← C5×#60332 #11983052
Subgroups — C5×#60332 #11983052
Order 1280.
1628 conjugacy classes of subgroups.
The subgroup lattice has 184 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C5×#3531 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#2995 | C2 | 1 | 10 | yes | maximal, complemented |
| 3 | C5×#2987 | C2 | 1 | 5 | yes | maximal, complemented |
| 4 | C5×#2966 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | C5×#2960 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | C5×#564 | C4 | 1 | 1 | yes | characteristic |
| 7 | C5×#563 | C4 | 1 | 10 | yes | — |
| 8 | C5×#562 | C4 | 1 | 5 | yes | — |
| 9 | C5×#533 | C22 | 1 | 5 | yes | — |
| 10 | C5×#529 | C22 | 1 | 10 | yes | — |
| 11 | C5×#446 | C22 | 1 | 10 | yes | — |
| 12 | C5×#446 | C22 | 1 | 20 | yes | — |
| 13 | C5×C8×Q8 | C22 | 1 | 10 | yes | — |
| 14 | C5×#436 | C22 | 1 | 10 | yes | — |
| 15 | C5×#435 | C22 | 1 | 20 | yes | — |
| 16 | C5×C8×D4 | C22 | 1 | 10 | yes | — |
| 17 | C5×#433 | C22 | 1 | 20 | yes | — |
| 18 | C5×#432 | C22 | 1 | 10 | yes | — |
| 19 | C5×#424 | C22 | 1 | 10 | yes | — |
| 20 | C5×#423 | C22 | 1 | 5 | yes | — |
| 21 | C5×#405 | C22 | 1 | 10 | yes | — |
| 22 | C2×C4×C5×C8 | C22 | 1 | 5 | yes | — |
| 23 | #60332 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 24 | C2×C5×M16 | C23 | 1 | 10 | yes | — |
| 25 | C22×C5×C8 | C23 | 1 | 5 | yes | — |
| 26 | C22×C5×C8 | C23 | 1 | 5 | yes | — |
| 27 | C5×C4⋊Q8 | C2×C4 | 1 | 10 | yes | — |
| 28 | C5×#126 | C2×C4 | 1 | 20 | yes | — |
| 29 | C5×#125 | C2×C4 | 1 | 10 | yes | — |
| 30 | C5×#125 | C2×C4 | 1 | 5 | yes | — |
| 31 | C5×#125 | C2×C4 | 1 | 5 | yes | — |
| 32 | C5×#124 | C2×C4 | 1 | 10 | yes | — |
| 33 | C5×#123 | C2×C4 | 1 | 20 | yes | — |
| 34 | C5×C22⋊Q8 | C2×C4 | 1 | 10 | yes | — |
| 35 | C5×C22⋊Q8 | C2×C4 | 1 | 20 | yes | — |
| 36 | C5×#121 | C2×C4 | 1 | 10 | yes | — |
| 37 | C4×C5×Q8 | C23 | 1 | 10 | yes | — |
| 38 | C4×C5×D4 | C23 | 1 | 10 | yes | — |
| 39 | C5×#117 | C23 | 1 | 10 | yes | — |
| 40 | C2×C42×C5 | C23 | 1 | 5 | yes | — |
| 41 | C5×C4⋊C8 | C23 | 1 | 20 | yes | — |
| 42 | C5×C4⋊C8 | C23 | 1 | 10 | yes | — |
| 43 | C5×C4⋊C8 | C23 | 1 | 10 | yes | — |
| 44 | C5×C22⋊C8 | C23 | 1 | 20 | yes | — |
| 45 | C5×#97 | C23 | 1 | 20 | yes | — |
| 46 | C4×C5×C8 | C23 | 1 | 10 | yes | — |
| 47 | C4×C5×C8 | C23 | 1 | 10 | yes | — |
| 48 | #3531 | C2×C5 | 1 | 1 | yes | characteristic |
| 49 | #2995 | C2×C5 | 1 | 10 | yes | complemented |
| 50 | #2987 | C2×C5 | 1 | 5 | yes | complemented |
| 51 | #2966 | C2×C5 | 1 | 10 | yes | complemented |
| 52 | #2960 | C2×C5 | 1 | 5 | yes | complemented |
| 53 | C2×C5×Q8 | C22×C4 | 1 | 10 | yes | — |
| 54 | C2×C5×D4 | C22×C4 | 1 | 10 | yes | — |
| 55 | C22×C4×C5 | C22×C4 | 1 | 10 | yes | — |
| 56 | C22×C4×C5 | C24 | 1 | 5 | yes | — |
| 57 | C5×M16 | — | 4 | 10 | no | — |
| 58 | C2×C5×C8 | — | 2 | 10 | no | — |
| 59 | C2×C5×C8 | — | 4 | 5 | no | — |
| 60 | C2×C5×C8 | C24 | 1 | 10 | yes | — |
| 61 | C2×C5×C8 | C24 | 1 | 5 | yes | — |
| 62 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 63 | C5×C4⋊C4 | C22×C4 | 1 | 10 | yes | — |
| 64 | C5×C4⋊C4 | C22×C4 | 1 | 10 | yes | — |
| 65 | C5×C4⋊C4 | C22×C4 | 1 | 10 | yes | — |
| 66 | C5×C4⋊C4 | C22×C4 | 1 | 10 | yes | — |
| 67 | C5×C4⋊C4 | C22×C4 | 1 | 20 | yes | — |
| 68 | C5×C22⋊C4 | C22×C4 | 1 | 20 | yes | — |
| 69 | C5×C22⋊C4 | C22×C4 | 1 | 20 | yes | — |
| 70 | C42×C5 | C22×C4 | 1 | 5 | yes | — |
| 71 | C42×C5 | C22×C4 | 1 | 5 | yes | — |
| 72 | C42×C5 | C24 | 1 | 10 | yes | — |
| 73 | #564 | C4×C5 | 1 | 1 | yes | characteristic |
| 74 | #563 | C4×C5 | 1 | 10 | yes | — |
| 75 | #562 | C4×C5 | 1 | 5 | yes | — |
| 76 | #533 | C22×C5 | 1 | 5 | yes | — |
| 77 | #529 | C22×C5 | 1 | 10 | yes | — |
| 78 | #446 | C22×C5 | 1 | 20 | yes | — |
| 79 | #446 | C22×C5 | 1 | 10 | yes | — |
| 80 | C8×Q8 | C22×C5 | 1 | 10 | yes | — |
| 81 | #436 | C22×C5 | 1 | 10 | yes | — |
| 82 | #435 | C22×C5 | 1 | 20 | yes | — |
| 83 | C8×D4 | C22×C5 | 1 | 10 | yes | — |
| 84 | #433 | C22×C5 | 1 | 20 | yes | — |
| 85 | #432 | C22×C5 | 1 | 10 | yes | — |
| 86 | #424 | C22×C5 | 1 | 10 | yes | — |
| 87 | #423 | C22×C5 | 1 | 5 | yes | — |
| 88 | #405 | C22×C5 | 1 | 10 | yes | — |
| 89 | C2×C4×C8 | C22×C5 | 1 | 5 | yes | — |
| 90 | C23×C5 | C23×C4 | 1 | 5 | yes | — |
| 91 | C5×Q8 | — | 4 | 10 | no | — |
| 92 | C5×D4 | — | 4 | 10 | no | — |
| 93 | C2×C4×C5 | — | 2 | 5 | no | — |
| 94 | C2×C4×C5 | — | 2 | 5 | no | — |
| 95 | C2×C4×C5 | — | 4 | 10 | no | — |
| 96 | C2×C4×C5 | C23×C4 | 1 | 5 | yes | — |
| 97 | C2×C4×C5 | C23×C4 | 1 | 10 | yes | — |
| 98 | C2×C4×C5 | C23×C4 | 1 | 10 | yes | — |
| 99 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 100 | C5×C8 | — | 2 | 5 | no | — |
| 101 | C5×C8 | — | 2 | 10 | no | — |
| 102 | C5×C8 | 2−1+4 | 1 | 2 | yes | — |
| 103 | C2×M16 | C23×C5 | 1 | 10 | yes | — |
| 104 | C22×C8 | C23×C5 | 1 | 5 | yes | — |
| 105 | C22×C8 | C23×C5 | 1 | 5 | yes | — |
| 106 | C4⋊Q8 | C2×C4×C5 | 1 | 10 | yes | — |
| 107 | #126 | C2×C4×C5 | 1 | 20 | yes | — |
| 108 | #125 | C2×C4×C5 | 1 | 10 | yes | — |
| 109 | #125 | C2×C4×C5 | 1 | 5 | yes | — |
| 110 | #125 | C2×C4×C5 | 1 | 5 | yes | — |
| 111 | #124 | C2×C4×C5 | 1 | 10 | yes | — |
| 112 | #123 | C2×C4×C5 | 1 | 20 | yes | — |
| 113 | C22⋊Q8 | C2×C4×C5 | 1 | 10 | yes | — |
| 114 | C22⋊Q8 | C2×C4×C5 | 1 | 20 | yes | — |
| 115 | #121 | C2×C4×C5 | 1 | 10 | yes | — |
| 116 | C4×Q8 | C23×C5 | 1 | 10 | yes | — |
| 117 | C4×D4 | C23×C5 | 1 | 10 | yes | — |
| 118 | #117 | C23×C5 | 1 | 10 | yes | — |
| 119 | C2×C42 | C23×C5 | 1 | 5 | yes | — |
| 120 | C4⋊C8 | C23×C5 | 1 | 20 | yes | — |
| 121 | C4⋊C8 | C23×C5 | 1 | 10 | yes | — |
| 122 | C4⋊C8 | C23×C5 | 1 | 10 | yes | — |
| 123 | C22⋊C8 | C23×C5 | 1 | 20 | yes | — |
| 124 | #97 | C23×C5 | 1 | 20 | yes | — |
| 125 | C4×C8 | C23×C5 | 1 | 10 | yes | — |
| 126 | C4×C8 | C23×C5 | 1 | 10 | yes | — |
| 127 | C22×C5 | — | 2 | 5 | no | — |
| 128 | C22×C5 | — | 2 | 10 | no | — |
| 129 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 130 | C4×C5 | — | 2 | 5 | no | — |
| 131 | C4×C5 | — | 2 | 10 | no | — |
| 132 | C4×C5 | — | 2 | 10 | no | — |
| 133 | C4×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 134 | C4×C5 | #585 | 1 | 1 | yes | characteristic |
| 135 | C2×Q8 | C22×C4×C5 | 1 | 10 | yes | — |
| 136 | C2×D4 | C22×C4×C5 | 1 | 10 | yes | — |
| 137 | C22×C4 | C22×C4×C5 | 1 | 10 | yes | — |
| 138 | C22×C4 | C24×C5 | 1 | 5 | yes | — |
| 139 | M16 | — | 4 | 10 | no | — |
| 140 | C2×C8 | — | 2 | 10 | no | — |
| 141 | C2×C8 | — | 4 | 5 | no | — |
| 142 | C2×C8 | C24×C5 | 1 | 5 | yes | — |
| 143 | C2×C8 | C24×C5 | 1 | 10 | yes | — |
| 144 | C2×C8 | C24×C5 | 1 | 1 | yes | characteristic |
| 145 | C4⋊C4 | C22×C4×C5 | 1 | 10 | yes | — |
| 146 | C4⋊C4 | C22×C4×C5 | 1 | 10 | yes | — |
| 147 | C4⋊C4 | C22×C4×C5 | 1 | 10 | yes | — |
| 148 | C4⋊C4 | C22×C4×C5 | 1 | 10 | yes | — |
| 149 | C4⋊C4 | C22×C4×C5 | 1 | 20 | yes | — |
| 150 | C22⋊C4 | C22×C4×C5 | 1 | 20 | yes | — |
| 151 | C22⋊C4 | C22×C4×C5 | 1 | 20 | yes | — |
| 152 | C42 | C22×C4×C5 | 1 | 5 | yes | — |
| 153 | C42 | C22×C4×C5 | 1 | 5 | yes | — |
| 154 | C42 | C24×C5 | 1 | 10 | yes | — |
| 155 | C2×C5 | — | 4 | 5 | no | — |
| 156 | C2×C5 | C4×2−1+4 | 1 | 1 | yes | characteristic |
| 157 | C2×C5 | #3573 | 1 | 2 | yes | — |
| 158 | C23 | C23×C4×C5 | 1 | 5 | yes | — |
| 159 | Q8 | — | 4 | 10 | no | — |
| 160 | D4 | — | 4 | 10 | no | — |
| 161 | C2×C4 | — | 2 | 5 | no | — |
| 162 | C2×C4 | — | 2 | 5 | no | — |
| 163 | C2×C4 | — | 4 | 10 | no | — |
| 164 | C2×C4 | C23×C4×C5 | 1 | 5 | yes | — |
| 165 | C2×C4 | C23×C4×C5 | 1 | 10 | yes | — |
| 166 | C2×C4 | C23×C4×C5 | 1 | 10 | yes | — |
| 167 | C2×C4 | C25×C5 | 1 | 1 | yes | characteristic |
| 168 | C8 | — | 2 | 5 | no | — |
| 169 | C8 | — | 2 | 10 | no | — |
| 170 | C8 | C5×2−1+4 | 1 | 2 | yes | — |
| 171 | C5 | #60332 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 172 | C22 | — | 2 | 5 | no | — |
| 173 | C22 | — | 2 | 10 | no | — |
| 174 | C22 | C24×C4×C5 | 1 | 1 | yes | characteristic |
| 175 | C4 | — | 2 | 5 | no | — |
| 176 | C4 | — | 2 | 10 | no | — |
| 177 | C4 | — | 2 | 10 | no | — |
| 178 | C4 | C2×C5×2−1+4 | 1 | 1 | yes | characteristic |
| 179 | C4 | C5×#585 | 1 | 1 | yes | characteristic |
| 180 | C2 | — | 4 | 5 | no | — |
| 181 | C2 | C4×C5×2−1+4 | 1 | 1 | yes | characteristic |
| 182 | C2 | C5×#3573 | 1 | 2 | yes | — |
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