Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
223 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 25 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 | C4×#6732 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C8×SL(2,𝔽5) | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#6732 | C4 | 1 | 1 | yes | characteristic |
| 4 | C4×SL(2,𝔽5) | C4 | 1 | 1 | yes | characteristic |
| 5 | C4×SL(2,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 6 | #2991⋊C3 | — | 5 | 1 | no | maximal, Hall |
| 7 | #65122 | — | 6 | 1 | no | maximal |
| 8 | C2×SL(2,𝔽5) | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | #6732 | — | 2 | 1 | no | — |
| 10 | C4×#41⋊C3 | — | 5 | 1 | no | — |
| 11 | #4833 | — | 10 | 1 | no | maximal |
| 12 | C8×SL(2,𝔽3) | — | 5 | 2 | no | — |
| 13 | C42×D5 | — | 6 | 1 | no | — |
| 14 | C5×C4⋊C8 | — | 6 | 1 | no | — |
| 15 | #3952 | — | 6 | 2 | no | — |
| 16 | C8×Dic5 | — | 6 | 2 | no | — |
| 17 | C4⋊#168 | — | 6 | 1 | no | — |
| 18 | #2991 | — | 5 | 1 | no | Sylow |
| 19 | SL(2,𝔽5) | M16 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 21 | C42×D3 | — | 10 | 1 | no | — |
| 22 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 23 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 24 | C3×C4⋊C8 | — | 10 | 1 | no | — |
| 25 | (C2×D3)⋊C8 | — | 10 | 2 | no | — |
| 26 | C8×Dic3 | — | 10 | 2 | no | — |
| 27 | C4⋊(C3⋊C8) | — | 10 | 1 | no | — |
| 28 | C2×C4×D5 | — | 6 | 1 | no | — |
| 29 | C2×C4×D5 | — | 6 | 1 | no | — |
| 30 | C2×C4×D5 | — | 6 | 1 | no | — |
| 31 | C2×C5×C8 | — | 6 | 2 | no | — |
| 32 | C42×C5 | — | 6 | 1 | no | — |
| 33 | C4×Dic5 | — | 6 | 1 | no | — |
| 34 | C4×Dic5 | — | 6 | 1 | no | — |
| 35 | C4×Dic5 | — | 6 | 1 | no | — |
| 36 | C2×#168 | — | 6 | 2 | no | — |
| 37 | C4×#41 | — | 5 | 1 | no | — |
| 38 | C8×Q8 | — | 5 | 2 | no | — |
| 39 | #436 | — | 15 | 2 | no | — |
| 40 | #431 | — | 15 | 1 | no | — |
| 41 | #423 | — | 15 | 1 | no | — |
| 42 | C2×C4×D3 | — | 10 | 1 | no | — |
| 43 | C2×C4×D3 | — | 10 | 1 | no | — |
| 44 | C2×C4×D3 | — | 10 | 1 | no | — |
| 45 | #41⋊C3 | — | 10 | 1 | no | — |
| 46 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 47 | C2×C3×C8 | — | 10 | 2 | no | — |
| 48 | C3×C42 | — | 10 | 1 | no | — |
| 49 | C4×Dic3 | — | 10 | 1 | no | — |
| 50 | C4×Dic3 | — | 10 | 1 | no | — |
| 51 | C4×Dic3 | — | 10 | 1 | no | — |
| 52 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 53 | C22×D5 | — | 6 | 1 | no | — |
| 54 | C2×C4×C5 | — | 6 | 1 | no | — |
| 55 | C2×C4×C5 | — | 6 | 1 | no | — |
| 56 | C2×C4×C5 | — | 6 | 1 | no | — |
| 57 | C2×Dic5 | — | 6 | 1 | no | — |
| 58 | C2×Dic5 | — | 6 | 1 | no | — |
| 59 | C2×Dic5 | — | 6 | 1 | no | — |
| 60 | C4×D5 | — | 6 | 4 | no | — |
| 61 | C4×D5 | — | 12 | 1 | no | — |
| 62 | C4×D5 | — | 12 | 1 | no | — |
| 63 | C4×D5 | — | 12 | 1 | no | — |
| 64 | C4×D5 | — | 12 | 1 | no | — |
| 65 | C5×C8 | — | 12 | 2 | no | — |
| 66 | #168 | — | 12 | 2 | no | — |
| 67 | C2×#41 | — | 5 | 1 | no | — |
| 68 | C2×M16 | — | 15 | 2 | no | — |
| 69 | C4×Q8 | — | 5 | 1 | no | — |
| 70 | C4×Q8 | — | 5 | 1 | no | — |
| 71 | C4×D4 | — | 15 | 1 | no | — |
| 72 | C4×D4 | — | 15 | 1 | no | — |
| 73 | #117 | — | 15 | 1 | no | — |
| 74 | C2×C42 | — | 15 | 1 | no | — |
| 75 | C4⋊C8 | — | 15 | 2 | no | — |
| 76 | C4⋊C8 | — | 15 | 1 | no | — |
| 77 | C4⋊C8 | A5 | 1 | 1 | yes | maximal normal, characteristic |
| 78 | C22⋊C8 | — | 15 | 2 | no | — |
| 79 | C4×C8 | — | 15 | 2 | no | — |
| 80 | C22×D3 | — | 10 | 1 | no | — |
| 81 | C2×C3×C4 | — | 10 | 1 | no | — |
| 82 | C2×C3×C4 | — | 10 | 1 | no | — |
| 83 | C2×C3×C4 | — | 10 | 1 | no | — |
| 84 | C2×Dic3 | — | 10 | 1 | no | — |
| 85 | C2×Dic3 | — | 10 | 1 | no | — |
| 86 | C2×Dic3 | — | 10 | 1 | no | — |
| 87 | C4×D3 | — | 10 | 4 | no | — |
| 88 | C4×D3 | — | 20 | 1 | no | — |
| 89 | C4×D3 | — | 20 | 1 | no | — |
| 90 | C4×D3 | — | 20 | 1 | no | — |
| 91 | C4×D3 | — | 20 | 1 | no | — |
| 92 | SL(2,𝔽3) | — | 5 | 1 | no | — |
| 93 | C3×C8 | — | 20 | 2 | no | — |
| 94 | C3⋊C8 | — | 20 | 2 | no | — |
| 95 | C22×C5 | — | 6 | 1 | no | — |
| 96 | C2×D5 | — | 6 | 2 | no | — |
| 97 | C2×D5 | — | 12 | 1 | no | — |
| 98 | C2×D5 | — | 12 | 1 | no | — |
| 99 | C4×C5 | — | 6 | 2 | no | — |
| 100 | C4×C5 | — | 6 | 1 | no | — |
| 101 | C4×C5 | — | 6 | 1 | no | — |
| 102 | C4×C5 | — | 12 | 1 | no | — |
| 103 | Dic5 | — | 6 | 1 | no | — |
| 104 | Dic5 | — | 6 | 1 | no | — |
| 105 | Dic5 | — | 6 | 2 | no | — |
| 106 | Dic5 | — | 12 | 1 | no | — |
| 107 | #41 | — | 10 | 1 | no | — |
| 108 | #41 | — | 30 | 1 | no | — |
| 109 | C2×Q8 | — | 5 | 1 | no | — |
| 110 | C2×D4 | — | 15 | 1 | no | — |
| 111 | C22×C4 | — | 15 | 1 | no | — |
| 112 | C22×C4 | — | 15 | 1 | no | — |
| 113 | C22×C4 | — | 15 | 1 | no | — |
| 114 | M16 | — | 60 | 2 | no | — |
| 115 | C2×C8 | — | 15 | 2 | no | — |
| 116 | C2×C8 | C2×A5 | 1 | 2 | yes | — |
| 117 | C4⋊C4 | — | 15 | 1 | no | — |
| 118 | C4⋊C4 | — | 15 | 1 | no | — |
| 119 | C22⋊C4 | — | 15 | 2 | no | — |
| 120 | C42 | — | 15 | 1 | no | — |
| 121 | C42 | — | 15 | 1 | no | — |
| 122 | C42 | — | 15 | 1 | no | — |
| 123 | C42 | C2×A5 | 1 | 1 | yes | characteristic |
| 124 | C22×C3 | — | 10 | 1 | no | — |
| 125 | C2×D3 | — | 10 | 2 | no | — |
| 126 | C2×D3 | — | 20 | 1 | no | — |
| 127 | C2×D3 | — | 20 | 1 | no | — |
| 128 | C3×C4 | — | 10 | 2 | no | — |
| 129 | C3×C4 | — | 10 | 1 | no | — |
| 130 | C3×C4 | — | 10 | 1 | no | — |
| 131 | C3×C4 | — | 20 | 1 | no | — |
| 132 | Dic3 | — | 10 | 1 | no | — |
| 133 | Dic3 | — | 10 | 1 | no | — |
| 134 | Dic3 | — | 10 | 2 | no | — |
| 135 | Dic3 | — | 20 | 1 | no | — |
| 136 | C2×C5 | — | 6 | 1 | no | — |
| 137 | C2×C5 | — | 6 | 1 | no | — |
| 138 | C2×C5 | — | 6 | 1 | no | — |
| 139 | D5 | — | 12 | 2 | no | — |
| 140 | C23 | — | 15 | 1 | no | — |
| 141 | Q8 | — | 5 | 1 | no | — |
| 142 | Q8 | — | 15 | 1 | no | — |
| 143 | D4 | — | 30 | 1 | no | — |
| 144 | D4 | — | 30 | 1 | no | — |
| 145 | C2×C4 | — | 15 | 1 | no | — |
| 146 | C2×C4 | — | 15 | 1 | no | — |
| 147 | C2×C4 | — | 15 | 1 | no | — |
| 148 | C2×C4 | — | 30 | 1 | no | — |
| 149 | C2×C4 | — | 30 | 1 | no | — |
| 150 | C2×C4 | — | 30 | 2 | no | — |
| 151 | C2×C4 | — | 30 | 1 | no | — |
| 152 | C2×C4 | — | 30 | 1 | no | — |
| 153 | C2×C4 | C4×A5 | 1 | 1 | yes | characteristic |
| 154 | C2×C4 | C4×A5 | 1 | 1 | yes | characteristic |
| 155 | C2×C4 | C22×A5 | 1 | 1 | yes | characteristic |
| 156 | C8 | — | 2 | 2 | no | — |
| 157 | C8 | — | 30 | 2 | no | — |
| 158 | C2×C3 | — | 10 | 1 | no | — |
| 159 | C2×C3 | — | 10 | 1 | no | — |
| 160 | C2×C3 | — | 10 | 1 | no | — |
| 161 | D3 | — | 20 | 2 | no | — |
| 162 | C5 | — | 6 | 1 | no | Sylow |
| 163 | C22 | — | 30 | 1 | no | — |
| 164 | C22 | — | 30 | 1 | no | — |
| 165 | C22 | — | 30 | 1 | no | — |
| 166 | C22 | C2×C4×A5 | 1 | 1 | yes | characteristic |
| 167 | C4 | — | 2 | 1 | no | — |
| 168 | C4 | — | 15 | 1 | no | — |
| 169 | C4 | — | 15 | 1 | no | — |
| 170 | C4 | — | 30 | 1 | no | — |
| 171 | C4 | — | 30 | 1 | no | — |
| 172 | C4 | #91145 | 1 | 2 | yes | — |
| 173 | C4 | #91881 | 1 | 1 | yes | characteristic |
| 174 | C4 | #91883 | 1 | 1 | yes | characteristic |
| 175 | C3 | — | 10 | 1 | no | Sylow |
| 176 | C2 | — | 60 | 1 | no | — |
| 177 | C2 | #11751539 | 1 | 1 | yes | characteristic |
| 178 | C2 | C2×#91145 | 1 | 1 | yes | characteristic |
| 179 | C2 | M16×A5 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×SL(2,𝔽5) | C2 | semidirect |
| 19. SL(2,𝔽5) | M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6732 | 2 |
| C8×SL(2,𝔽5) | 2 |
| #2991⋊C3 | 5 |
| #65122 | 6 |
| #4833 | 10 |