Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
730 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 87 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 | C2×#4150⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C5⋊#994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C4×C5×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #65910⋊C3 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10617748 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 6 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 7 | #4150⋊C3 | — | 2 | 2 | no | — |
| 8 | C5⋊#994 | — | 2 | 2 | no | — |
| 9 | C2×D5×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 10 | C2×C5⋊(#41⋊C3) | C22 | 1 | 2 | yes | — |
| 11 | C3×#4021 | — | 4 | 1 | no | maximal |
| 12 | C4×C5×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 13 | #3500⋊C3 | — | 5 | 1 | no | maximal, Hall |
| 14 | C2×#4150 | C2×C3 | 1 | 1 | yes | characteristic |
| 15 | C2×#4149 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C4×C5×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | #65910 | C2×C3 | 1 | 4 | yes | complemented |
| 18 | #65888 | — | 3 | 4 | no | — |
| 19 | #65860 | — | 3 | 1 | no | — |
| 20 | #65859 | — | 3 | 1 | no | — |
| 21 | #65811 | — | 3 | 1 | no | — |
| 22 | C2×#4021 | — | 3 | 1 | no | — |
| 23 | C2×C3×D20 | — | 4 | 1 | no | — |
| 24 | C2×C3×Dic10 | — | 4 | 1 | no | — |
| 25 | C5×#41⋊C3 | D4 | 1 | 2 | yes | complemented |
| 26 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 27 | D5×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 28 | C5⋊(#41⋊C3) | — | 2 | 2 | no | — |
| 29 | C3×C42×C5 | — | 4 | 1 | no | — |
| 30 | C3×#685 | — | 4 | 4 | no | — |
| 31 | C2×2−1+4⋊C3 | — | 5 | 1 | no | — |
| 32 | C2×#994 | — | 5 | 1 | no | — |
| 33 | #548⋊C3 | — | 5 | 4 | no | — |
| 34 | C4×#41⋊C3 | D5 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×C5×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 36 | #4150 | — | 2 | 2 | no | — |
| 37 | #4150 | — | 6 | 2 | no | — |
| 38 | #4149 | — | 2 | 2 | no | — |
| 39 | #4149 | — | 6 | 2 | no | — |
| 40 | C2×#713 | C22×C3 | 1 | 2 | yes | — |
| 41 | C2×Q8×D5 | C22×C3 | 1 | 2 | yes | — |
| 42 | C2×#711 | — | 3 | 2 | no | — |
| 43 | C2×D4×D5 | — | 3 | 2 | no | — |
| 44 | C2×#709 | — | 3 | 1 | no | — |
| 45 | C2×#709 | — | 3 | 1 | no | — |
| 46 | C22×D20 | — | 3 | 1 | no | — |
| 47 | C22×Dic10 | — | 3 | 1 | no | — |
| 48 | C4×C5×Q8 | C22×C3 | 1 | 2 | yes | — |
| 49 | C4×C5×D4 | — | 3 | 2 | no | — |
| 50 | C5×#117 | — | 3 | 1 | no | — |
| 51 | C2×C42×C5 | — | 3 | 1 | no | — |
| 52 | #4076 | — | 3 | 4 | no | — |
| 53 | C2×#685 | — | 3 | 4 | no | — |
| 54 | #4043 | — | 3 | 4 | no | — |
| 55 | #4041 | — | 3 | 4 | no | — |
| 56 | #4032 | — | 3 | 4 | no | — |
| 57 | #4028 | — | 3 | 4 | no | — |
| 58 | #4021 | — | 3 | 2 | no | — |
| 59 | #4021 | — | 3 | 1 | no | — |
| 60 | #4021 | — | 3 | 4 | no | — |
| 61 | #4021 | A4 | 1 | 1 | yes | characteristic |
| 62 | #4020 | — | 3 | 1 | no | — |
| 63 | C4×D20 | — | 3 | 4 | no | — |
| 64 | #4015 | — | 3 | 1 | no | — |
| 65 | #3500 | — | 5 | 1 | no | Sylow |
| 66 | C22×C3×D5 | — | 4 | 2 | no | — |
| 67 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 68 | C2×C3×C4×C5 | — | 4 | 2 | no | — |
| 69 | C2×C3×Dic5 | — | 4 | 2 | no | — |
| 70 | C3×D20 | — | 8 | 2 | no | — |
| 71 | C3×Dic10 | — | 8 | 2 | no | — |
| 72 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | 2−1+4⋊C3 | — | 10 | 2 | no | — |
| 74 | #994 | — | 10 | 2 | no | — |
| 75 | C2×#41⋊C3 | — | 5 | 2 | no | — |
| 76 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 77 | C22×SL(2,𝔽3) | — | 5 | 2 | no | — |
| 78 | C3×#124 | — | 20 | 1 | no | — |
| 79 | C4×SL(2,𝔽3) | C2×D5 | 1 | 2 | yes | complemented |
| 80 | C23×D5 | — | 3 | 2 | no | — |
| 81 | C5×#41 | — | 3 | 2 | no | — |
| 82 | C5×#41 | C3×D4 | 1 | 2 | yes | — |
| 83 | C2×C5×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 84 | C2×C5×D4 | — | 3 | 1 | no | — |
| 85 | C22×C4×C5 | — | 3 | 1 | no | — |
| 86 | C22×C4×C5 | — | 3 | 2 | no | — |
| 87 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 88 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 89 | C22×Dic5 | — | 3 | 2 | no | — |
| 90 | #713 | — | 2 | 2 | no | — |
| 91 | #713 | — | 6 | 2 | no | — |
| 92 | Q8×D5 | — | 2 | 2 | no | — |
| 93 | Q8×D5 | — | 6 | 2 | no | — |
| 94 | #711 | — | 6 | 4 | no | — |
| 95 | #711 | — | 6 | 4 | no | — |
| 96 | D4×D5 | — | 6 | 4 | no | — |
| 97 | D4×D5 | — | 6 | 4 | no | — |
| 98 | #709 | — | 6 | 2 | no | — |
| 99 | #709 | — | 6 | 2 | no | — |
| 100 | #709 | — | 6 | 2 | no | — |
| 101 | #709 | — | 6 | 2 | no | — |
| 102 | C2×D20 | — | 3 | 2 | no | — |
| 103 | C2×D20 | — | 3 | 1 | no | — |
| 104 | C2×D20 | — | 3 | 4 | no | — |
| 105 | C2×D20 | — | 6 | 2 | no | — |
| 106 | C2×D20 | — | 6 | 2 | no | — |
| 107 | C2×D20 | C2×A4 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×D5 | — | 3 | 2 | no | — |
| 109 | C2×C4×D5 | — | 3 | 2 | no | — |
| 110 | C2×Dic10 | — | 3 | 1 | no | — |
| 111 | C2×Dic10 | — | 3 | 2 | no | — |
| 112 | C2×Dic10 | — | 6 | 2 | no | — |
| 113 | C2×Dic10 | — | 6 | 2 | no | — |
| 114 | C2×Dic10 | C2×A4 | 1 | 1 | yes | characteristic |
| 115 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 116 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 117 | C42×C5 | — | 3 | 1 | no | — |
| 118 | C42×C5 | — | 3 | 2 | no | — |
| 119 | C42×C5 | C2×A4 | 1 | 1 | yes | characteristic |
| 120 | #685 | — | 3 | 8 | no | — |
| 121 | #685 | — | 3 | 4 | no | — |
| 122 | #685 | C2×A4 | 1 | 4 | yes | — |
| 123 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 124 | C2×2−1+4 | — | 5 | 1 | no | — |
| 125 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 126 | #548 | — | 5 | 4 | no | — |
| 127 | #546 | — | 15 | 4 | no | — |
| 128 | #536 | — | 15 | 1 | no | — |
| 129 | #535 | — | 15 | 1 | no | — |
| 130 | #532 | — | 15 | 1 | no | — |
| 131 | C2×#124 | — | 15 | 1 | no | — |
| 132 | C4×#41 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 133 | C22×C3×C5 | — | 4 | 1 | no | — |
| 134 | C2×C3×D5 | — | 8 | 2 | no | — |
| 135 | C2×C3×D5 | — | 8 | 4 | no | — |
| 136 | C3×C4×C5 | — | 4 | 2 | no | — |
| 137 | C3×C4×C5 | — | 8 | 2 | no | — |
| 138 | C3×Dic5 | — | 8 | 2 | no | — |
| 139 | C2×C3×Q8 | — | 20 | 1 | no | — |
| 140 | C2×C3×D4 | — | 20 | 1 | no | — |
| 141 | #41⋊C3 | — | 10 | 2 | no | — |
| 142 | #41⋊C3 | D20 | 1 | 2 | yes | complemented |
| 143 | C2×SL(2,𝔽3) | — | 10 | 2 | no | — |
| 144 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 145 | C3×C22⋊C4 | — | 20 | 4 | no | — |
| 146 | C3×C42 | — | 4 | 1 | no | — |
| 147 | C23×C5 | — | 3 | 1 | no | — |
| 148 | C22×D5 | — | 3 | 2 | no | — |
| 149 | C22×D5 | — | 6 | 4 | no | — |
| 150 | C22×D5 | — | 12 | 4 | no | — |
| 151 | C22×D5 | C22×A4 | 1 | 2 | yes | — |
| 152 | C5×Q8 | — | 3 | 1 | no | — |
| 153 | C5×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 154 | C5×D4 | — | 3 | 2 | no | — |
| 155 | C5×D4 | — | 3 | 2 | no | — |
| 156 | C2×C4×C5 | — | 3 | 1 | no | — |
| 157 | C2×C4×C5 | — | 3 | 2 | no | — |
| 158 | C2×C4×C5 | — | 3 | 2 | no | — |
| 159 | C2×C4×C5 | — | 3 | 2 | no | — |
| 160 | C2×C4×C5 | — | 12 | 2 | no | — |
| 161 | C2×C4×C5 | C22×A4 | 1 | 2 | yes | — |
| 162 | C2×C4×C5 | C22×A4 | 1 | 1 | yes | characteristic |
| 163 | C22⋊D5 | — | 6 | 4 | no | — |
| 164 | C22⋊D5 | — | 6 | 4 | no | — |
| 165 | C2×Dic5 | — | 3 | 2 | no | — |
| 166 | C2×Dic5 | — | 6 | 4 | no | — |
| 167 | C2×Dic5 | C22×A4 | 1 | 2 | yes | — |
| 168 | D20 | — | 2 | 2 | no | — |
| 169 | D20 | — | 6 | 2 | no | — |
| 170 | D20 | — | 6 | 2 | no | — |
| 171 | D20 | — | 6 | 2 | no | — |
| 172 | D20 | — | 12 | 4 | no | — |
| 173 | C4×D5 | — | 6 | 2 | no | — |
| 174 | C4×D5 | — | 6 | 2 | no | — |
| 175 | C4×D5 | — | 6 | 2 | no | — |
| 176 | C4×D5 | — | 6 | 2 | no | — |
| 177 | Dic10 | — | 2 | 2 | no | — |
| 178 | Dic10 | — | 6 | 2 | no | — |
| 179 | Dic10 | — | 6 | 2 | no | — |
| 180 | Dic10 | — | 6 | 2 | no | — |
| 181 | 2−1+4 | — | 10 | 2 | no | — |
| 182 | 2−1+4 | — | 30 | 2 | no | — |
| 183 | H(5,𝔽2) | — | 10 | 2 | no | — |
| 184 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 185 | C2×#41 | — | 5 | 2 | no | — |
| 186 | C2×#41 | — | 15 | 1 | no | — |
| 187 | C2×#41 | — | 15 | 1 | no | — |
| 188 | C2×#41 | — | 15 | 2 | no | — |
| 189 | C2×#41 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 190 | C22×Q8 | — | 5 | 2 | no | — |
| 191 | C22×Q8 | — | 15 | 1 | no | — |
| 192 | C22×D4 | — | 15 | 1 | no | — |
| 193 | C22×D4 | — | 15 | 2 | no | — |
| 194 | C4⋊Q8 | — | 15 | 1 | no | — |
| 195 | #127 | — | 15 | 1 | no | — |
| 196 | #124 | — | 5 | 1 | no | — |
| 197 | #124 | — | 15 | 2 | no | — |
| 198 | #124 | — | 15 | 4 | no | — |
| 199 | #124 | — | 15 | 1 | no | — |
| 200 | #123 | — | 15 | 4 | no | — |
| 201 | C22⋊Q8 | — | 15 | 4 | no | — |
| 202 | #121 | — | 15 | 4 | no | — |
| 203 | #121 | — | 15 | 4 | no | — |
| 204 | #120 | — | 15 | 4 | no | — |
| 205 | C4×Q8 | C2×C3×D5 | 1 | 2 | yes | — |
| 206 | C4×D4 | — | 3 | 2 | no | — |
| 207 | C4×D4 | — | 15 | 4 | no | — |
| 208 | #117 | — | 3 | 1 | no | — |
| 209 | C2×C22⋊C4 | — | 15 | 4 | no | — |
| 210 | C2×C42 | — | 3 | 1 | no | — |
| 211 | C2×C3×C5 | — | 4 | 1 | no | — |
| 212 | C2×C3×C5 | — | 4 | 2 | no | — |
| 213 | C3×D5 | — | 16 | 2 | no | — |
| 214 | C23×C3 | — | 20 | 2 | no | — |
| 215 | C3×Q8 | — | 40 | 2 | no | — |
| 216 | C3×D4 | — | 40 | 2 | no | — |
| 217 | C2×C3×C4 | — | 4 | 1 | no | — |
| 218 | C2×C3×C4 | — | 4 | 2 | no | — |
| 219 | C2×C3×C4 | — | 20 | 2 | no | — |
| 220 | SL(2,𝔽3) | C2×D20 | 1 | 1 | yes | characteristic |
| 221 | C22×C5 | — | 3 | 2 | no | — |
| 222 | C22×C5 | — | 6 | 2 | no | — |
| 223 | C22×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 224 | C2×D5 | — | 2 | 2 | no | — |
| 225 | C2×D5 | — | 2 | 4 | no | — |
| 226 | C2×D5 | — | 6 | 2 | no | — |
| 227 | C2×D5 | — | 6 | 4 | no | — |
| 228 | C2×D5 | — | 24 | 4 | no | — |
| 229 | C4×C5 | — | 2 | 2 | no | — |
| 230 | C4×C5 | — | 3 | 1 | no | — |
| 231 | C4×C5 | — | 3 | 1 | no | — |
| 232 | C4×C5 | — | 6 | 2 | no | — |
| 233 | C4×C5 | D4×A4 | 1 | 2 | yes | — |
| 234 | Dic5 | — | 2 | 2 | no | — |
| 235 | Dic5 | — | 6 | 2 | no | — |
| 236 | C24 | — | 15 | 2 | no | — |
| 237 | #41 | — | 3 | 2 | no | — |
| 238 | #41 | — | 10 | 2 | no | — |
| 239 | #41 | — | 30 | 2 | no | — |
| 240 | #41 | — | 30 | 2 | no | — |
| 241 | #41 | — | 30 | 2 | no | — |
| 242 | #41 | — | 30 | 2 | no | — |
| 243 | #41 | — | 30 | 4 | no | — |
| 244 | #41 | — | 30 | 4 | no | — |
| 245 | #41 | — | 30 | 2 | no | — |
| 246 | #41 | C3×D20 | 1 | 2 | yes | — |
| 247 | C2×Q8 | — | 5 | 1 | no | — |
| 248 | C2×Q8 | — | 10 | 2 | no | — |
| 249 | C2×Q8 | — | 15 | 2 | no | — |
| 250 | C2×Q8 | — | 15 | 1 | no | — |
| 251 | C2×Q8 | — | 30 | 2 | no | — |
| 252 | C2×Q8 | — | 30 | 2 | no | — |
| 253 | C2×Q8 | — | 30 | 2 | no | — |
| 254 | C2×Q8 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 255 | C2×D4 | — | 3 | 1 | no | — |
| 256 | C2×D4 | — | 5 | 1 | no | — |
| 257 | C2×D4 | — | 15 | 2 | no | — |
| 258 | C2×D4 | — | 15 | 4 | no | — |
| 259 | C2×D4 | — | 15 | 2 | no | — |
| 260 | C2×D4 | — | 15 | 2 | no | — |
| 261 | C2×D4 | — | 15 | 1 | no | — |
| 262 | C2×D4 | — | 30 | 2 | no | — |
| 263 | C2×D4 | — | 30 | 2 | no | — |
| 264 | C2×D4 | — | 30 | 4 | no | — |
| 265 | C2×D4 | — | 30 | 4 | no | — |
| 266 | C22×C4 | — | 3 | 1 | no | — |
| 267 | C22×C4 | — | 3 | 2 | no | — |
| 268 | C22×C4 | — | 15 | 2 | no | — |
| 269 | C22×C4 | — | 15 | 2 | no | — |
| 270 | C22×C4 | — | 15 | 2 | no | — |
| 271 | C4⋊C4 | — | 3 | 2 | no | — |
| 272 | C4⋊C4 | — | 15 | 4 | no | — |
| 273 | C22⋊C4 | — | 3 | 2 | no | — |
| 274 | C22⋊C4 | — | 5 | 4 | no | — |
| 275 | C22⋊C4 | — | 15 | 8 | no | — |
| 276 | C22⋊C4 | — | 15 | 4 | no | — |
| 277 | C42 | — | 3 | 1 | no | — |
| 278 | C42 | — | 3 | 2 | no | — |
| 279 | C42 | D5×A4 | 1 | 1 | yes | characteristic |
| 280 | C3×C5 | — | 4 | 1 | no | Hall |
| 281 | C22×C3 | — | 4 | 1 | no | — |
| 282 | C22×C3 | — | 40 | 2 | no | — |
| 283 | C22×C3 | — | 40 | 4 | no | — |
| 284 | C3×C4 | — | 4 | 2 | no | — |
| 285 | C3×C4 | — | 8 | 2 | no | — |
| 286 | C3×C4 | — | 40 | 2 | no | — |
| 287 | C2×C5 | — | 6 | 2 | no | — |
| 288 | C2×C5 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 289 | C2×C5 | #5945 | 1 | 2 | yes | — |
| 290 | D5 | — | 4 | 2 | no | — |
| 291 | D5 | — | 12 | 2 | no | — |
| 292 | C23 | — | 3 | 1 | no | — |
| 293 | C23 | — | 5 | 2 | no | — |
| 294 | C23 | — | 15 | 2 | no | — |
| 295 | C23 | — | 30 | 4 | no | — |
| 296 | C23 | — | 60 | 4 | no | — |
| 297 | Q8 | — | 3 | 1 | no | — |
| 298 | Q8 | — | 10 | 2 | no | — |
| 299 | Q8 | — | 30 | 2 | no | — |
| 300 | Q8 | — | 30 | 2 | no | — |
| 301 | Q8 | — | 30 | 2 | no | — |
| 302 | Q8 | C2×C3×D20 | 1 | 1 | yes | characteristic |
| 303 | D4 | — | 3 | 2 | no | — |
| 304 | D4 | — | 3 | 2 | no | — |
| 305 | D4 | — | 10 | 2 | no | — |
| 306 | D4 | — | 30 | 2 | no | — |
| 307 | D4 | — | 30 | 2 | no | — |
| 308 | D4 | — | 30 | 4 | no | — |
| 309 | D4 | — | 30 | 4 | no | — |
| 310 | D4 | — | 30 | 2 | no | — |
| 311 | D4 | — | 60 | 4 | no | — |
| 312 | C2×C4 | — | 3 | 1 | no | — |
| 313 | C2×C4 | — | 3 | 2 | no | — |
| 314 | C2×C4 | — | 3 | 2 | no | — |
| 315 | C2×C4 | — | 3 | 2 | no | — |
| 316 | C2×C4 | — | 5 | 2 | no | — |
| 317 | C2×C4 | — | 12 | 2 | no | — |
| 318 | C2×C4 | — | 15 | 2 | no | — |
| 319 | C2×C4 | — | 30 | 2 | no | — |
| 320 | C2×C4 | — | 30 | 2 | no | — |
| 321 | C2×C4 | — | 30 | 2 | no | — |
| 322 | C2×C4 | — | 30 | 2 | no | — |
| 323 | C2×C4 | — | 30 | 4 | no | — |
| 324 | C2×C4 | C2×D5×A4 | 1 | 2 | yes | — |
| 325 | C2×C4 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 326 | C2×C3 | — | 4 | 1 | no | — |
| 327 | C2×C3 | — | 4 | 2 | no | — |
| 328 | C2×C3 | — | 80 | 2 | no | — |
| 329 | C5 | #3500⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 330 | C22 | — | 3 | 2 | no | — |
| 331 | C22 | — | 6 | 2 | no | — |
| 332 | C22 | — | 10 | 2 | no | — |
| 333 | C22 | — | 10 | 4 | no | — |
| 334 | C22 | — | 30 | 2 | no | — |
| 335 | C22 | — | 30 | 4 | no | — |
| 336 | C22 | — | 120 | 4 | no | — |
| 337 | C22 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 338 | C4 | — | 2 | 2 | no | — |
| 339 | C4 | — | 3 | 1 | no | — |
| 340 | C4 | — | 3 | 1 | no | — |
| 341 | C4 | — | 6 | 2 | no | — |
| 342 | C4 | — | 10 | 2 | no | — |
| 343 | C4 | — | 30 | 2 | no | — |
| 344 | C4 | A4×D20 | 1 | 2 | yes | — |
| 345 | C3 | — | 4 | 1 | no | Sylow |
| 346 | C2 | — | 6 | 2 | no | — |
| 347 | C2 | — | 20 | 2 | no | — |
| 348 | C2 | — | 60 | 2 | no | — |
| 349 | C2 | C2×A4×D20 | 1 | 1 | yes | characteristic |
| 350 | C2 | #66283⋊C3 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×A4 |
| commutator, cosocle | C2×C5×Q8 | C23×C3 |
| Fitting | C4×C5×#41 | C2×C3 |
| socle | C22×C5 | C23×A4 |
| hypercenter | C42 | D5×A4 |
| hypocenter | C5×Q8 | C2×C3×D4 |
| LCS | G ▷ C2×C5×Q8 ▷ C5×Q8 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4150⋊C3 | C2 | semidirect |
| 2. C2×C5⋊#994 | C2 | semidirect |
| 3. C4×C5×#41⋊C3 | C2 | semidirect |
| 4. #65910⋊C3 | C2 | semidirect |
| 5. #10617748 | C3 | semidirect |
| 9. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 15. C2×#4149 | C2×C3 | semidirect |
| 16. C4×C5×#41 | C2×C3 | semidirect |
| 17. #65910 | C2×C3 | semidirect |
| 25. C5×#41⋊C3 | D4 | semidirect |
| 34. C4×#41⋊C3 | D5 | semidirect |
| 79. C4×SL(2,𝔽3) | C2×D5 | semidirect |
| 132. C4×#41 | C3×D5 | semidirect |
| 142. #41⋊C3 | D20 | semidirect |
| 329. C5 | #3500⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4150⋊C3 | 2 |
| C2×C5⋊#994 | 2 |
| C4×C5×#41⋊C3 | 2 |
| #65910⋊C3 | 2 |
| #10617748 | 3 |
| C3×#4021 | 4 |
| #3500⋊C3 | 5 |