← C5×D5⋊#131 #13107730
Subgroups — C5×D5⋊#131 #13107730
Order 1600.
552 conjugacy classes of subgroups.
The subgroup lattice has 194 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C5×D5×#41 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#4133 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C5×#4131 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C5×D5⋊M16 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×C5×D5⋊C8 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C52×#41 | C4 | 1 | 1 | yes | characteristic |
| 7 | C5×#713 | C22 | 1 | 1 | yes | characteristic |
| 8 | C5×Q8×D5 | C4 | 1 | 1 | yes | characteristic |
| 9 | C5×#711 | C22 | 1 | 3 | yes | — |
| 10 | C5×D4×D5 | C4 | 1 | 3 | yes | — |
| 11 | C5×#709 | C4 | 1 | 3 | yes | — |
| 12 | C2×C4×C5×D5 | C22 | 1 | 3 | yes | — |
| 13 | C5×#704 | C22 | 1 | 6 | yes | complemented |
| 14 | C2×C5×#170 | C22 | 1 | 6 | yes | complemented |
| 15 | C5×#700 | C22 | 1 | 6 | yes | complemented |
| 16 | C5×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | C5×D5⋊C8 | C22 | 1 | 3 | yes | — |
| 18 | C5×D5⋊C8 | C22 | 1 | 6 | yes | complemented |
| 19 | D5⋊#131 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 20 | C2×C5×#131 | — | 5 | 1 | no | maximal |
| 21 | C22×C5×D5 | C2×C4 | 1 | 3 | yes | — |
| 22 | C52×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C52×D4 | C2×C4 | 1 | 3 | yes | — |
| 24 | C2×C4×C52 | C2×C4 | 1 | 3 | yes | — |
| 25 | C5×C22⋊D5 | C2×C4 | 1 | 6 | yes | — |
| 26 | C2×C5×Dic5 | C23 | 1 | 3 | yes | — |
| 27 | C5×D20 | C2×C4 | 1 | 3 | yes | — |
| 28 | C4×C5×D5 | C2×C4 | 1 | 3 | yes | — |
| 29 | C4×C5×D5 | C2×C4 | 1 | 3 | yes | — |
| 30 | C4×C5×D5 | C23 | 1 | 1 | yes | characteristic |
| 31 | C4×C5×D5 | C23 | 1 | 3 | yes | — |
| 32 | C5×Dic10 | C2×C4 | 1 | 3 | yes | — |
| 33 | C5×#170 | C23 | 1 | 2 | yes | — |
| 34 | C5×#170 | C23 | 1 | 6 | yes | — |
| 35 | C2×C5×#41 | — | 5 | 1 | no | — |
| 36 | D5×#41 | C2×C5 | 1 | 1 | yes | characteristic |
| 37 | #4133 | C2×C5 | 1 | 2 | yes | complemented |
| 38 | #4131 | C2×C5 | 1 | 6 | yes | complemented |
| 39 | D5⋊M16 | C2×C5 | 1 | 3 | yes | complemented |
| 40 | C2×D5⋊C8 | C2×C5 | 1 | 3 | yes | complemented |
| 41 | C5×#131 | — | 5 | 6 | no | — |
| 42 | C5×#131 | — | 5 | 2 | no | — |
| 43 | C2×C5×M16 | — | 5 | 3 | no | — |
| 44 | C22×C5×C8 | — | 5 | 3 | no | — |
| 45 | C22×C52 | C22×C4 | 1 | 3 | yes | — |
| 46 | C2×C5×D5 | — | 2 | 6 | no | — |
| 47 | C2×C5×D5 | C22×C4 | 1 | 3 | yes | — |
| 48 | C2×C5×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 49 | C4×C52 | C22×C4 | 1 | 3 | yes | — |
| 50 | C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 51 | C5×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 52 | C5×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 53 | C5×#41 | — | 4 | 1 | no | — |
| 54 | C5×#41 | — | 5 | 1 | no | — |
| 55 | C5×#41 | — | 5 | 3 | no | — |
| 56 | C5×#41 | — | 5 | 3 | no | — |
| 57 | C5×#41 | C4×C5 | 1 | 1 | yes | characteristic |
| 58 | C5×#41 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 59 | C2×C5×Q8 | — | 5 | 1 | no | — |
| 60 | C2×C5×D4 | — | 5 | 3 | no | — |
| 61 | C22×C4×C5 | — | 5 | 3 | no | — |
| 62 | #713 | C22×C5 | 1 | 1 | yes | characteristic |
| 63 | Q8×D5 | C4×C5 | 1 | 1 | yes | characteristic |
| 64 | #711 | C22×C5 | 1 | 3 | yes | — |
| 65 | D4×D5 | C4×C5 | 1 | 3 | yes | — |
| 66 | #709 | C4×C5 | 1 | 3 | yes | — |
| 67 | C2×C4×D5 | C22×C5 | 1 | 3 | yes | — |
| 68 | #704 | C22×C5 | 1 | 6 | yes | complemented |
| 69 | C2×#170 | C22×C5 | 1 | 6 | yes | complemented |
| 70 | #700 | C22×C5 | 1 | 6 | yes | complemented |
| 71 | D5⋊C8 | C22×C5 | 1 | 1 | yes | characteristic |
| 72 | D5⋊C8 | C22×C5 | 1 | 3 | yes | — |
| 73 | D5⋊C8 | C22×C5 | 1 | 6 | yes | complemented |
| 74 | C5×M16 | — | 5 | 6 | no | — |
| 75 | C5×M16 | — | 5 | 6 | no | — |
| 76 | C2×C5×C8 | — | 5 | 1 | no | — |
| 77 | C2×C5×C8 | — | 5 | 3 | no | — |
| 78 | C2×C5×C8 | — | 5 | 6 | no | — |
| 79 | C2×C5×C8 | — | 5 | 6 | no | — |
| 80 | C2×#131 | — | 5 | 1 | no | Sylow |
| 81 | C2×C52 | — | 2 | 3 | no | — |
| 82 | C2×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 83 | C5×D5 | — | 2 | 3 | no | — |
| 84 | C5×D5 | #131 | 1 | 2 | yes | complemented |
| 85 | C23×C5 | — | 5 | 3 | no | — |
| 86 | C22×D5 | C2×C4×C5 | 1 | 3 | yes | — |
| 87 | C5×Q8 | — | 4 | 1 | no | — |
| 88 | C5×Q8 | — | 5 | 3 | no | — |
| 89 | C5×Q8 | C2×C4×C5 | 1 | 1 | yes | characteristic |
| 90 | C5×Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 91 | C5×D4 | — | 4 | 3 | no | — |
| 92 | C5×D4 | — | 5 | 6 | no | — |
| 93 | C5×D4 | — | 5 | 3 | no | — |
| 94 | C5×D4 | C2×C4×C5 | 1 | 3 | yes | — |
| 95 | C5×D4 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 96 | C2×C4×C5 | — | 4 | 3 | no | — |
| 97 | C2×C4×C5 | — | 5 | 3 | no | — |
| 98 | C2×C4×C5 | — | 5 | 3 | no | — |
| 99 | C2×C4×C5 | — | 5 | 3 | no | — |
| 100 | C2×C4×C5 | — | 5 | 3 | no | — |
| 101 | C2×C4×C5 | — | 5 | 1 | no | — |
| 102 | C2×C4×C5 | C2×C4×C5 | 1 | 3 | yes | — |
| 103 | C2×C4×C5 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 104 | C22⋊D5 | C2×C4×C5 | 1 | 6 | yes | — |
| 105 | C2×Dic5 | C23×C5 | 1 | 3 | yes | — |
| 106 | D20 | C2×C4×C5 | 1 | 3 | yes | — |
| 107 | C4×D5 | C2×C4×C5 | 1 | 3 | yes | — |
| 108 | C4×D5 | C2×C4×C5 | 1 | 3 | yes | — |
| 109 | C4×D5 | C23×C5 | 1 | 1 | yes | characteristic |
| 110 | C4×D5 | C23×C5 | 1 | 3 | yes | — |
| 111 | Dic10 | C2×C4×C5 | 1 | 3 | yes | — |
| 112 | #170 | C23×C5 | 1 | 2 | yes | — |
| 113 | #170 | C23×C5 | 1 | 6 | yes | — |
| 114 | C5×C8 | — | 5 | 2 | no | — |
| 115 | C5×C8 | — | 5 | 6 | no | — |
| 116 | C2×#41 | — | 5 | 1 | no | — |
| 117 | #131 | — | 5 | 6 | no | — |
| 118 | #131 | — | 5 | 2 | no | — |
| 119 | C2×M16 | — | 5 | 3 | no | — |
| 120 | C22×C8 | — | 5 | 3 | no | — |
| 121 | C52 | C2×#131 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 122 | C22×C5 | — | 4 | 3 | no | — |
| 123 | C22×C5 | — | 5 | 1 | no | — |
| 124 | C22×C5 | — | 5 | 3 | no | — |
| 125 | C22×C5 | — | 10 | 6 | no | — |
| 126 | C22×C5 | C22×C4×C5 | 1 | 3 | yes | — |
| 127 | C22×C5 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 128 | C2×D5 | — | 2 | 6 | no | — |
| 129 | C2×D5 | C22×C4×C5 | 1 | 3 | yes | — |
| 130 | C2×D5 | C22×C4×C5 | 1 | 1 | yes | characteristic |
| 131 | C4×C5 | — | 4 | 1 | no | — |
| 132 | C4×C5 | — | 4 | 3 | no | — |
| 133 | C4×C5 | — | 5 | 3 | no | — |
| 134 | C4×C5 | — | 5 | 1 | no | — |
| 135 | C4×C5 | C22×C4×C5 | 1 | 3 | yes | — |
| 136 | C4×C5 | C22×C4×C5 | 1 | 1 | yes | characteristic |
| 137 | C4×C5 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 138 | C4×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 139 | Dic5 | C22×C4×C5 | 1 | 3 | yes | — |
| 140 | Dic5 | C24×C5 | 1 | 1 | yes | characteristic |
| 141 | #41 | — | 5 | 1 | no | — |
| 142 | #41 | — | 5 | 3 | no | — |
| 143 | #41 | — | 5 | 3 | no | — |
| 144 | #41 | C5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 145 | C2×Q8 | — | 5 | 1 | no | — |
| 146 | C2×D4 | — | 5 | 3 | no | — |
| 147 | C22×C4 | — | 5 | 3 | no | — |
| 148 | M16 | — | 5 | 6 | no | — |
| 149 | M16 | — | 5 | 6 | no | — |
| 150 | C2×C8 | — | 5 | 1 | no | — |
| 151 | C2×C8 | — | 5 | 3 | no | — |
| 152 | C2×C8 | — | 5 | 6 | no | — |
| 153 | C2×C8 | — | 5 | 6 | no | — |
| 154 | C2×C5 | — | 2 | 3 | no | — |
| 155 | C2×C5 | — | 2 | 3 | no | — |
| 156 | C2×C5 | — | 4 | 1 | no | — |
| 157 | C2×C5 | — | 5 | 2 | no | — |
| 158 | C2×C5 | — | 8 | 3 | no | — |
| 159 | C2×C5 | — | 10 | 3 | no | — |
| 160 | C2×C5 | C23×C4×C5 | 1 | 1 | yes | characteristic |
| 161 | C2×C5 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 162 | D5 | — | 2 | 3 | no | — |
| 163 | D5 | C5×#131 | 1 | 2 | yes | complemented |
| 164 | C23 | — | 5 | 3 | no | — |
| 165 | Q8 | — | 5 | 3 | no | — |
| 166 | Q8 | C2×C5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 167 | D4 | — | 5 | 6 | no | — |
| 168 | D4 | — | 5 | 3 | no | — |
| 169 | D4 | C2×C5×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 170 | C2×C4 | — | 5 | 3 | no | — |
| 171 | C2×C4 | — | 5 | 1 | no | — |
| 172 | C2×C4 | — | 5 | 3 | no | — |
| 173 | C2×C4 | — | 5 | 3 | no | — |
| 174 | C2×C4 | — | 5 | 3 | no | — |
| 175 | C2×C4 | C2×C5×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 176 | C8 | — | 5 | 2 | no | — |
| 177 | C8 | — | 5 | 6 | no | — |
| 178 | C5 | — | 4 | 1 | no | — |
| 179 | C5 | C2×C5×#131 | 1 | 1 | yes | characteristic, complemented |
| 180 | C5 | D5⋊#131 | 1 | 1 | yes | characteristic, direct product factor |
| 181 | C22 | — | 5 | 1 | no | — |
| 182 | C22 | — | 5 | 3 | no | — |
| 183 | C22 | — | 10 | 6 | no | — |
| 184 | C22 | C22×C5×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 185 | C4 | — | 5 | 1 | no | — |
| 186 | C4 | — | 5 | 3 | no | — |
| 187 | C4 | C22×C5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 188 | C4 | C22×C5×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 189 | C2 | — | 2 | 3 | no | — |
| 190 | C2 | — | 5 | 2 | no | — |
| 191 | C2 | — | 10 | 3 | no | — |
| 192 | C2 | C23×C5×AGL(1,𝔽5) | 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