Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 26 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 | C5×#376⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#4621 | C2 | 1 | 2 | yes | maximal |
| 3 | C5×#1506 | — | 3 | 1 | no | maximal, Hall |
| 4 | C5×A4⋊Q8 | — | 4 | 1 | no | maximal |
| 5 | C5×#95⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 6 | #72986 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 7 | C5×#533 | — | 3 | 1 | no | — |
| 8 | C5×#432 | — | 3 | 1 | no | — |
| 9 | C5×#376 | D3 | 1 | 1 | yes | characteristic |
| 10 | C5×#328 | — | 3 | 2 | no | — |
| 11 | C5×#328 | — | 3 | 2 | no | — |
| 12 | C4×C5×A4 | — | 4 | 1 | no | — |
| 13 | C5×SL(2,ℤ/4) | — | 4 | 2 | no | — |
| 14 | #376⋊C3 | C2×C5 | 1 | 1 | yes | characteristic |
| 15 | #4621 | C2×C5 | 1 | 2 | yes | — |
| 16 | C5×C4⋊Q8 | — | 3 | 1 | no | — |
| 17 | C5×C4⋊Q8 | — | 3 | 1 | no | — |
| 18 | C5×#125 | — | 6 | 1 | no | — |
| 19 | C5×C22⋊Q8 | — | 3 | 2 | no | — |
| 20 | C5×C22⋊Q8 | — | 6 | 1 | no | — |
| 21 | C4×C5×Q8 | — | 3 | 2 | no | — |
| 22 | C4×C5×Q8 | — | 6 | 1 | no | — |
| 23 | C5×#117 | — | 6 | 1 | no | — |
| 24 | C2×C42×C5 | — | 3 | 1 | no | — |
| 25 | C5×C4⋊C8 | — | 6 | 1 | no | — |
| 26 | C5×C22⋊C8 | — | 3 | 2 | no | — |
| 27 | C5×#97 | — | 6 | 1 | no | — |
| 28 | C5×#95 | — | 3 | 1 | no | — |
| 29 | C5×#95 | C2×D3 | 1 | 1 | yes | characteristic |
| 30 | #1506 | — | 3 | 1 | no | Sylow |
| 31 | C2×C5×A4 | — | 4 | 1 | no | — |
| 32 | C5×Dic6 | — | 16 | 1 | no | — |
| 33 | A4⋊Q8 | — | 4 | 1 | no | — |
| 34 | #95⋊C3 | C22×C5 | 1 | 1 | yes | characteristic |
| 35 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 36 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 37 | C22×C4×C5 | — | 3 | 1 | no | — |
| 38 | C22×C4×C5 | — | 3 | 1 | no | — |
| 39 | C22×C4×C5 | S4 | 1 | 1 | yes | characteristic |
| 40 | C2×C5×C8 | — | 6 | 2 | no | — |
| 41 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 42 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 43 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 44 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 45 | C5×C4⋊C4 | — | 6 | 2 | no | — |
| 46 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 47 | C5×C22⋊C4 | — | 6 | 2 | no | — |
| 48 | C42×C5 | — | 3 | 1 | no | — |
| 49 | C42×C5 | — | 3 | 1 | no | — |
| 50 | C42×C5 | — | 3 | 1 | no | — |
| 51 | C42×C5 | — | 3 | 1 | no | — |
| 52 | C42×C5 | — | 6 | 2 | no | — |
| 53 | #533 | — | 3 | 1 | no | — |
| 54 | #432 | — | 3 | 1 | no | — |
| 55 | #376 | C5×D3 | 1 | 1 | yes | characteristic |
| 56 | #328 | — | 3 | 2 | no | — |
| 57 | #328 | — | 3 | 2 | no | — |
| 58 | C5×A4 | — | 4 | 1 | no | — |
| 59 | C3×C4×C5 | — | 16 | 1 | no | — |
| 60 | C5×Dic3 | — | 16 | 2 | no | — |
| 61 | C4×A4 | — | 4 | 1 | no | — |
| 62 | SL(2,ℤ/4) | — | 4 | 2 | no | — |
| 63 | C23×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 64 | C5×Q8 | — | 12 | 1 | no | — |
| 65 | C5×Q8 | — | 12 | 2 | no | — |
| 66 | C5×Q8 | — | 12 | 1 | no | — |
| 67 | C2×C4×C5 | — | 3 | 1 | no | — |
| 68 | C2×C4×C5 | — | 3 | 1 | no | — |
| 69 | C2×C4×C5 | — | 3 | 1 | no | — |
| 70 | C2×C4×C5 | — | 3 | 1 | no | — |
| 71 | C2×C4×C5 | — | 3 | 1 | no | — |
| 72 | C2×C4×C5 | — | 3 | 1 | no | — |
| 73 | C2×C4×C5 | — | 6 | 1 | no | — |
| 74 | C2×C4×C5 | — | 6 | 1 | no | — |
| 75 | C2×C4×C5 | — | 6 | 2 | no | — |
| 76 | C2×C4×C5 | — | 6 | 2 | no | — |
| 77 | C2×C4×C5 | — | 12 | 1 | no | — |
| 78 | C5×C8 | — | 12 | 2 | no | — |
| 79 | C4⋊Q8 | — | 3 | 1 | no | — |
| 80 | C4⋊Q8 | — | 3 | 1 | no | — |
| 81 | #125 | — | 6 | 1 | no | — |
| 82 | C22⋊Q8 | — | 3 | 2 | no | — |
| 83 | C22⋊Q8 | — | 6 | 1 | no | — |
| 84 | C4×Q8 | — | 3 | 2 | no | — |
| 85 | C4×Q8 | — | 6 | 1 | no | — |
| 86 | #117 | — | 6 | 1 | no | — |
| 87 | C2×C42 | — | 3 | 1 | no | — |
| 88 | C4⋊C8 | — | 6 | 1 | no | — |
| 89 | C22⋊C8 | — | 3 | 2 | no | — |
| 90 | #97 | — | 6 | 1 | no | — |
| 91 | #95 | — | 3 | 1 | no | — |
| 92 | #95 | C2×C5×D3 | 1 | 1 | yes | characteristic |
| 93 | C2×C3×C5 | — | 16 | 1 | no | — |
| 94 | C2×A4 | — | 4 | 1 | no | — |
| 95 | Dic6 | — | 16 | 1 | no | — |
| 96 | C22×C5 | — | 3 | 1 | no | — |
| 97 | C22×C5 | — | 3 | 1 | no | — |
| 98 | C22×C5 | #984 | 1 | 1 | yes | characteristic |
| 99 | C4×C5 | — | 3 | 1 | no | — |
| 100 | C4×C5 | — | 6 | 1 | no | — |
| 101 | C4×C5 | — | 6 | 1 | no | — |
| 102 | C4×C5 | — | 6 | 1 | no | — |
| 103 | C4×C5 | — | 6 | 1 | no | — |
| 104 | C4×C5 | — | 12 | 2 | no | — |
| 105 | C4×C5 | — | 12 | 2 | no | — |
| 106 | C4×C5 | #857 | 1 | 1 | yes | characteristic |
| 107 | C2×Q8 | — | 3 | 2 | no | — |
| 108 | C2×Q8 | — | 6 | 1 | no | — |
| 109 | C22×C4 | — | 3 | 1 | no | — |
| 110 | C22×C4 | — | 3 | 1 | no | — |
| 111 | C22×C4 | C5×S4 | 1 | 1 | yes | characteristic |
| 112 | C2×C8 | — | 6 | 2 | no | — |
| 113 | C4⋊C4 | — | 3 | 2 | no | — |
| 114 | C4⋊C4 | — | 6 | 1 | no | — |
| 115 | C4⋊C4 | — | 6 | 1 | no | — |
| 116 | C4⋊C4 | — | 6 | 2 | no | — |
| 117 | C4⋊C4 | — | 6 | 2 | no | — |
| 118 | C4⋊C4 | — | 6 | 1 | no | — |
| 119 | C22⋊C4 | — | 6 | 2 | no | — |
| 120 | C42 | — | 3 | 1 | no | — |
| 121 | C42 | — | 3 | 1 | no | — |
| 122 | C42 | — | 3 | 1 | no | — |
| 123 | C42 | — | 3 | 1 | no | — |
| 124 | C42 | — | 6 | 2 | no | — |
| 125 | C3×C5 | — | 16 | 1 | no | Hall |
| 126 | A4 | — | 4 | 1 | no | — |
| 127 | C3×C4 | — | 16 | 1 | no | — |
| 128 | Dic3 | — | 16 | 2 | no | — |
| 129 | C2×C5 | — | 3 | 1 | no | — |
| 130 | C2×C5 | — | 3 | 1 | no | — |
| 131 | C2×C5 | C2×#857 | 1 | 1 | yes | characteristic |
| 132 | C23 | C2×C5×S4 | 1 | 1 | yes | characteristic |
| 133 | Q8 | — | 12 | 1 | no | — |
| 134 | Q8 | — | 12 | 2 | no | — |
| 135 | Q8 | — | 12 | 1 | no | — |
| 136 | C2×C4 | — | 3 | 1 | no | — |
| 137 | C2×C4 | — | 3 | 1 | no | — |
| 138 | C2×C4 | — | 3 | 1 | no | — |
| 139 | C2×C4 | — | 3 | 1 | no | — |
| 140 | C2×C4 | — | 3 | 1 | no | — |
| 141 | C2×C4 | — | 3 | 1 | no | — |
| 142 | C2×C4 | — | 6 | 1 | no | — |
| 143 | C2×C4 | — | 6 | 1 | no | — |
| 144 | C2×C4 | — | 6 | 2 | no | — |
| 145 | C2×C4 | — | 6 | 2 | no | — |
| 146 | C2×C4 | — | 12 | 1 | no | — |
| 147 | C8 | — | 12 | 2 | no | — |
| 148 | C2×C3 | — | 16 | 1 | no | — |
| 149 | C5 | #72986 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 150 | C22 | — | 3 | 1 | no | — |
| 151 | C22 | — | 3 | 1 | no | — |
| 152 | C22 | C5×#984 | 1 | 1 | yes | characteristic |
| 153 | C4 | — | 3 | 1 | no | — |
| 154 | C4 | — | 6 | 1 | no | — |
| 155 | C4 | — | 6 | 1 | no | — |
| 156 | C4 | — | 6 | 1 | no | — |
| 157 | C4 | — | 6 | 1 | no | — |
| 158 | C4 | — | 12 | 2 | no | — |
| 159 | C4 | — | 12 | 2 | no | — |
| 160 | C4 | C5×#857 | 1 | 1 | yes | characteristic |
| 161 | C3 | — | 16 | 1 | no | Sylow |
| 162 | C2 | — | 3 | 1 | no | — |
| 163 | C2 | — | 3 | 1 | no | — |
| 164 | C2 | C2×C5×#857 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #72986 | C5 | direct (N × H) |
| 149. C5 | #72986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#376⋊C3 | 2 |
| C5×#4621 | 2 |
| C5×#1506 | 3 |
| C5×A4⋊Q8 | 4 |
| #72986 | 5 |