Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 80 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 | A4×#713 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11756716 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | D5⋊(A4⋊C8) | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #10617517 | — | 3 | 1 | no | maximal, Hall |
| 5 | C5×Q8×A4 | C4 | 1 | 1 | yes | characteristic |
| 6 | #91992 | — | 4 | 1 | no | maximal |
| 7 | A4×D20 | C4 | 1 | 3 | yes | — |
| 8 | C4×D5×A4 | C22 | 1 | 3 | yes | — |
| 9 | A4⋊#170 | C22 | 1 | 1 | yes | characteristic |
| 10 | A4⋊#170 | C22 | 1 | 3 | yes | — |
| 11 | #85511 | — | 5 | 1 | no | maximal, Hall |
| 12 | C22×#713 | D3 | 1 | 1 | yes | characteristic |
| 13 | C2×#4133 | — | 3 | 1 | no | — |
| 14 | C2×#4133 | — | 3 | 1 | no | — |
| 15 | #65787 | — | 3 | 3 | no | — |
| 16 | #65787 | — | 3 | 3 | no | — |
| 17 | #65756 | — | 3 | 3 | no | — |
| 18 | D5⋊(C22⋊C8) | — | 3 | 3 | no | — |
| 19 | C2×D5×A4 | C2×C4 | 1 | 3 | yes | — |
| 20 | C3×#713 | — | 4 | 1 | no | — |
| 21 | C4×C5×A4 | C2×C4 | 1 | 3 | yes | — |
| 22 | #6758 | — | 4 | 3 | no | — |
| 23 | D5⋊(C3⋊C8) | — | 4 | 3 | no | — |
| 24 | A4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 25 | A4×#41 | — | 5 | 1 | no | — |
| 26 | #5409 | — | 5 | 3 | no | — |
| 27 | C2×A4⋊C8 | — | 5 | 3 | no | — |
| 28 | C22×C5×Q8 | Dic3 | 1 | 1 | yes | characteristic |
| 29 | C2×#713 | — | 3 | 1 | no | — |
| 30 | C2×#713 | — | 3 | 3 | no | — |
| 31 | C2×#713 | — | 3 | 1 | no | — |
| 32 | C2×#713 | — | 3 | 3 | no | — |
| 33 | C22×D20 | Dic3 | 1 | 3 | yes | — |
| 34 | C22×C4×D5 | C2×D3 | 1 | 3 | yes | — |
| 35 | #4133 | — | 6 | 1 | no | — |
| 36 | #4133 | — | 6 | 3 | no | — |
| 37 | #4133 | — | 6 | 3 | no | — |
| 38 | #4133 | — | 6 | 1 | no | — |
| 39 | C2×#700 | — | 3 | 3 | no | — |
| 40 | C2×#700 | — | 3 | 3 | no | — |
| 41 | C2×D5⋊C8 | — | 3 | 3 | no | — |
| 42 | C2×D5⋊C8 | — | 3 | 3 | no | — |
| 43 | C22⋊#170 | — | 3 | 1 | no | — |
| 44 | C22⋊#170 | — | 3 | 3 | no | — |
| 45 | #4003 | — | 3 | 3 | no | — |
| 46 | #4003 | — | 3 | 3 | no | — |
| 47 | #4003 | — | 3 | 6 | no | — |
| 48 | #2880 | — | 15 | 1 | no | Sylow |
| 49 | C2×C5×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 50 | D5×A4 | — | 2 | 3 | no | — |
| 51 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 52 | C3×D20 | — | 4 | 3 | no | — |
| 53 | C3×C4×D5 | — | 4 | 3 | no | — |
| 54 | C3⋊#170 | — | 4 | 1 | no | — |
| 55 | C3⋊#170 | — | 4 | 3 | no | — |
| 56 | Q8×A4 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 57 | D4×A4 | — | 5 | 3 | no | — |
| 58 | C2×C4×A4 | — | 5 | 3 | no | — |
| 59 | #948 | — | 20 | 1 | no | — |
| 60 | A4⋊C8 | — | 5 | 1 | no | — |
| 61 | A4⋊C8 | — | 5 | 3 | no | — |
| 62 | C23×D5 | C2×Dic3 | 1 | 3 | yes | — |
| 63 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 64 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 65 | C22×C4×C5 | C2×Dic3 | 1 | 3 | yes | — |
| 66 | C22×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 67 | #713 | — | 3 | 1 | no | — |
| 68 | #713 | — | 3 | 3 | no | — |
| 69 | #713 | — | 3 | 3 | no | — |
| 70 | #713 | — | 6 | 1 | no | — |
| 71 | #713 | — | 6 | 3 | no | — |
| 72 | #713 | — | 6 | 3 | no | — |
| 73 | #713 | S4 | 1 | 1 | yes | characteristic |
| 74 | C2×D20 | — | 3 | 3 | no | — |
| 75 | C2×D20 | — | 3 | 6 | no | — |
| 76 | C2×D20 | — | 3 | 3 | no | — |
| 77 | C2×C4×D5 | — | 3 | 3 | no | — |
| 78 | C2×C4×D5 | — | 3 | 3 | no | — |
| 79 | C2×C4×D5 | — | 3 | 3 | no | — |
| 80 | C2×C4×D5 | — | 3 | 3 | no | — |
| 81 | C2×#170 | — | 3 | 1 | no | — |
| 82 | C2×#170 | — | 3 | 1 | no | — |
| 83 | C2×#170 | — | 3 | 3 | no | — |
| 84 | C2×#170 | — | 3 | 3 | no | — |
| 85 | #700 | — | 6 | 3 | no | — |
| 86 | #700 | — | 6 | 3 | no | — |
| 87 | #700 | — | 6 | 3 | no | — |
| 88 | #700 | — | 6 | 3 | no | — |
| 89 | D5⋊C8 | — | 6 | 3 | no | — |
| 90 | D5⋊C8 | — | 6 | 3 | no | — |
| 91 | D5⋊C8 | — | 6 | 3 | no | — |
| 92 | D5⋊C8 | — | 6 | 3 | no | — |
| 93 | C22×#41 | — | 5 | 1 | no | — |
| 94 | C2×#131 | — | 15 | 1 | no | — |
| 95 | C2×#131 | — | 15 | 1 | no | — |
| 96 | #408 | — | 15 | 3 | no | — |
| 97 | #408 | — | 15 | 3 | no | — |
| 98 | #407 | — | 15 | 3 | no | — |
| 99 | C2×C22⋊C8 | — | 15 | 3 | no | — |
| 100 | C2×C3×D5 | — | 4 | 3 | no | — |
| 101 | C5×A4 | #131 | 1 | 1 | yes | characteristic, complemented |
| 102 | C3×C4×C5 | — | 4 | 3 | no | — |
| 103 | C3×Dic5 | — | 4 | 1 | no | — |
| 104 | C22×A4 | — | 5 | 3 | no | — |
| 105 | C3×#41 | — | 20 | 1 | no | — |
| 106 | C4×A4 | — | 5 | 1 | no | — |
| 107 | C4×A4 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 108 | #208 | — | 20 | 3 | no | — |
| 109 | C2×C3⋊C8 | — | 20 | 3 | no | — |
| 110 | C23×C5 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 111 | C22×D5 | — | 2 | 3 | no | — |
| 112 | C22×D5 | — | 3 | 3 | no | — |
| 113 | C22×D5 | — | 3 | 3 | no | — |
| 114 | C22×D5 | — | 6 | 3 | no | — |
| 115 | C5×Q8 | — | 3 | 3 | no | — |
| 116 | C5×Q8 | — | 6 | 1 | no | — |
| 117 | C5×Q8 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C5 | — | 3 | 3 | no | — |
| 119 | C2×C4×C5 | — | 3 | 3 | no | — |
| 120 | C2×Dic5 | — | 3 | 1 | no | — |
| 121 | C2×Dic5 | — | 3 | 1 | no | — |
| 122 | D20 | — | 3 | 6 | no | — |
| 123 | D20 | — | 3 | 3 | no | — |
| 124 | D20 | — | 6 | 3 | no | — |
| 125 | D20 | SL(2,ℤ/4) | 1 | 3 | yes | — |
| 126 | C4×D5 | — | 3 | 3 | no | — |
| 127 | C4×D5 | — | 3 | 3 | no | — |
| 128 | C4×D5 | — | 3 | 3 | no | — |
| 129 | C4×D5 | — | 6 | 3 | no | — |
| 130 | C4×D5 | C2×S4 | 1 | 3 | yes | — |
| 131 | #170 | — | 6 | 1 | no | — |
| 132 | #170 | — | 6 | 3 | no | — |
| 133 | #170 | — | 6 | 1 | no | — |
| 134 | #170 | — | 6 | 3 | no | — |
| 135 | C2×#41 | — | 15 | 1 | no | — |
| 136 | C2×#41 | — | 15 | 3 | no | — |
| 137 | C2×#41 | — | 15 | 1 | no | — |
| 138 | C2×#41 | — | 15 | 3 | no | — |
| 139 | C22×Q8 | ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 140 | C22×D4 | — | 5 | 3 | no | — |
| 141 | C23×C4 | — | 5 | 3 | no | — |
| 142 | #131 | — | 30 | 1 | no | — |
| 143 | #131 | — | 30 | 3 | no | — |
| 144 | #131 | — | 30 | 3 | no | — |
| 145 | #131 | — | 30 | 1 | no | — |
| 146 | C2×M16 | — | 15 | 3 | no | — |
| 147 | C2×M16 | — | 15 | 3 | no | — |
| 148 | C22×C8 | — | 15 | 3 | no | — |
| 149 | C22×C8 | — | 15 | 3 | no | — |
| 150 | C22⋊C8 | — | 15 | 1 | no | — |
| 151 | C22⋊C8 | — | 15 | 3 | no | — |
| 152 | C22⋊C8 | — | 15 | 3 | no | — |
| 153 | C22⋊C8 | — | 15 | 3 | no | — |
| 154 | C22⋊C8 | — | 15 | 6 | no | — |
| 155 | C2×C3×C5 | — | 4 | 1 | no | — |
| 156 | C3×D5 | — | 8 | 3 | no | — |
| 157 | C2×A4 | — | 10 | 3 | no | — |
| 158 | C2×A4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 159 | C3×Q8 | — | 4 | 1 | no | — |
| 160 | C3×D4 | — | 20 | 3 | no | — |
| 161 | C2×C3×C4 | — | 20 | 3 | no | — |
| 162 | C3⋊C8 | — | 20 | 1 | no | — |
| 163 | C3⋊C8 | — | 20 | 3 | no | — |
| 164 | C22×C5 | — | 3 | 1 | no | — |
| 165 | C22×C5 | — | 3 | 1 | no | — |
| 166 | C22×C5 | #948 | 1 | 1 | yes | characteristic, complemented |
| 167 | C2×D5 | — | 3 | 3 | no | — |
| 168 | C2×D5 | — | 6 | 3 | no | — |
| 169 | C2×D5 | — | 6 | 3 | no | — |
| 170 | C2×D5 | — | 6 | 3 | no | — |
| 171 | C2×D5 | — | 6 | 3 | no | — |
| 172 | C2×D5 | C2×SL(2,ℤ/4) | 1 | 3 | yes | — |
| 173 | C4×C5 | — | 3 | 3 | no | — |
| 174 | C4×C5 | C2×SL(2,ℤ/4) | 1 | 3 | yes | — |
| 175 | Dic5 | — | 3 | 1 | no | — |
| 176 | Dic5 | C22×S4 | 1 | 1 | yes | characteristic |
| 177 | C24 | — | 5 | 3 | no | — |
| 178 | #41 | — | 5 | 1 | no | — |
| 179 | #41 | — | 15 | 3 | no | — |
| 180 | #41 | — | 15 | 3 | no | — |
| 181 | #41 | — | 15 | 1 | no | — |
| 182 | #41 | — | 30 | 1 | no | — |
| 183 | #41 | — | 30 | 3 | no | — |
| 184 | #41 | — | 30 | 3 | no | — |
| 185 | C2×Q8 | — | 3 | 1 | no | — |
| 186 | C2×Q8 | — | 3 | 3 | no | — |
| 187 | C2×D4 | — | 15 | 3 | no | — |
| 188 | C2×D4 | — | 15 | 3 | no | — |
| 189 | C2×D4 | — | 15 | 6 | no | — |
| 190 | C22×C4 | — | 5 | 1 | no | — |
| 191 | C22×C4 | — | 15 | 3 | no | — |
| 192 | C22×C4 | — | 15 | 3 | no | — |
| 193 | C22×C4 | — | 15 | 3 | no | — |
| 194 | C22×C4 | — | 15 | 3 | no | — |
| 195 | C22×C4 | C2×ΓL(1,𝔽16) | 1 | 3 | yes | — |
| 196 | M16 | — | 30 | 3 | no | — |
| 197 | M16 | — | 30 | 3 | no | — |
| 198 | M16 | — | 30 | 3 | no | — |
| 199 | M16 | — | 30 | 3 | no | — |
| 200 | C2×C8 | — | 15 | 1 | no | — |
| 201 | C2×C8 | — | 15 | 1 | no | — |
| 202 | C2×C8 | — | 15 | 3 | no | — |
| 203 | C2×C8 | — | 15 | 3 | no | — |
| 204 | C2×C8 | — | 30 | 3 | no | — |
| 205 | C2×C8 | — | 30 | 3 | no | — |
| 206 | C2×C8 | — | 30 | 3 | no | — |
| 207 | C2×C8 | — | 30 | 3 | no | — |
| 208 | C3×C5 | — | 4 | 1 | no | Hall |
| 209 | C22×C3 | — | 20 | 3 | no | — |
| 210 | A4 | #4133 | 1 | 1 | yes | characteristic, complemented |
| 211 | C3×C4 | — | 4 | 3 | no | — |
| 212 | C3×C4 | — | 20 | 1 | no | — |
| 213 | C2×C5 | — | 3 | 1 | no | — |
| 214 | C2×C5 | — | 3 | 1 | no | — |
| 215 | C2×C5 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 216 | D5 | — | 2 | 3 | no | — |
| 217 | D5 | — | 6 | 3 | no | — |
| 218 | C23 | — | 10 | 3 | no | — |
| 219 | C23 | — | 15 | 3 | no | — |
| 220 | C23 | — | 15 | 3 | no | — |
| 221 | C23 | — | 30 | 3 | no | — |
| 222 | C23 | C22×ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 223 | Q8 | — | 3 | 3 | no | — |
| 224 | Q8 | — | 6 | 1 | no | — |
| 225 | Q8 | A4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 226 | D4 | — | 5 | 3 | no | — |
| 227 | D4 | — | 15 | 6 | no | — |
| 228 | D4 | — | 15 | 3 | no | — |
| 229 | D4 | — | 30 | 3 | no | — |
| 230 | C2×C4 | — | 3 | 3 | no | — |
| 231 | C2×C4 | — | 3 | 3 | no | — |
| 232 | C2×C4 | — | 5 | 3 | no | — |
| 233 | C2×C4 | — | 15 | 3 | no | — |
| 234 | C2×C4 | — | 15 | 3 | no | — |
| 235 | C2×C4 | — | 15 | 1 | no | — |
| 236 | C2×C4 | — | 15 | 3 | no | — |
| 237 | C2×C4 | — | 15 | 1 | no | — |
| 238 | C2×C4 | — | 30 | 3 | no | — |
| 239 | C8 | — | 30 | 1 | no | — |
| 240 | C8 | — | 30 | 3 | no | — |
| 241 | C8 | — | 30 | 1 | no | — |
| 242 | C8 | — | 30 | 3 | no | — |
| 243 | C2×C3 | — | 4 | 1 | no | — |
| 244 | C2×C3 | — | 40 | 3 | no | — |
| 245 | C5 | #85511 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 246 | C22 | — | 3 | 1 | no | — |
| 247 | C22 | — | 3 | 1 | no | — |
| 248 | C22 | — | 5 | 3 | no | — |
| 249 | C22 | — | 15 | 3 | no | — |
| 250 | C22 | — | 30 | 3 | no | — |
| 251 | C22 | — | 30 | 3 | no | — |
| 252 | C22 | — | 30 | 3 | no | — |
| 253 | C22 | — | 30 | 3 | no | — |
| 254 | C22 | #91992 | 1 | 1 | yes | characteristic, complemented |
| 255 | C4 | — | 3 | 3 | no | — |
| 256 | C4 | — | 5 | 1 | no | — |
| 257 | C4 | — | 15 | 1 | no | — |
| 258 | C4 | C2×A4⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 259 | C3 | — | 4 | 1 | no | Sylow |
| 260 | C2 | — | 3 | 1 | no | — |
| 261 | C2 | — | 3 | 1 | no | — |
| 262 | C2 | — | 10 | 3 | no | — |
| 263 | C2 | — | 30 | 3 | no | — |
| 264 | C2 | C22×A4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11756716 | C2 | semidirect |
| 3. D5⋊(A4⋊C8) | C2 | semidirect |
| 101. C5×A4 | #131 | semidirect |
| 166. C22×C5 | #948 | semidirect |
| 210. A4 | #4133 | semidirect |
| 245. C5 | #85511 | semidirect |
| 254. C22 | #91992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#713 | 2 |
| #11756716 | 2 |
| D5⋊(A4⋊C8) | 2 |
| #10617517 | 3 |
| #91992 | 4 |
| #85511 | 5 |