Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 62 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 | #10613531 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10603834 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10598757 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10598756 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#4064 | — | 2 | 2 | no | — |
| 6 | #66059 | C4 | 1 | 1 | yes | characteristic |
| 7 | D5×C4⋊Q8 | C4 | 1 | 1 | yes | characteristic |
| 8 | C5×#494 | C4 | 1 | 1 | yes | characteristic |
| 9 | #65479 | — | 2 | 2 | no | — |
| 10 | #65381 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65374 | C22 | 1 | 1 | yes | characteristic |
| 12 | #64982 | C4 | 1 | 1 | yes | characteristic |
| 13 | C4×#676 | C22 | 1 | 1 | yes | characteristic |
| 14 | #64891 | — | 2 | 2 | no | — |
| 15 | #64890 | — | 2 | 2 | no | — |
| 16 | #64861 | C22 | 1 | 4 | yes | — |
| 17 | #11993 | — | 5 | 1 | no | maximal, Sylow |
| 18 | C2×#713 | — | 2 | 1 | no | — |
| 19 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 20 | C2×C5×Q16 | — | 2 | 2 | no | — |
| 21 | C5×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C5×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | #4093 | — | 2 | 1 | no | — |
| 24 | #4090 | — | 2 | 1 | no | — |
| 25 | C2×#689 | — | 2 | 2 | no | — |
| 26 | C2×#688 | — | 2 | 2 | no | — |
| 27 | #4064 | — | 4 | 8 | no | — |
| 28 | C2×#677 | — | 2 | 2 | no | — |
| 29 | C2×#676 | D4 | 1 | 2 | yes | — |
| 30 | #4041 | — | 4 | 1 | no | — |
| 31 | #4039 | — | 4 | 1 | no | — |
| 32 | D5×C4⋊C4 | — | 4 | 1 | no | — |
| 33 | #4034 | — | 4 | 1 | no | — |
| 34 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C42×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #4015 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | #3998 | — | 2 | 4 | no | — |
| 38 | C4×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #3947 | D4 | 1 | 2 | yes | — |
| 40 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 41 | #3152 | — | 5 | 1 | no | — |
| 42 | #2165 | — | 5 | 2 | no | — |
| 43 | #1359 | — | 5 | 2 | no | — |
| 44 | #1358 | — | 5 | 2 | no | — |
| 45 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 46 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 47 | #713 | — | 4 | 4 | no | — |
| 48 | Q8×D5 | — | 4 | 4 | no | — |
| 49 | C2×D20 | — | 2 | 1 | no | — |
| 50 | C2×D20 | — | 4 | 1 | no | — |
| 51 | C2×D20 | — | 4 | 1 | no | — |
| 52 | C2×C4×D5 | — | 2 | 1 | no | — |
| 53 | C2×C4×D5 | — | 4 | 1 | no | — |
| 54 | C2×C4×D5 | — | 4 | 1 | no | — |
| 55 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 56 | C2×Dic10 | — | 2 | 1 | no | — |
| 57 | C2×Dic10 | — | 4 | 1 | no | — |
| 58 | C5×Q16 | — | 4 | 4 | no | — |
| 59 | C2×C5×C8 | C22⋊C4 | 1 | 2 | yes | — |
| 60 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 61 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 62 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 63 | #689 | — | 4 | 4 | no | — |
| 64 | #688 | — | 4 | 4 | no | — |
| 65 | #685 | — | 4 | 2 | no | — |
| 66 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 67 | #683 | — | 4 | 2 | no | — |
| 68 | C4×Dic5 | — | 2 | 1 | no | — |
| 69 | C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 70 | C2×#168 | C2×D4 | 1 | 2 | yes | — |
| 71 | #677 | — | 4 | 4 | no | — |
| 72 | #676 | — | 2 | 4 | no | — |
| 73 | #674 | — | 4 | 4 | no | — |
| 74 | C2×#137 | — | 10 | 2 | no | — |
| 75 | #532 | — | 5 | 1 | no | — |
| 76 | C2×C4⋊Q8 | — | 5 | 1 | no | — |
| 77 | #497 | — | 10 | 2 | no | — |
| 78 | #494 | — | 5 | 1 | no | — |
| 79 | #494 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 80 | #492 | — | 5 | 1 | no | — |
| 81 | #492 | — | 5 | 1 | no | — |
| 82 | C4×M16 | — | 5 | 1 | no | — |
| 83 | #364 | — | 5 | 4 | no | — |
| 84 | #349 | — | 10 | 2 | no | — |
| 85 | #347 | — | 10 | 2 | no | — |
| 86 | C22×D5 | — | 4 | 1 | no | — |
| 87 | C22×D5 | #100 | 1 | 1 | yes | characteristic |
| 88 | C5×Q8 | — | 4 | 2 | no | — |
| 89 | C5×Q8 | — | 4 | 2 | no | — |
| 90 | C2×C4×C5 | — | 2 | 1 | no | — |
| 91 | C2×C4×C5 | — | 4 | 1 | no | — |
| 92 | C2×C4×C5 | — | 4 | 1 | no | — |
| 93 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic5 | — | 2 | 1 | no | — |
| 95 | C2×Dic5 | — | 4 | 1 | no | — |
| 96 | C2×Dic5 | #100 | 1 | 1 | yes | characteristic |
| 97 | D20 | — | 4 | 2 | no | — |
| 98 | D20 | — | 8 | 2 | no | — |
| 99 | D20 | — | 8 | 2 | no | — |
| 100 | C4×D5 | — | 2 | 2 | no | — |
| 101 | C4×D5 | — | 4 | 2 | no | — |
| 102 | C4×D5 | — | 8 | 2 | no | — |
| 103 | C4×D5 | — | 8 | 2 | no | — |
| 104 | Dic10 | — | 4 | 2 | no | — |
| 105 | Dic10 | — | 8 | 2 | no | — |
| 106 | C5×C8 | — | 2 | 2 | no | — |
| 107 | #168 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 108 | C2×#41 | — | 10 | 1 | no | — |
| 109 | C22×Q8 | — | 10 | 1 | no | — |
| 110 | #137 | — | 20 | 8 | no | — |
| 111 | C2×Q16 | — | 2 | 2 | no | — |
| 112 | C2×Q16 | — | 10 | 2 | no | — |
| 113 | C2×SD16 | — | 10 | 2 | no | — |
| 114 | C2×SD16 | — | 10 | 2 | no | — |
| 115 | C2×M16 | — | 5 | 2 | no | — |
| 116 | C4⋊Q8 | — | 5 | 1 | no | — |
| 117 | C4⋊Q8 | — | 10 | 1 | no | — |
| 118 | C4⋊Q8 | — | 20 | 1 | no | — |
| 119 | C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 120 | C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 121 | #127 | — | 5 | 1 | no | — |
| 122 | #124 | — | 10 | 1 | no | — |
| 123 | #121 | — | 20 | 1 | no | — |
| 124 | C4×D4 | — | 20 | 1 | no | — |
| 125 | C2×C4⋊C4 | — | 20 | 1 | no | — |
| 126 | C2×C42 | — | 5 | 1 | no | — |
| 127 | M32 | — | 10 | 4 | no | — |
| 128 | #97 | — | 5 | 2 | no | — |
| 129 | C4×C8 | — | 5 | 1 | no | — |
| 130 | C4×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 131 | C22×C5 | C2×#100 | 1 | 1 | yes | characteristic |
| 132 | C2×D5 | — | 2 | 1 | no | — |
| 133 | C2×D5 | — | 4 | 1 | no | — |
| 134 | C2×D5 | — | 8 | 2 | no | — |
| 135 | C2×D5 | — | 8 | 1 | no | — |
| 136 | C4×C5 | — | 2 | 2 | no | — |
| 137 | C4×C5 | — | 8 | 1 | no | — |
| 138 | C4×C5 | — | 8 | 1 | no | — |
| 139 | C4×C5 | #418 | 1 | 2 | yes | — |
| 140 | Dic5 | — | 2 | 1 | no | — |
| 141 | Dic5 | — | 4 | 1 | no | — |
| 142 | Dic5 | — | 8 | 1 | no | — |
| 143 | #41 | — | 20 | 4 | no | — |
| 144 | C2×Q8 | — | 2 | 1 | no | — |
| 145 | C2×Q8 | — | 2 | 1 | no | — |
| 146 | C2×Q8 | — | 10 | 1 | no | — |
| 147 | C2×Q8 | — | 20 | 1 | no | — |
| 148 | C2×Q8 | — | 20 | 4 | no | — |
| 149 | C2×D4 | — | 10 | 1 | no | — |
| 150 | C2×D4 | — | 20 | 1 | no | — |
| 151 | C2×D4 | — | 20 | 1 | no | — |
| 152 | C22×C4 | — | 5 | 1 | no | — |
| 153 | C22×C4 | — | 10 | 1 | no | — |
| 154 | C22×C4 | — | 20 | 1 | no | — |
| 155 | C22×C4 | — | 20 | 1 | no | — |
| 156 | Q16 | — | 4 | 4 | no | — |
| 157 | Q16 | — | 20 | 4 | no | — |
| 158 | SD16 | — | 20 | 4 | no | — |
| 159 | SD16 | — | 20 | 4 | no | — |
| 160 | M16 | — | 10 | 4 | no | — |
| 161 | C2×C8 | — | 5 | 2 | no | — |
| 162 | C2×C8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 163 | C4⋊C4 | — | 4 | 1 | no | — |
| 164 | C4⋊C4 | — | 4 | 1 | no | — |
| 165 | C4⋊C4 | — | 20 | 1 | no | — |
| 166 | C4⋊C4 | — | 20 | 2 | no | — |
| 167 | C22⋊C4 | — | 20 | 2 | no | — |
| 168 | C42 | — | 5 | 1 | no | — |
| 169 | C42 | — | 10 | 1 | no | — |
| 170 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 171 | C16 | — | 20 | 4 | no | — |
| 172 | C2×C5 | — | 2 | 1 | no | — |
| 173 | C2×C5 | #1555 | 1 | 1 | yes | characteristic |
| 174 | D5 | — | 4 | 1 | no | — |
| 175 | D5 | — | 16 | 1 | no | — |
| 176 | C23 | — | 5 | 1 | no | — |
| 177 | C23 | — | 20 | 1 | no | — |
| 178 | Q8 | — | 4 | 2 | no | — |
| 179 | Q8 | — | 4 | 2 | no | — |
| 180 | Q8 | — | 20 | 2 | no | — |
| 181 | Q8 | — | 40 | 2 | no | — |
| 182 | D4 | — | 20 | 2 | no | — |
| 183 | D4 | — | 40 | 2 | no | — |
| 184 | D4 | — | 40 | 2 | no | — |
| 185 | C2×C4 | — | 2 | 1 | no | — |
| 186 | C2×C4 | — | 4 | 1 | no | — |
| 187 | C2×C4 | — | 4 | 1 | no | — |
| 188 | C2×C4 | — | 5 | 1 | no | — |
| 189 | C2×C4 | — | 10 | 2 | no | — |
| 190 | C2×C4 | — | 10 | 1 | no | — |
| 191 | C2×C4 | — | 20 | 2 | no | — |
| 192 | C2×C4 | — | 20 | 1 | no | — |
| 193 | C2×C4 | — | 40 | 2 | no | — |
| 194 | C2×C4 | — | 40 | 2 | no | — |
| 195 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 196 | C8 | — | 2 | 2 | no | — |
| 197 | C8 | — | 5 | 4 | no | — |
| 198 | C5 | #11993 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 199 | C22 | — | 10 | 1 | no | — |
| 200 | C22 | — | 20 | 1 | no | — |
| 201 | C22 | — | 40 | 2 | no | — |
| 202 | C22 | — | 40 | 1 | no | — |
| 203 | C22 | D5⋊#100 | 1 | 1 | yes | characteristic |
| 204 | C4 | — | 2 | 2 | no | — |
| 205 | C4 | — | 8 | 1 | no | — |
| 206 | C4 | — | 8 | 1 | no | — |
| 207 | C4 | — | 10 | 1 | no | — |
| 208 | C4 | — | 20 | 1 | no | — |
| 209 | C4 | — | 40 | 1 | no | — |
| 210 | C4 | #65767 | 1 | 2 | yes | — |
| 211 | C2 | — | 2 | 1 | no | — |
| 212 | C2 | — | 20 | 1 | no | — |
| 213 | C2 | — | 80 | 1 | no | — |
| 214 | C2 | #10604610 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10603834 | C2 | semidirect |
| 3. #10598757 | C2 | semidirect |
| 4. #10598756 | C2 | semidirect |
| 198. C5 | #11993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613531 | 2 |
| #10603834 | 2 |
| #10598757 | 2 |
| #10598756 | 2 |
| #11993 | 5 |