Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
170 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 27 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 | #11752122 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5407 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #65429⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10601886 | — | 3 | 1 | no | maximal, Hall |
| 5 | #91954 | — | 2 | 1 | no | — |
| 6 | C5×#986 | — | 2 | 1 | no | — |
| 7 | C5×#131⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | #90944 | — | 4 | 1 | no | maximal |
| 9 | #73041 | — | 5 | 1 | no | maximal, Hall |
| 10 | C5×#472 | — | 3 | 1 | no | — |
| 11 | C2×#3959 | — | 3 | 1 | no | — |
| 12 | #65432 | — | 3 | 1 | no | — |
| 13 | #65429 | D3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #64783 | — | 3 | 1 | no | — |
| 15 | #64716 | — | 3 | 1 | no | — |
| 16 | #64713 | — | 3 | 1 | no | — |
| 17 | C5×#41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 18 | C5⋊#226 | — | 4 | 1 | no | — |
| 19 | C5×GL(2,𝔽3) | — | 4 | 1 | no | — |
| 20 | Dic60 | — | 4 | 1 | no | — |
| 21 | C5×D24 | — | 4 | 1 | no | — |
| 22 | C3×#672 | — | 4 | 1 | no | — |
| 23 | #5407 | D5 | 1 | 1 | yes | characteristic |
| 24 | #5403 | — | 5 | 1 | no | — |
| 25 | #504⋊C3 | — | 5 | 1 | no | — |
| 26 | C5×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 27 | C2×C5×D8 | — | 3 | 1 | no | — |
| 28 | C5×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 29 | #4097 | — | 6 | 1 | no | — |
| 30 | C2×Dic20 | — | 3 | 1 | no | — |
| 31 | C5×#108 | — | 3 | 1 | no | — |
| 32 | C5×#100 | — | 6 | 1 | no | — |
| 33 | #3959 | — | 6 | 1 | no | — |
| 34 | #3959 | — | 6 | 1 | no | — |
| 35 | #3956 | — | 6 | 1 | no | — |
| 36 | #3951 | — | 3 | 1 | no | — |
| 37 | #3944 | — | 3 | 1 | no | — |
| 38 | C2×#672 | — | 3 | 1 | no | — |
| 39 | #2223 | — | 15 | 1 | no | Sylow |
| 40 | Dic30 | — | 8 | 1 | no | — |
| 41 | C5×D12 | — | 8 | 1 | no | — |
| 42 | C5×SL(2,𝔽3) | D8 | 1 | 1 | yes | characteristic |
| 43 | C3×C5×C8 | — | 4 | 1 | no | — |
| 44 | #986 | — | 2 | 1 | no | — |
| 45 | #984 | — | 10 | 1 | no | — |
| 46 | #131⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 47 | #800 | — | 20 | 1 | no | — |
| 48 | C5×#41 | D12 | 1 | 1 | yes | characteristic |
| 49 | C2×C5×D4 | — | 6 | 1 | no | — |
| 50 | C2×Dic10 | — | 6 | 1 | no | — |
| 51 | C5×SD16 | — | 12 | 1 | no | — |
| 52 | C5×D8 | — | 6 | 1 | no | — |
| 53 | C5×D8 | — | 6 | 1 | no | — |
| 54 | C5×D8 | — | 12 | 1 | no | — |
| 55 | C5×M16 | — | 3 | 1 | no | — |
| 56 | C5×M16 | — | 6 | 1 | no | — |
| 57 | C2×C5×C8 | — | 3 | 1 | no | — |
| 58 | #689 | — | 12 | 1 | no | — |
| 59 | #687 | — | 12 | 1 | no | — |
| 60 | #681 | — | 6 | 1 | no | — |
| 61 | Dic20 | — | 6 | 1 | no | — |
| 62 | Dic20 | — | 6 | 1 | no | — |
| 63 | #672 | — | 3 | 1 | no | — |
| 64 | #672 | S4 | 1 | 1 | yes | characteristic |
| 65 | C2×SD32 | — | 15 | 1 | no | — |
| 66 | #504 | — | 5 | 1 | no | — |
| 67 | #473 | — | 15 | 1 | no | — |
| 68 | #472 | — | 3 | 1 | no | — |
| 69 | #368 | — | 15 | 1 | no | — |
| 70 | #362 | — | 15 | 1 | no | — |
| 71 | #361 | — | 15 | 1 | no | — |
| 72 | C2×C5×D3 | — | 16 | 1 | no | — |
| 73 | C3×C4×C5 | — | 4 | 1 | no | — |
| 74 | Dic15 | — | 16 | 1 | no | — |
| 75 | #41⋊C3 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 76 | GL(2,𝔽3) | — | 4 | 1 | no | — |
| 77 | #226 | — | 20 | 1 | no | — |
| 78 | Dic12 | — | 20 | 1 | no | — |
| 79 | D24 | — | 4 | 1 | no | — |
| 80 | C3×C16 | — | 20 | 1 | no | — |
| 81 | C23×C5 | — | 12 | 1 | no | — |
| 82 | C5×Q8 | D24 | 1 | 1 | yes | characteristic |
| 83 | C5×D4 | — | 3 | 1 | no | — |
| 84 | C5×D4 | — | 12 | 1 | no | — |
| 85 | C5×D4 | — | 12 | 1 | no | — |
| 86 | C2×C4×C5 | — | 3 | 1 | no | — |
| 87 | C2×Dic5 | — | 12 | 1 | no | — |
| 88 | Dic10 | — | 12 | 1 | no | — |
| 89 | Dic10 | — | 12 | 1 | no | — |
| 90 | C5×C8 | — | 3 | 1 | no | — |
| 91 | C5×C8 | — | 12 | 1 | no | — |
| 92 | C5×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 93 | #168 | — | 12 | 1 | no | — |
| 94 | #137 | — | 30 | 1 | no | — |
| 95 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 96 | C2×Q16 | — | 15 | 1 | no | — |
| 97 | C2×D8 | — | 3 | 1 | no | — |
| 98 | #131 | D3×D5 | 1 | 1 | yes | characteristic |
| 99 | SD32 | — | 30 | 1 | no | — |
| 100 | SD32 | — | 30 | 1 | no | — |
| 101 | M32 | — | 15 | 1 | no | — |
| 102 | C2×C16 | — | 15 | 1 | no | — |
| 103 | #108 | — | 3 | 1 | no | — |
| 104 | #108 | — | 15 | 1 | no | — |
| 105 | #101 | — | 30 | 1 | no | — |
| 106 | #100 | — | 6 | 1 | no | — |
| 107 | C2×C3×C5 | — | 4 | 1 | no | — |
| 108 | C5×D3 | — | 32 | 1 | no | — |
| 109 | D12 | — | 8 | 1 | no | — |
| 110 | Dic6 | — | 40 | 1 | no | — |
| 111 | SL(2,𝔽3) | #686 | 1 | 1 | yes | characteristic |
| 112 | C3×C8 | — | 4 | 1 | no | — |
| 113 | C22×C5 | — | 3 | 1 | no | — |
| 114 | C22×C5 | — | 24 | 1 | no | — |
| 115 | C22×C5 | — | 48 | 1 | no | — |
| 116 | C4×C5 | — | 3 | 1 | no | — |
| 117 | C4×C5 | C4⋊S4 | 1 | 1 | yes | characteristic |
| 118 | Dic5 | — | 24 | 1 | no | — |
| 119 | #41 | #1203 | 1 | 1 | yes | characteristic |
| 120 | C2×Q8 | — | 30 | 1 | no | — |
| 121 | C2×D4 | — | 6 | 1 | no | — |
| 122 | Q16 | — | 30 | 1 | no | — |
| 123 | Q16 | — | 30 | 1 | no | — |
| 124 | Q16 | — | 60 | 1 | no | — |
| 125 | SD16 | — | 12 | 1 | no | — |
| 126 | SD16 | — | 60 | 1 | no | — |
| 127 | D8 | — | 6 | 1 | no | — |
| 128 | D8 | — | 6 | 1 | no | — |
| 129 | D8 | — | 12 | 1 | no | — |
| 130 | M16 | — | 3 | 1 | no | — |
| 131 | M16 | — | 6 | 1 | no | — |
| 132 | M16 | — | 30 | 1 | no | — |
| 133 | C2×C8 | — | 3 | 1 | no | — |
| 134 | C16 | — | 5 | 1 | no | — |
| 135 | C16 | — | 15 | 1 | no | — |
| 136 | C3×C5 | — | 4 | 1 | no | Hall |
| 137 | C2×D3 | — | 16 | 1 | no | — |
| 138 | C3×C4 | — | 4 | 1 | no | — |
| 139 | Dic3 | — | 80 | 1 | no | — |
| 140 | C2×C5 | — | 6 | 1 | no | — |
| 141 | C2×C5 | — | 48 | 1 | no | — |
| 142 | C2×C5 | #5402 | 1 | 1 | yes | characteristic |
| 143 | C23 | — | 12 | 1 | no | — |
| 144 | Q8 | — | 60 | 1 | no | — |
| 145 | Q8 | — | 60 | 1 | no | — |
| 146 | Q8 | #6654 | 1 | 1 | yes | characteristic |
| 147 | D4 | — | 3 | 1 | no | — |
| 148 | D4 | — | 12 | 1 | no | — |
| 149 | D4 | — | 12 | 1 | no | — |
| 150 | C2×C4 | — | 3 | 1 | no | — |
| 151 | C2×C4 | — | 60 | 1 | no | — |
| 152 | C8 | — | 3 | 1 | no | — |
| 153 | C8 | — | 12 | 1 | no | — |
| 154 | C8 | — | 60 | 1 | no | — |
| 155 | C8 | D5×S4 | 1 | 1 | yes | characteristic |
| 156 | C2×C3 | — | 4 | 1 | no | — |
| 157 | D3 | — | 32 | 1 | no | — |
| 158 | C5 | #73041 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 159 | C22 | — | 3 | 1 | no | — |
| 160 | C22 | — | 24 | 1 | no | — |
| 161 | C22 | — | 48 | 1 | no | — |
| 162 | C4 | — | 3 | 1 | no | — |
| 163 | C4 | — | 120 | 1 | no | — |
| 164 | C4 | #91902 | 1 | 1 | yes | characteristic |
| 165 | C3 | — | 4 | 1 | no | Sylow |
| 166 | C2 | — | 6 | 1 | no | — |
| 167 | C2 | — | 48 | 1 | no | — |
| 168 | C2 | #11751575 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11752122 | C2 | semidirect |
| 3. #65429⋊C3 | C2 | semidirect |
| 13. #65429 | D3 | semidirect |
| 158. C5 | #73041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752122 | 2 |
| C5×#5407 | 2 |
| #65429⋊C3 | 2 |
| #10601886 | 3 |
| #90944 | 4 |
| #73041 | 5 |