Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
894 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 160 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 | #10619197 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10605010 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10605007 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C5×#585 | C4 | 1 | 1 | yes | characteristic |
| 5 | #66153 | — | 2 | 6 | no | — |
| 6 | #66153 | C4 | 1 | 3 | yes | — |
| 7 | C2×#4094 | — | 2 | 6 | no | — |
| 8 | C2×#4094 | C22 | 1 | 3 | yes | — |
| 9 | C2×#3998 | C22 | 1 | 3 | yes | complemented |
| 10 | C22×#674 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #64912 | — | 2 | 6 | no | — |
| 12 | C22⋊#674 | — | 2 | 6 | no | — |
| 13 | #12684 | — | 5 | 1 | no | maximal, Sylow |
| 14 | C5×2−1+4 | — | 2 | 3 | no | — |
| 15 | C5×H(5,𝔽2) | — | 2 | 3 | no | — |
| 16 | C5×H(5,𝔽2) | C8 | 1 | 4 | yes | — |
| 17 | C2×C5×#41 | — | 2 | 6 | no | — |
| 18 | C2×C5×#41 | C2×C4 | 1 | 3 | yes | — |
| 19 | #4094 | — | 2 | 4 | no | — |
| 20 | #4094 | — | 2 | 12 | no | — |
| 21 | #4094 | — | 2 | 12 | no | — |
| 22 | #4094 | — | 2 | 6 | no | — |
| 23 | #4094 | — | 2 | 6 | no | — |
| 24 | C2×#681 | — | 2 | 12 | no | — |
| 25 | C2×#681 | — | 2 | 6 | no | — |
| 26 | C2×#681 | C2×C4 | 1 | 3 | yes | — |
| 27 | C2×#681 | D4 | 1 | 6 | yes | — |
| 28 | C22×#168 | — | 2 | 4 | no | — |
| 29 | C22×#168 | D4 | 1 | 6 | yes | — |
| 30 | C22×#168 | C23 | 1 | 1 | yes | characteristic |
| 31 | #3998 | — | 2 | 6 | no | — |
| 32 | C2×#674 | — | 2 | 3 | no | — |
| 33 | C2×#674 | — | 2 | 3 | no | — |
| 34 | #3573 | — | 5 | 1 | no | — |
| 35 | #2115 | — | 5 | 3 | no | — |
| 36 | #2113 | — | 5 | 3 | no | — |
| 37 | C5×#41 | — | 2 | 4 | no | — |
| 38 | C5×#41 | — | 2 | 12 | no | — |
| 39 | C5×#41 | — | 2 | 12 | no | — |
| 40 | C5×#41 | — | 2 | 6 | no | — |
| 41 | C5×#41 | — | 2 | 6 | no | — |
| 42 | C2×C5×Q8 | — | 2 | 6 | no | — |
| 43 | C2×C5×Q8 | M16 | 1 | 3 | yes | — |
| 44 | C2×C5×D4 | — | 2 | 6 | no | — |
| 45 | C2×C5×D4 | — | 2 | 12 | no | — |
| 46 | C2×C5×D4 | C2×C8 | 1 | 6 | yes | — |
| 47 | C2×C5×D4 | M16 | 1 | 3 | yes | — |
| 48 | C22×C4×C5 | — | 2 | 4 | no | — |
| 49 | C22×C4×C5 | C22⋊C4 | 1 | 6 | yes | — |
| 50 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 51 | #681 | — | 2 | 12 | no | — |
| 52 | #681 | — | 2 | 6 | no | — |
| 53 | #681 | — | 2 | 12 | no | — |
| 54 | C2×#168 | — | 2 | 12 | no | — |
| 55 | C2×#168 | — | 2 | 6 | no | — |
| 56 | C2×#168 | — | 2 | 6 | no | — |
| 57 | C2×#168 | C22⋊C4 | 1 | 6 | yes | — |
| 58 | C2×#168 | C2×D4 | 1 | 3 | yes | — |
| 59 | C2×#168 | C2×D4 | 1 | 3 | yes | — |
| 60 | #674 | — | 4 | 1 | no | — |
| 61 | #674 | — | 4 | 3 | no | — |
| 62 | #585 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 63 | #568 | — | 5 | 3 | no | — |
| 64 | #568 | — | 10 | 6 | no | — |
| 65 | C2×#131 | — | 5 | 3 | no | — |
| 66 | C2×#131 | — | 10 | 6 | no | — |
| 67 | C2×M32 | — | 5 | 3 | no | — |
| 68 | C22×C16 | — | 5 | 1 | no | — |
| 69 | #349 | — | 10 | 6 | no | — |
| 70 | C22⋊C16 | — | 10 | 6 | no | — |
| 71 | C23×C5 | — | 2 | 4 | no | — |
| 72 | C23×C5 | C22⋊C8 | 1 | 6 | yes | — |
| 73 | C23×C5 | C22×C8 | 1 | 1 | yes | characteristic |
| 74 | C5×Q8 | — | 2 | 4 | no | — |
| 75 | C5×Q8 | — | 2 | 6 | no | — |
| 76 | C5×D4 | — | 2 | 12 | no | — |
| 77 | C5×D4 | — | 2 | 12 | no | — |
| 78 | C5×D4 | — | 2 | 6 | no | — |
| 79 | C2×C4×C5 | — | 2 | 12 | no | — |
| 80 | C2×C4×C5 | — | 2 | 6 | no | — |
| 81 | C2×C4×C5 | — | 2 | 6 | no | — |
| 82 | C2×C4×C5 | C22⋊C8 | 1 | 6 | yes | — |
| 83 | C2×C4×C5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 84 | C2×C4×C5 | C2×M16 | 1 | 3 | yes | — |
| 85 | #168 | — | 2 | 6 | no | — |
| 86 | #168 | #120 | 1 | 1 | yes | characteristic |
| 87 | #168 | #120 | 1 | 3 | yes | — |
| 88 | 2−1+4 | — | 2 | 3 | no | — |
| 89 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 90 | H(5,𝔽2) | #170 | 1 | 4 | yes | — |
| 91 | C2×#41 | — | 2 | 6 | no | — |
| 92 | C2×#41 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 93 | #131 | — | 10 | 6 | no | — |
| 94 | #131 | — | 10 | 6 | no | — |
| 95 | #131 | — | 10 | 12 | no | — |
| 96 | #131 | — | 10 | 4 | no | — |
| 97 | #131 | — | 10 | 12 | no | — |
| 98 | C2×M16 | — | 5 | 6 | no | — |
| 99 | C2×M16 | — | 5 | 3 | no | — |
| 100 | C2×M16 | — | 10 | 12 | no | — |
| 101 | C2×M16 | — | 10 | 6 | no | — |
| 102 | C22×C8 | — | 5 | 1 | no | — |
| 103 | C22×C8 | — | 5 | 6 | no | — |
| 104 | C22×C8 | — | 10 | 4 | no | — |
| 105 | M32 | — | 10 | 6 | no | — |
| 106 | C2×C16 | — | 10 | 3 | no | — |
| 107 | C2×C16 | — | 10 | 3 | no | — |
| 108 | C22×C5 | — | 2 | 6 | no | — |
| 109 | C22×C5 | — | 4 | 1 | no | — |
| 110 | C22×C5 | — | 4 | 6 | no | — |
| 111 | C22×C5 | — | 8 | 4 | no | — |
| 112 | C22×C5 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 113 | C4×C5 | — | 2 | 6 | no | — |
| 114 | C4×C5 | #379 | 1 | 1 | yes | characteristic |
| 115 | C4×C5 | #407 | 1 | 3 | yes | — |
| 116 | #41 | — | 2 | 4 | no | — |
| 117 | #41 | — | 2 | 12 | no | — |
| 118 | #41 | — | 2 | 6 | no | — |
| 119 | #41 | — | 2 | 6 | no | — |
| 120 | #41 | — | 2 | 12 | no | — |
| 121 | C2×Q8 | — | 2 | 6 | no | — |
| 122 | C2×Q8 | #704 | 1 | 3 | yes | — |
| 123 | C2×D4 | — | 2 | 6 | no | — |
| 124 | C2×D4 | — | 2 | 12 | no | — |
| 125 | C2×D4 | C2×#170 | 1 | 6 | yes | — |
| 126 | C2×D4 | #704 | 1 | 3 | yes | — |
| 127 | C22×C4 | — | 2 | 4 | no | — |
| 128 | C22×C4 | C22⋊AGL(1,𝔽5) | 1 | 6 | yes | — |
| 129 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 130 | M16 | — | 10 | 12 | no | — |
| 131 | M16 | — | 10 | 12 | no | — |
| 132 | M16 | — | 10 | 6 | no | — |
| 133 | C2×C8 | — | 5 | 3 | no | — |
| 134 | C2×C8 | — | 5 | 3 | no | — |
| 135 | C2×C8 | — | 5 | 6 | no | — |
| 136 | C2×C8 | — | 10 | 6 | no | — |
| 137 | C2×C8 | — | 10 | 6 | no | — |
| 138 | C2×C8 | — | 10 | 12 | no | — |
| 139 | C16 | — | 20 | 1 | no | — |
| 140 | C16 | — | 20 | 3 | no | — |
| 141 | C2×C5 | — | 2 | 3 | no | — |
| 142 | C2×C5 | — | 4 | 6 | no | — |
| 143 | C2×C5 | #1779 | 1 | 1 | yes | characteristic |
| 144 | C23 | — | 2 | 4 | no | — |
| 145 | C23 | C22⋊#170 | 1 | 6 | yes | — |
| 146 | C23 | C22×#170 | 1 | 1 | yes | characteristic |
| 147 | Q8 | — | 2 | 4 | no | — |
| 148 | Q8 | — | 2 | 6 | no | — |
| 149 | D4 | — | 2 | 12 | no | — |
| 150 | D4 | — | 2 | 12 | no | — |
| 151 | D4 | — | 2 | 6 | no | — |
| 152 | C2×C4 | — | 2 | 12 | no | — |
| 153 | C2×C4 | — | 2 | 6 | no | — |
| 154 | C2×C4 | — | 2 | 6 | no | — |
| 155 | C2×C4 | C22⋊#170 | 1 | 6 | yes | — |
| 156 | C2×C4 | C2×#704 | 1 | 3 | yes | — |
| 157 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 158 | C8 | — | 5 | 1 | no | — |
| 159 | C8 | — | 5 | 3 | no | — |
| 160 | C8 | — | 10 | 6 | no | — |
| 161 | C5 | #12684 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 162 | C22 | — | 2 | 6 | no | — |
| 163 | C22 | — | 4 | 1 | no | — |
| 164 | C22 | — | 4 | 6 | no | — |
| 165 | C22 | — | 8 | 4 | no | — |
| 166 | C22 | C2×C22⋊#170 | 1 | 3 | yes | — |
| 167 | C4 | — | 2 | 6 | no | — |
| 168 | C4 | #65798 | 1 | 3 | yes | — |
| 169 | C4 | #65800 | 1 | 1 | yes | characteristic |
| 170 | C2 | — | 2 | 3 | no | — |
| 171 | C2 | — | 4 | 6 | no | — |
| 172 | C2 | #10605025 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10605010 | C2 | semidirect |
| 3. #10605007 | C2 | semidirect |
| 9. C2×#3998 | C22 | semidirect |
| 10. C22×#674 | C22 | semidirect |
| 161. C5 | #12684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619197 | 2 |
| #10605010 | 2 |
| #10605007 | 2 |
| #12684 | 5 |