Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
516 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #11752556 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11751863 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11746724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#64853 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11746556 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10604640 | — | 3 | 1 | no | maximal, Hall |
| 7 | C2×#6766 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C2×#6766 | C22 | 1 | 1 | yes | characteristic |
| 9 | #91923 | — | 2 | 2 | no | — |
| 10 | C42×D15 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#869 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×#4020 | C22 | 1 | 1 | yes | characteristic |
| 13 | #91465 | — | 2 | 2 | no | — |
| 14 | #91434 | — | 2 | 2 | no | — |
| 15 | #91368 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #91368 | C22 | 1 | 1 | yes | characteristic |
| 17 | #91228 | C22 | 1 | 2 | yes | — |
| 18 | C3×#3999 | C22 | 1 | 2 | yes | — |
| 19 | #91173 | — | 2 | 2 | no | — |
| 20 | #69151 | — | 5 | 1 | no | maximal, Hall |
| 21 | #66059 | — | 3 | 1 | no | — |
| 22 | #65785 | — | 3 | 2 | no | — |
| 23 | #64928 | — | 3 | 2 | no | — |
| 24 | #64853 | — | 3 | 1 | no | — |
| 25 | #64853 | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C4×D15 | — | 2 | 1 | no | — |
| 27 | C2×C4×D15 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×C5×Dic6 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×C5×Dic6 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C3×D20 | — | 2 | 2 | no | — |
| 31 | C2×C3×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×C3×D20 | C23 | 1 | 1 | yes | characteristic |
| 33 | C2×#1202 | — | 2 | 1 | no | — |
| 34 | C2×#1202 | D4 | 1 | 2 | yes | — |
| 35 | C2×D5×Dic3 | — | 2 | 1 | no | — |
| 36 | C2×D5×Dic3 | D4 | 1 | 2 | yes | — |
| 37 | #6766 | — | 4 | 1 | no | — |
| 38 | #6766 | — | 4 | 1 | no | — |
| 39 | #6766 | — | 4 | 1 | no | — |
| 40 | #6766 | — | 4 | 1 | no | — |
| 41 | #6763 | — | 2 | 2 | no | — |
| 42 | C3×C22⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 43 | Dic3⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 44 | Dic3×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 45 | C3×C42×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C4×Dic15 | — | 2 | 1 | no | — |
| 47 | C4×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C5×C4⋊Dic3 | — | 2 | 2 | no | — |
| 49 | #6665 | — | 2 | 2 | no | — |
| 50 | #6665 | — | 2 | 2 | no | — |
| 51 | #5716 | — | 5 | 1 | no | — |
| 52 | #4740 | — | 5 | 2 | no | — |
| 53 | C3×#353 | — | 5 | 1 | no | — |
| 54 | #4545 | — | 5 | 1 | no | — |
| 55 | #4473 | — | 5 | 2 | no | — |
| 56 | C2×#713 | — | 3 | 1 | no | — |
| 57 | C2×#713 | — | 3 | 1 | no | — |
| 58 | #4130 | — | 6 | 2 | no | — |
| 59 | C5×C4⋊Q8 | — | 3 | 1 | no | — |
| 60 | #4093 | — | 3 | 1 | no | — |
| 61 | #4093 | — | 3 | 1 | no | — |
| 62 | #4041 | — | 6 | 2 | no | — |
| 63 | #4039 | — | 6 | 2 | no | — |
| 64 | #4020 | C2×D3 | 1 | 1 | yes | characteristic |
| 65 | C42×D5 | — | 3 | 1 | no | — |
| 66 | #3999 | — | 3 | 2 | no | — |
| 67 | #3999 | — | 6 | 2 | no | — |
| 68 | #3999 | C2×D3 | 1 | 2 | yes | — |
| 69 | #2126 | — | 15 | 1 | no | Sylow |
| 70 | C22×D15 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 71 | C22×C3×D5 | — | 2 | 1 | no | — |
| 72 | C22×C3×D5 | C2×D4 | 1 | 2 | yes | — |
| 73 | C2×ΓL(1,𝔽16) | — | 4 | 2 | no | — |
| 74 | C2×C3×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 75 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 76 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | C2×Dic15 | — | 2 | 1 | no | — |
| 78 | C2×Dic15 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 79 | C4×D15 | — | 2 | 1 | no | — |
| 80 | C4×D15 | — | 2 | 1 | no | — |
| 81 | C4×D15 | — | 4 | 2 | no | — |
| 82 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 83 | C2×C5×Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 84 | C5×Dic6 | — | 4 | 1 | no | — |
| 85 | C5×Dic6 | — | 4 | 1 | no | — |
| 86 | C3×D20 | — | 4 | 1 | no | — |
| 87 | C3×D20 | — | 4 | 4 | no | — |
| 88 | C3×D20 | — | 4 | 1 | no | — |
| 89 | #1202 | — | 4 | 2 | no | — |
| 90 | #1202 | — | 4 | 2 | no | — |
| 91 | D5×Dic3 | — | 2 | 2 | no | — |
| 92 | D5×Dic3 | — | 2 | 2 | no | — |
| 93 | D5×Dic3 | — | 4 | 1 | no | — |
| 94 | D5×Dic3 | — | 4 | 1 | no | — |
| 95 | C2×#237 | — | 5 | 1 | no | — |
| 96 | C2×#237 | — | 5 | 1 | no | — |
| 97 | C3×#127 | — | 5 | 1 | no | — |
| 98 | #938 | — | 10 | 2 | no | — |
| 99 | #936 | — | 5 | 1 | no | — |
| 100 | #936 | — | 5 | 1 | no | — |
| 101 | D4×Dic3 | — | 10 | 2 | no | — |
| 102 | #877 | — | 10 | 2 | no | — |
| 103 | C42×D3 | — | 5 | 1 | no | — |
| 104 | #869 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 105 | C3×#99 | — | 5 | 2 | no | — |
| 106 | #834 | — | 5 | 2 | no | — |
| 107 | #806 | — | 10 | 2 | no | — |
| 108 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 109 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 110 | #713 | — | 12 | 1 | no | — |
| 111 | #713 | — | 12 | 1 | no | — |
| 112 | #713 | — | 12 | 1 | no | — |
| 113 | #713 | — | 12 | 1 | no | — |
| 114 | C2×D20 | — | 2 | 2 | no | — |
| 115 | C2×D20 | — | 3 | 2 | no | — |
| 116 | C2×D20 | — | 6 | 1 | no | — |
| 117 | C2×D20 | C4×D3 | 1 | 1 | yes | characteristic |
| 118 | C2×D20 | C22×D3 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×D5 | — | 3 | 2 | no | — |
| 120 | C2×C4×D5 | — | 3 | 1 | no | — |
| 121 | C2×C4×D5 | — | 6 | 1 | no | — |
| 122 | C2×C4×D5 | — | 6 | 1 | no | — |
| 123 | C22⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 124 | C22⋊AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 125 | C4⋊AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 126 | C4×AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 127 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 128 | C42×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 129 | #685 | — | 6 | 2 | no | — |
| 130 | #685 | — | 6 | 2 | no | — |
| 131 | C4×Dic5 | — | 3 | 1 | no | — |
| 132 | C4×Dic5 | — | 6 | 1 | no | — |
| 133 | #532 | — | 15 | 1 | no | — |
| 134 | #410 | — | 15 | 2 | no | — |
| 135 | #354 | — | 15 | 2 | no | — |
| 136 | #353 | — | 5 | 1 | no | — |
| 137 | #353 | — | 15 | 1 | no | — |
| 138 | C22×C3×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×D15 | — | 2 | 1 | no | — |
| 140 | C2×D15 | — | 4 | 1 | no | — |
| 141 | C2×C3×D5 | — | 2 | 2 | no | — |
| 142 | C2×C3×D5 | — | 4 | 2 | no | — |
| 143 | C2×C3×D5 | — | 4 | 2 | no | — |
| 144 | C2×C3×D5 | — | 4 | 1 | no | — |
| 145 | ΓL(1,𝔽16) | — | 8 | 2 | no | — |
| 146 | C3×AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 147 | C3×C4×C5 | — | 2 | 2 | no | — |
| 148 | C3×C4×C5 | — | 2 | 1 | no | — |
| 149 | Dic15 | — | 4 | 1 | no | — |
| 150 | Dic15 | #99 | 1 | 1 | yes | characteristic |
| 151 | Dic15 | #99 | 1 | 1 | yes | characteristic |
| 152 | C5×Dic3 | — | 2 | 2 | no | — |
| 153 | C5×Dic3 | — | 4 | 1 | no | — |
| 154 | C2×C3×D4 | — | 5 | 1 | no | — |
| 155 | C2×C3×D4 | — | 5 | 1 | no | — |
| 156 | C2×C3×D4 | — | 10 | 2 | no | — |
| 157 | C2×#67 | — | 5 | 2 | no | — |
| 158 | C2×#67 | — | 10 | 1 | no | — |
| 159 | C22×Dic3 | — | 5 | 2 | no | — |
| 160 | C22×Dic3 | — | 10 | 1 | no | — |
| 161 | #237 | — | 20 | 1 | no | — |
| 162 | #237 | — | 20 | 1 | no | — |
| 163 | #237 | — | 20 | 1 | no | — |
| 164 | #237 | — | 20 | 1 | no | — |
| 165 | C2×C4×D3 | — | 5 | 1 | no | — |
| 166 | C2×C4×D3 | — | 10 | 1 | no | — |
| 167 | C2×Dic6 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 168 | C2×Dic6 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 169 | C3×C22⋊C4 | — | 10 | 2 | no | — |
| 170 | C3×C42 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 171 | #217 | — | 10 | 2 | no | — |
| 172 | #217 | — | 10 | 2 | no | — |
| 173 | #217 | — | 10 | 2 | no | — |
| 174 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 175 | Dic3⋊C4 | — | 20 | 2 | no | — |
| 176 | C4×Dic3 | — | 5 | 1 | no | — |
| 177 | C4×Dic3 | — | 10 | 1 | no | — |
| 178 | C4×Dic3 | — | 20 | 2 | no | — |
| 179 | C22×D5 | — | 2 | 1 | no | — |
| 180 | C22×D5 | — | 3 | 1 | no | — |
| 181 | C22×D5 | D3×D4 | 1 | 2 | yes | — |
| 182 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 183 | C2×AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 184 | C5×Q8 | — | 12 | 1 | no | — |
| 185 | C5×Q8 | — | 12 | 1 | no | — |
| 186 | C2×C4×C5 | — | 2 | 1 | no | — |
| 187 | C2×C4×C5 | — | 3 | 2 | no | — |
| 188 | C2×C4×C5 | — | 6 | 1 | no | — |
| 189 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 190 | C2×Dic5 | — | 3 | 1 | no | — |
| 191 | C2×Dic5 | — | 6 | 1 | no | — |
| 192 | D20 | — | 4 | 1 | no | — |
| 193 | D20 | — | 4 | 1 | no | — |
| 194 | D20 | — | 4 | 4 | no | — |
| 195 | D20 | — | 12 | 2 | no | — |
| 196 | D20 | — | 12 | 2 | no | — |
| 197 | C4×D5 | — | 6 | 1 | no | — |
| 198 | C4×D5 | — | 6 | 1 | no | — |
| 199 | C4×D5 | — | 6 | 2 | no | — |
| 200 | C4×D5 | — | 6 | 2 | no | — |
| 201 | C4×D5 | — | 12 | 1 | no | — |
| 202 | C4×D5 | — | 12 | 1 | no | — |
| 203 | C4×D5 | — | 12 | 2 | no | — |
| 204 | C2×#41 | — | 15 | 1 | no | — |
| 205 | C2×#41 | — | 15 | 1 | no | — |
| 206 | C4⋊Q8 | — | 3 | 1 | no | — |
| 207 | #127 | — | 5 | 1 | no | — |
| 208 | #124 | — | 15 | 1 | no | — |
| 209 | #124 | — | 15 | 1 | no | — |
| 210 | #121 | — | 30 | 2 | no | — |
| 211 | C4×D4 | — | 30 | 2 | no | — |
| 212 | #117 | — | 30 | 2 | no | — |
| 213 | C2×C42 | — | 15 | 1 | no | — |
| 214 | #99 | — | 5 | 2 | no | — |
| 215 | #99 | — | 15 | 2 | no | — |
| 216 | #99 | — | 30 | 2 | no | — |
| 217 | C2×C3×C5 | — | 2 | 1 | no | — |
| 218 | C2×C3×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 219 | D15 | — | 4 | 1 | no | — |
| 220 | C3×D5 | — | 4 | 2 | no | — |
| 221 | C3×D5 | — | 8 | 1 | no | — |
| 222 | C23×C3 | — | 5 | 2 | no | — |
| 223 | C23×C3 | — | 10 | 1 | no | — |
| 224 | C22×D3 | — | 5 | 1 | no | — |
| 225 | C3×D4 | — | 20 | 1 | no | — |
| 226 | C3×D4 | — | 20 | 1 | no | — |
| 227 | C3×D4 | — | 20 | 4 | no | — |
| 228 | C2×C3×C4 | — | 2 | 1 | no | — |
| 229 | C2×C3×C4 | — | 20 | 2 | no | — |
| 230 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 231 | #67 | — | 20 | 2 | no | — |
| 232 | #67 | — | 20 | 2 | no | — |
| 233 | C2×Dic3 | — | 2 | 1 | no | — |
| 234 | C2×Dic3 | — | 5 | 1 | no | — |
| 235 | C2×Dic3 | — | 10 | 2 | no | — |
| 236 | C2×Dic3 | — | 10 | 2 | no | — |
| 237 | C2×Dic3 | — | 10 | 1 | no | — |
| 238 | C2×Dic3 | — | 20 | 1 | no | — |
| 239 | C2×Dic3 | — | 20 | 1 | no | — |
| 240 | C2×Dic3 | — | 20 | 2 | no | — |
| 241 | C2×Dic3 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 242 | C4×D3 | — | 10 | 1 | no | — |
| 243 | C4×D3 | — | 10 | 1 | no | — |
| 244 | C4×D3 | — | 20 | 2 | no | — |
| 245 | Dic6 | — | 4 | 1 | no | — |
| 246 | Dic6 | — | 4 | 1 | no | — |
| 247 | C22×C5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 248 | C2×D5 | — | 2 | 2 | no | — |
| 249 | C2×D5 | — | 4 | 2 | no | — |
| 250 | C2×D5 | — | 4 | 2 | no | — |
| 251 | C2×D5 | — | 4 | 1 | no | — |
| 252 | C2×D5 | — | 6 | 1 | no | — |
| 253 | C2×D5 | — | 12 | 1 | no | — |
| 254 | AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 255 | AGL(1,𝔽5) | — | 24 | 2 | no | — |
| 256 | C4×C5 | — | 2 | 2 | no | — |
| 257 | C4×C5 | — | 2 | 1 | no | — |
| 258 | C4×C5 | — | 6 | 2 | no | — |
| 259 | C4×C5 | — | 12 | 1 | no | — |
| 260 | Dic5 | — | 3 | 1 | no | — |
| 261 | Dic5 | — | 3 | 1 | no | — |
| 262 | Dic5 | — | 12 | 1 | no | — |
| 263 | #41 | — | 60 | 1 | no | — |
| 264 | #41 | — | 60 | 1 | no | — |
| 265 | #41 | — | 60 | 1 | no | — |
| 266 | #41 | — | 60 | 1 | no | — |
| 267 | C2×Q8 | — | 3 | 1 | no | — |
| 268 | C2×Q8 | — | 3 | 1 | no | — |
| 269 | C2×D4 | — | 5 | 1 | no | — |
| 270 | C2×D4 | — | 5 | 1 | no | — |
| 271 | C2×D4 | — | 10 | 2 | no | — |
| 272 | C2×D4 | — | 15 | 2 | no | — |
| 273 | C2×D4 | — | 30 | 1 | no | — |
| 274 | C22×C4 | — | 15 | 2 | no | — |
| 275 | C22×C4 | — | 15 | 1 | no | — |
| 276 | C22×C4 | — | 30 | 1 | no | — |
| 277 | C22×C4 | — | 30 | 1 | no | — |
| 278 | C4⋊C4 | — | 6 | 2 | no | — |
| 279 | C4⋊C4 | — | 60 | 2 | no | — |
| 280 | C22⋊C4 | — | 10 | 2 | no | — |
| 281 | C22⋊C4 | — | 30 | 2 | no | — |
| 282 | C22⋊C4 | — | 30 | 2 | no | — |
| 283 | C22⋊C4 | — | 30 | 2 | no | — |
| 284 | C42 | — | 15 | 1 | no | — |
| 285 | C42 | — | 30 | 1 | no | — |
| 286 | C42 | — | 60 | 2 | no | — |
| 287 | C42 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 288 | C3×C5 | #2126 | 1 | 1 | yes | characteristic, complemented, Hall |
| 289 | C22×C3 | — | 10 | 2 | no | — |
| 290 | C22×C3 | — | 20 | 2 | no | — |
| 291 | C22×C3 | — | 20 | 2 | no | — |
| 292 | C22×C3 | — | 20 | 1 | no | — |
| 293 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 294 | C2×D3 | — | 10 | 1 | no | — |
| 295 | C2×D3 | — | 20 | 1 | no | — |
| 296 | C3×C4 | — | 2 | 2 | no | — |
| 297 | C3×C4 | — | 2 | 1 | no | — |
| 298 | C3×C4 | — | 40 | 2 | no | — |
| 299 | Dic3 | — | 2 | 2 | no | — |
| 300 | Dic3 | — | 4 | 1 | no | — |
| 301 | Dic3 | — | 5 | 1 | no | — |
| 302 | Dic3 | — | 5 | 1 | no | — |
| 303 | Dic3 | — | 20 | 1 | no | — |
| 304 | Dic3 | — | 40 | 2 | no | — |
| 305 | C2×C5 | — | 2 | 1 | no | — |
| 306 | C2×C5 | D3×#99 | 1 | 1 | yes | characteristic |
| 307 | D5 | — | 4 | 2 | no | — |
| 308 | D5 | — | 8 | 1 | no | — |
| 309 | D5 | — | 12 | 1 | no | — |
| 310 | C23 | — | 5 | 2 | no | — |
| 311 | C23 | — | 10 | 1 | no | — |
| 312 | C23 | — | 15 | 1 | no | — |
| 313 | Q8 | — | 12 | 1 | no | — |
| 314 | Q8 | — | 12 | 1 | no | — |
| 315 | D4 | — | 20 | 1 | no | — |
| 316 | D4 | — | 20 | 1 | no | — |
| 317 | D4 | — | 20 | 4 | no | — |
| 318 | D4 | — | 60 | 2 | no | — |
| 319 | D4 | — | 60 | 2 | no | — |
| 320 | C2×C4 | — | 2 | 1 | no | — |
| 321 | C2×C4 | — | 3 | 2 | no | — |
| 322 | C2×C4 | — | 6 | 1 | no | — |
| 323 | C2×C4 | — | 15 | 1 | no | — |
| 324 | C2×C4 | — | 20 | 2 | no | — |
| 325 | C2×C4 | — | 30 | 1 | no | — |
| 326 | C2×C4 | — | 30 | 1 | no | — |
| 327 | C2×C4 | — | 30 | 2 | no | — |
| 328 | C2×C4 | — | 30 | 2 | no | — |
| 329 | C2×C4 | — | 30 | 1 | no | — |
| 330 | C2×C4 | — | 60 | 2 | no | — |
| 331 | C2×C4 | — | 60 | 1 | no | — |
| 332 | C2×C4 | — | 60 | 1 | no | — |
| 333 | C2×C4 | — | 60 | 2 | no | — |
| 334 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 335 | C2×C3 | — | 2 | 1 | no | — |
| 336 | C2×C3 | — | 20 | 2 | no | — |
| 337 | C2×C3 | — | 40 | 1 | no | — |
| 338 | C2×C3 | D5⋊#99 | 1 | 1 | yes | characteristic |
| 339 | D3 | — | 20 | 1 | no | — |
| 340 | C5 | #69151 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 341 | C22 | — | 10 | 2 | no | — |
| 342 | C22 | — | 20 | 2 | no | — |
| 343 | C22 | — | 20 | 2 | no | — |
| 344 | C22 | — | 20 | 1 | no | — |
| 345 | C22 | — | 30 | 1 | no | — |
| 346 | C22 | — | 60 | 1 | no | — |
| 347 | C22 | D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 348 | C4 | — | 2 | 2 | no | — |
| 349 | C4 | — | 2 | 1 | no | — |
| 350 | C4 | — | 6 | 2 | no | — |
| 351 | C4 | — | 12 | 1 | no | — |
| 352 | C4 | — | 15 | 1 | no | — |
| 353 | C4 | — | 15 | 1 | no | — |
| 354 | C4 | — | 40 | 2 | no | — |
| 355 | C4 | — | 60 | 1 | no | — |
| 356 | C4 | — | 120 | 2 | no | — |
| 357 | C3 | #10604640 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C2 | — | 2 | 1 | no | — |
| 359 | C2 | — | 20 | 2 | no | — |
| 360 | C2 | — | 40 | 1 | no | — |
| 361 | C2 | — | 60 | 1 | no | — |
| 362 | C2 | #11751852 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11751863 | C2 | semidirect |
| 3. #11746724 | C2 | semidirect |
| 4. C3×#64853 | C2 | semidirect |
| 5. #11746556 | C2 | semidirect |
| 7. C2×#6766 | C4 | semidirect |
| 10. C42×D15 | C4 | semidirect |
| 11. C5×#869 | C4 | semidirect |
| 15. #91368 | C4 | semidirect |
| 25. #64853 | D3 | semidirect |
| 104. #869 | AGL(1,𝔽5) | semidirect |
| 288. C3×C5 | #2126 | semidirect |
| 340. C5 | #69151 | semidirect |
| 357. C3 | #10604640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752556 | 2 |
| #11751863 | 2 |
| #11746724 | 2 |
| C3×#64853 | 2 |
| #11746556 | 2 |
| #10604640 | 3 |
| #69151 | 5 |