← #30593915
Subgroups — #30593915
Order 15616.
59452 conjugacy classes of subgroups.
The subgroup lattice has 250 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21460632 | C2 | 1 | 16 | yes | maximal, complemented |
| 2 | #21460631 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | #21460630 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | #21460629 | C2 | 1 | 20 | yes | maximal, complemented |
| 5 | C2×#16840598 | C2 | 1 | 30 | yes | maximal, complemented |
| 6 | #585×D61 | C2 | 1 | 32 | yes | maximal, complemented |
| 7 | C2×C61×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16840599 | C22 | 1 | 192 | yes | complemented |
| 9 | #16840598 | C22 | 1 | 240 | yes | complemented |
| 10 | #16840598 | C22 | 1 | 80 | yes | complemented |
| 11 | #16840598 | C22 | 1 | 240 | yes | complemented |
| 12 | #16840598 | C22 | 1 | 240 | yes | complemented |
| 13 | #16840597 | C22 | 1 | 320 | yes | complemented |
| 14 | C2×#14519825 | C22 | 1 | 60 | yes | complemented |
| 15 | C2×#14519824 | C22 | 1 | 120 | yes | complemented |
| 16 | 2−1+4×D61 | C22 | 1 | 192 | yes | complemented |
| 17 | C2×#14519823 | C22 | 1 | 120 | yes | complemented |
| 18 | C2×#14519822 | C22 | 1 | 180 | yes | complemented |
| 19 | H(5,𝔽2)×D61 | C22 | 1 | 320 | yes | complemented |
| 20 | C22×#11758222 | C22 | 1 | 60 | yes | complemented |
| 21 | C2×#41×D61 | C22 | 1 | 240 | yes | complemented |
| 22 | C61×#585 | C22 | 1 | 16 | yes | complemented |
| 23 | C61×#585 | C22 | 1 | 16 | yes | complemented |
| 24 | C2×2−1+4×C61 | C22 | 1 | 6 | yes | complemented |
| 25 | C2×H(5,𝔽2)×C61 | C22 | 1 | 10 | yes | complemented |
| 26 | C22×#41×C61 | C22 | 1 | 15 | yes | complemented |
| 27 | #14519825 | C23 | 1 | 480 | yes | complemented |
| 28 | #14519825 | C23 | 1 | 160 | yes | complemented |
| 29 | #14519824 | C23 | 1 | 960 | yes | complemented |
| 30 | #14519824 | C23 | 1 | 320 | yes | complemented |
| 31 | #14519823 | C23 | 1 | 960 | yes | complemented |
| 32 | #14519823 | C23 | 1 | 320 | yes | complemented |
| 33 | #14519822 | C23 | 1 | 1440 | yes | complemented |
| 34 | #14519822 | C23 | 1 | 480 | yes | complemented |
| 35 | C2×#11758226 | C23 | 1 | 240 | yes | complemented |
| 36 | C2×#11758222 | C23 | 1 | 360 | yes | complemented |
| 37 | C2×#11758222 | C23 | 1 | 120 | yes | complemented |
| 38 | C2×#11758222 | C23 | 1 | 360 | yes | complemented |
| 39 | C2×#11758222 | C23 | 1 | 360 | yes | complemented |
| 40 | C2×#11758224 | C23 | 1 | 720 | yes | complemented |
| 41 | #41×D61 | C23 | 1 | 640 | yes | complemented |
| 42 | #41×D61 | C23 | 1 | 1920 | yes | complemented |
| 43 | C22×Dic122 | C23 | 1 | 60 | yes | complemented |
| 44 | C2×Q8×D61 | C23 | 1 | 240 | yes | complemented |
| 45 | C22×D244 | C23 | 1 | 60 | yes | complemented |
| 46 | C22×C22⋊D61 | C23 | 1 | 120 | yes | complemented |
| 47 | C2×D4×D61 | C23 | 1 | 720 | yes | complemented |
| 48 | C22×C4×D61 | C23 | 1 | 120 | yes | complemented |
| 49 | 2−1+4×C61 | C23 | 1 | 96 | yes | complemented |
| 50 | H(5,𝔽2)×C61 | C23 | 1 | 160 | yes | complemented |
| 51 | C2×#41×C61 | C23 | 1 | 20 | yes | complemented |
| 52 | C2×#41×C61 | C23 | 1 | 60 | yes | complemented |
| 53 | C2×#41×C61 | C23 | 1 | 120 | yes | complemented |
| 54 | C2×#41×C61 | C23 | 1 | 120 | yes | complemented |
| 55 | C22×Q8×C61 | C23 | 1 | 15 | yes | complemented |
| 56 | C22×D4×C61 | C23 | 1 | 45 | yes | complemented |
| 57 | C23×C4×C61 | C23 | 1 | 15 | yes | complemented |
| 58 | C24×C61 | C24 | 1 | 15 | yes | — |
| 59 | C23×D61 | C24 | 1 | 120 | yes | — |
| 60 | #41×C61 | C24 | 1 | 80 | yes | — |
| 61 | #41×C61 | C24 | 1 | 480 | yes | — |
| 62 | #41×C61 | C24 | 1 | 80 | yes | — |
| 63 | C2×Q8×C61 | C24 | 1 | 120 | yes | — |
| 64 | C2×Q8×C61 | C24 | 1 | 20 | yes | — |
| 65 | C2×D4×C61 | C24 | 1 | 360 | yes | — |
| 66 | C2×D4×C61 | C24 | 1 | 60 | yes | — |
| 67 | C22×C4×C61 | C24 | 1 | 60 | yes | — |
| 68 | C22×C4×C61 | C24 | 1 | 60 | yes | — |
| 69 | C22×C4×C61 | C24 | 1 | 15 | yes | — |
| 70 | C22×C4×C61 | C24 | 1 | 45 | yes | — |
| 71 | C2×C22⋊D61 | C24 | 1 | 720 | yes | — |
| 72 | C2×C22⋊D61 | C24 | 1 | 240 | yes | — |
| 73 | C22×Dic61 | C24 | 1 | 120 | yes | — |
| 74 | #11758226 | C24 | 1 | 640 | yes | — |
| 75 | Q8×D61 | C24 | 1 | 640 | yes | — |
| 76 | #11758224 | C24 | 1 | 1920 | yes | — |
| 77 | D4×D61 | C24 | 1 | 1920 | yes | — |
| 78 | #11758222 | C24 | 1 | 240 | yes | — |
| 79 | #11758222 | C24 | 1 | 1440 | yes | — |
| 80 | #11758222 | C24 | 1 | 16 | yes | — |
| 81 | #11758222 | C24 | 1 | 240 | yes | — |
| 82 | #11758222 | C24 | 1 | 240 | yes | — |
| 83 | C2×D244 | C24 | 1 | 360 | yes | — |
| 84 | C2×D244 | C24 | 1 | 120 | yes | — |
| 85 | C2×C4×D61 | C24 | 1 | 240 | yes | — |
| 86 | C2×C4×D61 | C24 | 1 | 720 | yes | — |
| 87 | C2×Dic122 | C24 | 1 | 360 | yes | — |
| 88 | C2×Dic122 | C24 | 1 | 120 | yes | — |
| 89 | C23×C61 | — | 8 | 15 | no | — |
| 90 | C23×C61 | C25 | 1 | 60 | yes | — |
| 91 | C23×C61 | C25 | 1 | 15 | yes | — |
| 92 | C22×D61 | — | 8 | 120 | no | — |
| 93 | C22×D61 | C25 | 1 | 240 | yes | — |
| 94 | Q8×C61 | C25 | 1 | 80 | yes | — |
| 95 | D4×C61 | C25 | 1 | 240 | yes | — |
| 96 | C2×C4×C61 | C25 | 1 | 30 | yes | — |
| 97 | C2×C4×C61 | C25 | 1 | 180 | yes | — |
| 98 | C2×C4×C61 | C25 | 1 | 30 | yes | — |
| 99 | C2×C4×C61 | C25 | 1 | 1 | yes | characteristic |
| 100 | C2×C4×C61 | C25 | 1 | 15 | yes | — |
| 101 | C22⋊D61 | C25 | 1 | 32 | yes | — |
| 102 | C22⋊D61 | C25 | 1 | 480 | yes | — |
| 103 | C2×Dic61 | C25 | 1 | 240 | yes | — |
| 104 | D244 | C25 | 1 | 16 | yes | — |
| 105 | D244 | C25 | 1 | 240 | yes | — |
| 106 | C4×D61 | C25 | 1 | 32 | yes | — |
| 107 | C4×D61 | C25 | 1 | 480 | yes | — |
| 108 | Dic122 | C25 | 1 | 16 | yes | — |
| 109 | Dic122 | C25 | 1 | 240 | yes | — |
| 110 | #63103 | — | 61 | 1 | no | maximal, Sylow |
| 111 | C22×C61 | — | 4 | 60 | no | — |
| 112 | C22×C61 | — | 4 | 15 | no | — |
| 113 | C22×C61 | C26 | 1 | 30 | yes | — |
| 114 | C22×C61 | C26 | 1 | 1 | yes | characteristic |
| 115 | C2×D61 | — | 4 | 240 | no | — |
| 116 | C2×D61 | C26 | 1 | 32 | yes | — |
| 117 | C4×C61 | C26 | 1 | 1 | yes | characteristic |
| 118 | C4×C61 | C26 | 1 | 30 | yes | — |
| 119 | C4×C61 | C26 | 1 | 1 | yes | characteristic |
| 120 | Dic61 | C26 | 1 | 32 | yes | — |
| 121 | 2−1+6 | — | 61 | 16 | no | — |
| 122 | 2−1+6 | — | 61 | 12 | no | — |
| 123 | H(7,𝔽2) | — | 61 | 16 | no | — |
| 124 | H(7,𝔽2) | — | 61 | 20 | no | — |
| 125 | C2×#585 | — | 61 | 32 | no | — |
| 126 | C2×#585 | — | 61 | 30 | no | — |
| 127 | C2×#585 | D61 | 1 | 1 | yes | characteristic, complemented |
| 128 | C2×C61 | — | 2 | 30 | no | — |
| 129 | C2×C61 | — | 2 | 1 | no | — |
| 130 | C2×C61 | C27 | 1 | 1 | yes | characteristic |
| 131 | D61 | — | 2 | 32 | no | — |
| 132 | #585 | — | 61 | 192 | no | — |
| 133 | #585 | — | 61 | 320 | no | — |
| 134 | #585 | — | 61 | 240 | no | — |
| 135 | #585 | — | 61 | 80 | no | — |
| 136 | #585 | — | 61 | 240 | no | — |
| 137 | #585 | — | 61 | 240 | no | — |
| 138 | #585 | C2×D61 | 1 | 16 | yes | complemented |
| 139 | #585 | C2×D61 | 1 | 16 | yes | complemented |
| 140 | C2×2−1+4 | — | 61 | 192 | no | — |
| 141 | C2×2−1+4 | — | 61 | 120 | no | — |
| 142 | C2×2−1+4 | — | 61 | 60 | no | — |
| 143 | C2×2−1+4 | C2×D61 | 1 | 6 | yes | complemented |
| 144 | C2×H(5,𝔽2) | — | 61 | 320 | no | — |
| 145 | C2×H(5,𝔽2) | — | 61 | 120 | no | — |
| 146 | C2×H(5,𝔽2) | — | 61 | 180 | no | — |
| 147 | C2×H(5,𝔽2) | C2×D61 | 1 | 10 | yes | complemented |
| 148 | C22×#41 | — | 61 | 240 | no | — |
| 149 | C22×#41 | — | 61 | 60 | no | — |
| 150 | C22×#41 | C2×D61 | 1 | 15 | yes | complemented |
| 151 | C61 | #63103 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 152 | 2−1+4 | — | 61 | 960 | no | — |
| 153 | 2−1+4 | — | 61 | 320 | no | — |
| 154 | 2−1+4 | — | 61 | 480 | no | — |
| 155 | 2−1+4 | — | 61 | 160 | no | — |
| 156 | 2−1+4 | C22×D61 | 1 | 96 | yes | complemented |
| 157 | H(5,𝔽2) | — | 61 | 960 | no | — |
| 158 | H(5,𝔽2) | — | 61 | 320 | no | — |
| 159 | H(5,𝔽2) | — | 61 | 1440 | no | — |
| 160 | H(5,𝔽2) | — | 61 | 480 | no | — |
| 161 | H(5,𝔽2) | C22×D61 | 1 | 160 | yes | complemented |
| 162 | C2×#41 | — | 61 | 640 | no | — |
| 163 | C2×#41 | — | 61 | 1920 | no | — |
| 164 | C2×#41 | — | 61 | 240 | no | — |
| 165 | C2×#41 | — | 61 | 720 | no | — |
| 166 | C2×#41 | — | 61 | 360 | no | — |
| 167 | C2×#41 | — | 61 | 120 | no | — |
| 168 | C2×#41 | — | 61 | 360 | no | — |
| 169 | C2×#41 | — | 61 | 360 | no | — |
| 170 | C2×#41 | C22×D61 | 1 | 120 | yes | complemented |
| 171 | C2×#41 | C22×D61 | 1 | 20 | yes | complemented |
| 172 | C2×#41 | C22×D61 | 1 | 120 | yes | complemented |
| 173 | C2×#41 | C22×D61 | 1 | 60 | yes | complemented |
| 174 | C22×Q8 | — | 61 | 240 | no | — |
| 175 | C22×Q8 | — | 61 | 60 | no | — |
| 176 | C22×Q8 | C22×D61 | 1 | 15 | yes | complemented |
| 177 | C22×D4 | — | 61 | 120 | no | — |
| 178 | C22×D4 | — | 61 | 720 | no | — |
| 179 | C22×D4 | — | 61 | 60 | no | — |
| 180 | C22×D4 | C22×D61 | 1 | 45 | yes | complemented |
| 181 | C23×C4 | — | 61 | 120 | no | — |
| 182 | C23×C4 | C22×D61 | 1 | 15 | yes | complemented |
| 183 | C24 | — | 61 | 120 | no | — |
| 184 | C24 | C23×D61 | 1 | 15 | yes | — |
| 185 | #41 | — | 61 | 640 | no | — |
| 186 | #41 | — | 61 | 1920 | no | — |
| 187 | #41 | — | 61 | 240 | no | — |
| 188 | #41 | — | 61 | 16 | no | — |
| 189 | #41 | — | 61 | 1440 | no | — |
| 190 | #41 | — | 61 | 240 | no | — |
| 191 | #41 | — | 61 | 240 | no | — |
| 192 | #41 | C23×D61 | 1 | 80 | yes | — |
| 193 | #41 | C23×D61 | 1 | 480 | yes | — |
| 194 | #41 | C23×D61 | 1 | 80 | yes | — |
| 195 | C2×Q8 | — | 61 | 640 | no | — |
| 196 | C2×Q8 | — | 61 | 360 | no | — |
| 197 | C2×Q8 | — | 61 | 120 | no | — |
| 198 | C2×Q8 | C23×D61 | 1 | 120 | yes | — |
| 199 | C2×Q8 | C23×D61 | 1 | 20 | yes | — |
| 200 | C2×D4 | — | 61 | 720 | no | — |
| 201 | C2×D4 | — | 61 | 240 | no | — |
| 202 | C2×D4 | — | 61 | 1920 | no | — |
| 203 | C2×D4 | — | 61 | 360 | no | — |
| 204 | C2×D4 | — | 61 | 120 | no | — |
| 205 | C2×D4 | C23×D61 | 1 | 360 | yes | — |
| 206 | C2×D4 | C23×D61 | 1 | 60 | yes | — |
| 207 | C22×C4 | — | 61 | 120 | no | — |
| 208 | C22×C4 | — | 61 | 240 | no | — |
| 209 | C22×C4 | — | 61 | 720 | no | — |
| 210 | C22×C4 | C23×D61 | 1 | 60 | yes | — |
| 211 | C22×C4 | C23×D61 | 1 | 15 | yes | — |
| 212 | C22×C4 | C23×D61 | 1 | 60 | yes | — |
| 213 | C22×C4 | C23×D61 | 1 | 45 | yes | — |
| 214 | C23 | — | 8 | 15 | no | — |
| 215 | C23 | — | 61 | 240 | no | — |
| 216 | C23 | — | 488 | 120 | no | — |
| 217 | C23 | C24×D61 | 1 | 60 | yes | — |
| 218 | C23 | C24×D61 | 1 | 15 | yes | — |
| 219 | Q8 | — | 61 | 240 | no | — |
| 220 | Q8 | — | 61 | 16 | no | — |
| 221 | Q8 | C24×D61 | 1 | 80 | yes | — |
| 222 | D4 | — | 61 | 480 | no | — |
| 223 | D4 | — | 61 | 32 | no | — |
| 224 | D4 | — | 61 | 240 | no | — |
| 225 | D4 | — | 61 | 16 | no | — |
| 226 | D4 | C24×D61 | 1 | 240 | yes | — |
| 227 | C2×C4 | — | 61 | 240 | no | — |
| 228 | C2×C4 | — | 61 | 480 | no | — |
| 229 | C2×C4 | — | 61 | 32 | no | — |
| 230 | C2×C4 | C24×D61 | 1 | 180 | yes | — |
| 231 | C2×C4 | C24×D61 | 1 | 30 | yes | — |
| 232 | C2×C4 | C24×D61 | 1 | 15 | yes | — |
| 233 | C2×C4 | C24×D61 | 1 | 30 | yes | — |
| 234 | C2×C4 | C24×D61 | 1 | 1 | yes | characteristic |
| 235 | C22 | — | 4 | 15 | no | — |
| 236 | C22 | — | 4 | 60 | no | — |
| 237 | C22 | — | 61 | 32 | no | — |
| 238 | C22 | — | 244 | 240 | no | — |
| 239 | C22 | C25×D61 | 1 | 30 | yes | — |
| 240 | C22 | C25×D61 | 1 | 1 | yes | characteristic |
| 241 | C4 | — | 61 | 32 | no | — |
| 242 | C4 | C25×D61 | 1 | 30 | yes | — |
| 243 | C4 | C25×D61 | 1 | 1 | yes | characteristic |
| 244 | C4 | C25×D61 | 1 | 1 | yes | characteristic |
| 245 | C2 | — | 2 | 1 | no | — |
| 246 | C2 | — | 2 | 30 | no | — |
| 247 | C2 | — | 122 | 32 | no | — |
| 248 | C2 | C26×D61 | 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