Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #11756525 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C5×#828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11748090 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11747547 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#64785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11745907 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11745889 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10602282 | — | 3 | 1 | no | maximal, Hall |
| 9 | #92098 | — | 2 | 1 | no | — |
| 10 | C2×C3×C5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 11 | #91831 | — | 2 | 1 | no | — |
| 12 | #91808 | — | 2 | 1 | no | — |
| 13 | #91807 | — | 2 | 2 | no | — |
| 14 | Q16×D15 | — | 2 | 1 | no | — |
| 15 | #91793 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91790 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C5×D24 | C22 | 1 | 1 | yes | characteristic |
| 18 | #91304 | — | 2 | 1 | no | — |
| 19 | C5×#828 | — | 2 | 2 | no | — |
| 20 | C2×C5×C3⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#3951 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#3944 | C22 | 1 | 1 | yes | characteristic |
| 23 | #90959 | — | 2 | 1 | no | — |
| 24 | #90944 | — | 2 | 1 | no | — |
| 25 | #90939 | — | 2 | 1 | no | — |
| 26 | #69268 | — | 5 | 1 | no | maximal, Hall |
| 27 | #66100 | — | 3 | 1 | no | — |
| 28 | C2×C5×SD32 | — | 3 | 1 | no | — |
| 29 | #65449 | — | 3 | 1 | no | — |
| 30 | #65436 | — | 3 | 1 | no | — |
| 31 | #64785 | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #64730 | — | 3 | 1 | no | — |
| 33 | #64728 | — | 3 | 1 | no | — |
| 34 | C2×C3×C5×Q8 | — | 2 | 1 | no | — |
| 35 | #6821 | — | 2 | 2 | no | — |
| 36 | #6821 | — | 4 | 1 | no | — |
| 37 | Q8×D15 | — | 2 | 2 | no | — |
| 38 | Q8×D15 | — | 4 | 1 | no | — |
| 39 | #6817 | — | 2 | 1 | no | — |
| 40 | #6817 | — | 4 | 2 | no | — |
| 41 | #6817 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C5×D12 | — | 2 | 1 | no | — |
| 43 | C3×C5×Q16 | — | 2 | 1 | no | — |
| 44 | C3×C5×Q16 | D4 | 1 | 2 | yes | — |
| 45 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 46 | #6718 | — | 2 | 2 | no | — |
| 47 | #6717 | — | 2 | 2 | no | — |
| 48 | #6710 | D4 | 1 | 1 | yes | characteristic |
| 49 | Dic60 | D4 | 1 | 1 | yes | characteristic |
| 50 | D120 | D4 | 1 | 1 | yes | characteristic |
| 51 | #6706 | — | 2 | 1 | no | — |
| 52 | #6705 | — | 2 | 1 | no | — |
| 53 | C8×D15 | — | 2 | 1 | no | — |
| 54 | C5×D24 | — | 2 | 1 | no | — |
| 55 | C5×D24 | — | 2 | 1 | no | — |
| 56 | C3×#681 | — | 2 | 1 | no | — |
| 57 | #6659 | — | 4 | 1 | no | — |
| 58 | #6654 | — | 4 | 1 | no | — |
| 59 | C3×#672 | — | 2 | 1 | no | — |
| 60 | C5×C3⋊C16 | — | 2 | 1 | no | — |
| 61 | #5766 | — | 5 | 1 | no | — |
| 62 | C2×#828 | D5 | 1 | 1 | yes | characteristic, complemented |
| 63 | #4908 | — | 5 | 1 | no | — |
| 64 | #4897 | — | 5 | 1 | no | — |
| 65 | C3×#362 | — | 5 | 1 | no | — |
| 66 | #4515 | — | 5 | 1 | no | — |
| 67 | #4497 | — | 5 | 1 | no | — |
| 68 | #4147 | — | 6 | 1 | no | — |
| 69 | C2×C5×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C2×C5×D8 | — | 3 | 1 | no | — |
| 71 | #4088 | — | 6 | 1 | no | — |
| 72 | #4078 | — | 6 | 1 | no | — |
| 73 | #4065 | — | 6 | 1 | no | — |
| 74 | #4064 | — | 6 | 2 | no | — |
| 75 | D5×Q16 | — | 6 | 1 | no | — |
| 76 | #4050 | — | 3 | 1 | no | — |
| 77 | #4047 | — | 3 | 1 | no | — |
| 78 | C5×SD32 | — | 6 | 2 | no | — |
| 79 | C2×C5×C16 | — | 3 | 1 | no | — |
| 80 | #3965 | — | 6 | 1 | no | — |
| 81 | #3959 | — | 6 | 1 | no | — |
| 82 | #3958 | — | 6 | 1 | no | — |
| 83 | #3951 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | #3944 | C2×D3 | 1 | 1 | yes | characteristic |
| 85 | #2193 | — | 15 | 1 | no | Sylow |
| 86 | C22×C5×D3 | — | 4 | 1 | no | — |
| 87 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 88 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 89 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 90 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | #1220 | — | 2 | 1 | no | — |
| 92 | #1220 | — | 4 | 1 | no | — |
| 93 | D60 | — | 2 | 1 | no | — |
| 94 | D60 | — | 4 | 2 | no | — |
| 95 | D60 | D8 | 1 | 1 | yes | characteristic |
| 96 | C4×D15 | — | 2 | 1 | no | — |
| 97 | C4×D15 | — | 4 | 2 | no | — |
| 98 | C4×D15 | — | 4 | 2 | no | — |
| 99 | C4×D15 | — | 4 | 1 | no | — |
| 100 | Dic30 | — | 2 | 1 | no | — |
| 101 | Dic30 | — | 4 | 2 | no | — |
| 102 | Dic30 | D8 | 1 | 1 | yes | characteristic |
| 103 | C5×D12 | — | 4 | 1 | no | — |
| 104 | C5×D12 | — | 4 | 1 | no | — |
| 105 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C3⋊#168 | — | 2 | 1 | no | — |
| 108 | C3×#168 | — | 4 | 1 | no | — |
| 109 | #1007 | — | 10 | 1 | no | — |
| 110 | C2×C3×Q16 | C2×D5 | 1 | 1 | yes | characteristic |
| 111 | #942 | — | 10 | 1 | no | — |
| 112 | #919 | — | 10 | 1 | no | — |
| 113 | #918 | — | 10 | 2 | no | — |
| 114 | D3×Q16 | — | 10 | 1 | no | — |
| 115 | #908 | — | 10 | 1 | no | — |
| 116 | #904 | — | 5 | 1 | no | — |
| 117 | C2×D24 | C2×D5 | 1 | 1 | yes | characteristic |
| 118 | #901 | — | 5 | 1 | no | — |
| 119 | C3×M32 | — | 5 | 1 | no | — |
| 120 | C3×#108 | — | 5 | 1 | no | — |
| 121 | #828 | — | 2 | 2 | no | — |
| 122 | #823 | — | 10 | 1 | no | — |
| 123 | C2×C3⋊C16 | C2×D5 | 1 | 1 | yes | characteristic |
| 124 | #800 | — | 10 | 1 | no | — |
| 125 | D48 | — | 10 | 1 | no | — |
| 126 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 127 | C2×C5×D4 | — | 6 | 1 | no | — |
| 128 | #713 | — | 6 | 2 | no | — |
| 129 | #713 | — | 12 | 1 | no | — |
| 130 | Q8×D5 | — | 6 | 2 | no | — |
| 131 | Q8×D5 | — | 12 | 1 | no | — |
| 132 | #709 | — | 3 | 1 | no | — |
| 133 | #709 | — | 6 | 1 | no | — |
| 134 | #709 | — | 12 | 2 | no | — |
| 135 | C5×Q16 | — | 2 | 1 | no | — |
| 136 | C5×Q16 | D12 | 1 | 2 | yes | — |
| 137 | C5×D8 | — | 6 | 1 | no | — |
| 138 | C5×D8 | — | 6 | 1 | no | — |
| 139 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | #689 | — | 6 | 2 | no | — |
| 141 | #688 | — | 6 | 2 | no | — |
| 142 | #687 | — | 12 | 1 | no | — |
| 143 | #686 | — | 12 | 1 | no | — |
| 144 | #681 | — | 2 | 1 | no | — |
| 145 | #681 | — | 3 | 1 | no | — |
| 146 | Dic20 | — | 3 | 1 | no | — |
| 147 | D40 | — | 3 | 1 | no | — |
| 148 | #677 | — | 6 | 1 | no | — |
| 149 | #676 | — | 6 | 1 | no | — |
| 150 | C8×D5 | — | 6 | 1 | no | — |
| 151 | C5×C16 | — | 6 | 1 | no | — |
| 152 | #672 | — | 2 | 1 | no | — |
| 153 | #578 | — | 15 | 1 | no | — |
| 154 | #509 | — | 15 | 1 | no | — |
| 155 | C2×SD32 | — | 3 | 1 | no | — |
| 156 | #472 | — | 15 | 1 | no | — |
| 157 | #362 | — | 5 | 1 | no | — |
| 158 | #359 | — | 15 | 1 | no | — |
| 159 | #350 | — | 15 | 1 | no | — |
| 160 | C22×C3×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 161 | C2×D15 | — | 2 | 1 | no | — |
| 162 | C2×D15 | — | 4 | 1 | no | — |
| 163 | C2×C5×D3 | — | 8 | 1 | no | — |
| 164 | C2×C5×D3 | — | 16 | 1 | no | — |
| 165 | C3×C4×C5 | — | 4 | 2 | no | — |
| 166 | C3×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 167 | C3×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 168 | Dic15 | — | 2 | 1 | no | — |
| 169 | Dic15 | — | 4 | 1 | no | — |
| 170 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 171 | #239 | — | 10 | 2 | no | — |
| 172 | #239 | — | 20 | 1 | no | — |
| 173 | D3×Q8 | — | 10 | 2 | no | — |
| 174 | D3×Q8 | — | 20 | 1 | no | — |
| 175 | #235 | — | 5 | 1 | no | — |
| 176 | #235 | — | 10 | 1 | no | — |
| 177 | #235 | — | 20 | 2 | no | — |
| 178 | C2×D12 | — | 2 | 1 | no | — |
| 179 | C3×Q16 | — | 2 | 1 | no | — |
| 180 | C3×Q16 | C22⋊D5 | 1 | 2 | yes | — |
| 181 | C3×M16 | — | 10 | 1 | no | — |
| 182 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 183 | #216 | — | 10 | 2 | no | — |
| 184 | #215 | — | 10 | 2 | no | — |
| 185 | #208 | — | 5 | 1 | no | — |
| 186 | Dic12 | — | 5 | 1 | no | — |
| 187 | D24 | — | 2 | 1 | no | — |
| 188 | D24 | — | 2 | 1 | no | — |
| 189 | D24 | — | 5 | 1 | no | — |
| 190 | D24 | — | 20 | 1 | no | — |
| 191 | #204 | — | 10 | 1 | no | — |
| 192 | #204 | — | 20 | 1 | no | — |
| 193 | ΓL(1,𝔽25) | — | 10 | 1 | no | — |
| 194 | D3×C8 | — | 10 | 1 | no | — |
| 195 | C3×C16 | — | 10 | 1 | no | — |
| 196 | C3⋊C16 | — | 2 | 1 | no | — |
| 197 | C23×C5 | — | 12 | 1 | no | — |
| 198 | C5×Q8 | — | 2 | 2 | no | — |
| 199 | C5×Q8 | — | 4 | 1 | no | — |
| 200 | C5×D4 | — | 12 | 1 | no | — |
| 201 | C5×D4 | — | 12 | 1 | no | — |
| 202 | C2×C4×C5 | — | 4 | 1 | no | — |
| 203 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 204 | C22⋊D5 | — | 6 | 1 | no | — |
| 205 | C22⋊D5 | — | 12 | 1 | no | — |
| 206 | D20 | — | 3 | 1 | no | — |
| 207 | D20 | — | 6 | 1 | no | — |
| 208 | D20 | — | 12 | 2 | no | — |
| 209 | C4×D5 | — | 6 | 1 | no | — |
| 210 | C4×D5 | — | 12 | 2 | no | — |
| 211 | C4×D5 | — | 12 | 2 | no | — |
| 212 | C4×D5 | — | 12 | 1 | no | — |
| 213 | Dic10 | — | 3 | 1 | no | — |
| 214 | Dic10 | — | 6 | 1 | no | — |
| 215 | Dic10 | — | 12 | 2 | no | — |
| 216 | C5×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 217 | C5×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 218 | #168 | — | 4 | 1 | no | — |
| 219 | #168 | — | 6 | 1 | no | — |
| 220 | 2−1+4 | — | 30 | 1 | no | — |
| 221 | #137 | — | 30 | 1 | no | — |
| 222 | #137 | — | 30 | 2 | no | — |
| 223 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 224 | #135 | — | 15 | 1 | no | — |
| 225 | #135 | — | 30 | 1 | no | — |
| 226 | C2×Q16 | — | 30 | 1 | no | — |
| 227 | C2×Q16 | D3×D5 | 1 | 1 | yes | characteristic |
| 228 | C2×D8 | — | 3 | 1 | no | — |
| 229 | #131 | — | 15 | 1 | no | — |
| 230 | SD32 | — | 6 | 2 | no | — |
| 231 | SD32 | — | 30 | 1 | no | — |
| 232 | D16 | — | 30 | 1 | no | — |
| 233 | M32 | — | 5 | 1 | no | — |
| 234 | C2×C16 | — | 3 | 1 | no | — |
| 235 | #108 | — | 5 | 1 | no | — |
| 236 | #100 | — | 30 | 1 | no | — |
| 237 | C2×C3×C5 | — | 2 | 1 | no | — |
| 238 | C2×C3×C5 | #447 | 1 | 1 | yes | characteristic |
| 239 | D15 | — | 4 | 1 | no | — |
| 240 | D15 | — | 8 | 1 | no | — |
| 241 | C5×D3 | — | 16 | 1 | no | — |
| 242 | C22×D3 | — | 4 | 1 | no | — |
| 243 | C3×Q8 | — | 2 | 2 | no | — |
| 244 | C3×Q8 | — | 4 | 1 | no | — |
| 245 | C2×C3×C4 | — | 4 | 1 | no | — |
| 246 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 247 | #67 | — | 10 | 1 | no | — |
| 248 | #67 | — | 20 | 1 | no | — |
| 249 | D12 | — | 4 | 1 | no | — |
| 250 | D12 | — | 4 | 1 | no | — |
| 251 | D12 | — | 5 | 1 | no | — |
| 252 | D12 | — | 10 | 1 | no | — |
| 253 | D12 | — | 20 | 2 | no | — |
| 254 | C4×D3 | — | 10 | 1 | no | — |
| 255 | C4×D3 | — | 20 | 2 | no | — |
| 256 | C4×D3 | — | 20 | 2 | no | — |
| 257 | C4×D3 | — | 20 | 1 | no | — |
| 258 | Dic6 | — | 5 | 1 | no | — |
| 259 | Dic6 | — | 10 | 1 | no | — |
| 260 | Dic6 | — | 20 | 2 | no | — |
| 261 | C3×C8 | — | 20 | 1 | no | — |
| 262 | C3×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 263 | C3×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 264 | C3⋊C8 | — | 10 | 1 | no | — |
| 265 | C22×C5 | — | 24 | 1 | no | — |
| 266 | C22×C5 | — | 48 | 1 | no | — |
| 267 | C22×C5 | #914 | 1 | 1 | yes | characteristic |
| 268 | C2×D5 | — | 6 | 1 | no | — |
| 269 | C2×D5 | — | 12 | 1 | no | — |
| 270 | C4×C5 | — | 4 | 2 | no | — |
| 271 | C4×C5 | #882 | 1 | 1 | yes | characteristic |
| 272 | C4×C5 | D3×D8 | 1 | 1 | yes | characteristic |
| 273 | Dic5 | — | 6 | 1 | no | — |
| 274 | Dic5 | — | 12 | 1 | no | — |
| 275 | #41 | — | 15 | 1 | no | — |
| 276 | #41 | — | 30 | 2 | no | — |
| 277 | #41 | — | 30 | 1 | no | — |
| 278 | #41 | — | 60 | 2 | no | — |
| 279 | #41 | — | 60 | 1 | no | — |
| 280 | C2×Q8 | — | 2 | 1 | no | — |
| 281 | C2×Q8 | — | 30 | 2 | no | — |
| 282 | C2×Q8 | — | 60 | 1 | no | — |
| 283 | C2×D4 | — | 6 | 1 | no | — |
| 284 | Q16 | — | 2 | 1 | no | — |
| 285 | Q16 | — | 15 | 1 | no | — |
| 286 | Q16 | — | 30 | 2 | no | — |
| 287 | Q16 | #1203 | 1 | 2 | yes | — |
| 288 | SD16 | — | 30 | 2 | no | — |
| 289 | SD16 | — | 30 | 1 | no | — |
| 290 | SD16 | — | 60 | 1 | no | — |
| 291 | D8 | — | 6 | 1 | no | — |
| 292 | D8 | — | 6 | 1 | no | — |
| 293 | D8 | — | 15 | 1 | no | — |
| 294 | D8 | — | 60 | 1 | no | — |
| 295 | M16 | — | 10 | 1 | no | — |
| 296 | M16 | — | 15 | 1 | no | — |
| 297 | M16 | — | 30 | 1 | no | — |
| 298 | C2×C8 | — | 30 | 1 | no | — |
| 299 | C2×C8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 300 | C16 | — | 6 | 1 | no | — |
| 301 | C16 | — | 10 | 1 | no | — |
| 302 | C3×C5 | #2193 | 1 | 1 | yes | characteristic, complemented, Hall |
| 303 | C22×C3 | #4057 | 1 | 1 | yes | characteristic |
| 304 | C2×D3 | — | 8 | 1 | no | — |
| 305 | C2×D3 | — | 10 | 1 | no | — |
| 306 | C2×D3 | — | 16 | 1 | no | — |
| 307 | C2×D3 | — | 20 | 1 | no | — |
| 308 | C3×C4 | — | 4 | 2 | no | — |
| 309 | C3×C4 | D5×D8 | 1 | 1 | yes | characteristic |
| 310 | C3×C4 | #4083 | 1 | 1 | yes | characteristic |
| 311 | Dic3 | — | 10 | 1 | no | — |
| 312 | Dic3 | — | 20 | 1 | no | — |
| 313 | C2×C5 | — | 2 | 1 | no | — |
| 314 | C2×C5 | — | 48 | 1 | no | — |
| 315 | C2×C5 | #4773 | 1 | 1 | yes | characteristic |
| 316 | D5 | — | 12 | 1 | no | — |
| 317 | D5 | — | 24 | 1 | no | — |
| 318 | C23 | — | 12 | 1 | no | — |
| 319 | Q8 | — | 2 | 2 | no | — |
| 320 | Q8 | — | 4 | 1 | no | — |
| 321 | Q8 | — | 15 | 1 | no | — |
| 322 | Q8 | — | 30 | 1 | no | — |
| 323 | Q8 | — | 60 | 2 | no | — |
| 324 | D4 | — | 12 | 1 | no | — |
| 325 | D4 | — | 12 | 1 | no | — |
| 326 | D4 | — | 15 | 1 | no | — |
| 327 | D4 | — | 30 | 1 | no | — |
| 328 | D4 | — | 30 | 1 | no | — |
| 329 | D4 | — | 60 | 2 | no | — |
| 330 | D4 | — | 60 | 1 | no | — |
| 331 | C2×C4 | — | 4 | 1 | no | — |
| 332 | C2×C4 | — | 30 | 1 | no | — |
| 333 | C2×C4 | — | 60 | 2 | no | — |
| 334 | C2×C4 | — | 60 | 2 | no | — |
| 335 | C2×C4 | — | 60 | 1 | no | — |
| 336 | C2×C4 | #6790 | 1 | 1 | yes | characteristic |
| 337 | C8 | — | 20 | 1 | no | — |
| 338 | C8 | — | 30 | 1 | no | — |
| 339 | C8 | C2×#1203 | 1 | 1 | yes | characteristic |
| 340 | C8 | #6790 | 1 | 1 | yes | characteristic |
| 341 | C2×C3 | — | 2 | 1 | no | — |
| 342 | C2×C3 | #65445 | 1 | 1 | yes | characteristic |
| 343 | D3 | — | 16 | 1 | no | — |
| 344 | D3 | — | 20 | 1 | no | — |
| 345 | D3 | — | 40 | 1 | no | — |
| 346 | C5 | #69268 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 347 | C22 | — | 24 | 1 | no | — |
| 348 | C22 | — | 30 | 1 | no | — |
| 349 | C22 | — | 48 | 1 | no | — |
| 350 | C22 | — | 60 | 1 | no | — |
| 351 | C22 | #91500 | 1 | 1 | yes | characteristic |
| 352 | C4 | — | 4 | 2 | no | — |
| 353 | C4 | — | 30 | 1 | no | — |
| 354 | C4 | — | 60 | 1 | no | — |
| 355 | C4 | #91481 | 1 | 1 | yes | characteristic |
| 356 | C4 | #91573 | 1 | 1 | yes | characteristic |
| 357 | C3 | #10602282 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C2 | — | 2 | 1 | no | — |
| 359 | C2 | — | 48 | 1 | no | — |
| 360 | C2 | — | 60 | 1 | no | — |
| 361 | C2 | — | 120 | 1 | no | — |
| 362 | C2 | #11749041 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756525 | C2 | semidirect |
| 2. C2×C5×#828 | C2 | semidirect |
| 3. #11748090 | C2 | semidirect |
| 4. #11747547 | C2 | semidirect |
| 5. C3×#64785 | C2 | semidirect |
| 6. #11745907 | C2 | semidirect |
| 7. #11745889 | C2 | semidirect |
| 31. #64785 | D3 | semidirect |
| 62. C2×#828 | D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #69268 | semidirect |
| 357. C3 | #10602282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756525 | 2 |
| C2×C5×#828 | 2 |
| #11748090 | 2 |
| #11747547 | 2 |
| C3×#64785 | 2 |
| #11745907 | 2 |
| #11745889 | 2 |
| #10602282 | 3 |
| #69268 | 5 |