Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
199 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 18 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 | D4×SL(2,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4⋊#6728 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | SL(2,𝔽5)⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×SL(2,𝔽5) | — | 2 | 1 | no | — |
| 5 | C2×#6728 | — | 2 | 1 | no | — |
| 6 | C4×SL(2,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 7 | #73085 | — | 5 | 1 | no | maximal, Hall |
| 8 | D4⋊#170 | — | 6 | 1 | no | maximal |
| 9 | C2×SL(2,𝔽5) | — | 4 | 1 | no | — |
| 10 | C2×SL(2,𝔽5) | D4 | 1 | 1 | yes | characteristic |
| 11 | #6728 | — | 4 | 1 | no | — |
| 12 | D4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 13 | C4⋊#226 | — | 5 | 1 | no | — |
| 14 | #4759 | — | 10 | 1 | no | maximal |
| 15 | SL(2,𝔽3)⋊C8 | — | 5 | 1 | no | — |
| 16 | D4×Dic5 | — | 6 | 1 | no | — |
| 17 | C4⋊#170 | — | 6 | 1 | no | — |
| 18 | C4×#170 | — | 6 | 1 | no | — |
| 19 | #1649 | — | 15 | 1 | no | Sylow |
| 20 | SL(2,𝔽5) | D8 | 1 | 1 | yes | characteristic |
| 21 | C22×SL(2,𝔽3) | — | 10 | 1 | no | — |
| 22 | C2×#226 | — | 10 | 1 | no | — |
| 23 | D4×Dic3 | — | 10 | 1 | no | — |
| 24 | #888 | — | 10 | 1 | no | — |
| 25 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 26 | C3×#102 | — | 10 | 1 | no | — |
| 27 | #832 | — | 10 | 1 | no | — |
| 28 | #818 | — | 10 | 1 | no | — |
| 29 | Dic3⋊C8 | — | 10 | 1 | no | — |
| 30 | #807 | — | 10 | 1 | no | — |
| 31 | C2×C5×D4 | — | 6 | 1 | no | — |
| 32 | C22×Dic5 | — | 12 | 1 | no | — |
| 33 | C2×#170 | — | 12 | 1 | no | — |
| 34 | C2×#170 | — | 12 | 1 | no | — |
| 35 | C22⋊Dic5 | — | 12 | 1 | no | — |
| 36 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 37 | C4×Dic5 | — | 6 | 1 | no | — |
| 38 | D4×Q8 | — | 5 | 1 | no | — |
| 39 | #500 | — | 15 | 1 | no | — |
| 40 | #474 | — | 15 | 1 | no | — |
| 41 | #462 | — | 15 | 1 | no | — |
| 42 | #332 | — | 15 | 1 | no | — |
| 43 | Q8⋊C8 | — | 15 | 1 | no | — |
| 44 | D4⋊C8 | — | 15 | 1 | no | — |
| 45 | C2×C3×D4 | — | 10 | 1 | no | — |
| 46 | C22×Dic3 | — | 20 | 1 | no | — |
| 47 | C2×Dic6 | — | 20 | 1 | no | — |
| 48 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 49 | C2×SL(2,𝔽3) | — | 20 | 1 | no | — |
| 50 | #226 | — | 20 | 1 | no | — |
| 51 | C2×C3×C8 | — | 10 | 1 | no | — |
| 52 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 53 | #217 | — | 20 | 1 | no | — |
| 54 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 55 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 56 | Dic3⋊C4 | — | 20 | 1 | no | — |
| 57 | C4×Dic3 | — | 10 | 1 | no | — |
| 58 | C2×C3⋊C8 | — | 10 | 1 | no | — |
| 59 | C23×C5 | — | 12 | 1 | no | — |
| 60 | C5×D4 | — | 6 | 2 | no | — |
| 61 | C5×D4 | — | 12 | 1 | no | — |
| 62 | C2×C4×C5 | — | 6 | 1 | no | — |
| 63 | C2×Dic5 | — | 6 | 1 | no | — |
| 64 | C2×Dic5 | — | 6 | 1 | no | — |
| 65 | C2×Dic5 | — | 12 | 1 | no | — |
| 66 | C2×Dic5 | — | 24 | 1 | no | — |
| 67 | C2×Dic5 | — | 24 | 1 | no | — |
| 68 | #170 | — | 12 | 2 | no | — |
| 69 | #170 | — | 24 | 1 | no | — |
| 70 | C22×Q8 | — | 10 | 1 | no | — |
| 71 | C2×Q16 | — | 30 | 1 | no | — |
| 72 | C4⋊Q8 | — | 15 | 1 | no | — |
| 73 | C4⋊Q8 | — | 15 | 1 | no | — |
| 74 | C22⋊Q8 | — | 30 | 1 | no | — |
| 75 | C4×Q8 | — | 5 | 1 | no | — |
| 76 | C4×D4 | — | 15 | 1 | no | — |
| 77 | #107 | — | 30 | 1 | no | — |
| 78 | #107 | — | 30 | 2 | no | — |
| 79 | C4⋊C8 | — | 15 | 1 | no | — |
| 80 | C4⋊C8 | — | 15 | 1 | no | — |
| 81 | #103 | — | 30 | 1 | no | — |
| 82 | #102 | — | 10 | 1 | no | — |
| 83 | C4×C8 | — | 15 | 1 | no | — |
| 84 | C23×C3 | — | 20 | 1 | no | — |
| 85 | C3×D4 | — | 10 | 2 | no | — |
| 86 | C3×D4 | — | 20 | 1 | no | — |
| 87 | C2×C3×C4 | — | 10 | 1 | no | — |
| 88 | C2×C3×C4 | — | 20 | 1 | no | — |
| 89 | C2×Dic3 | — | 10 | 1 | no | — |
| 90 | C2×Dic3 | — | 10 | 1 | no | — |
| 91 | C2×Dic3 | — | 20 | 1 | no | — |
| 92 | C2×Dic3 | — | 20 | 1 | no | — |
| 93 | C2×Dic3 | — | 40 | 1 | no | — |
| 94 | C2×Dic3 | — | 40 | 1 | no | — |
| 95 | Dic6 | — | 40 | 1 | no | — |
| 96 | Dic6 | — | 40 | 1 | no | — |
| 97 | SL(2,𝔽3) | — | 5 | 1 | no | — |
| 98 | C3×C8 | — | 20 | 1 | no | — |
| 99 | C3⋊C8 | — | 20 | 1 | no | — |
| 100 | C22×C5 | — | 6 | 1 | no | — |
| 101 | C22×C5 | — | 12 | 2 | no | — |
| 102 | C22×C5 | — | 24 | 1 | no | — |
| 103 | C22×C5 | — | 24 | 1 | no | — |
| 104 | C4×C5 | — | 6 | 1 | no | — |
| 105 | C4×C5 | — | 6 | 1 | no | — |
| 106 | Dic5 | — | 6 | 1 | no | — |
| 107 | Dic5 | — | 6 | 1 | no | — |
| 108 | Dic5 | — | 12 | 1 | no | — |
| 109 | Dic5 | — | 24 | 1 | no | — |
| 110 | C2×Q8 | — | 5 | 1 | no | — |
| 111 | C2×Q8 | — | 20 | 1 | no | — |
| 112 | C2×Q8 | — | 30 | 1 | no | — |
| 113 | C2×Q8 | — | 30 | 1 | no | — |
| 114 | C2×Q8 | — | 60 | 1 | no | — |
| 115 | C2×D4 | S5 | 1 | 1 | yes | characteristic |
| 116 | C22×C4 | — | 30 | 1 | no | — |
| 117 | Q16 | — | 60 | 1 | no | — |
| 118 | Q16 | — | 60 | 1 | no | — |
| 119 | C2×C8 | — | 10 | 1 | no | — |
| 120 | C2×C8 | — | 30 | 1 | no | — |
| 121 | C2×C8 | — | 30 | 1 | no | — |
| 122 | C4⋊C4 | — | 10 | 1 | no | — |
| 123 | C4⋊C4 | — | 15 | 1 | no | — |
| 124 | C4⋊C4 | — | 15 | 2 | no | — |
| 125 | C4⋊C4 | — | 15 | 1 | no | — |
| 126 | C4⋊C4 | — | 30 | 1 | no | — |
| 127 | C22⋊C4 | — | 30 | 1 | no | — |
| 128 | C42 | — | 15 | 1 | no | — |
| 129 | C22×C3 | — | 10 | 1 | no | — |
| 130 | C22×C3 | — | 20 | 2 | no | — |
| 131 | C22×C3 | — | 40 | 1 | no | — |
| 132 | C22×C3 | — | 40 | 1 | no | — |
| 133 | C3×C4 | — | 10 | 1 | no | — |
| 134 | C3×C4 | — | 10 | 1 | no | — |
| 135 | C3×C4 | — | 40 | 1 | no | — |
| 136 | Dic3 | — | 10 | 1 | no | — |
| 137 | Dic3 | — | 10 | 1 | no | — |
| 138 | Dic3 | — | 20 | 1 | no | — |
| 139 | Dic3 | — | 40 | 1 | no | — |
| 140 | Dic3 | — | 40 | 1 | no | — |
| 141 | C2×C5 | — | 6 | 1 | no | — |
| 142 | C2×C5 | — | 6 | 1 | no | — |
| 143 | C2×C5 | — | 6 | 1 | no | — |
| 144 | C2×C5 | — | 24 | 2 | no | — |
| 145 | C23 | — | 2 | 1 | no | — |
| 146 | Q8 | — | 5 | 1 | no | — |
| 147 | Q8 | — | 15 | 1 | no | — |
| 148 | Q8 | — | 60 | 1 | no | — |
| 149 | Q8 | — | 60 | 1 | no | — |
| 150 | Q8 | — | 60 | 1 | no | — |
| 151 | Q8 | — | 60 | 1 | no | — |
| 152 | D4 | — | 2 | 1 | no | — |
| 153 | D4 | #6728 | 1 | 2 | yes | complemented |
| 154 | C2×C4 | — | 15 | 1 | no | — |
| 155 | C2×C4 | — | 15 | 1 | no | — |
| 156 | C2×C4 | — | 20 | 1 | no | — |
| 157 | C2×C4 | — | 30 | 1 | no | — |
| 158 | C2×C4 | — | 60 | 1 | no | — |
| 159 | C2×C4 | — | 60 | 1 | no | — |
| 160 | C2×C4 | C2×S5 | 1 | 1 | yes | characteristic |
| 161 | C8 | — | 20 | 1 | no | — |
| 162 | C8 | — | 30 | 2 | no | — |
| 163 | C8 | — | 60 | 1 | no | — |
| 164 | C2×C3 | — | 10 | 1 | no | — |
| 165 | C2×C3 | — | 10 | 1 | no | — |
| 166 | C2×C3 | — | 10 | 1 | no | — |
| 167 | C2×C3 | — | 40 | 2 | no | — |
| 168 | C5 | — | 6 | 1 | no | Sylow |
| 169 | C22 | — | 2 | 2 | no | — |
| 170 | C22 | — | 4 | 1 | no | — |
| 171 | C22 | — | 4 | 1 | no | — |
| 172 | C22 | C22⋊S5 | 1 | 1 | yes | characteristic |
| 173 | C4 | — | 15 | 1 | no | — |
| 174 | C4 | — | 15 | 1 | no | — |
| 175 | C4 | — | 30 | 1 | no | — |
| 176 | C4 | — | 40 | 1 | no | — |
| 177 | C4 | — | 60 | 1 | no | — |
| 178 | C4 | C2×#6728 | 1 | 1 | yes | characteristic |
| 179 | C4 | #91877 | 1 | 1 | yes | characteristic |
| 180 | C3 | — | 10 | 1 | no | Sylow |
| 181 | C2 | — | 4 | 2 | no | — |
| 182 | C2 | #11751518 | 1 | 1 | yes | characteristic |
| 183 | C2 | #11751520 | 1 | 1 | yes | characteristic |
| 184 | C2 | C22⋊#6728 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4⋊#6728 | C2 | semidirect |
| 3. SL(2,𝔽5)⋊C8 | C2 | semidirect |
| 153. D4 | #6728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×SL(2,𝔽5) | 2 |
| C4⋊#6728 | 2 |
| SL(2,𝔽5)⋊C8 | 2 |
| #73085 | 5 |
| D4⋊#170 | 6 |
| #4759 | 10 |