Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
418 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 48 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 | Q8×D5×A4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4⋊(A4⋊AGL(1,𝔽5)) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | D5⋊(A4⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10604973 | — | 3 | 1 | no | maximal, Hall |
| 5 | C2×A4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 6 | C5×Q8×A4 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C4×D5×A4 | — | 2 | 1 | no | — |
| 8 | C4×D5×A4 | C22 | 1 | 1 | yes | characteristic |
| 9 | A4×Dic10 | — | 2 | 1 | no | — |
| 10 | A4×Dic10 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | A4⋊#170 | — | 2 | 1 | no | — |
| 12 | #91238 | — | 4 | 1 | no | maximal |
| 13 | #73147 | — | 5 | 1 | no | maximal, Hall |
| 14 | C22×Q8×D5 | D3 | 1 | 1 | yes | characteristic |
| 15 | C2×#4009 | — | 3 | 1 | no | — |
| 16 | C2×#4009 | — | 3 | 1 | no | — |
| 17 | C2×#4009 | — | 3 | 1 | no | — |
| 18 | C2×#4009 | — | 3 | 1 | no | — |
| 19 | #65765 | — | 3 | 1 | no | — |
| 20 | D5⋊(C22⋊C8) | — | 3 | 1 | no | — |
| 21 | C2×D5×A4 | D4 | 1 | 1 | yes | characteristic |
| 22 | A4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 23 | C3×Q8×D5 | — | 4 | 1 | no | — |
| 24 | C4×C5×A4 | — | 2 | 1 | no | — |
| 25 | C4×C5×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C4⋊ΓL(1,𝔽16) | — | 4 | 1 | no | — |
| 27 | D5⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 28 | A4×Dic5 | — | 2 | 1 | no | — |
| 29 | A4×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×Q8×A4 | — | 5 | 1 | no | — |
| 31 | C4⋊SL(2,ℤ/4) | — | 5 | 1 | no | — |
| 32 | C2×A4⋊C8 | — | 5 | 1 | no | — |
| 33 | C22×C5×Q8 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 35 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 36 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 37 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 38 | C2×Q8×D5 | — | 6 | 1 | no | — |
| 39 | C2×Q8×D5 | — | 6 | 1 | no | — |
| 40 | C22×C4×D5 | — | 2 | 1 | no | — |
| 41 | C22×C4×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 42 | C22×Dic10 | — | 2 | 1 | no | — |
| 43 | C22×Dic10 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×C22⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 45 | C2×C4⋊AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 46 | C2×C4⋊AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 47 | C2×D5⋊C8 | — | 3 | 1 | no | — |
| 48 | C2×D5⋊C8 | — | 3 | 1 | no | — |
| 49 | C22⋊#170 | — | 6 | 1 | no | — |
| 50 | #4009 | — | 6 | 2 | no | — |
| 51 | #4009 | — | 6 | 2 | no | — |
| 52 | #4009 | — | 6 | 1 | no | — |
| 53 | #4009 | — | 6 | 1 | no | — |
| 54 | #4009 | — | 6 | 1 | no | — |
| 55 | #4009 | — | 6 | 1 | no | — |
| 56 | (C2×AGL(1,𝔽5))⋊C4 | — | 6 | 1 | no | — |
| 57 | #4003 | — | 6 | 1 | no | — |
| 58 | #1787 | — | 15 | 1 | no | Sylow |
| 59 | C2×C5×A4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 60 | C2×ΓL(1,𝔽16) | — | 8 | 1 | no | — |
| 61 | D5×A4 | SD16 | 1 | 1 | yes | characteristic |
| 62 | D5×A4 | Q16 | 1 | 1 | yes | characteristic |
| 63 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 64 | C3×C4×D5 | — | 4 | 1 | no | — |
| 65 | C3×C4×D5 | — | 8 | 1 | no | — |
| 66 | C3×Dic10 | — | 4 | 1 | no | — |
| 67 | C3×Dic10 | — | 8 | 1 | no | — |
| 68 | C3⋊#170 | — | 8 | 1 | no | — |
| 69 | Q8×A4 | — | 5 | 1 | no | — |
| 70 | Q8×A4 | — | 10 | 1 | no | — |
| 71 | Q8×A4 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 72 | C2×C4×A4 | — | 5 | 1 | no | — |
| 73 | C2×C4×A4 | — | 10 | 1 | no | — |
| 74 | C2×SL(2,ℤ/4) | — | 10 | 1 | no | — |
| 75 | A4⋊C8 | — | 10 | 1 | no | — |
| 76 | #835 | — | 20 | 1 | no | — |
| 77 | C23×D5 | #67 | 1 | 1 | yes | characteristic |
| 78 | C22×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 79 | C22×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 80 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 81 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 82 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 83 | C22×C4×C5 | — | 2 | 1 | no | — |
| 84 | C22×C4×C5 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 85 | C22×Dic5 | — | 2 | 1 | no | — |
| 86 | C22×Dic5 | #67 | 1 | 1 | yes | characteristic |
| 87 | Q8×D5 | — | 3 | 2 | no | — |
| 88 | Q8×D5 | — | 3 | 2 | no | — |
| 89 | Q8×D5 | — | 3 | 1 | no | — |
| 90 | Q8×D5 | — | 3 | 1 | no | — |
| 91 | Q8×D5 | — | 3 | 1 | no | — |
| 92 | Q8×D5 | — | 6 | 1 | no | — |
| 93 | Q8×D5 | — | 6 | 1 | no | — |
| 94 | Q8×D5 | — | 6 | 2 | no | — |
| 95 | Q8×D5 | — | 6 | 1 | no | — |
| 96 | Q8×D5 | — | 6 | 2 | no | — |
| 97 | Q8×D5 | S4 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×D5 | — | 3 | 1 | no | — |
| 99 | C2×C4×D5 | — | 3 | 1 | no | — |
| 100 | C2×C4×D5 | — | 3 | 1 | no | — |
| 101 | C2×C4×D5 | — | 3 | 1 | no | — |
| 102 | C2×C4×D5 | — | 6 | 1 | no | — |
| 103 | C2×C4×D5 | — | 6 | 1 | no | — |
| 104 | C2×C4×D5 | — | 6 | 1 | no | — |
| 105 | C2×C4×D5 | — | 6 | 1 | no | — |
| 106 | C2×Dic10 | — | 3 | 1 | no | — |
| 107 | C2×Dic10 | — | 3 | 1 | no | — |
| 108 | C2×Dic10 | — | 6 | 1 | no | — |
| 109 | C2×Dic10 | — | 6 | 1 | no | — |
| 110 | C2×Dic10 | — | 6 | 1 | no | — |
| 111 | C2×Dic10 | — | 6 | 1 | no | — |
| 112 | C2×Dic10 | — | 6 | 1 | no | — |
| 113 | C22⋊AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 114 | C22⋊AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 115 | C2×#170 | — | 6 | 1 | no | — |
| 116 | C2×#170 | — | 6 | 1 | no | — |
| 117 | C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 118 | C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 119 | C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 120 | C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 121 | D5⋊C8 | — | 6 | 1 | no | — |
| 122 | D5⋊C8 | — | 6 | 1 | no | — |
| 123 | D5⋊C8 | — | 6 | 1 | no | — |
| 124 | D5⋊C8 | — | 6 | 1 | no | — |
| 125 | C23×Q8 | — | 5 | 1 | no | — |
| 126 | C2×#103 | — | 15 | 1 | no | — |
| 127 | C2×#103 | — | 15 | 1 | no | — |
| 128 | C2×#103 | — | 15 | 1 | no | — |
| 129 | C2×#103 | — | 15 | 1 | no | — |
| 130 | C2×C22⋊C8 | — | 15 | 1 | no | — |
| 131 | #380 | — | 15 | 1 | no | — |
| 132 | C2×C3×D5 | — | 4 | 1 | no | — |
| 133 | C5×A4 | #103 | 1 | 1 | yes | characteristic, complemented |
| 134 | ΓL(1,𝔽16) | — | 16 | 1 | no | — |
| 135 | C3×C4×C5 | — | 4 | 1 | no | — |
| 136 | C3×C4×C5 | — | 8 | 1 | no | — |
| 137 | C3×Dic5 | — | 4 | 1 | no | — |
| 138 | C3×Dic5 | — | 8 | 1 | no | — |
| 139 | C22×A4 | — | 5 | 1 | no | — |
| 140 | C2×C3×Q8 | — | 20 | 1 | no | — |
| 141 | C4×A4 | — | 2 | 1 | no | — |
| 142 | C4×A4 | — | 5 | 1 | no | — |
| 143 | C4×A4 | — | 10 | 1 | no | — |
| 144 | C4×A4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 145 | SL(2,ℤ/4) | — | 20 | 1 | no | — |
| 146 | C4⋊Dic3 | — | 20 | 1 | no | — |
| 147 | C2×C3⋊C8 | — | 20 | 1 | no | — |
| 148 | C23×C5 | #217 | 1 | 1 | yes | characteristic |
| 149 | C22×D5 | — | 3 | 1 | no | — |
| 150 | C22×D5 | — | 3 | 1 | no | — |
| 151 | C22×D5 | — | 3 | 1 | no | — |
| 152 | C22×D5 | — | 3 | 1 | no | — |
| 153 | C22×D5 | #215 | 1 | 1 | yes | characteristic |
| 154 | C22×D5 | #216 | 1 | 1 | yes | characteristic |
| 155 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 156 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 157 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 158 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 159 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 160 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 161 | C5×Q8 | — | 3 | 2 | no | — |
| 162 | C5×Q8 | — | 3 | 1 | no | — |
| 163 | C5×Q8 | — | 6 | 1 | no | — |
| 164 | C5×Q8 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic, complemented |
| 165 | C2×C4×C5 | — | 3 | 1 | no | — |
| 166 | C2×C4×C5 | — | 3 | 1 | no | — |
| 167 | C2×C4×C5 | — | 6 | 1 | no | — |
| 168 | C2×C4×C5 | — | 6 | 1 | no | — |
| 169 | C2×Dic5 | — | 3 | 1 | no | — |
| 170 | C2×Dic5 | — | 3 | 1 | no | — |
| 171 | C2×Dic5 | — | 6 | 1 | no | — |
| 172 | C2×Dic5 | — | 6 | 1 | no | — |
| 173 | C4×D5 | — | 2 | 1 | no | — |
| 174 | C4×D5 | — | 3 | 1 | no | — |
| 175 | C4×D5 | — | 3 | 1 | no | — |
| 176 | C4×D5 | — | 3 | 1 | no | — |
| 177 | C4×D5 | — | 6 | 1 | no | — |
| 178 | C4×D5 | — | 6 | 1 | no | — |
| 179 | C4×D5 | — | 6 | 1 | no | — |
| 180 | C4×D5 | — | 6 | 2 | no | — |
| 181 | C4×D5 | — | 6 | 1 | no | — |
| 182 | C4×D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 183 | Dic10 | — | 2 | 1 | no | — |
| 184 | Dic10 | — | 3 | 2 | no | — |
| 185 | Dic10 | — | 3 | 1 | no | — |
| 186 | Dic10 | — | 6 | 1 | no | — |
| 187 | Dic10 | — | 6 | 1 | no | — |
| 188 | Dic10 | — | 6 | 1 | no | — |
| 189 | Dic10 | — | 6 | 2 | no | — |
| 190 | Dic10 | — | 6 | 1 | no | — |
| 191 | Dic10 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic, complemented |
| 192 | #170 | — | 12 | 1 | no | — |
| 193 | #170 | — | 12 | 1 | no | — |
| 194 | C22×Q8 | — | 5 | 1 | no | — |
| 195 | C22×Q8 | — | 10 | 1 | no | — |
| 196 | C22×Q8 | — | 15 | 1 | no | — |
| 197 | C22×Q8 | — | 15 | 1 | no | — |
| 198 | C22×Q8 | — | 15 | 1 | no | — |
| 199 | C22×Q8 | — | 15 | 1 | no | — |
| 200 | C22×Q8 | — | 30 | 1 | no | — |
| 201 | C22×Q8 | — | 30 | 1 | no | — |
| 202 | C22×Q8 | ΓL(1,𝔽16) | 1 | 1 | yes | characteristic, complemented |
| 203 | C23×C4 | — | 5 | 1 | no | — |
| 204 | C23×C4 | — | 10 | 1 | no | — |
| 205 | C22×C8 | — | 15 | 1 | no | — |
| 206 | C22×C8 | — | 15 | 1 | no | — |
| 207 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 208 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 209 | C2×C22⋊C4 | — | 30 | 1 | no | — |
| 210 | #103 | — | 30 | 1 | no | — |
| 211 | #103 | — | 30 | 1 | no | — |
| 212 | #103 | — | 30 | 1 | no | — |
| 213 | #103 | — | 30 | 2 | no | — |
| 214 | #103 | — | 30 | 2 | no | — |
| 215 | #103 | — | 30 | 1 | no | — |
| 216 | C22⋊C8 | — | 30 | 1 | no | — |
| 217 | C22⋊C8 | — | 30 | 1 | no | — |
| 218 | #95 | — | 30 | 1 | no | — |
| 219 | C2×C3×C5 | — | 4 | 1 | no | — |
| 220 | C3×D5 | — | 4 | 1 | no | — |
| 221 | C3×D5 | — | 4 | 1 | no | — |
| 222 | C2×A4 | — | 5 | 1 | no | — |
| 223 | C2×A4 | — | 5 | 1 | no | — |
| 224 | C2×A4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 225 | C3×Q8 | — | 4 | 1 | no | — |
| 226 | C3×Q8 | — | 20 | 1 | no | — |
| 227 | C3×Q8 | — | 40 | 1 | no | — |
| 228 | C2×C3×C4 | — | 20 | 1 | no | — |
| 229 | C2×C3×C4 | — | 40 | 1 | no | — |
| 230 | C2×Dic3 | — | 40 | 1 | no | — |
| 231 | C3⋊C8 | — | 40 | 1 | no | — |
| 232 | C22×C5 | — | 3 | 1 | no | — |
| 233 | C22×C5 | — | 3 | 1 | no | — |
| 234 | C22×C5 | #835 | 1 | 1 | yes | characteristic, complemented |
| 235 | C2×D5 | — | 3 | 1 | no | — |
| 236 | C2×D5 | — | 3 | 1 | no | — |
| 237 | C2×D5 | — | 3 | 1 | no | — |
| 238 | C2×D5 | — | 3 | 1 | no | — |
| 239 | C2×D5 | — | 3 | 1 | no | — |
| 240 | C2×D5 | — | 3 | 1 | no | — |
| 241 | C2×D5 | — | 3 | 1 | no | — |
| 242 | C2×D5 | — | 6 | 1 | no | — |
| 243 | C2×D5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 244 | AGL(1,𝔽5) | — | 24 | 1 | no | — |
| 245 | AGL(1,𝔽5) | — | 24 | 1 | no | — |
| 246 | C4×C5 | — | 2 | 1 | no | — |
| 247 | C4×C5 | — | 3 | 1 | no | — |
| 248 | C4×C5 | — | 6 | 1 | no | — |
| 249 | C4×C5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 250 | Dic5 | — | 2 | 1 | no | — |
| 251 | Dic5 | — | 3 | 1 | no | — |
| 252 | Dic5 | — | 6 | 1 | no | — |
| 253 | Dic5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 254 | C24 | — | 5 | 1 | no | — |
| 255 | C2×Q8 | — | 3 | 1 | no | — |
| 256 | C2×Q8 | — | 3 | 1 | no | — |
| 257 | C2×Q8 | — | 5 | 1 | no | — |
| 258 | C2×Q8 | — | 6 | 1 | no | — |
| 259 | C2×Q8 | — | 15 | 1 | no | — |
| 260 | C2×Q8 | — | 15 | 1 | no | — |
| 261 | C2×Q8 | — | 15 | 1 | no | — |
| 262 | C2×Q8 | — | 15 | 1 | no | — |
| 263 | C2×Q8 | — | 15 | 2 | no | — |
| 264 | C2×Q8 | — | 15 | 2 | no | — |
| 265 | C2×Q8 | — | 15 | 1 | no | — |
| 266 | C2×Q8 | — | 30 | 1 | no | — |
| 267 | C2×Q8 | — | 30 | 1 | no | — |
| 268 | C2×Q8 | — | 30 | 1 | no | — |
| 269 | C2×Q8 | — | 30 | 1 | no | — |
| 270 | C2×Q8 | — | 30 | 1 | no | — |
| 271 | C2×Q8 | — | 30 | 1 | no | — |
| 272 | C2×Q8 | — | 30 | 1 | no | — |
| 273 | C2×Q8 | — | 30 | 1 | no | — |
| 274 | C2×Q8 | — | 30 | 2 | no | — |
| 275 | C2×Q8 | — | 30 | 2 | no | — |
| 276 | C22×C4 | — | 2 | 1 | no | — |
| 277 | C22×C4 | — | 5 | 1 | no | — |
| 278 | C22×C4 | — | 10 | 1 | no | — |
| 279 | C22×C4 | — | 15 | 1 | no | — |
| 280 | C22×C4 | — | 15 | 1 | no | — |
| 281 | C22×C4 | — | 15 | 1 | no | — |
| 282 | C22×C4 | — | 15 | 1 | no | — |
| 283 | C22×C4 | — | 30 | 1 | no | — |
| 284 | C22×C4 | — | 30 | 1 | no | — |
| 285 | C22×C4 | — | 30 | 1 | no | — |
| 286 | C22×C4 | — | 30 | 1 | no | — |
| 287 | C22×C4 | — | 30 | 1 | no | — |
| 288 | C22×C4 | — | 30 | 1 | no | — |
| 289 | C22×C4 | C2×ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | — | 30 | 1 | no | — |
| 291 | C2×C8 | — | 30 | 1 | no | — |
| 292 | C2×C8 | — | 30 | 1 | no | — |
| 293 | C2×C8 | — | 30 | 1 | no | — |
| 294 | C2×C8 | — | 30 | 1 | no | — |
| 295 | C2×C8 | — | 30 | 1 | no | — |
| 296 | C4⋊C4 | — | 30 | 1 | no | — |
| 297 | C4⋊C4 | — | 30 | 1 | no | — |
| 298 | C4⋊C4 | — | 30 | 1 | no | — |
| 299 | C4⋊C4 | — | 30 | 1 | no | — |
| 300 | C22⋊C4 | — | 60 | 1 | no | — |
| 301 | C22⋊C4 | — | 60 | 1 | no | — |
| 302 | C3×C5 | — | 4 | 1 | no | Hall |
| 303 | C22×C3 | — | 20 | 1 | no | — |
| 304 | A4 | #4009 | 1 | 1 | yes | characteristic, complemented |
| 305 | C3×C4 | — | 4 | 1 | no | — |
| 306 | C3×C4 | — | 8 | 1 | no | — |
| 307 | C3×C4 | — | 20 | 1 | no | — |
| 308 | C3×C4 | — | 40 | 1 | no | — |
| 309 | Dic3 | — | 80 | 1 | no | — |
| 310 | C2×C5 | — | 3 | 1 | no | — |
| 311 | C2×C5 | — | 3 | 1 | no | — |
| 312 | C2×C5 | #5432 | 1 | 1 | yes | characteristic |
| 313 | D5 | — | 3 | 1 | no | — |
| 314 | D5 | — | 3 | 1 | no | — |
| 315 | D5 | #5416 | 1 | 1 | yes | characteristic |
| 316 | D5 | #5417 | 1 | 1 | yes | characteristic |
| 317 | C23 | — | 5 | 1 | no | — |
| 318 | C23 | — | 5 | 1 | no | — |
| 319 | C23 | — | 15 | 1 | no | — |
| 320 | C23 | — | 15 | 1 | no | — |
| 321 | C23 | — | 15 | 1 | no | — |
| 322 | C23 | — | 15 | 1 | no | — |
| 323 | C23 | #6763 | 1 | 1 | yes | characteristic |
| 324 | Q8 | — | 3 | 2 | no | — |
| 325 | Q8 | — | 3 | 1 | no | — |
| 326 | Q8 | — | 5 | 1 | no | — |
| 327 | Q8 | — | 6 | 1 | no | — |
| 328 | Q8 | — | 10 | 1 | no | — |
| 329 | Q8 | — | 15 | 2 | no | — |
| 330 | Q8 | — | 15 | 1 | no | — |
| 331 | Q8 | — | 30 | 1 | no | — |
| 332 | Q8 | — | 30 | 1 | no | — |
| 333 | Q8 | — | 30 | 1 | no | — |
| 334 | Q8 | — | 30 | 1 | no | — |
| 335 | Q8 | — | 30 | 2 | no | — |
| 336 | Q8 | A4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 337 | C2×C4 | — | 3 | 1 | no | — |
| 338 | C2×C4 | — | 3 | 1 | no | — |
| 339 | C2×C4 | — | 5 | 1 | no | — |
| 340 | C2×C4 | — | 6 | 1 | no | — |
| 341 | C2×C4 | — | 6 | 1 | no | — |
| 342 | C2×C4 | — | 10 | 1 | no | — |
| 343 | C2×C4 | — | 15 | 1 | no | — |
| 344 | C2×C4 | — | 15 | 1 | no | — |
| 345 | C2×C4 | — | 15 | 1 | no | — |
| 346 | C2×C4 | — | 15 | 1 | no | — |
| 347 | C2×C4 | — | 15 | 1 | no | — |
| 348 | C2×C4 | — | 30 | 1 | no | — |
| 349 | C2×C4 | — | 30 | 1 | no | — |
| 350 | C2×C4 | — | 30 | 1 | no | — |
| 351 | C2×C4 | — | 30 | 1 | no | — |
| 352 | C2×C4 | — | 30 | 2 | no | — |
| 353 | C2×C4 | — | 30 | 1 | no | — |
| 354 | C2×C4 | — | 30 | 1 | no | — |
| 355 | C2×C4 | — | 60 | 1 | no | — |
| 356 | C2×C4 | — | 60 | 1 | no | — |
| 357 | C2×C4 | — | 60 | 1 | no | — |
| 358 | C2×C4 | — | 60 | 1 | no | — |
| 359 | C2×C4 | — | 60 | 1 | no | — |
| 360 | C2×C4 | — | 60 | 1 | no | — |
| 361 | C8 | — | 60 | 1 | no | — |
| 362 | C8 | — | 60 | 1 | no | — |
| 363 | C2×C3 | — | 4 | 1 | no | — |
| 364 | C2×C3 | — | 20 | 1 | no | — |
| 365 | C2×C3 | — | 20 | 1 | no | — |
| 366 | C5 | #73147 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 367 | C22 | — | 3 | 1 | no | — |
| 368 | C22 | — | 3 | 1 | no | — |
| 369 | C22 | — | 5 | 1 | no | — |
| 370 | C22 | — | 15 | 1 | no | — |
| 371 | C22 | — | 15 | 1 | no | — |
| 372 | C22 | — | 15 | 1 | no | — |
| 373 | C22 | — | 15 | 1 | no | — |
| 374 | C22 | — | 15 | 1 | no | — |
| 375 | C22 | — | 15 | 1 | no | — |
| 376 | C22 | — | 15 | 1 | no | — |
| 377 | C22 | — | 30 | 1 | no | — |
| 378 | C22 | #91238 | 1 | 1 | yes | characteristic, complemented |
| 379 | C4 | — | 2 | 1 | no | — |
| 380 | C4 | — | 3 | 1 | no | — |
| 381 | C4 | — | 5 | 1 | no | — |
| 382 | C4 | — | 6 | 1 | no | — |
| 383 | C4 | — | 10 | 1 | no | — |
| 384 | C4 | — | 15 | 1 | no | — |
| 385 | C4 | — | 30 | 1 | no | — |
| 386 | C4 | — | 120 | 1 | no | — |
| 387 | C4 | — | 120 | 1 | no | — |
| 388 | C4 | C2×A4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 389 | C3 | — | 4 | 1 | no | Sylow |
| 390 | C2 | — | 3 | 1 | no | — |
| 391 | C2 | — | 3 | 1 | no | — |
| 392 | C2 | — | 5 | 1 | no | — |
| 393 | C2 | — | 5 | 1 | no | — |
| 394 | C2 | — | 15 | 1 | no | — |
| 395 | C2 | — | 15 | 1 | no | — |
| 396 | C2 | #11756729 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C5×Q8×A4 | C4 | semidirect |
| 10. A4×Dic10 | C4 | semidirect |
| 33. C22×C5×Q8 | Dic3 | semidirect |
| 43. C22×Dic10 | Dic3 | semidirect |
| 71. Q8×A4 | AGL(1,𝔽5) | semidirect |
| 133. C5×A4 | #103 | semidirect |
| 164. C5×Q8 | SL(2,ℤ/4) | semidirect |
| 191. Dic10 | SL(2,ℤ/4) | semidirect |
| 202. C22×Q8 | ΓL(1,𝔽16) | semidirect |
| 234. C22×C5 | #835 | semidirect |
| 304. A4 | #4009 | semidirect |
| 336. Q8 | A4⋊AGL(1,𝔽5) | semidirect |
| 366. C5 | #73147 | semidirect |
| 378. C22 | #91238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D5×A4 | 2 |
| C4⋊(A4⋊AGL(1,𝔽5)) | 2 |
| D5⋊(A4⋊C8) | 2 |
| #10604973 | 3 |
| #91238 | 4 |
| #73147 | 5 |