← C32×C4×C52×C16 #72192549
Subgroups — C32×C4×C52×C16 #72192549
Order 14400.
1392 conjugacy classes of subgroups.
The subgroup lattice has 162 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C32×C4×C52×C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C32×C52×C16 | C2 | 1 | 2 | yes | maximal |
| 3 | C3×C4×C52×C16 | C3 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C32×C42×C52 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×C32×C52×C8 | C4 | 1 | 1 | yes | characteristic |
| 6 | C2×C32×C52×C8 | C22 | 1 | 1 | yes | characteristic |
| 7 | C32×C52×C16 | C4 | 1 | 4 | yes | direct product factor |
| 8 | C32×C4×C5×C16 | C5 | 1 | 6 | yes | maximal, direct product factor |
| 9 | C3×C4×C52×C8 | C2×C3 | 1 | 4 | yes | — |
| 10 | C2×C3×C52×C16 | C2×C3 | 1 | 8 | yes | — |
| 11 | C2×C32×C4×C52 | C8 | 1 | 2 | yes | — |
| 12 | C2×C32×C4×C52 | C2×C4 | 1 | 1 | yes | characteristic |
| 13 | C32×C52×C8 | C8 | 1 | 2 | yes | — |
| 14 | C32×C52×C8 | C2×C4 | 1 | 2 | yes | — |
| 15 | C4×C52×C16 | C32 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 16 | C2×C32×C5×C16 | C2×C5 | 1 | 12 | yes | — |
| 17 | C32×C4×C5×C8 | C2×C5 | 1 | 6 | yes | — |
| 18 | C2×C3×C52×C8 | C3×C4 | 1 | 4 | yes | — |
| 19 | C2×C3×C52×C8 | C22×C3 | 1 | 4 | yes | — |
| 20 | C3×C42×C52 | C3×C4 | 1 | 4 | yes | — |
| 21 | C3×C52×C16 | C3×C4 | 1 | 16 | yes | direct product factor |
| 22 | C3×C4×C5×C16 | C3×C5 | 1 | 24 | yes | direct product factor |
| 23 | C22×C32×C52 | C2×C8 | 1 | 1 | yes | characteristic |
| 24 | C32×C4×C52 | C16 | 1 | 4 | yes | direct product factor |
| 25 | C32×C4×C52 | C42 | 1 | 1 | yes | characteristic |
| 26 | C32×C4×C52 | C2×C8 | 1 | 1 | yes | characteristic |
| 27 | C2×C52×C16 | C2×C32 | 1 | 2 | yes | — |
| 28 | C4×C52×C8 | C2×C32 | 1 | 1 | yes | characteristic |
| 29 | C2×C32×C5×C8 | C4×C5 | 1 | 6 | yes | — |
| 30 | C2×C32×C5×C8 | C22×C5 | 1 | 6 | yes | — |
| 31 | C32×C42×C5 | C4×C5 | 1 | 6 | yes | — |
| 32 | C32×C5×C16 | C4×C5 | 1 | 24 | yes | direct product factor |
| 33 | C2×C3×C4×C52 | C3×C8 | 1 | 8 | yes | — |
| 34 | C2×C3×C4×C52 | C2×C3×C4 | 1 | 4 | yes | — |
| 35 | C3×C52×C8 | C3×C8 | 1 | 8 | yes | — |
| 36 | C3×C52×C8 | C2×C3×C4 | 1 | 8 | yes | — |
| 37 | C32×C4×C16 | C52 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 38 | C2×C3×C5×C16 | C2×C3×C5 | 1 | 48 | yes | — |
| 39 | C3×C4×C5×C8 | C2×C3×C5 | 1 | 24 | yes | — |
| 40 | C2×C32×C52 | C4×C8 | 1 | 1 | yes | characteristic |
| 41 | C2×C32×C52 | C2×C16 | 1 | 2 | yes | — |
| 42 | C2×C52×C8 | C32×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×C52×C8 | C22×C32 | 1 | 1 | yes | characteristic |
| 44 | C42×C52 | C32×C4 | 1 | 1 | yes | characteristic |
| 45 | C52×C16 | C32×C4 | 1 | 4 | yes | direct product factor |
| 46 | C2×C32×C4×C5 | C5×C8 | 1 | 12 | yes | — |
| 47 | C2×C32×C4×C5 | C2×C4×C5 | 1 | 6 | yes | — |
| 48 | C32×C5×C8 | C5×C8 | 1 | 12 | yes | — |
| 49 | C32×C5×C8 | C2×C4×C5 | 1 | 12 | yes | — |
| 50 | C4×C5×C16 | C32×C5 | 1 | 6 | yes | direct product factor |
| 51 | C22×C3×C52 | C2×C3×C8 | 1 | 4 | yes | — |
| 52 | C3×C4×C52 | C3×C16 | 1 | 16 | yes | direct product factor |
| 53 | C3×C4×C52 | C3×C42 | 1 | 4 | yes | — |
| 54 | C3×C4×C52 | C2×C3×C8 | 1 | 4 | yes | — |
| 55 | C2×C32×C16 | C2×C52 | 1 | 2 | yes | — |
| 56 | C32×C4×C8 | C2×C52 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×C5×C8 | C3×C4×C5 | 1 | 24 | yes | — |
| 58 | C2×C3×C5×C8 | C22×C3×C5 | 1 | 24 | yes | — |
| 59 | C3×C42×C5 | C3×C4×C5 | 1 | 24 | yes | — |
| 60 | C3×C5×C16 | C3×C4×C5 | 1 | 96 | yes | direct product factor |
| 61 | C32×C52 | C4×C16 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 62 | C2×C4×C52 | C32×C8 | 1 | 2 | yes | — |
| 63 | C2×C4×C52 | C2×C32×C4 | 1 | 1 | yes | characteristic |
| 64 | C52×C8 | C32×C8 | 1 | 2 | yes | — |
| 65 | C52×C8 | C2×C32×C4 | 1 | 2 | yes | — |
| 66 | C3×C4×C16 | C3×C52 | 1 | 4 | yes | direct product factor |
| 67 | C22×C32×C5 | C2×C5×C8 | 1 | 6 | yes | — |
| 68 | C32×C4×C5 | C5×C16 | 1 | 24 | yes | direct product factor |
| 69 | C32×C4×C5 | C42×C5 | 1 | 6 | yes | — |
| 70 | C32×C4×C5 | C2×C5×C8 | 1 | 6 | yes | — |
| 71 | C2×C5×C16 | C2×C32×C5 | 1 | 12 | yes | — |
| 72 | C4×C5×C8 | C2×C32×C5 | 1 | 6 | yes | — |
| 73 | C2×C3×C52 | C3×C4×C8 | 1 | 4 | yes | — |
| 74 | C2×C3×C52 | C2×C3×C16 | 1 | 8 | yes | — |
| 75 | C2×C32×C8 | C4×C52 | 1 | 1 | yes | characteristic |
| 76 | C2×C32×C8 | C22×C52 | 1 | 1 | yes | characteristic |
| 77 | C32×C42 | C4×C52 | 1 | 1 | yes | characteristic |
| 78 | C32×C16 | C4×C52 | 1 | 4 | yes | direct product factor |
| 79 | C2×C3×C4×C5 | C3×C5×C8 | 1 | 48 | yes | — |
| 80 | C2×C3×C4×C5 | C2×C3×C4×C5 | 1 | 24 | yes | — |
| 81 | C3×C5×C8 | C3×C5×C8 | 1 | 48 | yes | — |
| 82 | C3×C5×C8 | C2×C3×C4×C5 | 1 | 48 | yes | — |
| 83 | C22×C52 | C2×C32×C8 | 1 | 1 | yes | characteristic |
| 84 | C4×C52 | C32×C16 | 1 | 4 | yes | direct product factor |
| 85 | C4×C52 | C32×C42 | 1 | 1 | yes | characteristic |
| 86 | C4×C52 | C2×C32×C8 | 1 | 1 | yes | characteristic |
| 87 | C2×C3×C16 | C2×C3×C52 | 1 | 8 | yes | — |
| 88 | C3×C4×C8 | C2×C3×C52 | 1 | 4 | yes | — |
| 89 | C2×C32×C5 | C4×C5×C8 | 1 | 6 | yes | — |
| 90 | C2×C32×C5 | C2×C5×C16 | 1 | 12 | yes | — |
| 91 | C2×C5×C8 | C32×C4×C5 | 1 | 6 | yes | — |
| 92 | C2×C5×C8 | C22×C32×C5 | 1 | 6 | yes | — |
| 93 | C42×C5 | C32×C4×C5 | 1 | 6 | yes | — |
| 94 | C5×C16 | C32×C4×C5 | 1 | 24 | yes | direct product factor |
| 95 | C3×C52 | C3×C4×C16 | 1 | 4 | yes | direct product factor |
| 96 | C2×C32×C4 | C52×C8 | 1 | 2 | yes | — |
| 97 | C2×C32×C4 | C2×C4×C52 | 1 | 1 | yes | characteristic |
| 98 | C32×C8 | C52×C8 | 1 | 2 | yes | — |
| 99 | C32×C8 | C2×C4×C52 | 1 | 2 | yes | — |
| 100 | C4×C16 | C32×C52 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 101 | C22×C3×C5 | C2×C3×C5×C8 | 1 | 24 | yes | — |
| 102 | C3×C4×C5 | C3×C5×C16 | 1 | 96 | yes | direct product factor |
| 103 | C3×C4×C5 | C3×C42×C5 | 1 | 24 | yes | — |
| 104 | C3×C4×C5 | C2×C3×C5×C8 | 1 | 24 | yes | — |
| 105 | C2×C52 | C32×C4×C8 | 1 | 1 | yes | characteristic |
| 106 | C2×C52 | C2×C32×C16 | 1 | 2 | yes | — |
| 107 | C2×C3×C8 | C3×C4×C52 | 1 | 4 | yes | — |
| 108 | C2×C3×C8 | C22×C3×C52 | 1 | 4 | yes | — |
| 109 | C3×C42 | C3×C4×C52 | 1 | 4 | yes | — |
| 110 | C3×C16 | C3×C4×C52 | 1 | 16 | yes | direct product factor |
| 111 | C32×C5 | C4×C5×C16 | 1 | 6 | yes | direct product factor |
| 112 | C2×C4×C5 | C32×C5×C8 | 1 | 12 | yes | — |
| 113 | C2×C4×C5 | C2×C32×C4×C5 | 1 | 6 | yes | — |
| 114 | C5×C8 | C32×C5×C8 | 1 | 12 | yes | — |
| 115 | C5×C8 | C2×C32×C4×C5 | 1 | 12 | yes | — |
| 116 | C22×C32 | C2×C52×C8 | 1 | 1 | yes | characteristic |
| 117 | C32×C4 | C52×C16 | 1 | 4 | yes | direct product factor |
| 118 | C32×C4 | C42×C52 | 1 | 1 | yes | characteristic |
| 119 | C32×C4 | C2×C52×C8 | 1 | 1 | yes | characteristic |
| 120 | C2×C16 | C2×C32×C52 | 1 | 2 | yes | — |
| 121 | C4×C8 | C2×C32×C52 | 1 | 1 | yes | characteristic |
| 122 | C2×C3×C5 | C3×C4×C5×C8 | 1 | 24 | yes | — |
| 123 | C2×C3×C5 | C2×C3×C5×C16 | 1 | 48 | yes | — |
| 124 | C52 | C32×C4×C16 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 125 | C2×C3×C4 | C3×C52×C8 | 1 | 8 | yes | — |
| 126 | C2×C3×C4 | C2×C3×C4×C52 | 1 | 4 | yes | — |
| 127 | C3×C8 | C3×C52×C8 | 1 | 8 | yes | — |
| 128 | C3×C8 | C2×C3×C4×C52 | 1 | 8 | yes | — |
| 129 | C22×C5 | C2×C32×C5×C8 | 1 | 6 | yes | — |
| 130 | C4×C5 | C32×C5×C16 | 1 | 24 | yes | direct product factor |
| 131 | C4×C5 | C32×C42×C5 | 1 | 6 | yes | — |
| 132 | C4×C5 | C2×C32×C5×C8 | 1 | 6 | yes | — |
| 133 | C2×C32 | C4×C52×C8 | 1 | 1 | yes | characteristic |
| 134 | C2×C32 | C2×C52×C16 | 1 | 2 | yes | — |
| 135 | C2×C8 | C32×C4×C52 | 1 | 1 | yes | characteristic |
| 136 | C2×C8 | C22×C32×C52 | 1 | 1 | yes | characteristic |
| 137 | C42 | C32×C4×C52 | 1 | 1 | yes | characteristic |
| 138 | C16 | C32×C4×C52 | 1 | 4 | yes | direct product factor |
| 139 | C3×C5 | C3×C4×C5×C16 | 1 | 24 | yes | direct product factor |
| 140 | C22×C3 | C2×C3×C52×C8 | 1 | 4 | yes | — |
| 141 | C3×C4 | C3×C52×C16 | 1 | 16 | yes | direct product factor |
| 142 | C3×C4 | C3×C42×C52 | 1 | 4 | yes | — |
| 143 | C3×C4 | C2×C3×C52×C8 | 1 | 4 | yes | — |
| 144 | C2×C5 | C32×C4×C5×C8 | 1 | 6 | yes | — |
| 145 | C2×C5 | C2×C32×C5×C16 | 1 | 12 | yes | — |
| 146 | C32 | C4×C52×C16 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 147 | C2×C4 | C32×C52×C8 | 1 | 2 | yes | — |
| 148 | C2×C4 | C2×C32×C4×C52 | 1 | 1 | yes | characteristic |
| 149 | C8 | C32×C52×C8 | 1 | 2 | yes | — |
| 150 | C8 | C2×C32×C4×C52 | 1 | 2 | yes | — |
| 151 | C2×C3 | C2×C3×C52×C16 | 1 | 8 | yes | — |
| 152 | C2×C3 | C3×C4×C52×C8 | 1 | 4 | yes | — |
| 153 | C5 | C32×C4×C5×C16 | 1 | 6 | yes | direct product factor |
| 154 | C22 | C2×C32×C52×C8 | 1 | 1 | yes | characteristic |
| 155 | C4 | C32×C52×C16 | 1 | 4 | yes | direct product factor |
| 156 | C4 | C2×C32×C52×C8 | 1 | 1 | yes | characteristic |
| 157 | C4 | C32×C42×C52 | 1 | 1 | yes | characteristic |
| 158 | C3 | C3×C4×C52×C16 | 1 | 4 | yes | direct product factor |
| 159 | C2 | C2×C32×C52×C16 | 1 | 2 | yes | — |
| 160 | C2 | C32×C4×C52×C8 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta