Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
198 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10599512 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10598794 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10598784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #66082 | C4 | 1 | 1 | yes | characteristic |
| 5 | #65758 | — | 2 | 1 | no | — |
| 6 | C2×#3957 | — | 2 | 1 | no | — |
| 7 | #65421 | — | 2 | 1 | no | — |
| 8 | #65407 | C22 | 1 | 1 | yes | characteristic |
| 9 | #64912 | — | 2 | 1 | no | — |
| 10 | C5×#338 | C4 | 1 | 1 | yes | characteristic |
| 11 | #7414 | — | 5 | 1 | no | maximal, Sylow |
| 12 | C2×#709 | — | 2 | 1 | no | — |
| 13 | C2×#704 | — | 2 | 2 | no | — |
| 14 | C2×C5×M16 | — | 2 | 1 | no | — |
| 15 | C2×C5×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C2×C4×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×#681 | D4 | 1 | 1 | yes | characteristic |
| 18 | #4055 | — | 4 | 1 | no | — |
| 19 | #4054 | — | 4 | 1 | no | — |
| 20 | #4050 | — | 4 | 1 | no | — |
| 21 | #4004 | — | 4 | 1 | no | — |
| 22 | C4⋊#170 | — | 4 | 1 | no | — |
| 23 | #3998 | — | 4 | 1 | no | — |
| 24 | #3957 | — | 4 | 1 | no | — |
| 25 | #3957 | — | 4 | 1 | no | — |
| 26 | #3956 | — | 4 | 1 | no | — |
| 27 | #3955 | — | 4 | 1 | no | — |
| 28 | #3946 | — | 4 | 1 | no | — |
| 29 | #2050 | — | 5 | 1 | no | — |
| 30 | #1327 | — | 5 | 1 | no | — |
| 31 | #1309 | — | 5 | 1 | no | — |
| 32 | C22×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 33 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 34 | C22×Dic5 | — | 2 | 1 | no | — |
| 35 | #709 | — | 4 | 1 | no | — |
| 36 | #709 | — | 4 | 1 | no | — |
| 37 | #709 | — | 4 | 1 | no | — |
| 38 | #709 | — | 4 | 1 | no | — |
| 39 | C2×D20 | — | 2 | 1 | no | — |
| 40 | C2×C4×D5 | — | 4 | 1 | no | — |
| 41 | C2×Dic10 | — | 2 | 1 | no | — |
| 42 | #704 | — | 8 | 2 | no | — |
| 43 | C2×#170 | — | 4 | 2 | no | — |
| 44 | C5×M16 | — | 4 | 1 | no | — |
| 45 | C5×M16 | — | 4 | 1 | no | — |
| 46 | C5×M16 | — | 4 | 1 | no | — |
| 47 | C2×C5×C8 | — | 2 | 1 | no | — |
| 48 | C2×C5×C8 | — | 4 | 1 | no | — |
| 49 | C4×Dic5 | — | 2 | 1 | no | — |
| 50 | C4×Dic5 | D8 | 1 | 1 | yes | characteristic |
| 51 | C4×Dic5 | SD16 | 1 | 1 | yes | characteristic |
| 52 | #681 | — | 4 | 1 | no | — |
| 53 | C2×#168 | — | 2 | 1 | no | — |
| 54 | Dic20 | — | 4 | 1 | no | — |
| 55 | D40 | — | 4 | 1 | no | — |
| 56 | #677 | — | 4 | 2 | no | — |
| 57 | #674 | — | 8 | 1 | no | — |
| 58 | #575 | — | 5 | 1 | no | — |
| 59 | #423 | — | 5 | 1 | no | — |
| 60 | #423 | — | 10 | 1 | no | — |
| 61 | C2×#104 | — | 10 | 1 | no | — |
| 62 | #413 | — | 10 | 1 | no | — |
| 63 | #349 | — | 10 | 1 | no | — |
| 64 | #338 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 65 | C23×C5 | #104 | 1 | 1 | yes | characteristic |
| 66 | C22×D5 | — | 4 | 1 | no | — |
| 67 | C2×C4×C5 | — | 2 | 1 | no | — |
| 68 | C2×C4×C5 | — | 2 | 1 | no | — |
| 69 | C2×C4×C5 | #99 | 1 | 1 | yes | characteristic |
| 70 | C2×C4×C5 | #102 | 1 | 1 | yes | characteristic |
| 71 | C22⋊D5 | — | 8 | 1 | no | — |
| 72 | C22⋊D5 | — | 8 | 1 | no | — |
| 73 | C2×Dic5 | — | 2 | 1 | no | — |
| 74 | C2×Dic5 | — | 2 | 1 | no | — |
| 75 | C2×Dic5 | — | 4 | 1 | no | — |
| 76 | C2×Dic5 | — | 4 | 1 | no | — |
| 77 | C2×Dic5 | — | 4 | 1 | no | — |
| 78 | D20 | — | 4 | 1 | no | — |
| 79 | D20 | — | 4 | 1 | no | — |
| 80 | C4×D5 | — | 8 | 1 | no | — |
| 81 | C4×D5 | — | 8 | 1 | no | — |
| 82 | Dic10 | — | 4 | 1 | no | — |
| 83 | Dic10 | — | 4 | 1 | no | — |
| 84 | #170 | — | 8 | 2 | no | — |
| 85 | C5×C8 | — | 4 | 1 | no | — |
| 86 | C5×C8 | — | 8 | 1 | no | — |
| 87 | #168 | — | 4 | 1 | no | — |
| 88 | C2×#41 | — | 10 | 1 | no | — |
| 89 | #137 | — | 20 | 1 | no | — |
| 90 | AGL(1,ℤ/8) | — | 20 | 1 | no | — |
| 91 | #135 | — | 20 | 1 | no | — |
| 92 | C2×M16 | — | 2 | 1 | no | — |
| 93 | C2×M16 | — | 5 | 1 | no | — |
| 94 | C2×M16 | — | 10 | 2 | no | — |
| 95 | C2×M16 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 96 | C2×C42 | — | 5 | 1 | no | — |
| 97 | M32 | — | 20 | 1 | no | — |
| 98 | C4⋊C8 | — | 20 | 1 | no | — |
| 99 | C4⋊C8 | — | 20 | 1 | no | — |
| 100 | C4⋊C8 | — | 20 | 1 | no | — |
| 101 | #104 | — | 20 | 1 | no | — |
| 102 | #104 | — | 20 | 1 | no | — |
| 103 | #101 | — | 20 | 1 | no | — |
| 104 | #100 | — | 20 | 1 | no | — |
| 105 | C22×C5 | — | 2 | 1 | no | — |
| 106 | C22×C5 | — | 4 | 1 | no | — |
| 107 | C22×C5 | #327 | 1 | 1 | yes | characteristic |
| 108 | C2×D5 | — | 8 | 1 | no | — |
| 109 | C2×D5 | — | 16 | 1 | no | — |
| 110 | C4×C5 | — | 2 | 1 | no | — |
| 111 | C4×C5 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 112 | C4×C5 | #355 | 1 | 1 | yes | characteristic |
| 113 | Dic5 | — | 2 | 1 | no | — |
| 114 | Dic5 | — | 2 | 1 | no | — |
| 115 | Dic5 | — | 4 | 1 | no | — |
| 116 | Dic5 | — | 8 | 1 | no | — |
| 117 | #41 | — | 20 | 1 | no | — |
| 118 | #41 | — | 20 | 1 | no | — |
| 119 | #41 | — | 20 | 1 | no | — |
| 120 | #41 | — | 20 | 1 | no | — |
| 121 | C2×Q8 | — | 10 | 1 | no | — |
| 122 | C2×D4 | — | 10 | 1 | no | — |
| 123 | C2×D4 | — | 20 | 1 | no | — |
| 124 | C22×C4 | — | 10 | 1 | no | — |
| 125 | C22×C4 | — | 20 | 1 | no | — |
| 126 | C22×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 127 | Q16 | — | 20 | 1 | no | — |
| 128 | SD16 | — | 20 | 2 | no | — |
| 129 | D8 | — | 20 | 1 | no | — |
| 130 | M16 | — | 4 | 1 | no | — |
| 131 | M16 | — | 4 | 1 | no | — |
| 132 | M16 | — | 4 | 1 | no | — |
| 133 | M16 | — | 20 | 1 | no | — |
| 134 | M16 | — | 40 | 2 | no | — |
| 135 | C2×C8 | — | 2 | 1 | no | — |
| 136 | C2×C8 | — | 4 | 1 | no | — |
| 137 | C2×C8 | — | 10 | 1 | no | — |
| 138 | C2×C8 | — | 20 | 2 | no | — |
| 139 | C42 | — | 5 | 1 | no | — |
| 140 | C42 | — | 5 | 1 | no | — |
| 141 | C42 | — | 10 | 1 | no | — |
| 142 | C16 | — | 40 | 1 | no | — |
| 143 | C2×C5 | — | 2 | 1 | no | — |
| 144 | C2×C5 | — | 4 | 1 | no | — |
| 145 | C2×C5 | #1345 | 1 | 1 | yes | characteristic |
| 146 | D5 | — | 16 | 1 | no | — |
| 147 | C23 | — | 20 | 1 | no | — |
| 148 | C23 | #4010 | 1 | 1 | yes | characteristic |
| 149 | Q8 | — | 20 | 1 | no | — |
| 150 | Q8 | — | 20 | 1 | no | — |
| 151 | D4 | — | 20 | 1 | no | — |
| 152 | D4 | — | 20 | 1 | no | — |
| 153 | D4 | — | 40 | 1 | no | — |
| 154 | D4 | — | 40 | 1 | no | — |
| 155 | C2×C4 | — | 2 | 1 | no | — |
| 156 | C2×C4 | — | 2 | 1 | no | — |
| 157 | C2×C4 | — | 10 | 1 | no | — |
| 158 | C2×C4 | — | 10 | 1 | no | — |
| 159 | C2×C4 | — | 20 | 1 | no | — |
| 160 | C2×C4 | — | 20 | 1 | no | — |
| 161 | C2×C4 | — | 20 | 1 | no | — |
| 162 | C2×C4 | — | 40 | 1 | no | — |
| 163 | C2×C4 | — | 40 | 1 | no | — |
| 164 | C2×C4 | #3999 | 1 | 1 | yes | characteristic |
| 165 | C2×C4 | #4007 | 1 | 1 | yes | characteristic |
| 166 | C8 | — | 4 | 1 | no | — |
| 167 | C8 | — | 8 | 1 | no | — |
| 168 | C8 | — | 20 | 1 | no | — |
| 169 | C8 | — | 40 | 2 | no | — |
| 170 | C5 | #7414 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 171 | C22 | — | 2 | 1 | no | — |
| 172 | C22 | — | 4 | 1 | no | — |
| 173 | C22 | — | 40 | 1 | no | — |
| 174 | C22 | — | 80 | 1 | no | — |
| 175 | C22 | #64868 | 1 | 1 | yes | characteristic |
| 176 | C4 | — | 2 | 1 | no | — |
| 177 | C4 | — | 10 | 1 | no | — |
| 178 | C4 | — | 10 | 1 | no | — |
| 179 | C4 | — | 20 | 1 | no | — |
| 180 | C4 | — | 40 | 1 | no | — |
| 181 | C4 | #64856 | 1 | 1 | yes | characteristic |
| 182 | C4 | #64864 | 1 | 1 | yes | characteristic |
| 183 | C2 | — | 2 | 1 | no | — |
| 184 | C2 | — | 4 | 1 | no | — |
| 185 | C2 | — | 80 | 1 | no | — |
| 186 | C2 | #10598499 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10598794 | C2 | semidirect |
| 3. #10598784 | C2 | semidirect |
| 170. C5 | #7414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599512 | 2 |
| #10598794 | 2 |
| #10598784 | 2 |
| #7414 | 5 |