← C13×#63070 #15749409
Subgroups — C13×#63070 #15749409
Order 3328.
6588 conjugacy classes of subgroups.
The subgroup lattice has 212 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C13×#3559 | C2 | 1 | 30 | yes | maximal, complemented |
| 2 | C13×#3548 | C2 | 1 | 15 | yes | maximal, complemented |
| 3 | C13×#3531 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C13×#3517 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | C13×#3504 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | C13×#564 | C22 | 1 | 1 | yes | characteristic |
| 7 | C13×#563 | C22 | 1 | 30 | yes | — |
| 8 | C13×#562 | C22 | 1 | 15 | yes | — |
| 9 | C13×#562 | C22 | 1 | 30 | yes | — |
| 10 | C13×#557 | C22 | 1 | 10 | yes | — |
| 11 | C13×#554 | C22 | 1 | 60 | yes | — |
| 12 | C13×#553 | C22 | 1 | 60 | yes | — |
| 13 | C13×#550 | C22 | 1 | 30 | yes | — |
| 14 | C13×#550 | C22 | 1 | 10 | yes | — |
| 15 | C13×#547 | C22 | 1 | 60 | yes | — |
| 16 | C13×#547 | C22 | 1 | 30 | yes | — |
| 17 | C13×#544 | C22 | 1 | 30 | yes | — |
| 18 | C13×#540 | C22 | 1 | 60 | yes | — |
| 19 | C13×#539 | C22 | 1 | 60 | yes | — |
| 20 | C13×#537 | C22 | 1 | 60 | yes | — |
| 21 | C13×#533 | C22 | 1 | 15 | yes | — |
| 22 | C13×#532 | C22 | 1 | 30 | yes | — |
| 23 | C13×#529 | C22 | 1 | 30 | yes | — |
| 24 | C2×C13×#125 | C22 | 1 | 15 | yes | — |
| 25 | C13×#520 | C22 | 1 | 10 | yes | — |
| 26 | C4×C13×#41 | C22 | 1 | 5 | yes | — |
| 27 | C2×C13×#41 | C23 | 1 | 5 | yes | — |
| 28 | C2×C13×#41 | C23 | 1 | 60 | yes | — |
| 29 | C13×C4⋊Q8 | C23 | 1 | 30 | yes | — |
| 30 | C13×C4⋊Q8 | C23 | 1 | 30 | yes | — |
| 31 | C13×#127 | C23 | 1 | 30 | yes | — |
| 32 | C13×#126 | C23 | 1 | 60 | yes | — |
| 33 | C13×#125 | C23 | 1 | 15 | yes | — |
| 34 | C13×#125 | C23 | 1 | 30 | yes | — |
| 35 | C13×#125 | C23 | 1 | 60 | yes | — |
| 36 | C13×#125 | C23 | 1 | 10 | yes | — |
| 37 | C13×#125 | C23 | 1 | 5 | yes | — |
| 38 | C13×#124 | C23 | 1 | 30 | yes | — |
| 39 | C13×#123 | C23 | 1 | 60 | yes | — |
| 40 | C13×#123 | C23 | 1 | 120 | yes | — |
| 41 | C13×C22⋊Q8 | C23 | 1 | 30 | yes | — |
| 42 | C13×C22⋊Q8 | C23 | 1 | 60 | yes | — |
| 43 | C13×C22⋊Q8 | C23 | 1 | 120 | yes | — |
| 44 | C13×#121 | C23 | 1 | 30 | yes | — |
| 45 | C13×#121 | C23 | 1 | 60 | yes | — |
| 46 | C13×#121 | C23 | 1 | 60 | yes | — |
| 47 | C13×#121 | C23 | 1 | 120 | yes | — |
| 48 | C4×Q8×C13 | C23 | 1 | 10 | yes | — |
| 49 | C4×Q8×C13 | C23 | 1 | 30 | yes | — |
| 50 | C4×D4×C13 | C23 | 1 | 30 | yes | — |
| 51 | C4×D4×C13 | C23 | 1 | 60 | yes | — |
| 52 | C4×D4×C13 | C23 | 1 | 30 | yes | — |
| 53 | C4×D4×C13 | C23 | 1 | 60 | yes | — |
| 54 | C13×#117 | C23 | 1 | 15 | yes | — |
| 55 | C13×#117 | C23 | 1 | 30 | yes | — |
| 56 | C2×C13×C4⋊C4 | C23 | 1 | 30 | yes | — |
| 57 | C2×C13×C4⋊C4 | C23 | 1 | 60 | yes | — |
| 58 | C2×C42×C13 | C23 | 1 | 15 | yes | — |
| 59 | #63070 | C13 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 60 | C13×#41 | — | 2 | 20 | no | — |
| 61 | C13×#41 | — | 8 | 60 | no | — |
| 62 | C2×Q8×C13 | C24 | 1 | 30 | yes | — |
| 63 | C2×Q8×C13 | C24 | 1 | 1 | yes | characteristic |
| 64 | C2×D4×C13 | C24 | 1 | 15 | yes | — |
| 65 | C2×D4×C13 | C24 | 1 | 60 | yes | — |
| 66 | C2×D4×C13 | C24 | 1 | 30 | yes | — |
| 67 | C22×C4×C13 | C24 | 1 | 15 | yes | — |
| 68 | C22×C4×C13 | C24 | 1 | 30 | yes | — |
| 69 | C22×C4×C13 | C24 | 1 | 60 | yes | — |
| 70 | C13×C4⋊C4 | C24 | 1 | 30 | yes | — |
| 71 | C13×C4⋊C4 | C24 | 1 | 30 | yes | — |
| 72 | C13×C4⋊C4 | C24 | 1 | 60 | yes | — |
| 73 | C13×C4⋊C4 | C24 | 1 | 60 | yes | — |
| 74 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 75 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 76 | C13×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 77 | C13×C22⋊C4 | C24 | 1 | 60 | yes | — |
| 78 | C13×C22⋊C4 | C24 | 1 | 30 | yes | — |
| 79 | C13×C22⋊C4 | C24 | 1 | 60 | yes | — |
| 80 | C42×C13 | C24 | 1 | 5 | yes | — |
| 81 | C42×C13 | C24 | 1 | 30 | yes | — |
| 82 | C42×C13 | C24 | 1 | 15 | yes | — |
| 83 | #3559 | C2×C13 | 1 | 30 | yes | complemented |
| 84 | #3548 | C2×C13 | 1 | 15 | yes | complemented |
| 85 | #3531 | C2×C13 | 1 | 3 | yes | complemented |
| 86 | #3517 | C2×C13 | 1 | 10 | yes | complemented |
| 87 | #3504 | C2×C13 | 1 | 5 | yes | complemented |
| 88 | C23×C13 | C25 | 1 | 15 | yes | — |
| 89 | Q8×C13 | — | 4 | 30 | no | — |
| 90 | Q8×C13 | 2−1+4 | 1 | 4 | yes | — |
| 91 | D4×C13 | — | 2 | 30 | no | — |
| 92 | D4×C13 | — | 4 | 60 | no | — |
| 93 | D4×C13 | — | 4 | 30 | no | — |
| 94 | C2×C4×C13 | — | 2 | 30 | no | — |
| 95 | C2×C4×C13 | — | 4 | 60 | no | — |
| 96 | C2×C4×C13 | — | 4 | 30 | no | — |
| 97 | C2×C4×C13 | C25 | 1 | 5 | yes | — |
| 98 | C2×C4×C13 | C25 | 1 | 10 | yes | — |
| 99 | C2×C4×C13 | C25 | 1 | 30 | yes | — |
| 100 | C2×C4×C13 | C25 | 1 | 3 | yes | — |
| 101 | #564 | C22×C13 | 1 | 1 | yes | characteristic |
| 102 | #563 | C22×C13 | 1 | 30 | yes | — |
| 103 | #562 | C22×C13 | 1 | 15 | yes | — |
| 104 | #562 | C22×C13 | 1 | 30 | yes | — |
| 105 | #557 | C22×C13 | 1 | 10 | yes | — |
| 106 | #554 | C22×C13 | 1 | 60 | yes | — |
| 107 | #553 | C22×C13 | 1 | 60 | yes | — |
| 108 | #550 | C22×C13 | 1 | 10 | yes | — |
| 109 | #550 | C22×C13 | 1 | 30 | yes | — |
| 110 | #547 | C22×C13 | 1 | 30 | yes | — |
| 111 | #547 | C22×C13 | 1 | 60 | yes | — |
| 112 | #544 | C22×C13 | 1 | 30 | yes | — |
| 113 | #540 | C22×C13 | 1 | 60 | yes | — |
| 114 | #539 | C22×C13 | 1 | 60 | yes | — |
| 115 | #537 | C22×C13 | 1 | 60 | yes | — |
| 116 | #533 | C22×C13 | 1 | 15 | yes | — |
| 117 | #532 | C22×C13 | 1 | 30 | yes | — |
| 118 | #529 | C22×C13 | 1 | 30 | yes | — |
| 119 | C2×#125 | C22×C13 | 1 | 15 | yes | — |
| 120 | #520 | C22×C13 | 1 | 10 | yes | — |
| 121 | C4×#41 | C22×C13 | 1 | 5 | yes | — |
| 122 | C22×C13 | — | 2 | 15 | no | — |
| 123 | C22×C13 | — | 2 | 30 | no | — |
| 124 | C22×C13 | C26 | 1 | 1 | yes | characteristic |
| 125 | C4×C13 | — | 2 | 5 | no | — |
| 126 | C4×C13 | — | 2 | 30 | no | — |
| 127 | C4×C13 | — | 2 | 10 | no | — |
| 128 | C4×C13 | C2×2−1+4 | 1 | 6 | yes | — |
| 129 | C2×#41 | C23×C13 | 1 | 5 | yes | — |
| 130 | C2×#41 | C23×C13 | 1 | 60 | yes | — |
| 131 | C4⋊Q8 | C23×C13 | 1 | 30 | yes | — |
| 132 | C4⋊Q8 | C23×C13 | 1 | 30 | yes | — |
| 133 | #127 | C23×C13 | 1 | 30 | yes | — |
| 134 | #126 | C23×C13 | 1 | 60 | yes | — |
| 135 | #125 | C23×C13 | 1 | 15 | yes | — |
| 136 | #125 | C23×C13 | 1 | 30 | yes | — |
| 137 | #125 | C23×C13 | 1 | 60 | yes | — |
| 138 | #125 | C23×C13 | 1 | 10 | yes | — |
| 139 | #125 | C23×C13 | 1 | 5 | yes | — |
| 140 | #124 | C23×C13 | 1 | 30 | yes | — |
| 141 | #123 | C23×C13 | 1 | 60 | yes | — |
| 142 | #123 | C23×C13 | 1 | 120 | yes | — |
| 143 | C22⋊Q8 | C23×C13 | 1 | 30 | yes | — |
| 144 | C22⋊Q8 | C23×C13 | 1 | 60 | yes | — |
| 145 | C22⋊Q8 | C23×C13 | 1 | 120 | yes | — |
| 146 | #121 | C23×C13 | 1 | 30 | yes | — |
| 147 | #121 | C23×C13 | 1 | 60 | yes | — |
| 148 | #121 | C23×C13 | 1 | 60 | yes | — |
| 149 | #121 | C23×C13 | 1 | 120 | yes | — |
| 150 | C4×Q8 | C23×C13 | 1 | 10 | yes | — |
| 151 | C4×Q8 | C23×C13 | 1 | 30 | yes | — |
| 152 | C4×D4 | C23×C13 | 1 | 30 | yes | — |
| 153 | C4×D4 | C23×C13 | 1 | 60 | yes | — |
| 154 | C4×D4 | C23×C13 | 1 | 30 | yes | — |
| 155 | C4×D4 | C23×C13 | 1 | 60 | yes | — |
| 156 | #117 | C23×C13 | 1 | 15 | yes | — |
| 157 | #117 | C23×C13 | 1 | 30 | yes | — |
| 158 | C2×C4⋊C4 | C23×C13 | 1 | 30 | yes | — |
| 159 | C2×C4⋊C4 | C23×C13 | 1 | 60 | yes | — |
| 160 | C2×C42 | C23×C13 | 1 | 15 | yes | — |
| 161 | C2×C13 | — | 4 | 15 | no | — |
| 162 | C2×C13 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 163 | C2×C13 | H(7,𝔽2) | 1 | 2 | yes | — |
| 164 | #41 | — | 2 | 20 | no | — |
| 165 | #41 | — | 8 | 60 | no | — |
| 166 | C2×Q8 | C24×C13 | 1 | 30 | yes | — |
| 167 | C2×Q8 | C24×C13 | 1 | 1 | yes | characteristic |
| 168 | C2×D4 | C24×C13 | 1 | 15 | yes | — |
| 169 | C2×D4 | C24×C13 | 1 | 60 | yes | — |
| 170 | C2×D4 | C24×C13 | 1 | 30 | yes | — |
| 171 | C22×C4 | C24×C13 | 1 | 15 | yes | — |
| 172 | C22×C4 | C24×C13 | 1 | 30 | yes | — |
| 173 | C22×C4 | C24×C13 | 1 | 60 | yes | — |
| 174 | C4⋊C4 | C24×C13 | 1 | 30 | yes | — |
| 175 | C4⋊C4 | C24×C13 | 1 | 30 | yes | — |
| 176 | C4⋊C4 | C24×C13 | 1 | 60 | yes | — |
| 177 | C4⋊C4 | C24×C13 | 1 | 60 | yes | — |
| 178 | C4⋊C4 | C24×C13 | 1 | 10 | yes | — |
| 179 | C4⋊C4 | C24×C13 | 1 | 10 | yes | — |
| 180 | C4⋊C4 | C24×C13 | 1 | 10 | yes | — |
| 181 | C22⋊C4 | C24×C13 | 1 | 60 | yes | — |
| 182 | C22⋊C4 | C24×C13 | 1 | 30 | yes | — |
| 183 | C22⋊C4 | C24×C13 | 1 | 60 | yes | — |
| 184 | C42 | C24×C13 | 1 | 5 | yes | — |
| 185 | C42 | C24×C13 | 1 | 30 | yes | — |
| 186 | C42 | C24×C13 | 1 | 15 | yes | — |
| 187 | C13 | #63070 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 188 | C23 | C25×C13 | 1 | 15 | yes | — |
| 189 | Q8 | — | 4 | 30 | no | — |
| 190 | Q8 | C13×2−1+4 | 1 | 4 | yes | — |
| 191 | D4 | — | 2 | 30 | no | — |
| 192 | D4 | — | 4 | 60 | no | — |
| 193 | D4 | — | 4 | 30 | no | — |
| 194 | C2×C4 | — | 2 | 30 | no | — |
| 195 | C2×C4 | — | 4 | 60 | no | — |
| 196 | C2×C4 | — | 4 | 30 | no | — |
| 197 | C2×C4 | C25×C13 | 1 | 5 | yes | — |
| 198 | C2×C4 | C25×C13 | 1 | 10 | yes | — |
| 199 | C2×C4 | C25×C13 | 1 | 30 | yes | — |
| 200 | C2×C4 | C25×C13 | 1 | 3 | yes | — |
| 201 | C22 | — | 2 | 15 | no | — |
| 202 | C22 | — | 2 | 30 | no | — |
| 203 | C22 | C26×C13 | 1 | 1 | yes | characteristic |
| 204 | C4 | — | 2 | 5 | no | — |
| 205 | C4 | — | 2 | 30 | no | — |
| 206 | C4 | — | 2 | 10 | no | — |
| 207 | C4 | C2×C13×2−1+4 | 1 | 6 | yes | — |
| 208 | C2 | — | 4 | 15 | no | — |
| 209 | C2 | C22×C13×2−1+4 | 1 | 1 | yes | characteristic |
| 210 | C2 | C13×H(7,𝔽2) | 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