← #10610980
Subgroups — #10610980
Order 640.
452 conjugacy classes of subgroups.
The subgroup lattice has 204 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #66079 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#4050 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C5×#108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #65428 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #65390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #65184 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #65183 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C2×#709 | C22 | 1 | 2 | yes | — |
| 9 | C2×C5×M16 | C22 | 1 | 2 | yes | — |
| 10 | C22×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 11 | #4072 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#681 | C22 | 1 | 1 | yes | characteristic |
| 13 | #4053 | C22 | 1 | 8 | yes | complemented |
| 14 | D5×M16 | — | 2 | 4 | no | — |
| 15 | C2×Dic20 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #4050 | C4 | 1 | 2 | yes | complemented |
| 17 | #4050 | C4 | 1 | 2 | yes | complemented |
| 18 | #4050 | C22 | 1 | 2 | yes | — |
| 19 | #4050 | C22 | 1 | 2 | yes | — |
| 20 | C2×D40 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#677 | C4 | 1 | 2 | yes | complemented |
| 22 | #4047 | — | 2 | 4 | no | — |
| 23 | C5×#108 | C22 | 1 | 2 | yes | complemented |
| 24 | C5×#108 | C22 | 1 | 2 | yes | complemented |
| 25 | #3957 | C22 | 1 | 8 | yes | complemented |
| 26 | #3947 | C22 | 1 | 2 | yes | complemented |
| 27 | C8×Dic5 | C22 | 1 | 2 | yes | complemented |
| 28 | #2957 | — | 5 | 1 | no | maximal, Sylow |
| 29 | C22×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 30 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 31 | #709 | — | 2 | 2 | no | — |
| 32 | #709 | — | 2 | 2 | no | — |
| 33 | #709 | C2×C4 | 1 | 4 | yes | — |
| 34 | #709 | C23 | 1 | 4 | yes | — |
| 35 | C2×D20 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×C4×D5 | — | 2 | 2 | no | — |
| 37 | C2×Dic10 | C2×C4 | 1 | 2 | yes | — |
| 38 | C5×M16 | — | 2 | 2 | no | — |
| 39 | C5×M16 | C23 | 1 | 4 | yes | — |
| 40 | C2×C5×C8 | — | 2 | 2 | no | — |
| 41 | C2×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 47 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 48 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 49 | C4×Dic5 | C23 | 1 | 2 | yes | — |
| 50 | #681 | D4 | 1 | 2 | yes | — |
| 51 | #681 | D4 | 1 | 2 | yes | — |
| 52 | C2×#168 | C23 | 1 | 2 | yes | — |
| 53 | Dic20 | C2×C4 | 1 | 2 | yes | — |
| 54 | Dic20 | C2×C4 | 1 | 2 | yes | — |
| 55 | D40 | C2×C4 | 1 | 2 | yes | — |
| 56 | D40 | C2×C4 | 1 | 2 | yes | — |
| 57 | #677 | C2×C4 | 1 | 4 | yes | — |
| 58 | #677 | C2×C4 | 1 | 4 | yes | — |
| 59 | #676 | — | 2 | 8 | no | — |
| 60 | C8×D5 | — | 2 | 8 | no | — |
| 61 | C2×#135 | — | 5 | 1 | no | — |
| 62 | #568 | — | 5 | 2 | no | — |
| 63 | #444 | — | 5 | 4 | no | — |
| 64 | #443 | — | 5 | 4 | no | — |
| 65 | C2×#108 | D5 | 1 | 1 | yes | characteristic, complemented |
| 66 | #421 | — | 5 | 2 | no | — |
| 67 | #405 | — | 5 | 1 | no | — |
| 68 | C23×C5 | #41 | 1 | 1 | yes | characteristic |
| 69 | C22×D5 | — | 2 | 2 | no | — |
| 70 | C2×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | C2×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C2×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×C5 | #41 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 76 | C22⋊D5 | — | 2 | 4 | no | — |
| 77 | C22⋊D5 | — | 2 | 4 | no | — |
| 78 | C2×Dic5 | — | 2 | 2 | no | — |
| 79 | C2×Dic5 | — | 2 | 2 | no | — |
| 80 | D20 | — | 2 | 2 | no | — |
| 81 | D20 | C22×C4 | 1 | 4 | yes | — |
| 82 | C4×D5 | — | 2 | 4 | no | — |
| 83 | C4×D5 | — | 2 | 4 | no | — |
| 84 | Dic10 | — | 2 | 2 | no | — |
| 85 | Dic10 | C22×C4 | 1 | 4 | yes | — |
| 86 | C5×C8 | — | 2 | 4 | no | — |
| 87 | C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 88 | C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | #168 | C2×D4 | 1 | 4 | yes | — |
| 92 | C2×#41 | — | 5 | 2 | no | — |
| 93 | #135 | — | 5 | 2 | no | — |
| 94 | #135 | — | 5 | 2 | no | — |
| 95 | #135 | — | 5 | 2 | no | — |
| 96 | #135 | — | 5 | 2 | no | — |
| 97 | C2×Q16 | — | 5 | 1 | no | — |
| 98 | C2×SD16 | — | 5 | 2 | no | — |
| 99 | C2×D8 | — | 5 | 1 | no | — |
| 100 | #131 | — | 5 | 8 | no | — |
| 101 | #131 | — | 10 | 4 | no | — |
| 102 | C2×M16 | — | 5 | 1 | no | — |
| 103 | C2×M16 | — | 10 | 4 | no | — |
| 104 | C2×M16 | C2×D5 | 1 | 2 | yes | — |
| 105 | C22×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 106 | #117 | — | 5 | 1 | no | — |
| 107 | #108 | C2×D5 | 1 | 2 | yes | complemented |
| 108 | #108 | C2×D5 | 1 | 2 | yes | complemented |
| 109 | #104 | — | 5 | 8 | no | — |
| 110 | #97 | — | 5 | 2 | no | — |
| 111 | C4×C8 | — | 5 | 2 | no | — |
| 112 | C22×C5 | — | 4 | 1 | no | — |
| 113 | C22×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 114 | C22×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 116 | C2×D5 | — | 2 | 4 | no | — |
| 117 | C2×D5 | — | 8 | 2 | no | — |
| 118 | C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 119 | C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 120 | C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 121 | C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 122 | Dic5 | — | 2 | 4 | no | — |
| 123 | Dic5 | — | 4 | 2 | no | — |
| 124 | #41 | — | 5 | 4 | no | — |
| 125 | #41 | — | 5 | 4 | no | — |
| 126 | #41 | — | 10 | 2 | no | — |
| 127 | #41 | — | 10 | 2 | no | — |
| 128 | C2×Q8 | — | 5 | 2 | no | — |
| 129 | C2×D4 | — | 5 | 2 | no | — |
| 130 | C2×D4 | — | 10 | 2 | no | — |
| 131 | C22×C4 | — | 10 | 2 | no | — |
| 132 | C22×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 133 | Q16 | — | 5 | 2 | no | — |
| 134 | Q16 | — | 5 | 2 | no | — |
| 135 | SD16 | — | 5 | 4 | no | — |
| 136 | SD16 | — | 5 | 4 | no | — |
| 137 | D8 | — | 5 | 2 | no | — |
| 138 | D8 | — | 5 | 2 | no | — |
| 139 | M16 | — | 2 | 2 | no | — |
| 140 | M16 | — | 5 | 2 | no | — |
| 141 | M16 | — | 5 | 2 | no | — |
| 142 | M16 | — | 10 | 8 | no | — |
| 143 | M16 | C22×D5 | 1 | 4 | yes | — |
| 144 | C2×C8 | — | 2 | 2 | no | — |
| 145 | C2×C8 | — | 5 | 2 | no | — |
| 146 | C2×C8 | — | 10 | 8 | no | — |
| 147 | C2×C8 | C4×D5 | 1 | 1 | yes | characteristic |
| 148 | C2×C8 | C4×D5 | 1 | 1 | yes | characteristic |
| 149 | C2×C8 | C4×D5 | 1 | 1 | yes | characteristic |
| 150 | C2×C8 | C4×D5 | 1 | 1 | yes | characteristic |
| 151 | C2×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 152 | C2×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 153 | C4⋊C4 | — | 10 | 1 | no | — |
| 154 | C22⋊C4 | — | 10 | 1 | no | — |
| 155 | C42 | — | 5 | 2 | no | — |
| 156 | C2×C5 | — | 2 | 1 | no | — |
| 157 | C2×C5 | — | 2 | 1 | no | — |
| 158 | C2×C5 | — | 2 | 1 | no | — |
| 159 | C2×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 160 | D5 | — | 4 | 4 | no | — |
| 161 | C23 | — | 10 | 2 | no | — |
| 162 | C23 | #713 | 1 | 1 | yes | characteristic |
| 163 | Q8 | — | 5 | 4 | no | — |
| 164 | Q8 | — | 10 | 2 | no | — |
| 165 | D4 | — | 5 | 4 | no | — |
| 166 | D4 | — | 10 | 4 | no | — |
| 167 | D4 | — | 10 | 4 | no | — |
| 168 | D4 | — | 10 | 2 | no | — |
| 169 | C2×C4 | — | 10 | 2 | no | — |
| 170 | C2×C4 | — | 10 | 4 | no | — |
| 171 | C2×C4 | — | 10 | 4 | no | — |
| 172 | C2×C4 | — | 10 | 2 | no | — |
| 173 | C2×C4 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 174 | C2×C4 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 175 | C2×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 176 | C2×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 177 | C2×C4 | #713 | 1 | 1 | yes | characteristic |
| 178 | C2×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 179 | C8 | — | 2 | 4 | no | — |
| 180 | C8 | — | 5 | 4 | no | — |
| 181 | C8 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 182 | C8 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 183 | C8 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 184 | C8 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 185 | C5 | #2957 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 186 | C22 | — | 4 | 1 | no | — |
| 187 | C22 | — | 10 | 4 | no | — |
| 188 | C22 | — | 40 | 2 | no | — |
| 189 | C22 | #4039 | 1 | 1 | yes | characteristic |
| 190 | C22 | #4039 | 1 | 1 | yes | characteristic |
| 191 | C22 | C2×#713 | 1 | 1 | yes | characteristic |
| 192 | C4 | — | 10 | 4 | no | — |
| 193 | C4 | — | 20 | 2 | no | — |
| 194 | C4 | #4039 | 1 | 1 | yes | characteristic |
| 195 | C4 | #4039 | 1 | 1 | yes | characteristic |
| 196 | C4 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 197 | C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 198 | C2 | — | 2 | 1 | no | — |
| 199 | C2 | — | 2 | 1 | no | — |
| 200 | C2 | — | 2 | 1 | no | — |
| 201 | C2 | — | 20 | 4 | no | — |
| 202 | C2 | C2×#4039 | 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