133 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 134 | #683 | — | 3 | 1 | no | — |
| 135 | #683 | — | 6 | 1 | no | — |
| 136 | #683 | — | 6 | 1 | no | — |
| 137 | #683 | — | 6 | 1 | no | — |
| 138 | #683 | — | 6 | 1 | no | — |
| 139 | #683 | S4 | 1 | 1 | yes | characteristic |
| 140 | C4×Dic5 | — | 3 | 1 | no | — |
| 141 | C4×Dic5 | — | 3 | 1 | no | — |
| 142 | C4×Dic5 | — | 6 | 1 | no | — |
| 143 | C4×Dic5 | — | 6 | 1 | no | — |
| 144 | C2×#168 | — | 3 | 1 | no | — |
| 145 | C2×#168 | — | 3 | 1 | no | — |
| 146 | #557 | — | 5 | 1 | no | — |
| 147 | #556 | — | 15 | 1 | no | — |
| 148 | #488 | — | 15 | 1 | no | — |
| 149 | #488 | — | 15 | 1 | no | — |
| 150 | #487 | — | 15 | 1 | no | — |
| 151 | #479 | — | 15 | 1 | no | — |
| 152 | #479 | — | 15 | 1 | no | — |
| 153 | #474 | — | 15 | 1 | no | — |
| 154 | #464 | — | 3 | 1 | no | — |
| 155 | #464 | — | 15 | 1 | no | — |
| 156 | #462 | — | 15 | 1 | no | — |
| 157 | C8×Q8 | — | 15 | 1 | no | — |
| 158 | C4×Q16 | — | 15 | 1 | no | — |
| 159 | C4×Q16 | — | 15 | 1 | no | — |
| 160 | C4×SD16 | — | 15 | 1 | no | — |
| 161 | C22×C3×C5 | — | 4 | 1 | no | — |
| 162 | C2×C5×D3 | — | 4 | 2 | no | — |
| 163 | C2×C5×D3 | — | 8 | 1 | no | — |
| 164 | C2×C5×D3 | — | 8 | 1 | no | — |
| 165 | C3×C4×C5 | — | 8 | 1 | no | — |
| 166 | Dic15 | — | 4 | 2 | no | — |
| 167 | Dic15 | — | 8 | 1 | no | — |
| 168 | C3×Dic5 | — | 4 | 2 | no | — |
| 169 | C3×Dic5 | — | 8 | 1 | no | — |
| 170 | C5×Dic3 | — | 8 | 1 | no | — |
| 171 | C2×C4×D3 | — | 20 | 1 | no | — |
| 172 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 173 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 174 | #226 | — | 2 | 1 | no | — |
| 175 | #226 | — | 10 | 1 | no | — |
| 176 | C3×C4⋊C4 | — | 20 | 1 | no | — |
| 177 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 178 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 179 | C4⋊Dic3 | — | 20 | 1 | no | — |
| 180 | C4×Dic3 | — | 20 | 1 | no | — |
| 181 | C4×Dic3 | — | 20 | 1 | no | — |
| 182 | C23×C5 | — | 6 | 1 | no | — |
| 183 | C5×Q8 | — | 3 | 1 | no | — |
| 184 | C5×Q8 | — | 6 | 1 | no | — |
| 185 | C5×Q8 | — | 6 | 1 | no | — |
| 186 | C5×Q8 | #239 | 1 | 1 | yes | characteristic |
| 187 | C5×D4 | — | 6 | 1 | no | — |
| 188 | C5×D4 | — | 6 | 1 | no | — |
| 189 | C2×C4×C5 | — | 3 | 1 | no | — |
| 190 | C2×C4×C5 | — | 3 | 1 | no | — |
| 191 | C2×C4×C5 | — | 6 | 1 | no | — |
| 192 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 193 | C2×Dic5 | — | 3 | 1 | no | — |
| 194 | C2×Dic5 | — | 3 | 1 | no | — |
| 195 | C2×Dic5 | — | 6 | 1 | no | — |
| 196 | C2×Dic5 | — | 6 | 1 | no | — |
| 197 | C2×Dic5 | — | 12 | 2 | no | — |
| 198 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 199 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 200 | Dic10 | — | 6 | 2 | no | — |
| 201 | Dic10 | — | 6 | 1 | no | — |
| 202 | Dic10 | — | 6 | 1 | no | — |
| 203 | C5×C8 | — | 6 | 1 | no | — |
| 204 | C5×C8 | — | 6 | 1 | no | — |
| 205 | #168 | — | 6 | 1 | no | — |
| 206 | #168 | — | 6 | 1 | no | — |
| 207 | C2×Q16 | — | 3 | 1 | no | — |
| 208 | C2×Q16 | — | 15 | 1 | no | — |
| 209 | C2×SD16 | — | 3 | 1 | no | — |
| 210 | C4⋊Q8 | — | 15 | 1 | no | — |
| 211 | C4⋊Q8 | — | 15 | 1 | no | — |
| 212 | #126 | — | 30 | 1 | no | — |
| 213 | #126 | — | 30 | 1 | no | — |
| 214 | #125 | — | 15 | 1 | no | — |
| 215 | #125 | — | 15 | 1 | no | — |
| 216 | #124 | — | 3 | 1 | no | — |
| 217 | #124 | — | 15 | 1 | no | — |
| 218 | C22⋊Q8 | — | 30 | 1 | no | — |
| 219 | C4×Q8 | — | 5 | 1 | no | — |
| 220 | C4×Q8 | — | 5 | 1 | no | — |
| 221 | C4×Q8 | — | 15 | 1 | no | — |
| 222 | C4×Q8 | — | 15 | 1 | no | — |
| 223 | C4×Q8 | — | 15 | 1 | no | — |
| 224 | C4×Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 225 | C4×D4 | — | 15 | 1 | no | — |
| 226 | #117 | — | 30 | 1 | no | — |
| 227 | #107 | — | 15 | 1 | no | — |
| 228 | #107 | — | 15 | 1 | no | — |
| 229 | #106 | — | 15 | 1 | no | — |
| 230 | C4⋊C8 | — | 3 | 1 | no | — |
| 231 | C4⋊C8 | — | 15 | 1 | no | — |
| 232 | C4⋊C8 | — | 15 | 1 | no | — |
| 233 | #103 | — | 3 | 1 | no | — |
| 234 | #103 | — | 15 | 1 | no | — |
| 235 | #103 | — | 15 | 1 | no | — |
| 236 | #103 | — | 15 | 1 | no | — |
| 237 | #103 | — | 15 | 1 | no | — |
| 238 | #103 | — | 15 | 1 | no | — |
| 239 | #103 | — | 15 | 1 | no | — |
| 240 | #102 | — | 3 | 1 | no | — |
| 241 | #102 | — | 15 | 1 | no | — |
| 242 | #102 | — | 15 | 1 | no | — |
| 243 | C4×C8 | — | 15 | 1 | no | — |
| 244 | C4×C8 | — | 15 | 1 | no | — |
| 245 | C4×C8 | — | 15 | 1 | no | — |
| 246 | C2×C3×C5 | — | 4 | 1 | no | — |
| 247 | C2×C3×C5 | — | 4 | 1 | no | — |
| 248 | C2×C3×C5 | — | 4 | 1 | no | — |
| 249 | C5×D3 | — | 8 | 2 | no | — |
| 250 | C22×D3 | — | 4 | 1 | no | — |
| 251 | C2×C3×C4 | — | 4 | 1 | no | — |
| 252 | C2×C3×C4 | — | 20 | 1 | no | — |
| 253 | C2×C3×C4 | — | 20 | 1 | no | — |
| 254 | C2×Dic3 | — | 4 | 1 | no | — |
| 255 | C2×Dic3 | — | 20 | 1 | no | — |
| 256 | C2×Dic3 | — | 20 | 1 | no | — |
| 257 | C4×D3 | — | 20 | 4 | no | — |
| 258 | SL(2,𝔽3) | #711 | 1 | 1 | yes | characteristic |
| 259 | C22×C5 | — | 12 | 1 | no | — |
| 260 | C22×C5 | — | 12 | 1 | no | — |
| 261 | C22×C5 | — | 12 | 1 | no | — |
| 262 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 263 | C4×C5 | — | 2 | 1 | no | — |
| 264 | C4×C5 | — | 3 | 1 | no | — |
| 265 | C4×C5 | — | 3 | 1 | no | — |
| 266 | C4×C5 | — | 6 | 1 | no | — |
| 267 | C4×C5 | — | 12 | 1 | no | — |
| 268 | Dic5 | — | 2 | 1 | no | — |
| 269 | Dic5 | — | 6 | 1 | no | — |
| 270 | Dic5 | — | 6 | 1 | no | — |
| 271 | Dic5 | — | 12 | 1 | no | — |
| 272 | Dic5 | — | 12 | 1 | no | — |
| 273 | Dic5 | #985 | 1 | 2 | yes | — |
| 274 | C2×Q8 | — | 3 | 1 | no | — |
| 275 | C2×Q8 | — | 15 | 1 | no | — |
| 276 | C2×Q8 | — | 15 | 1 | no | — |
| 277 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 278 | C2×D4 | — | 3 | 1 | no | — |
| 279 | C22×C4 | — | 30 | 1 | no | — |
| 280 | Q16 | — | 6 | 1 | no | — |
| 281 | Q16 | — | 6 | 1 | no | — |
| 282 | Q16 | — | 30 | 1 | no | — |
| 283 | Q16 | — | 30 | 1 | no | — |
| 284 | SD16 | — | 6 | 1 | no | — |
| 285 | SD16 | — | 6 | 1 | no | — |
| 286 | C2×C8 | — | 3 | 1 | no | — |
| 287 | C2×C8 | — | 3 | 1 | no | — |
| 288 | C2×C8 | — | 15 | 1 | no | — |
| 289 | C2×C8 | — | 15 | 1 | no | — |
| 290 | C4⋊C4 | — | 3 | 1 | no | — |
| 291 | C4⋊C4 | — | 5 | 1 | no | — |
| 292 | C4⋊C4 | — | 15 | 1 | no | — |
| 293 | C4⋊C4 | — | 15 | 1 | no | — |
| 294 | C4⋊C4 | — | 15 | 1 | no | — |
| 295 | C4⋊C4 | — | 15 | 1 | no | — |
| 296 | C4⋊C4 | — | 15 | 1 | no | — |
| 297 | C4⋊C4 | — | 30 | 1 | no | — |
| 298 | C4⋊C4 | — | 30 | 1 | no | — |
| 299 | C4⋊C4 | — | 30 | 1 | no | — |
| 300 | C4⋊C4 | — | 30 | 1 | no | — |
| 301 | C4⋊C4 | — | 30 | 1 | no | — |
| 302 | C22⋊C4 | — | 6 | 1 | no | — |
| 303 | C22⋊C4 | — | 6 | 1 | no | — |
| 304 | C22⋊C4 | — | 30 | 1 | no | — |
| 305 | C22⋊C4 | — | 30 | 1 | no | — |
| 306 | C22⋊C4 | — | 30 | 1 | no | — |
| 307 | C42 | — | 3 | 1 | no | — |
| 308 | C42 | — | 15 | 1 | no | — |
| 309 | C42 | — | 15 | 1 | no | — |
| 310 | C42 | — | 30 | 1 | no | — |
| 311 | C42 | — | 30 | 1 | no | — |
| 312 | C3×C5 | — | 4 | 1 | no | Hall |
| 313 | C22×C3 | — | 4 | 1 | no | — |
| 314 | C2×D3 | — | 4 | 2 | no | — |
| 315 | C2×D3 | — | 8 | 1 | no | — |
| 316 | C2×D3 | — | 8 | 1 | no | — |
| 317 | C3×C4 | — | 8 | 1 | no | — |
| 318 | C3×C4 | — | 20 | 2 | no | — |
| 319 | C3×C4 | — | 40 | 1 | no | — |
| 320 | Dic3 | — | 8 | 1 | no | — |
| 321 | Dic3 | — | 20 | 2 | no | — |
| 322 | Dic3 | — | 40 | 1 | no | — |
| 323 | C2×C5 | — | 24 | 1 | no | — |
| 324 | C2×C5 | #5919 | 1 | 1 | yes | characteristic |
| 325 | C2×C5 | C2×#985 | 1 | 1 | yes | characteristic |
| 326 | C2×C5 | #5927 | 1 | 1 | yes | characteristic |
| 327 | C23 | — | 6 | 1 | no | — |
| 328 | Q8 | — | 3 | 1 | no | — |
| 329 | Q8 | — | 6 | 1 | no | — |
| 330 | Q8 | — | 6 | 1 | no | — |
| 331 | Q8 | — | 30 | 1 | no | — |
| 332 | Q8 | — | 30 | 1 | no | — |
| 333 | Q8 | — | 30 | 2 | no | — |
| 334 | Q8 | #6768 | 1 | 1 | yes | characteristic |
| 335 | D4 | — | 6 | 1 | no | — |
| 336 | D4 | — | 6 | 1 | no | — |
| 337 | C2×C4 | — | 3 | 1 | no | — |
| 338 | C2×C4 | — | 3 | 1 | no | — |
| 339 | C2×C4 | — | 5 | 1 | no | — |
| 340 | C2×C4 | — | 5 | 1 | no | — |
| 341 | C2×C4 | — | 6 | 1 | no | — |
| 342 | C2×C4 | — | 15 | 1 | no | — |
| 343 | C2×C4 | — | 15 | 1 | no | — |
| 344 | C2×C4 | — | 30 | 1 | no | — |
| 345 | C2×C4 | — | 30 | 1 | no | — |
| 346 | C2×C4 | — | 60 | 2 | no | — |
| 347 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 348 | C8 | — | 6 | 1 | no | — |
| 349 | C8 | — | 6 | 1 | no | — |
| 350 | C8 | — | 30 | 1 | no | — |
| 351 | C8 | — | 30 | 1 | no | — |
| 352 | C2×C3 | — | 4 | 1 | no | — |
| 353 | C2×C3 | — | 4 | 1 | no | — |
| 354 | C2×C3 | — | 4 | 1 | no | — |
| 355 | D3 | — | 8 | 2 | no | — |
| 356 | C5 | #85419 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 357 | C22 | — | 12 | 1 | no | — |
| 358 | C22 | — | 12 | 1 | no | — |
| 359 | C22 | — | 12 | 1 | no | — |
| 360 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 361 | C4 | — | 2 | 1 | no | — |
| 362 | C4 | — | 3 | 1 | no | — |
| 363 | C4 | — | 3 | 1 | no | — |
| 364 | C4 | — | 5 | 2 | no | — |
| 365 | C4 | — | 6 | 1 | no | — |
| 366 | C4 | — | 10 | 1 | no | — |
| 367 | C4 | — | 12 | 1 | no | — |
| 368 | C4 | — | 30 | 1 | no | — |
| 369 | C4 | — | 30 | 1 | no | — |
| 370 | C4 | — | 60 | 1 | no | — |
| 371 | C4 | — | 60 | 1 | no | — |
| 372 | C3 | — | 4 | 1 | no | Sylow |
| 373 | C2 | — | 24 | 1 | no | — |
| 374 | C2 | #11756746 | 1 | 1 | yes | characteristic |
| 375 | C2 | #11756766 | 1 | 1 | yes | characteristic |
| 376 | C2 | D5×#985 | 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. C4×C5⋊#226 | C2 | semidirect |
| 6. #11751597 | C2 | semidirect |
| 7. Dic5×#226 | C2 | semidirect |
| 19. #65903 | D3 | semidirect |
| 356. C5 | #85419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65903⋊C3 | 2 |
| C4×C5⋊#226 | 2 |
| C5×#5395 | 2 |
| Dic5×GL(2,𝔽3) | 2 |
| #11751601 | 2 |
| #11751597 | 2 |
| Dic5×#226 | 2 |
| #10612311 | 3 |
| #91400 | 4 |
| #85419 | 5 |