← C2×#10598798 #13027557
Subgroups — C2×#10598798 #13027557
Order 1280.
294 conjugacy classes of subgroups.
The subgroup lattice has 220 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#65429 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#64877 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C22×#3928 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10598798 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 5 | C2×C5×#131 | C4 | 1 | 1 | yes | characteristic |
| 6 | #65429 | — | 2 | 1 | no | — |
| 7 | #65429 | — | 2 | 1 | no | — |
| 8 | #65429 | C4 | 1 | 2 | yes | — |
| 9 | #65429 | C22 | 1 | 2 | yes | — |
| 10 | C2×#3944 | — | 2 | 1 | no | — |
| 11 | C2×#3944 | C4 | 1 | 1 | yes | characteristic |
| 12 | C22×#672 | — | 2 | 1 | no | — |
| 13 | C22×#672 | C22 | 1 | 1 | yes | characteristic |
| 14 | #64877 | — | 2 | 1 | no | — |
| 15 | #64877 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×#3928 | — | 2 | 1 | no | — |
| 17 | C2×#3928 | — | 2 | 1 | no | — |
| 18 | C2×#3928 | — | 2 | 1 | no | — |
| 19 | C2×#3928 | C22 | 1 | 2 | yes | complemented |
| 20 | C2×#1401 | — | 5 | 1 | no | maximal, Sylow |
| 21 | C2×C5×#41 | C8 | 1 | 1 | yes | characteristic |
| 22 | C5×#131 | — | 2 | 1 | no | — |
| 23 | C5×#131 | — | 2 | 1 | no | — |
| 24 | C5×#131 | C8 | 1 | 2 | yes | — |
| 25 | C5×#131 | C2×C4 | 1 | 2 | yes | — |
| 26 | C2×C5×M16 | — | 2 | 1 | no | — |
| 27 | C2×C5×M16 | C8 | 1 | 1 | yes | characteristic |
| 28 | C22×C5×C8 | — | 2 | 1 | no | — |
| 29 | C22×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #3944 | — | 2 | 1 | no | — |
| 31 | #3944 | — | 2 | 2 | no | — |
| 32 | #3944 | — | 2 | 2 | no | — |
| 33 | #3944 | C2×C4 | 1 | 2 | yes | — |
| 34 | C2×#672 | — | 2 | 1 | no | — |
| 35 | C2×#672 | — | 2 | 2 | no | — |
| 36 | C2×#672 | — | 2 | 2 | no | — |
| 37 | C2×#672 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×#672 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×#672 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×#672 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×#672 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×#672 | C23 | 1 | 1 | yes | characteristic |
| 43 | #3928 | — | 2 | 2 | no | — |
| 44 | #3928 | — | 2 | 2 | no | — |
| 45 | C2×#504 | — | 5 | 1 | no | — |
| 46 | C2×M64 | — | 5 | 1 | no | — |
| 47 | C22×C32 | — | 5 | 1 | no | — |
| 48 | #1401 | — | 5 | 4 | no | — |
| 49 | C5×#41 | — | 2 | 1 | no | — |
| 50 | C5×#41 | — | 2 | 1 | no | — |
| 51 | C5×#41 | C16 | 1 | 2 | yes | — |
| 52 | C5×#41 | C2×C8 | 1 | 2 | yes | — |
| 53 | C2×C5×Q8 | C16 | 1 | 1 | yes | characteristic |
| 54 | C2×C5×D4 | — | 2 | 1 | no | — |
| 55 | C2×C5×D4 | C16 | 1 | 1 | yes | characteristic |
| 56 | C22×C4×C5 | — | 2 | 1 | no | — |
| 57 | C22×C4×C5 | C2×C8 | 1 | 1 | yes | characteristic |
| 58 | C5×M16 | — | 2 | 1 | no | — |
| 59 | C5×M16 | — | 2 | 2 | no | — |
| 60 | C5×M16 | — | 2 | 2 | no | — |
| 61 | C5×M16 | C2×C8 | 1 | 2 | yes | — |
| 62 | C2×C5×C8 | — | 2 | 1 | no | — |
| 63 | C2×C5×C8 | — | 2 | 2 | no | — |
| 64 | C2×C5×C8 | — | 2 | 2 | no | — |
| 65 | C2×C5×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 66 | C2×C5×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 67 | C2×C5×C8 | C2×C8 | 1 | 1 | yes | characteristic |
| 68 | C2×C5×C8 | M16 | 1 | 1 | yes | characteristic |
| 69 | C2×C5×C8 | M16 | 1 | 1 | yes | characteristic |
| 70 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | #672 | — | 2 | 2 | no | — |
| 72 | #672 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 73 | #672 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | #672 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | #672 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×#131 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 77 | #504 | — | 5 | 2 | no | — |
| 78 | #504 | — | 5 | 2 | no | — |
| 79 | #504 | — | 10 | 1 | no | — |
| 80 | #504 | — | 10 | 1 | no | — |
| 81 | C2×M32 | — | 5 | 1 | no | — |
| 82 | C2×M32 | — | 10 | 1 | no | — |
| 83 | C22×C16 | — | 5 | 1 | no | — |
| 84 | C22×C16 | — | 10 | 1 | no | — |
| 85 | M64 | — | 5 | 2 | no | — |
| 86 | M64 | — | 10 | 1 | no | — |
| 87 | C2×C32 | — | 5 | 2 | no | — |
| 88 | C2×C32 | — | 10 | 1 | no | — |
| 89 | C2×C32 | — | 10 | 1 | no | — |
| 90 | C2×C32 | — | 10 | 1 | no | — |
| 91 | C23×C5 | — | 2 | 1 | no | — |
| 92 | C23×C5 | M32 | 1 | 1 | yes | characteristic |
| 93 | C5×Q8 | — | 2 | 1 | no | — |
| 94 | C5×Q8 | C2×C16 | 1 | 2 | yes | — |
| 95 | C5×D4 | — | 2 | 2 | no | — |
| 96 | C5×D4 | — | 2 | 2 | no | — |
| 97 | C5×D4 | — | 2 | 1 | no | — |
| 98 | C5×D4 | C2×C16 | 1 | 2 | yes | — |
| 99 | C2×C4×C5 | — | 2 | 1 | no | — |
| 100 | C2×C4×C5 | — | 2 | 2 | no | — |
| 101 | C2×C4×C5 | — | 2 | 2 | no | — |
| 102 | C2×C4×C5 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C5 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C5 | C2×C16 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C5 | C2×C16 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×C5 | M32 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×C5 | C22×C8 | 1 | 1 | yes | characteristic |
| 108 | C5×C8 | — | 2 | 2 | no | — |
| 109 | C5×C8 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 110 | C5×C8 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 111 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 112 | C5×C8 | C2×M16 | 1 | 1 | yes | characteristic |
| 113 | C2×#41 | #170 | 1 | 1 | yes | characteristic |
| 114 | #131 | — | 2 | 1 | no | — |
| 115 | #131 | — | 2 | 1 | no | — |
| 116 | #131 | #170 | 1 | 2 | yes | — |
| 117 | #131 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 118 | C2×M16 | — | 2 | 1 | no | — |
| 119 | C2×M16 | #170 | 1 | 1 | yes | characteristic |
| 120 | C22×C8 | — | 2 | 1 | no | — |
| 121 | C22×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 122 | M32 | — | 5 | 2 | no | — |
| 123 | M32 | — | 10 | 2 | no | — |
| 124 | M32 | — | 10 | 2 | no | — |
| 125 | M32 | — | 10 | 1 | no | — |
| 126 | C2×C16 | — | 5 | 1 | no | — |
| 127 | C2×C16 | — | 5 | 1 | no | — |
| 128 | C2×C16 | — | 5 | 1 | no | — |
| 129 | C2×C16 | — | 5 | 1 | no | — |
| 130 | C2×C16 | — | 5 | 1 | no | — |
| 131 | C2×C16 | — | 5 | 1 | no | — |
| 132 | C2×C16 | — | 10 | 2 | no | — |
| 133 | C2×C16 | — | 10 | 2 | no | — |
| 134 | C2×C16 | — | 10 | 1 | no | — |
| 135 | C32 | — | 10 | 2 | no | — |
| 136 | C32 | — | 10 | 2 | no | — |
| 137 | C22×C5 | — | 2 | 2 | no | — |
| 138 | C22×C5 | — | 2 | 2 | no | — |
| 139 | C22×C5 | — | 4 | 2 | no | — |
| 140 | C22×C5 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 141 | C22×C5 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 142 | C22×C5 | C2×M32 | 1 | 1 | yes | characteristic |
| 143 | C4×C5 | — | 2 | 2 | no | — |
| 144 | C4×C5 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 145 | C4×C5 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 146 | C4×C5 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 147 | C4×C5 | C22×C16 | 1 | 1 | yes | characteristic |
| 148 | #41 | — | 2 | 1 | no | — |
| 149 | #41 | — | 2 | 1 | no | — |
| 150 | #41 | #674 | 1 | 2 | yes | — |
| 151 | #41 | C2×#170 | 1 | 2 | yes | — |
| 152 | C2×Q8 | #674 | 1 | 1 | yes | characteristic |
| 153 | C2×D4 | — | 2 | 1 | no | — |
| 154 | C2×D4 | #674 | 1 | 1 | yes | characteristic |
| 155 | C22×C4 | — | 2 | 1 | no | — |
| 156 | C22×C4 | C2×#170 | 1 | 1 | yes | characteristic |
| 157 | M16 | — | 2 | 1 | no | — |
| 158 | M16 | — | 2 | 2 | no | — |
| 159 | M16 | — | 2 | 2 | no | — |
| 160 | M16 | C2×#170 | 1 | 2 | yes | — |
| 161 | C2×C8 | — | 2 | 1 | no | — |
| 162 | C2×C8 | — | 2 | 2 | no | — |
| 163 | C2×C8 | — | 2 | 2 | no | — |
| 164 | C2×C8 | C2×#170 | 1 | 1 | yes | characteristic |
| 165 | C2×C8 | #704 | 1 | 1 | yes | characteristic |
| 166 | C2×C8 | #704 | 1 | 1 | yes | characteristic |
| 167 | C2×C8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 168 | C2×C8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 169 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 170 | C16 | — | 5 | 1 | no | — |
| 171 | C16 | — | 5 | 1 | no | — |
| 172 | C16 | — | 5 | 1 | no | — |
| 173 | C16 | — | 5 | 1 | no | — |
| 174 | C16 | — | 10 | 2 | no | — |
| 175 | C2×C5 | — | 2 | 1 | no | — |
| 176 | C2×C5 | — | 2 | 1 | no | — |
| 177 | C2×C5 | — | 4 | 2 | no | — |
| 178 | C2×C5 | #1401 | 1 | 2 | yes | complemented |
| 179 | C2×C5 | C2×C22⋊C16 | 1 | 1 | yes | characteristic |
| 180 | C23 | — | 2 | 1 | no | — |
| 181 | C23 | #3998 | 1 | 1 | yes | characteristic |
| 182 | Q8 | — | 2 | 1 | no | — |
| 183 | Q8 | C2×#674 | 1 | 2 | yes | — |
| 184 | D4 | — | 2 | 2 | no | — |
| 185 | D4 | — | 2 | 2 | no | — |
| 186 | D4 | — | 2 | 1 | no | — |
| 187 | D4 | C2×#674 | 1 | 2 | yes | — |
| 188 | C2×C4 | — | 2 | 1 | no | — |
| 189 | C2×C4 | — | 2 | 2 | no | — |
| 190 | C2×C4 | — | 2 | 2 | no | — |
| 191 | C2×C4 | C2×#674 | 1 | 1 | yes | characteristic |
| 192 | C2×C4 | C2×#674 | 1 | 1 | yes | characteristic |
| 193 | C2×C4 | #3998 | 1 | 1 | yes | characteristic |
| 194 | C2×C4 | C22⋊#170 | 1 | 1 | yes | characteristic |
| 195 | C2×C4 | C22⋊#170 | 1 | 1 | yes | characteristic |
| 196 | C2×C4 | C22×#170 | 1 | 1 | yes | characteristic |
| 197 | C8 | — | 2 | 2 | no | — |
| 198 | C8 | C22⋊#170 | 1 | 1 | yes | characteristic |
| 199 | C8 | C22⋊#170 | 1 | 1 | yes | characteristic |
| 200 | C8 | C2×#704 | 1 | 1 | yes | characteristic |
| 201 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 202 | C5 | C2×#1401 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 203 | C22 | — | 2 | 2 | no | — |
| 204 | C22 | — | 2 | 2 | no | — |
| 205 | C22 | — | 4 | 2 | no | — |
| 206 | C22 | C22⋊#674 | 1 | 1 | yes | characteristic |
| 207 | C22 | C22⋊#674 | 1 | 1 | yes | characteristic |
| 208 | C22 | C2×#3998 | 1 | 1 | yes | characteristic |
| 209 | C4 | — | 2 | 2 | no | — |
| 210 | C4 | C22⋊#674 | 1 | 1 | yes | characteristic |
| 211 | C4 | C22⋊#674 | 1 | 1 | yes | characteristic |
| 212 | C4 | C22×#674 | 1 | 1 | yes | characteristic |
| 213 | C4 | C2×C22⋊#170 | 1 | 1 | yes | characteristic |
| 214 | C2 | — | 2 | 1 | no | — |
| 215 | C2 | — | 2 | 1 | no | — |
| 216 | C2 | — | 4 | 2 | no | — |
| 217 | C2 | #10598798 | 1 | 2 | yes | direct product factor |
| 218 | C2 | C2×C22⋊#674 | 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