Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #11752543 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11751917 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11746727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#64856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11746561 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10604145 | — | 3 | 1 | no | maximal, Hall |
| 7 | C2×#6769 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#6765 | C4 | 1 | 1 | yes | characteristic |
| 9 | #91931 | — | 2 | 2 | no | — |
| 10 | #91764 | C4 | 1 | 1 | yes | characteristic |
| 11 | C42×C5×D3 | C4 | 1 | 1 | yes | characteristic |
| 12 | C3×#4021 | C22 | 1 | 1 | yes | characteristic |
| 13 | #91458 | C4 | 1 | 1 | yes | characteristic |
| 14 | #91454 | — | 2 | 2 | no | — |
| 15 | #91395 | — | 2 | 2 | no | — |
| 16 | #91389 | C22 | 1 | 1 | yes | characteristic |
| 17 | #91234 | C22 | 1 | 2 | yes | — |
| 18 | C3×#4005 | C22 | 1 | 2 | yes | — |
| 19 | #91174 | — | 2 | 2 | no | — |
| 20 | #69165 | — | 5 | 1 | no | maximal, Hall |
| 21 | #65811 | — | 3 | 1 | no | — |
| 22 | #65761 | — | 3 | 2 | no | — |
| 23 | #64856 | — | 3 | 1 | no | — |
| 24 | #64856 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #64855 | — | 3 | 2 | no | — |
| 26 | C2×D60 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×Dic30 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×C4×C5×D3 | — | 2 | 1 | no | — |
| 29 | C2×C4×C5×D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C3×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C2×C3×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 32 | C2×#1203 | D4 | 1 | 2 | yes | — |
| 33 | C2×#1202 | — | 2 | 2 | no | — |
| 34 | C2×#1201 | — | 2 | 1 | no | — |
| 35 | C2×#1200 | D4 | 1 | 2 | yes | — |
| 36 | C2×D5×Dic3 | — | 2 | 1 | no | — |
| 37 | #6769 | — | 4 | 1 | no | — |
| 38 | #6769 | — | 4 | 1 | no | — |
| 39 | #6765 | — | 4 | 1 | no | — |
| 40 | #6765 | — | 4 | 1 | no | — |
| 41 | #6762 | — | 2 | 2 | no | — |
| 42 | C3×#704 | — | 2 | 2 | no | — |
| 43 | #6740 | — | 4 | 2 | no | — |
| 44 | #6738 | — | 4 | 2 | no | — |
| 45 | C3×C42×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | #6714 | — | 2 | 2 | no | — |
| 47 | C4×C5×Dic3 | — | 2 | 1 | no | — |
| 48 | C4×C5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C3×#685 | — | 2 | 2 | no | — |
| 50 | Dic3⋊Dic5 | — | 2 | 2 | no | — |
| 51 | #5668 | — | 5 | 1 | no | — |
| 52 | #4751 | — | 5 | 2 | no | — |
| 53 | C3×#355 | — | 5 | 1 | no | — |
| 54 | #4542 | — | 5 | 1 | no | — |
| 55 | #4478 | — | 5 | 2 | no | — |
| 56 | C2×#709 | — | 3 | 1 | no | — |
| 57 | C2×#709 | — | 3 | 1 | no | — |
| 58 | D5⋊M16 | — | 6 | 2 | no | — |
| 59 | C2×C42×C5 | — | 3 | 1 | no | — |
| 60 | #4076 | — | 6 | 2 | no | — |
| 61 | #4021 | — | 3 | 1 | no | — |
| 62 | #4021 | C2×D3 | 1 | 1 | yes | characteristic |
| 63 | #4020 | — | 3 | 1 | no | — |
| 64 | C4×D20 | — | 6 | 2 | no | — |
| 65 | #4015 | — | 3 | 1 | no | — |
| 66 | #4013 | — | 6 | 2 | no | — |
| 67 | #4005 | — | 3 | 2 | no | — |
| 68 | #4005 | C2×D3 | 1 | 2 | yes | — |
| 69 | #2132 | — | 15 | 1 | no | Sylow |
| 70 | C22×D15 | C22⋊C4 | 1 | 2 | yes | — |
| 71 | C22×C5×D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 72 | C22×C3×D5 | — | 2 | 1 | no | — |
| 73 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 74 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 75 | C2×Dic15 | — | 2 | 1 | no | — |
| 76 | D60 | — | 4 | 1 | no | — |
| 77 | Dic30 | — | 4 | 1 | no | — |
| 78 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 79 | C2×C5×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 80 | C4×C5×D3 | — | 2 | 1 | no | — |
| 81 | C4×C5×D3 | — | 2 | 1 | no | — |
| 82 | C4×C5×D3 | — | 4 | 2 | no | — |
| 83 | C2×C3×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 84 | C3×D20 | — | 4 | 1 | no | — |
| 85 | C3×Dic10 | — | 4 | 1 | no | — |
| 86 | #1203 | — | 4 | 2 | no | — |
| 87 | #1202 | — | 4 | 4 | no | — |
| 88 | #1201 | — | 4 | 2 | no | — |
| 89 | #1200 | — | 2 | 2 | no | — |
| 90 | #1200 | — | 2 | 2 | no | — |
| 91 | D5×Dic3 | — | 4 | 1 | no | — |
| 92 | D5×Dic3 | — | 4 | 1 | no | — |
| 93 | C3⋊#170 | — | 4 | 2 | no | — |
| 94 | C3×#170 | — | 4 | 2 | no | — |
| 95 | C2×#239 | — | 5 | 1 | no | — |
| 96 | C2×#237 | — | 5 | 1 | no | — |
| 97 | C3×#124 | — | 5 | 1 | no | — |
| 98 | #944 | — | 5 | 1 | no | — |
| 99 | #940 | — | 5 | 1 | no | — |
| 100 | D3×M16 | — | 10 | 2 | no | — |
| 101 | #884 | — | 10 | 2 | no | — |
| 102 | #67⋊C4 | — | 10 | 2 | no | — |
| 103 | #875 | — | 5 | 1 | no | — |
| 104 | C42×D3 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 105 | C3×#101 | — | 5 | 2 | no | — |
| 106 | #836 | — | 5 | 2 | no | — |
| 107 | #823 | — | 10 | 2 | no | — |
| 108 | C22×C4×C5 | — | 3 | 1 | no | — |
| 109 | C22×C4×C5 | — | 6 | 1 | no | — |
| 110 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 111 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 112 | #709 | — | 12 | 1 | no | — |
| 113 | #709 | — | 12 | 1 | no | — |
| 114 | #709 | — | 12 | 1 | no | — |
| 115 | #709 | — | 12 | 1 | no | — |
| 116 | C2×D20 | — | 3 | 1 | no | — |
| 117 | C2×D20 | — | 6 | 2 | no | — |
| 118 | C2×D20 | C4×D3 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×D5 | — | 3 | 2 | no | — |
| 120 | C2×C4×D5 | — | 6 | 1 | no | — |
| 121 | C2×Dic10 | — | 3 | 1 | no | — |
| 122 | C2×Dic10 | C22×D3 | 1 | 1 | yes | characteristic |
| 123 | #704 | — | 2 | 2 | no | — |
| 124 | #704 | — | 6 | 2 | no | — |
| 125 | #700 | — | 12 | 2 | no | — |
| 126 | D5⋊C8 | — | 12 | 2 | no | — |
| 127 | C42×C5 | — | 3 | 1 | no | — |
| 128 | C42×C5 | — | 6 | 1 | no | — |
| 129 | C42×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 130 | #685 | — | 2 | 2 | no | — |
| 131 | #685 | — | 6 | 2 | no | — |
| 132 | C4⋊Dic5 | — | 6 | 2 | no | — |
| 133 | #532 | — | 15 | 1 | no | — |
| 134 | #413 | — | 15 | 2 | no | — |
| 135 | #356 | — | 15 | 2 | no | — |
| 136 | #355 | — | 5 | 1 | no | — |
| 137 | #355 | — | 15 | 1 | no | — |
| 138 | C22×C3×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×D15 | — | 2 | 2 | no | — |
| 140 | C2×D15 | — | 4 | 2 | no | — |
| 141 | C2×C5×D3 | — | 2 | 1 | no | — |
| 142 | C2×C5×D3 | — | 4 | 1 | no | — |
| 143 | C2×C3×D5 | — | 4 | 2 | no | — |
| 144 | C2×C3×D5 | — | 4 | 1 | no | — |
| 145 | C3×C4×C5 | — | 2 | 1 | no | — |
| 146 | C3×C4×C5 | — | 4 | 1 | no | — |
| 147 | Dic15 | — | 4 | 1 | no | — |
| 148 | C3×Dic5 | — | 2 | 2 | no | — |
| 149 | C5×Dic3 | — | 2 | 2 | no | — |
| 150 | C5×Dic3 | #99 | 1 | 1 | yes | characteristic |
| 151 | C5×Dic3 | #99 | 1 | 1 | yes | characteristic |
| 152 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 153 | C2×C3×D4 | — | 5 | 1 | no | — |
| 154 | C2×#67 | — | 10 | 2 | no | — |
| 155 | C2×#67 | — | 10 | 1 | no | — |
| 156 | C22×Dic3 | — | 10 | 1 | no | — |
| 157 | #239 | — | 20 | 1 | no | — |
| 158 | #239 | — | 20 | 1 | no | — |
| 159 | #237 | — | 20 | 1 | no | — |
| 160 | #237 | — | 20 | 1 | no | — |
| 161 | C2×D12 | — | 5 | 2 | no | — |
| 162 | C2×D12 | — | 5 | 1 | no | — |
| 163 | C2×C4×D3 | — | 2 | 1 | no | — |
| 164 | C2×C4×D3 | — | 5 | 2 | no | — |
| 165 | C2×C4×D3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 166 | C2×Dic6 | — | 5 | 1 | no | — |
| 167 | C3×M16 | — | 10 | 2 | no | — |
| 168 | C3×C22⋊C4 | — | 10 | 2 | no | — |
| 169 | C3×C42 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 170 | (C2×D3)⋊C4 | — | 10 | 2 | no | — |
| 171 | Dic3⋊C4 | — | 10 | 2 | no | — |
| 172 | C4×Dic3 | — | 2 | 1 | no | — |
| 173 | C4×Dic3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 174 | #208 | — | 10 | 2 | no | — |
| 175 | ΓL(1,𝔽25) | — | 20 | 2 | no | — |
| 176 | D3×C8 | — | 20 | 2 | no | — |
| 177 | C23×C5 | — | 3 | 1 | no | — |
| 178 | C22×D5 | — | 2 | 1 | no | — |
| 179 | C22×D5 | — | 3 | 2 | no | — |
| 180 | C2×C4×C5 | — | 2 | 1 | no | — |
| 181 | C2×C4×C5 | — | 3 | 1 | no | — |
| 182 | C2×C4×C5 | — | 6 | 1 | no | — |
| 183 | C2×C4×C5 | — | 6 | 1 | no | — |
| 184 | C2×C4×C5 | — | 6 | 1 | no | — |
| 185 | C2×C4×C5 | — | 12 | 2 | no | — |
| 186 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 187 | C22⋊D5 | — | 12 | 2 | no | — |
| 188 | C22⋊D5 | — | 12 | 2 | no | — |
| 189 | C2×Dic5 | — | 6 | 1 | no | — |
| 190 | C2×Dic5 | D3×D4 | 1 | 2 | yes | — |
| 191 | D20 | — | 4 | 1 | no | — |
| 192 | D20 | — | 12 | 1 | no | — |
| 193 | D20 | — | 12 | 4 | no | — |
| 194 | C4×D5 | — | 6 | 2 | no | — |
| 195 | C4×D5 | — | 6 | 2 | no | — |
| 196 | C4×D5 | — | 12 | 1 | no | — |
| 197 | C4×D5 | — | 12 | 1 | no | — |
| 198 | Dic10 | — | 4 | 1 | no | — |
| 199 | Dic10 | — | 12 | 1 | no | — |
| 200 | #170 | — | 4 | 2 | no | — |
| 201 | #170 | — | 12 | 2 | no | — |
| 202 | C2×#41 | — | 15 | 1 | no | — |
| 203 | C2×#41 | — | 15 | 1 | no | — |
| 204 | C2×M16 | — | 30 | 2 | no | — |
| 205 | C4⋊Q8 | — | 15 | 1 | no | — |
| 206 | #127 | — | 15 | 1 | no | — |
| 207 | #124 | — | 5 | 1 | no | — |
| 208 | #124 | — | 15 | 1 | no | — |
| 209 | #121 | — | 30 | 2 | no | — |
| 210 | C4×D4 | — | 30 | 2 | no | — |
| 211 | C2×C42 | — | 3 | 1 | no | — |
| 212 | #101 | — | 5 | 2 | no | — |
| 213 | #101 | — | 15 | 2 | no | — |
| 214 | #100 | — | 30 | 2 | no | — |
| 215 | C2×C3×C5 | — | 2 | 1 | no | — |
| 216 | C2×C3×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 217 | D15 | — | 4 | 2 | no | — |
| 218 | C3×D5 | — | 8 | 1 | no | — |
| 219 | C5×D3 | — | 4 | 1 | no | — |
| 220 | C23×C3 | — | 10 | 1 | no | — |
| 221 | C22×D3 | — | 5 | 2 | no | — |
| 222 | C22×D3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 223 | C3×Q8 | — | 20 | 1 | no | — |
| 224 | C3×D4 | — | 20 | 1 | no | — |
| 225 | C2×C3×C4 | — | 2 | 1 | no | — |
| 226 | C2×C3×C4 | — | 5 | 2 | no | — |
| 227 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 228 | #67 | — | 20 | 4 | no | — |
| 229 | #67 | — | 20 | 2 | no | — |
| 230 | C2×Dic3 | — | 2 | 1 | no | — |
| 231 | C2×Dic3 | — | 10 | 1 | no | — |
| 232 | C2×Dic3 | — | 20 | 1 | no | — |
| 233 | C2×Dic3 | — | 20 | 1 | no | — |
| 234 | C2×Dic3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 235 | D12 | — | 20 | 1 | no | — |
| 236 | D12 | — | 20 | 2 | no | — |
| 237 | C4×D3 | — | 2 | 1 | no | — |
| 238 | C4×D3 | — | 2 | 1 | no | — |
| 239 | C4×D3 | — | 4 | 2 | no | — |
| 240 | C4×D3 | — | 10 | 2 | no | — |
| 241 | C4×D3 | — | 10 | 2 | no | — |
| 242 | Dic6 | — | 20 | 1 | no | — |
| 243 | C3×C8 | — | 20 | 2 | no | — |
| 244 | C3⋊C8 | — | 20 | 2 | no | — |
| 245 | C22×C5 | — | 6 | 1 | no | — |
| 246 | C22×C5 | — | 12 | 1 | no | — |
| 247 | C22×C5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 248 | C2×D5 | — | 4 | 2 | no | — |
| 249 | C2×D5 | — | 4 | 1 | no | — |
| 250 | C2×D5 | — | 6 | 2 | no | — |
| 251 | C2×D5 | — | 12 | 2 | no | — |
| 252 | C4×C5 | — | 2 | 1 | no | — |
| 253 | C4×C5 | — | 3 | 1 | no | — |
| 254 | C4×C5 | — | 3 | 1 | no | — |
| 255 | C4×C5 | — | 4 | 1 | no | — |
| 256 | C4×C5 | — | 6 | 2 | no | — |
| 257 | Dic5 | — | 2 | 2 | no | — |
| 258 | Dic5 | — | 12 | 1 | no | — |
| 259 | #41 | — | 60 | 1 | no | — |
| 260 | #41 | — | 60 | 1 | no | — |
| 261 | #41 | — | 60 | 1 | no | — |
| 262 | #41 | — | 60 | 1 | no | — |
| 263 | C2×Q8 | — | 5 | 1 | no | — |
| 264 | C2×Q8 | — | 15 | 1 | no | — |
| 265 | C2×D4 | — | 5 | 1 | no | — |
| 266 | C2×D4 | — | 15 | 2 | no | — |
| 267 | C2×D4 | — | 15 | 1 | no | — |
| 268 | C2×D4 | — | 30 | 2 | no | — |
| 269 | C2×D4 | — | 30 | 1 | no | — |
| 270 | C22×C4 | — | 3 | 1 | no | — |
| 271 | C22×C4 | — | 6 | 1 | no | — |
| 272 | C22×C4 | — | 15 | 2 | no | — |
| 273 | C22×C4 | — | 30 | 1 | no | — |
| 274 | M16 | — | 10 | 2 | no | — |
| 275 | M16 | — | 30 | 2 | no | — |
| 276 | M16 | — | 60 | 2 | no | — |
| 277 | C2×C8 | — | 60 | 2 | no | — |
| 278 | C4⋊C4 | — | 30 | 2 | no | — |
| 279 | C22⋊C4 | — | 10 | 2 | no | — |
| 280 | C22⋊C4 | — | 30 | 2 | no | — |
| 281 | C42 | — | 3 | 1 | no | — |
| 282 | C42 | — | 6 | 1 | no | — |
| 283 | C42 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 284 | C3×C5 | #2132 | 1 | 1 | yes | characteristic, complemented, Hall |
| 285 | C22×C3 | — | 20 | 2 | no | — |
| 286 | C22×C3 | — | 20 | 1 | no | — |
| 287 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 288 | C2×D3 | — | 2 | 1 | no | — |
| 289 | C2×D3 | — | 4 | 1 | no | — |
| 290 | C2×D3 | — | 10 | 2 | no | — |
| 291 | C2×D3 | — | 20 | 2 | no | — |
| 292 | C3×C4 | — | 2 | 1 | no | — |
| 293 | C3×C4 | — | 4 | 1 | no | — |
| 294 | C3×C4 | — | 10 | 2 | no | — |
| 295 | Dic3 | — | 2 | 2 | no | — |
| 296 | Dic3 | — | 20 | 1 | no | — |
| 297 | Dic3 | #3999 | 1 | 1 | yes | characteristic |
| 298 | Dic3 | #3999 | 1 | 1 | yes | characteristic |
| 299 | C2×C5 | — | 2 | 1 | no | — |
| 300 | C2×C5 | — | 12 | 1 | no | — |
| 301 | C2×C5 | D3×#99 | 1 | 1 | yes | characteristic |
| 302 | D5 | — | 8 | 1 | no | — |
| 303 | D5 | — | 12 | 2 | no | — |
| 304 | C23 | — | 3 | 1 | no | — |
| 305 | C23 | — | 10 | 1 | no | — |
| 306 | C23 | — | 15 | 2 | no | — |
| 307 | Q8 | — | 20 | 1 | no | — |
| 308 | Q8 | — | 60 | 1 | no | — |
| 309 | D4 | — | 20 | 1 | no | — |
| 310 | D4 | — | 60 | 1 | no | — |
| 311 | D4 | — | 60 | 4 | no | — |
| 312 | D4 | — | 60 | 2 | no | — |
| 313 | D4 | — | 60 | 2 | no | — |
| 314 | C2×C4 | — | 2 | 1 | no | — |
| 315 | C2×C4 | — | 3 | 1 | no | — |
| 316 | C2×C4 | — | 5 | 2 | no | — |
| 317 | C2×C4 | — | 6 | 1 | no | — |
| 318 | C2×C4 | — | 6 | 1 | no | — |
| 319 | C2×C4 | — | 6 | 1 | no | — |
| 320 | C2×C4 | — | 12 | 2 | no | — |
| 321 | C2×C4 | — | 30 | 2 | no | — |
| 322 | C2×C4 | — | 30 | 2 | no | — |
| 323 | C2×C4 | — | 30 | 1 | no | — |
| 324 | C2×C4 | — | 60 | 1 | no | — |
| 325 | C2×C4 | — | 60 | 1 | no | — |
| 326 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 327 | C8 | — | 20 | 2 | no | — |
| 328 | C8 | — | 60 | 2 | no | — |
| 329 | C2×C3 | — | 2 | 1 | no | — |
| 330 | C2×C3 | — | 40 | 1 | no | — |
| 331 | C2×C3 | C2×#3999 | 1 | 1 | yes | characteristic |
| 332 | D3 | — | 4 | 1 | no | — |
| 333 | D3 | — | 20 | 2 | no | — |
| 334 | C5 | #69165 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 335 | C22 | — | 6 | 1 | no | — |
| 336 | C22 | — | 12 | 1 | no | — |
| 337 | C22 | — | 20 | 2 | no | — |
| 338 | C22 | — | 20 | 1 | no | — |
| 339 | C22 | — | 30 | 2 | no | — |
| 340 | C22 | — | 60 | 2 | no | — |
| 341 | C22 | D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 342 | C4 | — | 2 | 1 | no | — |
| 343 | C4 | — | 3 | 1 | no | — |
| 344 | C4 | — | 3 | 1 | no | — |
| 345 | C4 | — | 4 | 1 | no | — |
| 346 | C4 | — | 6 | 2 | no | — |
| 347 | C4 | — | 10 | 2 | no | — |
| 348 | C4 | — | 60 | 1 | no | — |
| 349 | C3 | #10604145 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 350 | C2 | — | 2 | 1 | no | — |
| 351 | C2 | — | 12 | 1 | no | — |
| 352 | C2 | — | 40 | 1 | no | — |
| 353 | C2 | — | 60 | 2 | no | — |
| 354 | C2 | D3×#3999 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11751917 | C2 | semidirect |
| 3. #11746727 | C2 | semidirect |
| 4. C3×#64856 | C2 | semidirect |
| 5. #11746561 | C2 | semidirect |
| 24. #64856 | D3 | semidirect |
| 284. C3×C5 | #2132 | semidirect |
| 334. C5 | #69165 | semidirect |
| 349. C3 | #10604145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752543 | 2 |
| #11751917 | 2 |
| #11746727 | 2 |
| C3×#64856 | 2 |
| #11746561 | 2 |
| #10604145 | 3 |
| #69165 | 5 |