Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
572 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #66283⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#91954 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751632 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11751628 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10610726 | — | 3 | 1 | no | maximal, Hall |
| 7 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | #4150⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 9 | D5×#41⋊C3 | — | 2 | 1 | no | — |
| 10 | C5⋊#994 | C22 | 1 | 1 | yes | characteristic |
| 11 | #4147⋊C3 | — | 2 | 1 | no | — |
| 12 | #91954 | — | 2 | 1 | no | — |
| 13 | #91954 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×C5⋊#226 | — | 2 | 1 | no | — |
| 15 | #91313 | — | 4 | 1 | no | maximal |
| 16 | C5×GU(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 17 | #85542 | — | 5 | 1 | no | maximal, Hall |
| 18 | #66283 | D3 | 1 | 1 | yes | characteristic |
| 19 | C2×#4097 | — | 3 | 1 | no | — |
| 20 | C2×#4055 | — | 3 | 1 | no | — |
| 21 | #65860 | — | 3 | 1 | no | — |
| 22 | C5×#421 | — | 3 | 1 | no | — |
| 23 | #65421 | — | 3 | 1 | no | — |
| 24 | #65294 | — | 3 | 1 | no | — |
| 25 | #65115 | — | 3 | 2 | no | — |
| 26 | #65115 | — | 3 | 2 | no | — |
| 27 | #65114 | — | 3 | 2 | no | — |
| 28 | #65114 | — | 3 | 2 | no | — |
| 29 | C2×Dic30 | — | 4 | 1 | no | — |
| 30 | C3×#709 | — | 4 | 1 | no | — |
| 31 | C5×#41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 32 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 33 | C2×C5×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 34 | D5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 35 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 36 | C5⋊#226 | — | 2 | 2 | no | — |
| 37 | C5×#208 | — | 4 | 1 | no | — |
| 38 | #6662 | — | 4 | 2 | no | — |
| 39 | #6657 | — | 4 | 2 | no | — |
| 40 | #5945 | — | 5 | 1 | no | — |
| 41 | C2×#984 | — | 5 | 1 | no | — |
| 42 | #5430 | — | 5 | 2 | no | — |
| 43 | #5428 | — | 5 | 2 | no | — |
| 44 | #5423 | D5 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×C5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 46 | #4150 | — | 3 | 1 | no | — |
| 47 | #4150 | C2×D3 | 1 | 1 | yes | characteristic |
| 48 | #4149 | — | 3 | 1 | no | — |
| 49 | #4149 | C2×D3 | 1 | 1 | yes | characteristic |
| 50 | D5×#41 | — | 2 | 1 | no | — |
| 51 | D5×#41 | — | 6 | 1 | no | — |
| 52 | #4147 | — | 2 | 1 | no | — |
| 53 | #4144 | — | 6 | 1 | no | — |
| 54 | C2×#709 | — | 3 | 1 | no | — |
| 55 | C2×#709 | — | 3 | 1 | no | — |
| 56 | C22×Dic10 | — | 3 | 1 | no | — |
| 57 | C2×C5×M16 | — | 3 | 1 | no | — |
| 58 | C5×#117 | — | 3 | 1 | no | — |
| 59 | #4097 | — | 3 | 2 | no | — |
| 60 | #4097 | — | 3 | 2 | no | — |
| 61 | #4097 | — | 6 | 1 | no | — |
| 62 | #4097 | — | 6 | 1 | no | — |
| 63 | C2×#689 | — | 6 | 1 | no | — |
| 64 | C2×#687 | — | 6 | 1 | no | — |
| 65 | C2×#681 | — | 3 | 1 | no | — |
| 66 | #4055 | — | 3 | 2 | no | — |
| 67 | #4055 | — | 3 | 2 | no | — |
| 68 | #4055 | — | 6 | 1 | no | — |
| 69 | #4055 | — | 6 | 1 | no | — |
| 70 | C2×Dic20 | — | 6 | 1 | no | — |
| 71 | C2×#677 | — | 6 | 1 | no | — |
| 72 | #4043 | — | 6 | 2 | no | — |
| 73 | #4032 | — | 6 | 2 | no | — |
| 74 | #4021 | — | 3 | 2 | no | — |
| 75 | #4015 | — | 3 | 2 | no | — |
| 76 | C5×#104 | — | 3 | 2 | no | — |
| 77 | C5×#104 | — | 3 | 2 | no | — |
| 78 | #3956 | — | 3 | 2 | no | — |
| 79 | #3955 | — | 3 | 2 | no | — |
| 80 | #3937 | — | 3 | 2 | no | — |
| 81 | #3937 | — | 3 | 2 | no | — |
| 82 | #3022 | — | 15 | 1 | no | Sylow |
| 83 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 84 | C2×Dic15 | — | 8 | 1 | no | — |
| 85 | Dic30 | — | 4 | 2 | no | — |
| 86 | Dic30 | — | 8 | 1 | no | — |
| 87 | C3×C22⋊D5 | — | 8 | 1 | no | — |
| 88 | C3×D20 | — | 4 | 1 | no | — |
| 89 | C3×C4×D5 | — | 8 | 1 | no | — |
| 90 | C3×Dic10 | — | 4 | 1 | no | — |
| 91 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C5×C3⋊C8 | — | 4 | 2 | no | — |
| 93 | 2−1+4⋊C3 | — | 5 | 1 | no | — |
| 94 | 2−1+4⋊C3 | — | 10 | 1 | no | — |
| 95 | #994 | — | 5 | 1 | no | — |
| 96 | C2×#41⋊C3 | — | 10 | 1 | no | — |
| 97 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 98 | #984 | — | 5 | 2 | no | — |
| 99 | #984 | — | 10 | 1 | no | — |
| 100 | C2×#226 | — | 10 | 1 | no | — |
| 101 | #951 | — | 20 | 1 | no | — |
| 102 | GU(2,𝔽3) | C2×D5 | 1 | 2 | yes | complemented |
| 103 | C5×#41 | — | 3 | 1 | no | — |
| 104 | C5×#41 | — | 3 | 1 | no | — |
| 105 | C5×#41 | #67 | 1 | 1 | yes | characteristic |
| 106 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×C5×Q8 | #67 | 1 | 1 | yes | characteristic |
| 108 | C2×C5×D4 | — | 3 | 1 | no | — |
| 109 | C22×C4×C5 | — | 3 | 1 | no | — |
| 110 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 111 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 112 | C22×Dic5 | — | 6 | 1 | no | — |
| 113 | #713 | — | 2 | 1 | no | — |
| 114 | #713 | — | 6 | 1 | no | — |
| 115 | Q8×D5 | — | 2 | 1 | no | — |
| 116 | Q8×D5 | — | 6 | 1 | no | — |
| 117 | #711 | — | 6 | 1 | no | — |
| 118 | #711 | — | 6 | 2 | no | — |
| 119 | #711 | — | 6 | 1 | no | — |
| 120 | D4×D5 | — | 6 | 1 | no | — |
| 121 | D4×D5 | — | 6 | 2 | no | — |
| 122 | D4×D5 | — | 6 | 1 | no | — |
| 123 | #709 | — | 3 | 1 | no | — |
| 124 | #709 | — | 3 | 1 | no | — |
| 125 | #709 | — | 3 | 1 | no | — |
| 126 | #709 | — | 6 | 1 | no | — |
| 127 | #709 | — | 6 | 1 | no | — |
| 128 | #709 | — | 6 | 1 | no | — |
| 129 | #709 | — | 6 | 1 | no | — |
| 130 | #709 | — | 6 | 1 | no | — |
| 131 | #709 | S4 | 1 | 1 | yes | characteristic |
| 132 | C2×D20 | — | 3 | 1 | no | — |
| 133 | C2×D20 | — | 3 | 1 | no | — |
| 134 | C2×C4×D5 | — | 3 | 2 | no | — |
| 135 | C2×C4×D5 | — | 6 | 1 | no | — |
| 136 | C2×Dic10 | — | 3 | 1 | no | — |
| 137 | C2×Dic10 | — | 3 | 1 | no | — |
| 138 | C2×Dic10 | — | 3 | 2 | no | — |
| 139 | C2×Dic10 | — | 6 | 1 | no | — |
| 140 | C2×Dic10 | — | 6 | 1 | no | — |
| 141 | C2×Dic10 | — | 6 | 1 | no | — |
| 142 | C2×Dic10 | — | 6 | 1 | no | — |
| 143 | C2×Dic10 | — | 6 | 1 | no | — |
| 144 | C5×M16 | — | 3 | 2 | no | — |
| 145 | C5×M16 | — | 6 | 1 | no | — |
| 146 | C2×C5×C8 | — | 6 | 1 | no | — |
| 147 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 148 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 149 | C42×C5 | — | 3 | 2 | no | — |
| 150 | #689 | — | 6 | 2 | no | — |
| 151 | #689 | — | 6 | 2 | no | — |
| 152 | #687 | — | 6 | 2 | no | — |
| 153 | #687 | — | 6 | 2 | no | — |
| 154 | #685 | — | 6 | 4 | no | — |
| 155 | C4⋊Dic5 | — | 6 | 4 | no | — |
| 156 | #681 | — | 3 | 2 | no | — |
| 157 | #681 | — | 6 | 1 | no | — |
| 158 | C2×#168 | — | 6 | 1 | no | — |
| 159 | Dic20 | — | 6 | 2 | no | — |
| 160 | Dic20 | — | 6 | 2 | no | — |
| 161 | #677 | — | 6 | 2 | no | — |
| 162 | #677 | — | 6 | 2 | no | — |
| 163 | #585 | — | 5 | 1 | no | — |
| 164 | C2×#137 | — | 15 | 1 | no | — |
| 165 | C2×#137 | — | 15 | 1 | no | — |
| 166 | #536 | — | 15 | 1 | no | — |
| 167 | #456 | — | 15 | 2 | no | — |
| 168 | #456 | — | 15 | 2 | no | — |
| 169 | #455 | — | 15 | 2 | no | — |
| 170 | #455 | — | 15 | 2 | no | — |
| 171 | #421 | — | 3 | 1 | no | — |
| 172 | #421 | — | 15 | 1 | no | — |
| 173 | #413 | — | 15 | 1 | no | — |
| 174 | C22×C3×C5 | — | 4 | 1 | no | — |
| 175 | C2×C3×D5 | — | 8 | 1 | no | — |
| 176 | C3×C4×C5 | — | 4 | 1 | no | — |
| 177 | C3×C4×C5 | — | 4 | 1 | no | — |
| 178 | Dic15 | — | 8 | 2 | no | — |
| 179 | C3×Dic5 | — | 8 | 1 | no | — |
| 180 | C3×#41 | — | 20 | 1 | no | — |
| 181 | C2×Dic6 | — | 20 | 1 | no | — |
| 182 | #41⋊C3 | — | 10 | 1 | no | — |
| 183 | #41⋊C3 | D20 | 1 | 1 | yes | characteristic |
| 184 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 185 | C2×SL(2,𝔽3) | — | 10 | 1 | no | — |
| 186 | C2×SL(2,𝔽3) | D20 | 1 | 1 | yes | characteristic |
| 187 | #226 | — | 10 | 2 | no | — |
| 188 | #216 | — | 20 | 2 | no | — |
| 189 | #214 | — | 20 | 2 | no | — |
| 190 | #208 | — | 4 | 1 | no | — |
| 191 | C23×C5 | — | 3 | 1 | no | — |
| 192 | C22×D5 | — | 3 | 2 | no | — |
| 193 | C22×D5 | — | 6 | 1 | no | — |
| 194 | C5×Q8 | — | 3 | 1 | no | — |
| 195 | C5×Q8 | C2×#67 | 1 | 1 | yes | characteristic |
| 196 | C5×D4 | — | 3 | 1 | no | — |
| 197 | C5×D4 | — | 3 | 1 | no | — |
| 198 | C5×D4 | — | 6 | 1 | no | — |
| 199 | C2×C4×C5 | — | 3 | 1 | no | — |
| 200 | C2×C4×C5 | — | 3 | 1 | no | — |
| 201 | C2×C4×C5 | — | 3 | 1 | no | — |
| 202 | C2×C4×C5 | — | 3 | 1 | no | — |
| 203 | C2×C4×C5 | — | 3 | 1 | no | — |
| 204 | C2×C4×C5 | — | 6 | 2 | no | — |
| 205 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 206 | C22⋊D5 | — | 2 | 1 | no | — |
| 207 | C22⋊D5 | — | 6 | 1 | no | — |
| 208 | C22⋊D5 | — | 6 | 1 | no | — |
| 209 | C22⋊D5 | — | 6 | 2 | no | — |
| 210 | C22⋊D5 | — | 6 | 1 | no | — |
| 211 | C2×Dic5 | — | 3 | 2 | no | — |
| 212 | C2×Dic5 | — | 6 | 1 | no | — |
| 213 | C2×Dic5 | — | 6 | 2 | no | — |
| 214 | C2×Dic5 | — | 12 | 1 | no | — |
| 215 | C2×Dic5 | — | 12 | 1 | no | — |
| 216 | D20 | — | 3 | 1 | no | — |
| 217 | D20 | — | 6 | 1 | no | — |
| 218 | D20 | — | 6 | 1 | no | — |
| 219 | D20 | C2×S4 | 1 | 1 | yes | characteristic |
| 220 | C4×D5 | — | 2 | 1 | no | — |
| 221 | C4×D5 | — | 6 | 1 | no | — |
| 222 | C4×D5 | — | 6 | 1 | no | — |
| 223 | C4×D5 | — | 6 | 2 | no | — |
| 224 | C4×D5 | — | 6 | 1 | no | — |
| 225 | Dic10 | — | 3 | 1 | no | — |
| 226 | Dic10 | — | 6 | 1 | no | — |
| 227 | Dic10 | — | 6 | 1 | no | — |
| 228 | Dic10 | — | 6 | 2 | no | — |
| 229 | Dic10 | — | 6 | 2 | no | — |
| 230 | Dic10 | — | 12 | 1 | no | — |
| 231 | Dic10 | — | 12 | 1 | no | — |
| 232 | Dic10 | C2×S4 | 1 | 1 | yes | characteristic |
| 233 | C5×C8 | — | 6 | 2 | no | — |
| 234 | #168 | — | 6 | 2 | no | — |
| 235 | 2−1+4 | — | 5 | 1 | no | — |
| 236 | 2−1+4 | — | 10 | 1 | no | — |
| 237 | 2−1+4 | — | 15 | 1 | no | — |
| 238 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 239 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 240 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 241 | C2×#41 | — | 10 | 1 | no | — |
| 242 | C2×#41 | — | 15 | 1 | no | — |
| 243 | C2×#41 | — | 15 | 1 | no | — |
| 244 | C2×#41 | — | 30 | 1 | no | — |
| 245 | C2×#41 | D3×D5 | 1 | 1 | yes | characteristic |
| 246 | C22×Q8 | — | 15 | 1 | no | — |
| 247 | #137 | — | 15 | 2 | no | — |
| 248 | #137 | — | 15 | 2 | no | — |
| 249 | #137 | — | 15 | 2 | no | — |
| 250 | #137 | — | 15 | 2 | no | — |
| 251 | #137 | — | 30 | 1 | no | — |
| 252 | #137 | — | 30 | 1 | no | — |
| 253 | #137 | — | 30 | 1 | no | — |
| 254 | #137 | — | 30 | 1 | no | — |
| 255 | C2×Q16 | — | 30 | 1 | no | — |
| 256 | C2×Q16 | — | 30 | 1 | no | — |
| 257 | C2×SD16 | — | 30 | 1 | no | — |
| 258 | C2×SD16 | — | 30 | 1 | no | — |
| 259 | C2×M16 | — | 3 | 1 | no | — |
| 260 | C2×M16 | — | 15 | 1 | no | — |
| 261 | C4⋊Q8 | — | 15 | 2 | no | — |
| 262 | #124 | — | 15 | 2 | no | — |
| 263 | #123 | — | 30 | 2 | no | — |
| 264 | C22⋊Q8 | — | 30 | 2 | no | — |
| 265 | #117 | — | 3 | 1 | no | — |
| 266 | #104 | — | 3 | 2 | no | — |
| 267 | #104 | — | 3 | 2 | no | — |
| 268 | #104 | — | 15 | 2 | no | — |
| 269 | #104 | — | 15 | 2 | no | — |
| 270 | #101 | — | 15 | 2 | no | — |
| 271 | #100 | — | 15 | 2 | no | — |
| 272 | C2×C3×C5 | — | 4 | 1 | no | — |
| 273 | C2×C3×C5 | — | 8 | 1 | no | — |
| 274 | C3×D5 | — | 16 | 1 | no | — |
| 275 | C3×Q8 | — | 20 | 1 | no | — |
| 276 | C3×D4 | — | 20 | 1 | no | — |
| 277 | C3×D4 | — | 40 | 1 | no | — |
| 278 | C2×C3×C4 | — | 4 | 1 | no | — |
| 279 | C2×C3×C4 | — | 40 | 1 | no | — |
| 280 | C2×Dic3 | — | 40 | 1 | no | — |
| 281 | Dic6 | — | 20 | 2 | no | — |
| 282 | Dic6 | — | 40 | 1 | no | — |
| 283 | SL(2,𝔽3) | C2×D20 | 1 | 1 | yes | characteristic |
| 284 | C3⋊C8 | — | 4 | 2 | no | — |
| 285 | C22×C5 | — | 3 | 1 | no | — |
| 286 | C22×C5 | — | 3 | 1 | no | — |
| 287 | C22×C5 | — | 12 | 1 | no | — |
| 288 | C22×C5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 289 | C2×D5 | — | 2 | 1 | no | — |
| 290 | C2×D5 | — | 6 | 1 | no | — |
| 291 | C2×D5 | — | 12 | 2 | no | — |
| 292 | C2×D5 | — | 24 | 1 | no | — |
| 293 | C4×C5 | — | 3 | 1 | no | — |
| 294 | C4×C5 | — | 3 | 1 | no | — |
| 295 | C4×C5 | — | 12 | 2 | no | — |
| 296 | C4×C5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 297 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 298 | Dic5 | — | 2 | 1 | no | — |
| 299 | Dic5 | — | 6 | 1 | no | — |
| 300 | Dic5 | — | 12 | 2 | no | — |
| 301 | #41 | — | 3 | 1 | no | — |
| 302 | #41 | — | 3 | 1 | no | — |
| 303 | #41 | — | 5 | 1 | no | — |
| 304 | #41 | — | 10 | 1 | no | — |
| 305 | #41 | — | 15 | 1 | no | — |
| 306 | #41 | — | 15 | 1 | no | — |
| 307 | #41 | — | 15 | 1 | no | — |
| 308 | #41 | — | 30 | 1 | no | — |
| 309 | #41 | — | 30 | 1 | no | — |
| 310 | #41 | — | 30 | 1 | no | — |
| 311 | #41 | — | 30 | 1 | no | — |
| 312 | #41 | — | 30 | 1 | no | — |
| 313 | #41 | — | 30 | 1 | no | — |
| 314 | #41 | — | 30 | 2 | no | — |
| 315 | #41 | — | 30 | 1 | no | — |
| 316 | #41 | — | 30 | 1 | no | — |
| 317 | #41 | #1202 | 1 | 1 | yes | characteristic |
| 318 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 319 | C2×Q8 | — | 10 | 1 | no | — |
| 320 | C2×Q8 | — | 15 | 1 | no | — |
| 321 | C2×Q8 | — | 15 | 1 | no | — |
| 322 | C2×Q8 | — | 15 | 2 | no | — |
| 323 | C2×Q8 | — | 30 | 1 | no | — |
| 324 | C2×Q8 | — | 30 | 1 | no | — |
| 325 | C2×Q8 | — | 30 | 1 | no | — |
| 326 | C2×Q8 | — | 30 | 1 | no | — |
| 327 | C2×Q8 | — | 30 | 1 | no | — |
| 328 | C2×Q8 | — | 30 | 1 | no | — |
| 329 | C2×Q8 | #1202 | 1 | 1 | yes | characteristic |
| 330 | C2×D4 | — | 3 | 1 | no | — |
| 331 | C2×D4 | — | 15 | 1 | no | — |
| 332 | C2×D4 | — | 15 | 1 | no | — |
| 333 | C2×D4 | — | 15 | 2 | no | — |
| 334 | C2×D4 | — | 30 | 1 | no | — |
| 335 | C2×D4 | — | 30 | 1 | no | — |
| 336 | C2×D4 | — | 30 | 2 | no | — |
| 337 | C2×D4 | — | 30 | 1 | no | — |
| 338 | C22×C4 | — | 3 | 1 | no | — |
| 339 | C22×C4 | — | 15 | 2 | no | — |
| 340 | C22×C4 | — | 30 | 1 | no | — |
| 341 | C22×C4 | — | 30 | 1 | no | — |
| 342 | Q16 | — | 30 | 2 | no | — |
| 343 | Q16 | — | 30 | 2 | no | — |
| 344 | Q16 | — | 30 | 2 | no | — |
| 345 | Q16 | — | 30 | 2 | no | — |
| 346 | SD16 | — | 30 | 2 | no | — |
| 347 | SD16 | — | 30 | 2 | no | — |
| 348 | SD16 | — | 30 | 2 | no | — |
| 349 | SD16 | — | 30 | 2 | no | — |
| 350 | M16 | — | 3 | 2 | no | — |
| 351 | M16 | — | 6 | 1 | no | — |
| 352 | M16 | — | 15 | 2 | no | — |
| 353 | M16 | — | 30 | 1 | no | — |
| 354 | C2×C8 | — | 6 | 1 | no | — |
| 355 | C2×C8 | — | 30 | 1 | no | — |
| 356 | C4⋊C4 | — | 6 | 1 | no | — |
| 357 | C4⋊C4 | — | 30 | 4 | no | — |
| 358 | C22⋊C4 | — | 6 | 1 | no | — |
| 359 | C22⋊C4 | — | 30 | 4 | no | — |
| 360 | C42 | — | 3 | 2 | no | — |
| 361 | C3×C5 | — | 4 | 1 | no | Hall |
| 362 | C22×C3 | — | 4 | 1 | no | — |
| 363 | C22×C3 | — | 40 | 1 | no | — |
| 364 | C3×C4 | — | 4 | 1 | no | — |
| 365 | C3×C4 | — | 4 | 1 | no | — |
| 366 | C3×C4 | — | 40 | 1 | no | — |
| 367 | Dic3 | — | 40 | 2 | no | — |
| 368 | C2×C5 | — | 2 | 1 | no | — |
| 369 | C2×C5 | — | 6 | 1 | no | — |
| 370 | C2×C5 | — | 6 | 1 | no | — |
| 371 | C2×C5 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 372 | D5 | — | 4 | 1 | no | — |
| 373 | D5 | — | 12 | 1 | no | — |
| 374 | C23 | — | 3 | 1 | no | — |
| 375 | C23 | — | 15 | 2 | no | — |
| 376 | C23 | — | 30 | 1 | no | — |
| 377 | Q8 | — | 3 | 1 | no | — |
| 378 | Q8 | — | 5 | 1 | no | — |
| 379 | Q8 | — | 15 | 1 | no | — |
| 380 | Q8 | — | 30 | 1 | no | — |
| 381 | Q8 | — | 30 | 1 | no | — |
| 382 | Q8 | — | 30 | 2 | no | — |
| 383 | Q8 | — | 30 | 2 | no | — |
| 384 | Q8 | — | 60 | 1 | no | — |
| 385 | Q8 | — | 60 | 1 | no | — |
| 386 | Q8 | C2×#1202 | 1 | 1 | yes | characteristic |
| 387 | D4 | — | 3 | 1 | no | — |
| 388 | D4 | — | 3 | 1 | no | — |
| 389 | D4 | — | 5 | 1 | no | — |
| 390 | D4 | — | 6 | 1 | no | — |
| 391 | D4 | — | 10 | 1 | no | — |
| 392 | D4 | — | 15 | 1 | no | — |
| 393 | D4 | — | 30 | 1 | no | — |
| 394 | D4 | — | 30 | 1 | no | — |
| 395 | D4 | — | 30 | 1 | no | — |
| 396 | D4 | — | 30 | 1 | no | — |
| 397 | D4 | — | 30 | 2 | no | — |
| 398 | D4 | — | 30 | 1 | no | — |
| 399 | C2×C4 | — | 3 | 1 | no | — |
| 400 | C2×C4 | — | 3 | 1 | no | — |
| 401 | C2×C4 | — | 3 | 1 | no | — |
| 402 | C2×C4 | — | 3 | 1 | no | — |
| 403 | C2×C4 | — | 3 | 1 | no | — |
| 404 | C2×C4 | — | 6 | 2 | no | — |
| 405 | C2×C4 | — | 10 | 1 | no | — |
| 406 | C2×C4 | — | 15 | 2 | no | — |
| 407 | C2×C4 | — | 30 | 1 | no | — |
| 408 | C2×C4 | — | 30 | 1 | no | — |
| 409 | C2×C4 | — | 30 | 2 | no | — |
| 410 | C2×C4 | — | 30 | 1 | no | — |
| 411 | C2×C4 | — | 30 | 1 | no | — |
| 412 | C2×C4 | — | 30 | 2 | no | — |
| 413 | C2×C4 | — | 60 | 1 | no | — |
| 414 | C2×C4 | — | 60 | 1 | no | — |
| 415 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 416 | C8 | — | 6 | 2 | no | — |
| 417 | C8 | — | 30 | 2 | no | — |
| 418 | C2×C3 | — | 4 | 1 | no | — |
| 419 | C2×C3 | — | 8 | 1 | no | — |
| 420 | C2×C3 | — | 80 | 1 | no | — |
| 421 | C5 | #85542 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 422 | C22 | — | 3 | 1 | no | — |
| 423 | C22 | — | 3 | 1 | no | — |
| 424 | C22 | — | 10 | 1 | no | — |
| 425 | C22 | — | 12 | 1 | no | — |
| 426 | C22 | — | 30 | 1 | no | — |
| 427 | C22 | — | 60 | 2 | no | — |
| 428 | C22 | — | 120 | 1 | no | — |
| 429 | C22 | #91905 | 1 | 1 | yes | characteristic |
| 430 | C4 | — | 3 | 1 | no | — |
| 431 | C4 | — | 3 | 1 | no | — |
| 432 | C4 | — | 10 | 1 | no | — |
| 433 | C4 | — | 12 | 2 | no | — |
| 434 | C4 | — | 30 | 1 | no | — |
| 435 | C4 | — | 60 | 2 | no | — |
| 436 | C4 | #91905 | 1 | 1 | yes | characteristic |
| 437 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 438 | C3 | — | 4 | 1 | no | Sylow |
| 439 | C2 | — | 2 | 1 | no | — |
| 440 | C2 | — | 6 | 1 | no | — |
| 441 | C2 | — | 6 | 1 | no | — |
| 442 | C2 | — | 20 | 1 | no | — |
| 443 | C2 | — | 60 | 1 | no | — |
| 444 | C2 | C2×#91905 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#91954 | C2 | semidirect |
| 3. C5×#5423 | C2 | semidirect |
| 4. #11751632 | C2 | semidirect |
| 5. #11751628 | C2 | semidirect |
| 13. #91954 | C22 | semidirect |
| 16. C5×GU(2,𝔽3) | C22 | semidirect |
| 44. #5423 | D5 | semidirect |
| 102. GU(2,𝔽3) | C2×D5 | semidirect |
| 421. C5 | #85542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66283⋊C3 | 2 |
| C2×#91954 | 2 |
| C5×#5423 | 2 |
| #11751632 | 2 |
| #11751628 | 2 |
| #10610726 | 3 |
| #91313 | 4 |
| #85542 | 5 |