Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2482 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 2482 conjugacy classes of subgroups — too many to draw. Only its 255 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×C5×#994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756944 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 3 | C2×#4150⋊C3 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×D5×#41⋊C3 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×#66285 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 6 | C2×C3×#713 | — | 4 | 1 | no | maximal |
| 7 | C5×#994 | C22 | 1 | 4 | yes | complemented |
| 8 | C2×C5×#41⋊C3 | C22 | 1 | 3 | yes | complemented |
| 9 | #4150⋊C3 | C22 | 1 | 12 | yes | complemented |
| 10 | D5×#41⋊C3 | C22 | 1 | 12 | yes | complemented |
| 11 | C2×D5×SL(2,𝔽3) | C22 | 1 | 3 | yes | complemented |
| 12 | C2×C5⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×#5945 | — | 5 | 1 | no | maximal, Hall |
| 14 | C2×C5×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #66285 | — | 3 | 8 | no | — |
| 16 | #66285 | C2×C3 | 1 | 8 | yes | complemented |
| 17 | C2×#4150 | — | 3 | 1 | no | — |
| 18 | C2×#4150 | C2×C3 | 1 | 3 | yes | complemented |
| 19 | C2×D5×#41 | — | 3 | 1 | no | — |
| 20 | C2×D5×#41 | C2×C3 | 1 | 3 | yes | complemented |
| 21 | C2×#4144 | — | 3 | 3 | no | — |
| 22 | C22×#711 | — | 3 | 3 | no | — |
| 23 | C2×C3×C5×Q8 | — | 4 | 1 | no | — |
| 24 | C3×#713 | — | 4 | 8 | no | — |
| 25 | C2×C3×D20 | — | 4 | 3 | no | — |
| 26 | C2×C3×C4×D5 | — | 4 | 3 | no | — |
| 27 | C5×#41⋊C3 | C23 | 1 | 6 | yes | complemented |
| 28 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 29 | D5×SL(2,𝔽3) | C23 | 1 | 6 | yes | complemented |
| 30 | C5⋊(#41⋊C3) | C23 | 1 | 2 | yes | complemented |
| 31 | #5945 | — | 5 | 8 | no | — |
| 32 | C2×2−1+4⋊C3 | — | 5 | 3 | no | — |
| 33 | C2×#994 | D5 | 1 | 1 | yes | characteristic, complemented |
| 34 | C22×#41⋊C3 | — | 5 | 3 | no | — |
| 35 | C5×H(5,𝔽2) | — | 3 | 4 | no | — |
| 36 | C5×H(5,𝔽2) | C22×C3 | 1 | 4 | yes | complemented |
| 37 | C2×C5×#41 | — | 3 | 1 | no | — |
| 38 | C2×C5×#41 | C22×C3 | 1 | 3 | yes | — |
| 39 | C22×C5×D4 | — | 3 | 3 | no | — |
| 40 | C22×C22⋊D5 | — | 3 | 6 | no | — |
| 41 | C23×Dic5 | — | 3 | 2 | no | — |
| 42 | #4150 | — | 3 | 8 | no | — |
| 43 | #4150 | — | 3 | 8 | no | — |
| 44 | #4150 | — | 3 | 12 | no | — |
| 45 | #4150 | C22×C3 | 1 | 12 | yes | complemented |
| 46 | D5×#41 | — | 3 | 8 | no | — |
| 47 | D5×#41 | — | 3 | 8 | no | — |
| 48 | D5×#41 | — | 3 | 12 | no | — |
| 49 | D5×#41 | C22×C3 | 1 | 12 | yes | complemented |
| 50 | C2×#713 | A4 | 1 | 1 | yes | characteristic |
| 51 | C2×#713 | C22×C3 | 1 | 1 | yes | characteristic |
| 52 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 53 | C2×Q8×D5 | C22×C3 | 1 | 3 | yes | — |
| 54 | #4144 | — | 3 | 24 | no | — |
| 55 | #4144 | — | 3 | 24 | no | — |
| 56 | C2×#711 | — | 3 | 6 | no | — |
| 57 | C2×#711 | — | 3 | 24 | no | — |
| 58 | C2×#711 | — | 3 | 6 | no | — |
| 59 | C2×#711 | — | 3 | 3 | no | — |
| 60 | C2×#711 | — | 3 | 24 | no | — |
| 61 | C2×#711 | — | 3 | 3 | no | — |
| 62 | C2×D4×D5 | — | 3 | 3 | no | — |
| 63 | C2×D4×D5 | — | 3 | 3 | no | — |
| 64 | C2×#709 | — | 3 | 3 | no | — |
| 65 | C2×#709 | — | 3 | 3 | no | — |
| 66 | C22×C4×D5 | — | 3 | 3 | no | — |
| 67 | C22×Dic10 | — | 3 | 3 | no | — |
| 68 | C2×#585 | — | 5 | 1 | no | Sylow |
| 69 | C22×C3×D5 | — | 4 | 3 | no | — |
| 70 | C3×C5×Q8 | — | 4 | 4 | no | — |
| 71 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 72 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 73 | C3×D20 | — | 4 | 12 | no | — |
| 74 | C3×C4×D5 | — | 4 | 12 | no | — |
| 75 | C5×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 76 | C2×C3×#41 | — | 20 | 1 | no | — |
| 77 | 2−1+4⋊C3 | — | 5 | 12 | no | — |
| 78 | #994 | C2×D5 | 1 | 4 | yes | complemented |
| 79 | C2×#41⋊C3 | — | 5 | 12 | no | — |
| 80 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 81 | C2×#41⋊C3 | C2×D5 | 1 | 3 | yes | complemented |
| 82 | C22×SL(2,𝔽3) | — | 5 | 3 | no | — |
| 83 | C24×C5 | — | 3 | 2 | no | — |
| 84 | C23×D5 | — | 3 | 3 | no | — |
| 85 | C5×#41 | — | 3 | 4 | no | — |
| 86 | C5×#41 | — | 3 | 4 | no | — |
| 87 | C5×#41 | — | 3 | 6 | no | — |
| 88 | C5×#41 | C23×C3 | 1 | 6 | yes | — |
| 89 | C2×C5×Q8 | C2×A4 | 1 | 1 | yes | characteristic |
| 90 | C2×C5×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 91 | C2×C5×D4 | — | 3 | 3 | no | — |
| 92 | C2×C5×D4 | — | 3 | 12 | no | — |
| 93 | C2×C5×D4 | — | 3 | 12 | no | — |
| 94 | C2×C5×D4 | — | 3 | 3 | no | — |
| 95 | C22×C4×C5 | — | 3 | 3 | no | — |
| 96 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 97 | C2×C22⋊D5 | — | 3 | 48 | no | — |
| 98 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 99 | C22×Dic5 | — | 3 | 6 | no | — |
| 100 | C22×Dic5 | — | 3 | 16 | no | — |
| 101 | C22×Dic5 | — | 3 | 3 | no | — |
| 102 | #713 | — | 3 | 2 | no | — |
| 103 | #713 | C2×A4 | 1 | 8 | yes | — |
| 104 | #713 | C23×C3 | 1 | 2 | yes | — |
| 105 | Q8×D5 | — | 3 | 8 | no | — |
| 106 | Q8×D5 | — | 3 | 6 | no | — |
| 107 | Q8×D5 | C23×C3 | 1 | 6 | yes | — |
| 108 | #711 | — | 3 | 12 | no | — |
| 109 | #711 | — | 3 | 24 | no | — |
| 110 | #711 | — | 3 | 48 | no | — |
| 111 | #711 | — | 3 | 24 | no | — |
| 112 | #711 | — | 3 | 12 | no | — |
| 113 | #711 | — | 3 | 24 | no | — |
| 114 | D4×D5 | — | 3 | 12 | no | — |
| 115 | D4×D5 | — | 3 | 12 | no | — |
| 116 | D4×D5 | — | 3 | 24 | no | — |
| 117 | #709 | — | 3 | 12 | no | — |
| 118 | #709 | — | 3 | 12 | no | — |
| 119 | #709 | — | 3 | 12 | no | — |
| 120 | #709 | — | 3 | 12 | no | — |
| 121 | C2×D20 | — | 3 | 1 | no | — |
| 122 | C2×D20 | C2×A4 | 1 | 3 | yes | — |
| 123 | C2×C4×D5 | — | 3 | 3 | no | — |
| 124 | C2×C4×D5 | — | 3 | 3 | no | — |
| 125 | C2×C4×D5 | — | 3 | 1 | no | — |
| 126 | C2×C4×D5 | — | 3 | 12 | no | — |
| 127 | C2×C4×D5 | — | 3 | 12 | no | — |
| 128 | C2×C4×D5 | C2×A4 | 1 | 3 | yes | — |
| 129 | C2×Dic10 | — | 3 | 12 | no | — |
| 130 | C2×Dic10 | — | 3 | 3 | no | — |
| 131 | C2×Dic10 | — | 3 | 3 | no | — |
| 132 | C2×Dic10 | — | 3 | 12 | no | — |
| 133 | #585 | — | 5 | 8 | no | — |
| 134 | #585 | — | 15 | 8 | no | — |
| 135 | C2×2−1+4 | — | 5 | 3 | no | — |
| 136 | C2×2−1+4 | — | 15 | 1 | no | — |
| 137 | C2×H(5,𝔽2) | — | 15 | 3 | no | — |
| 138 | C2×H(5,𝔽2) | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 139 | C22×#41 | — | 5 | 3 | no | — |
| 140 | C22×#41 | — | 15 | 3 | no | — |
| 141 | C22×#41 | — | 15 | 1 | no | — |
| 142 | C22×C3×C5 | — | 4 | 1 | no | — |
| 143 | C2×C3×D5 | — | 4 | 6 | no | — |
| 144 | C2×C3×D5 | — | 8 | 6 | no | — |
| 145 | C3×C4×C5 | — | 4 | 6 | no | — |
| 146 | C3×Dic5 | — | 4 | 2 | no | — |
| 147 | C3×#41 | — | 20 | 8 | no | — |
| 148 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 149 | C2×C3×D4 | — | 20 | 3 | no | — |
| 150 | C22×C3×C4 | — | 20 | 3 | no | — |
| 151 | #41⋊C3 | — | 5 | 2 | no | — |
| 152 | #41⋊C3 | C22×D5 | 1 | 6 | yes | complemented |
| 153 | C2×SL(2,𝔽3) | — | 5 | 6 | no | — |
| 154 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 155 | C23×C5 | — | 3 | 8 | no | — |
| 156 | C23×C5 | — | 3 | 3 | no | — |
| 157 | C23×C5 | — | 12 | 4 | no | — |
| 158 | C22×D5 | — | 3 | 1 | no | — |
| 159 | C22×D5 | — | 3 | 12 | no | — |
| 160 | C22×D5 | — | 12 | 6 | no | — |
| 161 | C22×D5 | C22×A4 | 1 | 3 | yes | — |
| 162 | C5×Q8 | — | 3 | 1 | no | — |
| 163 | C5×Q8 | C22×A4 | 1 | 4 | yes | — |
| 164 | C5×Q8 | C24×C3 | 1 | 1 | yes | characteristic |
| 165 | C5×D4 | — | 3 | 6 | no | — |
| 166 | C5×D4 | — | 3 | 6 | no | — |
| 167 | C5×D4 | — | 3 | 12 | no | — |
| 168 | C2×C4×C5 | — | 3 | 1 | no | — |
| 169 | C2×C4×C5 | — | 3 | 6 | no | — |
| 170 | C2×C4×C5 | — | 3 | 6 | no | — |
| 171 | C2×C4×C5 | C22×A4 | 1 | 3 | yes | — |
| 172 | C22⋊D5 | — | 3 | 24 | no | — |
| 173 | C22⋊D5 | — | 3 | 24 | no | — |
| 174 | C2×Dic5 | — | 3 | 24 | no | — |
| 175 | C2×Dic5 | — | 3 | 3 | no | — |
| 176 | C2×Dic5 | — | 3 | 12 | no | — |
| 177 | C2×Dic5 | C22×A4 | 1 | 1 | yes | characteristic |
| 178 | D20 | — | 3 | 2 | no | — |
| 179 | D20 | — | 3 | 2 | no | — |
| 180 | D20 | C22×A4 | 1 | 12 | yes | — |
| 181 | C4×D5 | — | 3 | 6 | no | — |
| 182 | C4×D5 | — | 3 | 6 | no | — |
| 183 | C4×D5 | — | 3 | 12 | no | — |
| 184 | C4×D5 | — | 3 | 2 | no | — |
| 185 | C4×D5 | — | 3 | 2 | no | — |
| 186 | C4×D5 | C22×A4 | 1 | 12 | yes | — |
| 187 | Dic10 | — | 3 | 6 | no | — |
| 188 | Dic10 | — | 3 | 12 | no | — |
| 189 | Dic10 | — | 3 | 6 | no | — |
| 190 | 2−1+4 | — | 5 | 12 | no | — |
| 191 | 2−1+4 | — | 15 | 12 | no | — |
| 192 | 2−1+4 | — | 15 | 8 | no | — |
| 193 | 2−1+4 | — | 15 | 8 | no | — |
| 194 | H(5,𝔽2) | — | 3 | 4 | no | — |
| 195 | H(5,𝔽2) | — | 15 | 24 | no | — |
| 196 | H(5,𝔽2) | — | 15 | 24 | no | — |
| 197 | H(5,𝔽2) | C2×C3×D5 | 1 | 4 | yes | complemented |
| 198 | C2×#41 | — | 3 | 1 | no | — |
| 199 | C2×#41 | — | 5 | 1 | no | — |
| 200 | C2×#41 | — | 5 | 12 | no | — |
| 201 | C2×#41 | — | 5 | 1 | no | — |
| 202 | C2×#41 | — | 15 | 3 | no | — |
| 203 | C2×#41 | — | 15 | 3 | no | — |
| 204 | C2×#41 | — | 15 | 3 | no | — |
| 205 | C2×#41 | — | 15 | 24 | no | — |
| 206 | C2×#41 | — | 15 | 6 | no | — |
| 207 | C2×#41 | — | 15 | 24 | no | — |
| 208 | C2×#41 | — | 15 | 6 | no | — |
| 209 | C2×#41 | — | 15 | 8 | no | — |
| 210 | C2×#41 | — | 15 | 8 | no | — |
| 211 | C2×#41 | — | 15 | 3 | no | — |
| 212 | C2×#41 | — | 15 | 12 | no | — |
| 213 | C2×#41 | C2×C3×D5 | 1 | 3 | yes | — |
| 214 | C22×Q8 | — | 5 | 3 | no | — |
| 215 | C22×Q8 | — | 15 | 3 | no | — |
| 216 | C22×Q8 | — | 15 | 1 | no | — |
| 217 | C22×D4 | — | 3 | 3 | no | — |
| 218 | C22×D4 | — | 15 | 3 | no | — |
| 219 | C22×D4 | — | 15 | 3 | no | — |
| 220 | C22×D4 | — | 15 | 6 | no | — |
| 221 | C23×C4 | — | 15 | 3 | no | — |
| 222 | C23×C4 | — | 15 | 2 | no | — |
| 223 | C2×C3×C5 | — | 4 | 2 | no | — |
| 224 | C2×C3×C5 | — | 4 | 1 | no | — |
| 225 | C3×D5 | — | 8 | 6 | no | — |
| 226 | C23×C3 | — | 20 | 3 | no | — |
| 227 | C3×Q8 | — | 4 | 4 | no | — |
| 228 | C3×D4 | — | 20 | 12 | no | — |
| 229 | C2×C3×C4 | — | 4 | 3 | no | — |
| 230 | C2×C3×C4 | — | 20 | 12 | no | — |
| 231 | C2×C3×C4 | — | 20 | 1 | no | — |
| 232 | SL(2,𝔽3) | C23×D5 | 1 | 1 | yes | characteristic |
| 233 | C22×C5 | — | 3 | 6 | no | — |
| 234 | C22×C5 | — | 6 | 6 | no | — |
| 235 | C22×C5 | — | 12 | 8 | no | — |
| 236 | C22×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 237 | C2×D5 | — | 2 | 6 | no | — |
| 238 | C2×D5 | — | 3 | 2 | no | — |
| 239 | C2×D5 | — | 6 | 2 | no | — |
| 240 | C2×D5 | — | 12 | 12 | no | — |
| 241 | C2×D5 | C23×A4 | 1 | 6 | yes | — |
| 242 | C4×C5 | — | 3 | 1 | no | — |
| 243 | C4×C5 | — | 3 | 1 | no | — |
| 244 | C4×C5 | C23×A4 | 1 | 6 | yes | — |
| 245 | Dic5 | — | 3 | 6 | no | — |
| 246 | Dic5 | C23×A4 | 1 | 2 | yes | — |
| 247 | C24 | — | 3 | 2 | no | — |
| 248 | C24 | — | 15 | 3 | no | — |
| 249 | #41 | — | 3 | 4 | no | — |
| 250 | #41 | — | 3 | 4 | no | — |
| 251 | #41 | — | 3 | 6 | no | — |
| 252 | #41 | — | 5 | 8 | no | — |
| 253 | #41 | — | 5 | 2 | no | — |
| 254 | #41 | — | 15 | 12 | no | — |
| 255 | #41 | — | 15 | 12 | no | — |
| 256 | #41 | — | 15 | 12 | no | — |
| 257 | #41 | — | 15 | 12 | no | — |
| 258 | #41 | — | 15 | 24 | no | — |
| 259 | #41 | — | 15 | 12 | no | — |
| 260 | #41 | — | 15 | 24 | no | — |
| 261 | #41 | — | 15 | 48 | no | — |
| 262 | #41 | — | 15 | 24 | no | — |
| 263 | #41 | — | 15 | 12 | no | — |
| 264 | #41 | — | 15 | 2 | no | — |
| 265 | #41 | C22×C3×D5 | 1 | 6 | yes | — |
| 266 | C2×Q8 | — | 5 | 6 | no | — |
| 267 | C2×Q8 | — | 15 | 12 | no | — |
| 268 | C2×Q8 | — | 15 | 12 | no | — |
| 269 | C2×Q8 | — | 15 | 3 | no | — |
| 270 | C2×Q8 | — | 15 | 8 | no | — |
| 271 | C2×Q8 | — | 15 | 3 | no | — |
| 272 | C2×Q8 | — | 15 | 6 | no | — |
| 273 | C2×Q8 | D5×A4 | 1 | 1 | yes | characteristic |
| 274 | C2×Q8 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 275 | C2×D4 | — | 3 | 3 | no | — |
| 276 | C2×D4 | — | 3 | 12 | no | — |
| 277 | C2×D4 | — | 3 | 12 | no | — |
| 278 | C2×D4 | — | 3 | 3 | no | — |
| 279 | C2×D4 | — | 5 | 3 | no | — |
| 280 | C2×D4 | — | 15 | 1 | no | — |
| 281 | C2×D4 | — | 15 | 24 | no | — |
| 282 | C2×D4 | — | 15 | 12 | no | — |
| 283 | C2×D4 | — | 15 | 12 | no | — |
| 284 | C2×D4 | — | 15 | 6 | no | — |
| 285 | C2×D4 | — | 15 | 6 | no | — |
| 286 | C2×D4 | — | 15 | 48 | no | — |
| 287 | C22×C4 | — | 3 | 3 | no | — |
| 288 | C22×C4 | — | 5 | 3 | no | — |
| 289 | C22×C4 | — | 15 | 1 | no | — |
| 290 | C22×C4 | — | 15 | 12 | no | — |
| 291 | C22×C4 | — | 15 | 12 | no | — |
| 292 | C22×C4 | — | 15 | 3 | no | — |
| 293 | C22×C4 | — | 15 | 3 | no | — |
| 294 | C22×C4 | — | 15 | 6 | no | — |
| 295 | C22×C4 | — | 15 | 16 | no | — |
| 296 | C22×C4 | — | 15 | 3 | no | — |
| 297 | C3×C5 | — | 4 | 1 | no | Hall |
| 298 | C22×C3 | — | 4 | 1 | no | — |
| 299 | C22×C3 | — | 20 | 6 | no | — |
| 300 | C22×C3 | — | 40 | 6 | no | — |
| 301 | C3×C4 | — | 4 | 6 | no | — |
| 302 | C3×C4 | — | 20 | 2 | no | — |
| 303 | C2×C5 | — | 6 | 6 | no | — |
| 304 | C2×C5 | #5945 | 1 | 2 | yes | complemented |
| 305 | C2×C5 | C24×A4 | 1 | 1 | yes | characteristic |
| 306 | D5 | — | 2 | 6 | no | — |
| 307 | D5 | — | 6 | 2 | no | — |
| 308 | C23 | — | 3 | 8 | no | — |
| 309 | C23 | — | 3 | 3 | no | — |
| 310 | C23 | — | 5 | 3 | no | — |
| 311 | C23 | — | 12 | 4 | no | — |
| 312 | C23 | — | 15 | 12 | no | — |
| 313 | C23 | — | 15 | 1 | no | — |
| 314 | C23 | — | 60 | 6 | no | — |
| 315 | Q8 | — | 3 | 1 | no | — |
| 316 | Q8 | — | 15 | 6 | no | — |
| 317 | Q8 | — | 15 | 6 | no | — |
| 318 | Q8 | — | 15 | 12 | no | — |
| 319 | Q8 | C2×D5×A4 | 1 | 4 | yes | — |
| 320 | Q8 | C23×C3×D5 | 1 | 1 | yes | characteristic |
| 321 | D4 | — | 3 | 6 | no | — |
| 322 | D4 | — | 3 | 6 | no | — |
| 323 | D4 | — | 3 | 12 | no | — |
| 324 | D4 | — | 5 | 12 | no | — |
| 325 | D4 | — | 15 | 2 | no | — |
| 326 | D4 | — | 15 | 2 | no | — |
| 327 | D4 | — | 15 | 24 | no | — |
| 328 | D4 | — | 15 | 24 | no | — |
| 329 | C2×C4 | — | 3 | 1 | no | — |
| 330 | C2×C4 | — | 3 | 6 | no | — |
| 331 | C2×C4 | — | 3 | 6 | no | — |
| 332 | C2×C4 | — | 5 | 1 | no | — |
| 333 | C2×C4 | — | 5 | 12 | no | — |
| 334 | C2×C4 | — | 15 | 2 | no | — |
| 335 | C2×C4 | — | 15 | 2 | no | — |
| 336 | C2×C4 | — | 15 | 6 | no | — |
| 337 | C2×C4 | — | 15 | 6 | no | — |
| 338 | C2×C4 | — | 15 | 12 | no | — |
| 339 | C2×C4 | — | 15 | 24 | no | — |
| 340 | C2×C4 | — | 15 | 3 | no | — |
| 341 | C2×C4 | — | 15 | 12 | no | — |
| 342 | C2×C4 | C2×D5×A4 | 1 | 3 | yes | — |
| 343 | C2×C3 | — | 4 | 1 | no | — |
| 344 | C2×C3 | — | 4 | 2 | no | — |
| 345 | C2×C3 | — | 40 | 6 | no | — |
| 346 | C5 | C2×#5945 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 347 | C22 | — | 3 | 6 | no | — |
| 348 | C22 | — | 5 | 6 | no | — |
| 349 | C22 | — | 6 | 6 | no | — |
| 350 | C22 | — | 10 | 6 | no | — |
| 351 | C22 | — | 12 | 8 | no | — |
| 352 | C22 | — | 15 | 2 | no | — |
| 353 | C22 | — | 30 | 2 | no | — |
| 354 | C22 | — | 60 | 12 | no | — |
| 355 | C22 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 356 | C4 | — | 3 | 1 | no | — |
| 357 | C4 | — | 3 | 1 | no | — |
| 358 | C4 | — | 5 | 2 | no | — |
| 359 | C4 | — | 15 | 6 | no | — |
| 360 | C4 | C22×D5×A4 | 1 | 6 | yes | — |
| 361 | C3 | — | 4 | 1 | no | Sylow |
| 362 | C2 | — | 6 | 6 | no | — |
| 363 | C2 | — | 10 | 6 | no | — |
| 364 | C2 | — | 30 | 2 | no | — |
| 365 | C2 | #11756944 | 1 | 2 | yes | direct product factor |
| 366 | C2 | C23×D5×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C2×C5×H(5,𝔽2) | C2×C3 |
| socle | C22×C5 | C23×A4 |
| hypercenter | C2×Q8 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#994 | C2 | semidirect |
| 2. #11756944 | C2 | direct (N × H) |
| 3. C2×#4150⋊C3 | C2 | semidirect |
| 4. C2×D5×#41⋊C3 | C2 | semidirect |
| 5. C2×#66285 | C3 | semidirect |
| 7. C5×#994 | C22 | semidirect |
| 8. C2×C5×#41⋊C3 | C22 | semidirect |
| 9. #4150⋊C3 | C22 | semidirect |
| 10. D5×#41⋊C3 | C22 | semidirect |
| 11. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 12. C2×C5⋊(#41⋊C3) | C22 | semidirect |
| 14. C2×C5×H(5,𝔽2) | C2×C3 | semidirect |
| 16. #66285 | C2×C3 | semidirect |
| 18. C2×#4150 | C2×C3 | semidirect |
| 20. C2×D5×#41 | C2×C3 | semidirect |
| 27. C5×#41⋊C3 | C23 | semidirect |
| 29. D5×SL(2,𝔽3) | C23 | semidirect |
| 30. C5⋊(#41⋊C3) | C23 | semidirect |
| 33. C2×#994 | D5 | semidirect |
| 36. C5×H(5,𝔽2) | C22×C3 | semidirect |
| 45. #4150 | C22×C3 | semidirect |
| 49. D5×#41 | C22×C3 | semidirect |
| 78. #994 | C2×D5 | semidirect |
| 81. C2×#41⋊C3 | C2×D5 | semidirect |
| 138. C2×H(5,𝔽2) | C3×D5 | semidirect |
| 152. #41⋊C3 | C22×D5 | semidirect |
| 197. H(5,𝔽2) | C2×C3×D5 | semidirect |
| 304. C2×C5 | #5945 | semidirect |
| 346. C5 | C2×#5945 | semidirect |
| 365. C2 | #11756944 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#994 | 2 |
| #11756944 | 2 |
| C2×#4150⋊C3 | 2 |
| C2×D5×#41⋊C3 | 2 |
| C2×#66285 | 3 |
| C2×C3×#713 | 4 |
| C2×#5945 | 5 |