Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1456 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 85 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 | #41×A5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756681 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D4×S5 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C2×C4⋊S5 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11756669 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C22×S5 | C22 | 1 | 6 | yes | complemented |
| 7 | Q8×A5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | D4×A5 | C22 | 1 | 3 | yes | complemented |
| 9 | C2×C4×A5 | C22 | 1 | 3 | yes | complemented |
| 10 | C22⋊S5 | C22 | 1 | 6 | yes | complemented |
| 11 | A5⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C4⋊S5 | C22 | 1 | 3 | yes | complemented |
| 13 | C4⋊S5 | C22 | 1 | 6 | yes | complemented |
| 14 | C4×S5 | C22 | 1 | 6 | yes | complemented |
| 15 | #87489 | — | 5 | 1 | no | maximal, Hall |
| 16 | #66266 | — | 6 | 1 | no | maximal |
| 17 | C22×A5 | C23 | 1 | 3 | yes | — |
| 18 | C2×S5 | — | 4 | 6 | no | — |
| 19 | C2×S5 | C23 | 1 | 6 | yes | — |
| 20 | C4×A5 | C23 | 1 | 3 | yes | — |
| 21 | C4×A5 | C23 | 1 | 1 | yes | characteristic |
| 22 | A5⋊C4 | C23 | 1 | 2 | yes | — |
| 23 | D3×H(5,𝔽2) | — | 10 | 1 | no | maximal |
| 24 | A4×#41 | — | 5 | 1 | no | — |
| 25 | #5919 | — | 5 | 2 | no | — |
| 26 | D4×S4 | — | 5 | 6 | no | — |
| 27 | #5912 | — | 5 | 3 | no | — |
| 28 | C2×C4⋊S4 | — | 5 | 3 | no | — |
| 29 | D5×#41 | — | 6 | 1 | no | — |
| 30 | Q8×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 31 | D4×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 32 | #4130 | — | 6 | 3 | no | — |
| 33 | C2×C4⋊AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 34 | #3488 | — | 15 | 1 | no | Sylow |
| 35 | C2×A5 | — | 2 | 3 | no | — |
| 36 | C2×A5 | C24 | 1 | 1 | yes | characteristic |
| 37 | S5 | — | 2 | 6 | no | — |
| 38 | C22×S4 | — | 5 | 6 | no | — |
| 39 | C3×H(5,𝔽2) | — | 10 | 1 | no | — |
| 40 | #1009 | — | 10 | 1 | no | — |
| 41 | #1009 | — | 10 | 3 | no | — |
| 42 | #1009 | — | 10 | 2 | no | — |
| 43 | D3×#41 | — | 10 | 3 | no | — |
| 44 | D3×#41 | — | 10 | 2 | no | — |
| 45 | D3×#41 | — | 10 | 1 | no | — |
| 46 | #1004 | — | 10 | 6 | no | — |
| 47 | #1004 | — | 10 | 3 | no | — |
| 48 | C2×D3×D4 | — | 10 | 3 | no | — |
| 49 | C2×D3×D4 | — | 10 | 6 | no | — |
| 50 | Q8×A4 | — | 5 | 1 | no | — |
| 51 | D4×A4 | — | 5 | 3 | no | — |
| 52 | C2×C4×A4 | — | 5 | 3 | no | — |
| 53 | GL(2,ℤ/4) | — | 5 | 6 | no | — |
| 54 | C4⋊S4 | — | 5 | 3 | no | — |
| 55 | C4⋊S4 | — | 5 | 6 | no | — |
| 56 | C4×S4 | — | 5 | 6 | no | — |
| 57 | A4⋊Q8 | — | 5 | 1 | no | — |
| 58 | C22×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 59 | C5×#41 | — | 6 | 1 | no | — |
| 60 | #713 | — | 6 | 1 | no | — |
| 61 | Q8×D5 | — | 6 | 1 | no | — |
| 62 | #711 | — | 6 | 3 | no | — |
| 63 | D4×D5 | — | 6 | 3 | no | — |
| 64 | #709 | — | 6 | 3 | no | — |
| 65 | C2×C4×D5 | — | 6 | 3 | no | — |
| 66 | C22⋊AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 67 | C4⋊AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 68 | C4⋊AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 69 | C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 70 | C4×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 71 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 72 | C22×#41 | — | 5 | 1 | no | — |
| 73 | #550 | — | 15 | 2 | no | — |
| 74 | #548 | — | 15 | 2 | no | — |
| 75 | #546 | — | 15 | 6 | no | — |
| 76 | D42 | — | 15 | 6 | no | — |
| 77 | #537 | — | 15 | 3 | no | — |
| 78 | #535 | — | 15 | 3 | no | — |
| 79 | #525 | — | 15 | 3 | no | — |
| 80 | C2×#121 | — | 15 | 3 | no | — |
| 81 | #520 | — | 15 | 1 | no | — |
| 82 | A5 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 83 | C23×D3 | — | 10 | 6 | no | — |
| 84 | C22×A4 | — | 5 | 3 | no | — |
| 85 | C2×S4 | — | 5 | 6 | no | — |
| 86 | C2×S4 | — | 20 | 6 | no | — |
| 87 | C3×#41 | — | 10 | 2 | no | — |
| 88 | C3×#41 | — | 10 | 3 | no | — |
| 89 | C3×#41 | — | 10 | 1 | no | — |
| 90 | C2×C3×D4 | — | 10 | 6 | no | — |
| 91 | C2×C3×D4 | — | 10 | 3 | no | — |
| 92 | C2×#67 | — | 10 | 6 | no | — |
| 93 | C2×#67 | — | 10 | 12 | no | — |
| 94 | #239 | — | 10 | 2 | no | — |
| 95 | #239 | — | 10 | 1 | no | — |
| 96 | #239 | — | 10 | 3 | no | — |
| 97 | D3×Q8 | — | 10 | 1 | no | — |
| 98 | D3×Q8 | — | 10 | 1 | no | — |
| 99 | #237 | — | 10 | 3 | no | — |
| 100 | #237 | — | 10 | 6 | no | — |
| 101 | #237 | — | 10 | 6 | no | — |
| 102 | #237 | — | 10 | 3 | no | — |
| 103 | D3×D4 | — | 10 | 6 | no | — |
| 104 | D3×D4 | — | 10 | 3 | no | — |
| 105 | D3×D4 | — | 10 | 6 | no | — |
| 106 | D3×D4 | — | 10 | 6 | no | — |
| 107 | D3×D4 | — | 10 | 3 | no | — |
| 108 | D3×D4 | — | 10 | 6 | no | — |
| 109 | D3×D4 | — | 10 | 6 | no | — |
| 110 | D3×D4 | — | 10 | 6 | no | — |
| 111 | D3×D4 | — | 10 | 12 | no | — |
| 112 | #235 | — | 10 | 3 | no | — |
| 113 | #235 | — | 10 | 3 | no | — |
| 114 | #235 | — | 10 | 6 | no | — |
| 115 | #235 | — | 10 | 6 | no | — |
| 116 | C2×D12 | — | 10 | 3 | no | — |
| 117 | C2×D12 | — | 10 | 6 | no | — |
| 118 | C2×C4×D3 | — | 10 | 6 | no | — |
| 119 | C2×C4×D3 | — | 10 | 3 | no | — |
| 120 | C4×A4 | — | 5 | 1 | no | — |
| 121 | C4×A4 | — | 5 | 3 | no | — |
| 122 | SL(2,ℤ/4) | — | 5 | 2 | no | — |
| 123 | C22×D5 | — | 6 | 3 | no | — |
| 124 | C2×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 125 | C2×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 126 | C2×AGL(1,𝔽5) | — | 24 | 6 | no | — |
| 127 | C5×Q8 | — | 6 | 1 | no | — |
| 128 | C5×D4 | — | 6 | 3 | no | — |
| 129 | C2×C4×C5 | — | 6 | 3 | no | — |
| 130 | C22⋊D5 | — | 6 | 6 | no | — |
| 131 | C2×Dic5 | — | 6 | 3 | no | — |
| 132 | D20 | — | 6 | 3 | no | — |
| 133 | C4×D5 | — | 6 | 3 | no | — |
| 134 | C4×D5 | — | 6 | 1 | no | — |
| 135 | C4×D5 | — | 6 | 3 | no | — |
| 136 | C4×D5 | — | 6 | 3 | no | — |
| 137 | Dic10 | — | 6 | 3 | no | — |
| 138 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 139 | H(5,𝔽2) | — | 30 | 3 | no | — |
| 140 | H(5,𝔽2) | — | 30 | 3 | no | — |
| 141 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 142 | C2×#41 | — | 15 | 3 | no | — |
| 143 | C2×#41 | — | 15 | 2 | no | — |
| 144 | C2×#41 | — | 15 | 1 | no | — |
| 145 | C2×#41 | — | 15 | 3 | no | — |
| 146 | C2×#41 | — | 15 | 3 | no | — |
| 147 | C2×#41 | — | 15 | 1 | no | — |
| 148 | C22×Q8 | — | 5 | 1 | no | — |
| 149 | C22×D4 | — | 5 | 3 | no | — |
| 150 | C22×D4 | — | 15 | 3 | no | — |
| 151 | C22×D4 | — | 15 | 6 | no | — |
| 152 | C22×D4 | — | 15 | 6 | no | — |
| 153 | C23×C4 | — | 5 | 3 | no | — |
| 154 | #127 | — | 15 | 6 | no | — |
| 155 | #124 | — | 15 | 6 | no | — |
| 156 | #123 | — | 15 | 6 | no | — |
| 157 | C22⋊Q8 | — | 15 | 1 | no | — |
| 158 | C22⋊Q8 | — | 15 | 3 | no | — |
| 159 | C22⋊Q8 | — | 15 | 6 | no | — |
| 160 | #121 | — | 15 | 3 | no | — |
| 161 | #121 | — | 15 | 6 | no | — |
| 162 | #121 | — | 15 | 6 | no | — |
| 163 | #121 | — | 15 | 6 | no | — |
| 164 | #121 | — | 15 | 3 | no | — |
| 165 | #121 | — | 15 | 12 | no | — |
| 166 | #121 | — | 15 | 6 | no | — |
| 167 | #120 | — | 15 | 6 | no | — |
| 168 | #120 | — | 15 | 12 | no | — |
| 169 | C4×Q8 | — | 15 | 2 | no | — |
| 170 | C4×D4 | — | 15 | 6 | no | — |
| 171 | C4×D4 | — | 15 | 6 | no | — |
| 172 | C4×D4 | — | 15 | 6 | no | — |
| 173 | #117 | — | 15 | 3 | no | — |
| 174 | C2×C4⋊C4 | — | 15 | 3 | no | — |
| 175 | C2×C22⋊C4 | — | 15 | 6 | no | — |
| 176 | C23×C3 | — | 10 | 6 | no | — |
| 177 | C22×D3 | — | 10 | 6 | no | — |
| 178 | C22×D3 | — | 10 | 6 | no | — |
| 179 | C22×D3 | — | 10 | 3 | no | — |
| 180 | C22×D3 | — | 10 | 12 | no | — |
| 181 | C22×D3 | — | 40 | 6 | no | — |
| 182 | C22×D3 | — | 40 | 6 | no | — |
| 183 | C2×A4 | — | 5 | 1 | no | — |
| 184 | C2×A4 | — | 10 | 3 | no | — |
| 185 | S4 | — | 10 | 6 | no | — |
| 186 | C3×Q8 | — | 10 | 1 | no | — |
| 187 | C3×Q8 | — | 10 | 1 | no | — |
| 188 | C3×D4 | — | 10 | 6 | no | — |
| 189 | C3×D4 | — | 10 | 6 | no | — |
| 190 | C3×D4 | — | 10 | 3 | no | — |
| 191 | C3×D4 | — | 10 | 3 | no | — |
| 192 | C2×C3×C4 | — | 10 | 6 | no | — |
| 193 | C2×C3×C4 | — | 10 | 3 | no | — |
| 194 | #67 | — | 10 | 6 | no | — |
| 195 | #67 | — | 10 | 6 | no | — |
| 196 | #67 | — | 10 | 6 | no | — |
| 197 | #67 | — | 10 | 6 | no | — |
| 198 | #67 | — | 10 | 12 | no | — |
| 199 | C2×Dic3 | — | 10 | 3 | no | — |
| 200 | C2×Dic3 | — | 10 | 6 | no | — |
| 201 | D12 | — | 10 | 3 | no | — |
| 202 | D12 | — | 10 | 6 | no | — |
| 203 | D12 | — | 10 | 3 | no | — |
| 204 | D12 | — | 10 | 6 | no | — |
| 205 | C4×D3 | — | 10 | 6 | no | — |
| 206 | C4×D3 | — | 10 | 2 | no | — |
| 207 | C4×D3 | — | 10 | 3 | no | — |
| 208 | C4×D3 | — | 10 | 1 | no | — |
| 209 | C4×D3 | — | 10 | 3 | no | — |
| 210 | C4×D3 | — | 10 | 3 | no | — |
| 211 | C4×D3 | — | 10 | 6 | no | — |
| 212 | Dic6 | — | 10 | 1 | no | — |
| 213 | Dic6 | — | 10 | 3 | no | — |
| 214 | Dic6 | — | 10 | 2 | no | — |
| 215 | C22×C5 | — | 6 | 3 | no | — |
| 216 | C2×D5 | — | 6 | 1 | no | — |
| 217 | C2×D5 | — | 6 | 3 | no | — |
| 218 | C2×D5 | — | 12 | 3 | no | — |
| 219 | C2×D5 | — | 12 | 3 | no | — |
| 220 | AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 221 | AGL(1,𝔽5) | — | 12 | 6 | no | — |
| 222 | C4×C5 | — | 6 | 3 | no | — |
| 223 | C4×C5 | — | 6 | 1 | no | — |
| 224 | Dic5 | — | 6 | 3 | no | — |
| 225 | Dic5 | — | 6 | 1 | no | — |
| 226 | C24 | — | 5 | 3 | no | — |
| 227 | C24 | — | 15 | 6 | no | — |
| 228 | #41 | — | 10 | 2 | no | — |
| 229 | #41 | — | 10 | 3 | no | — |
| 230 | #41 | — | 15 | 1 | no | — |
| 231 | #41 | — | 15 | 3 | no | — |
| 232 | #41 | — | 15 | 3 | no | — |
| 233 | #41 | — | 30 | 3 | no | — |
| 234 | #41 | — | 30 | 6 | no | — |
| 235 | #41 | — | 30 | 1 | no | — |
| 236 | #41 | — | 30 | 3 | no | — |
| 237 | #41 | — | 30 | 3 | no | — |
| 238 | #41 | — | 30 | 3 | no | — |
| 239 | #41 | — | 30 | 3 | no | — |
| 240 | #41 | S5 | 1 | 1 | yes | characteristic, complemented |
| 241 | C2×Q8 | — | 15 | 1 | no | — |
| 242 | C2×Q8 | — | 15 | 1 | no | — |
| 243 | C2×Q8 | — | 15 | 3 | no | — |
| 244 | C2×D4 | — | 10 | 6 | no | — |
| 245 | C2×D4 | — | 10 | 3 | no | — |
| 246 | C2×D4 | — | 15 | 6 | no | — |
| 247 | C2×D4 | — | 15 | 3 | no | — |
| 248 | C2×D4 | — | 15 | 6 | no | — |
| 249 | C2×D4 | — | 15 | 3 | no | — |
| 250 | C2×D4 | — | 15 | 6 | no | — |
| 251 | C2×D4 | — | 15 | 3 | no | — |
| 252 | C2×D4 | — | 15 | 6 | no | — |
| 253 | C2×D4 | — | 15 | 6 | no | — |
| 254 | C2×D4 | — | 15 | 12 | no | — |
| 255 | C2×D4 | — | 30 | 6 | no | — |
| 256 | C2×D4 | — | 30 | 3 | no | — |
| 257 | C2×D4 | — | 30 | 3 | no | — |
| 258 | C2×D4 | — | 30 | 3 | no | — |
| 259 | C2×D4 | — | 30 | 12 | no | — |
| 260 | C2×D4 | — | 60 | 6 | no | — |
| 261 | C2×D4 | — | 60 | 6 | no | — |
| 262 | C22×C4 | — | 5 | 3 | no | — |
| 263 | C22×C4 | — | 5 | 1 | no | — |
| 264 | C22×C4 | — | 15 | 6 | no | — |
| 265 | C22×C4 | — | 15 | 3 | no | — |
| 266 | C22×C4 | — | 15 | 3 | no | — |
| 267 | C22×C4 | — | 15 | 3 | no | — |
| 268 | C22×C4 | — | 15 | 3 | no | — |
| 269 | C22×C4 | — | 15 | 6 | no | — |
| 270 | C4⋊C4 | — | 15 | 3 | no | — |
| 271 | C4⋊C4 | — | 15 | 6 | no | — |
| 272 | C4⋊C4 | — | 15 | 1 | no | — |
| 273 | C4⋊C4 | — | 15 | 2 | no | — |
| 274 | C4⋊C4 | — | 15 | 6 | no | — |
| 275 | C22⋊C4 | — | 15 | 2 | no | — |
| 276 | C22⋊C4 | — | 15 | 6 | no | — |
| 277 | C22⋊C4 | — | 15 | 12 | no | — |
| 278 | C22⋊C4 | — | 15 | 6 | no | — |
| 279 | C22⋊C4 | — | 15 | 6 | no | — |
| 280 | C22⋊C4 | — | 15 | 6 | no | — |
| 281 | C42 | — | 15 | 6 | no | — |
| 282 | C22×C3 | — | 10 | 6 | no | — |
| 283 | C22×C3 | — | 10 | 3 | no | — |
| 284 | C22×C3 | — | 40 | 6 | no | — |
| 285 | C2×D3 | — | 10 | 6 | no | — |
| 286 | C2×D3 | — | 10 | 1 | no | — |
| 287 | C2×D3 | — | 10 | 3 | no | — |
| 288 | C2×D3 | — | 20 | 3 | no | — |
| 289 | C2×D3 | — | 20 | 6 | no | — |
| 290 | C2×D3 | — | 20 | 6 | no | — |
| 291 | C2×D3 | — | 20 | 3 | no | — |
| 292 | C2×D3 | — | 40 | 6 | no | — |
| 293 | C2×D3 | — | 40 | 12 | no | — |
| 294 | A4 | — | 5 | 1 | no | — |
| 295 | C3×C4 | — | 10 | 2 | no | — |
| 296 | C3×C4 | — | 10 | 3 | no | — |
| 297 | C3×C4 | — | 10 | 1 | no | — |
| 298 | Dic3 | — | 10 | 2 | no | — |
| 299 | Dic3 | — | 10 | 1 | no | — |
| 300 | Dic3 | — | 10 | 3 | no | — |
| 301 | C2×C5 | — | 6 | 1 | no | — |
| 302 | C2×C5 | — | 12 | 3 | no | — |
| 303 | D5 | — | 6 | 1 | no | — |
| 304 | D5 | — | 6 | 1 | no | — |
| 305 | D5 | — | 12 | 3 | no | — |
| 306 | C23 | — | 5 | 1 | no | — |
| 307 | C23 | — | 10 | 3 | no | — |
| 308 | C23 | — | 10 | 6 | no | — |
| 309 | C23 | — | 15 | 6 | no | — |
| 310 | C23 | — | 15 | 3 | no | — |
| 311 | C23 | — | 15 | 3 | no | — |
| 312 | C23 | — | 30 | 6 | no | — |
| 313 | C23 | — | 30 | 3 | no | — |
| 314 | C23 | — | 60 | 6 | no | — |
| 315 | C23 | — | 60 | 6 | no | — |
| 316 | Q8 | — | 10 | 1 | no | — |
| 317 | Q8 | — | 15 | 3 | no | — |
| 318 | Q8 | — | 30 | 1 | no | — |
| 319 | Q8 | — | 30 | 1 | no | — |
| 320 | Q8 | C2×S5 | 1 | 1 | yes | characteristic, complemented |
| 321 | D4 | — | 10 | 6 | no | — |
| 322 | D4 | — | 10 | 6 | no | — |
| 323 | D4 | — | 10 | 3 | no | — |
| 324 | D4 | — | 15 | 6 | no | — |
| 325 | D4 | — | 15 | 3 | no | — |
| 326 | D4 | — | 30 | 6 | no | — |
| 327 | D4 | — | 30 | 3 | no | — |
| 328 | D4 | — | 30 | 6 | no | — |
| 329 | D4 | — | 30 | 3 | no | — |
| 330 | D4 | — | 30 | 6 | no | — |
| 331 | D4 | — | 30 | 6 | no | — |
| 332 | D4 | — | 60 | 6 | no | — |
| 333 | D4 | — | 60 | 12 | no | — |
| 334 | D4 | C2×S5 | 1 | 3 | yes | complemented |
| 335 | C2×C4 | — | 10 | 6 | no | — |
| 336 | C2×C4 | — | 15 | 2 | no | — |
| 337 | C2×C4 | — | 15 | 3 | no | — |
| 338 | C2×C4 | — | 15 | 3 | no | — |
| 339 | C2×C4 | — | 15 | 1 | no | — |
| 340 | C2×C4 | — | 15 | 3 | no | — |
| 341 | C2×C4 | — | 15 | 3 | no | — |
| 342 | C2×C4 | — | 15 | 1 | no | — |
| 343 | C2×C4 | — | 15 | 3 | no | — |
| 344 | C2×C4 | — | 15 | 2 | no | — |
| 345 | C2×C4 | — | 15 | 6 | no | — |
| 346 | C2×C4 | — | 30 | 6 | no | — |
| 347 | C2×C4 | — | 30 | 3 | no | — |
| 348 | C2×C4 | — | 60 | 6 | no | — |
| 349 | C2×C4 | C2×S5 | 1 | 3 | yes | complemented |
| 350 | C2×C3 | — | 10 | 1 | no | — |
| 351 | C2×C3 | — | 20 | 3 | no | — |
| 352 | C2×C3 | — | 20 | 6 | no | — |
| 353 | D3 | — | 10 | 1 | no | — |
| 354 | D3 | — | 10 | 1 | no | — |
| 355 | D3 | — | 20 | 6 | no | — |
| 356 | D3 | — | 20 | 3 | no | — |
| 357 | C5 | — | 6 | 1 | no | Sylow |
| 358 | C22 | — | 5 | 1 | no | — |
| 359 | C22 | — | 10 | 6 | no | — |
| 360 | C22 | — | 15 | 1 | no | — |
| 361 | C22 | — | 15 | 1 | no | — |
| 362 | C22 | — | 15 | 3 | no | — |
| 363 | C22 | — | 30 | 3 | no | — |
| 364 | C22 | — | 30 | 3 | no | — |
| 365 | C22 | — | 30 | 6 | no | — |
| 366 | C22 | — | 30 | 6 | no | — |
| 367 | C22 | — | 30 | 3 | no | — |
| 368 | C22 | — | 30 | 3 | no | — |
| 369 | C22 | — | 40 | 6 | no | — |
| 370 | C22 | — | 120 | 6 | no | — |
| 371 | C22 | C22×S5 | 1 | 3 | yes | — |
| 372 | C4 | — | 10 | 2 | no | — |
| 373 | C4 | — | 15 | 1 | no | — |
| 374 | C4 | — | 15 | 3 | no | — |
| 375 | C4 | — | 30 | 6 | no | — |
| 376 | C4 | — | 30 | 2 | no | — |
| 377 | C4 | C22×S5 | 1 | 3 | yes | — |
| 378 | C4 | C22×S5 | 1 | 1 | yes | characteristic |
| 379 | C3 | — | 10 | 1 | no | Sylow |
| 380 | C2 | — | 2 | 3 | no | — |
| 381 | C2 | — | 15 | 1 | no | — |
| 382 | C2 | — | 15 | 1 | no | — |
| 383 | C2 | — | 20 | 6 | no | — |
| 384 | C2 | — | 30 | 3 | no | — |
| 385 | C2 | C23×S5 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×S5 |
| commutator, socle, cosocle | C2×A5 | C24 |
| Fitting, hypercenter | #41 | S5 |
| hypocenter | A5 | H(5,𝔽2) |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×A5 | C2 | semidirect |
| 2. #11756681 | C2 | semidirect |
| 3. D4×S5 | C2 | semidirect |
| 4. C2×C4⋊S5 | C2 | semidirect |
| 5. #11756669 | C2 | semidirect |
| 6. C22×S5 | C22 | semidirect |
| 7. Q8×A5 | C22 | semidirect |
| 8. D4×A5 | C22 | semidirect |
| 9. C2×C4×A5 | C22 | semidirect |
| 10. C22⋊S5 | C22 | semidirect |
| 11. A5⋊Q8 | C22 | semidirect |
| 12. C4⋊S5 | C22 | semidirect |
| 13. C4⋊S5 | C22 | semidirect |
| 14. C4×S5 | C22 | semidirect |
| 82. A5 | H(5,𝔽2) | semidirect |
| 240. #41 | S5 | semidirect |
| 320. Q8 | C2×S5 | semidirect |
| 334. D4 | C2×S5 | semidirect |
| 349. C2×C4 | C2×S5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×A5 | 2 |
| #11756681 | 2 |
| D4×S5 | 2 |
| C2×C4⋊S5 | 2 |
| #11756669 | 2 |
| #87489 | 5 |
| #66266 | 6 |
| D3×H(5,𝔽2) | 10 |