Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 67 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 | C5×#3291 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10602047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10601712 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10598278 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598257 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C5×#577 | — | 2 | 2 | no | — |
| 7 | C5×#492 | C22 | 1 | 1 | yes | characteristic |
| 8 | C5×#471 | — | 2 | 2 | no | — |
| 9 | C5×#456 | — | 2 | 1 | no | — |
| 10 | C5×#453 | — | 2 | 1 | no | — |
| 11 | C5×#443 | C22 | 1 | 2 | yes | — |
| 12 | #65368 | — | 2 | 1 | no | — |
| 13 | #65365 | — | 2 | 1 | no | — |
| 14 | #64969 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #64786 | — | 2 | 2 | no | — |
| 16 | #64714 | — | 2 | 2 | no | — |
| 17 | #64683 | C22 | 1 | 2 | yes | complemented |
| 18 | C8×#168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #12364 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C5×2−1+4 | — | 2 | 1 | no | — |
| 21 | C5×H(5,𝔽2) | — | 2 | 1 | no | — |
| 22 | C5×#137 | — | 2 | 2 | no | — |
| 23 | C5×#137 | — | 4 | 2 | no | — |
| 24 | C5×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 25 | C5×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 26 | C5×#135 | — | 4 | 2 | no | — |
| 27 | C5×#135 | D4 | 1 | 2 | yes | — |
| 28 | C2×C5×SD16 | — | 2 | 2 | no | — |
| 29 | C2×C5×SD16 | — | 4 | 2 | no | — |
| 30 | C5×#131 | — | 2 | 2 | no | — |
| 31 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 32 | C5×#127 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×#687 | — | 4 | 2 | no | — |
| 34 | #4015 | — | 2 | 1 | no | — |
| 35 | C5×#108 | D4 | 1 | 2 | yes | — |
| 36 | C5×#104 | — | 2 | 2 | no | — |
| 37 | C5×#101 | — | 2 | 1 | no | — |
| 38 | C5×#100 | — | 2 | 1 | no | — |
| 39 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 40 | #3949 | — | 2 | 2 | no | — |
| 41 | #3944 | — | 2 | 2 | no | — |
| 42 | #3940 | — | 4 | 2 | no | — |
| 43 | C4×#168 | — | 2 | 1 | no | — |
| 44 | #3291 | D5 | 1 | 1 | yes | characteristic |
| 45 | #2230 | — | 5 | 2 | no | — |
| 46 | #1705 | — | 5 | 1 | no | — |
| 47 | #1359 | — | 5 | 1 | no | — |
| 48 | #1335 | — | 5 | 2 | no | — |
| 49 | C5×#41 | — | 2 | 2 | no | — |
| 50 | C5×#41 | — | 4 | 2 | no | — |
| 51 | C5×#41 | — | 4 | 2 | no | — |
| 52 | C5×#41 | — | 8 | 1 | no | — |
| 53 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 54 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 55 | C2×C5×D4 | — | 2 | 1 | no | — |
| 56 | C2×C5×D4 | — | 4 | 1 | no | — |
| 57 | C2×C5×D4 | — | 4 | 2 | no | — |
| 58 | C2×C5×D4 | — | 8 | 1 | no | — |
| 59 | C2×Dic10 | — | 4 | 1 | no | — |
| 60 | C5×Q16 | — | 4 | 2 | no | — |
| 61 | C5×Q16 | SD16 | 1 | 2 | yes | complemented |
| 62 | C5×SD16 | — | 2 | 2 | no | — |
| 63 | C5×SD16 | — | 4 | 2 | no | — |
| 64 | C5×SD16 | — | 4 | 2 | no | — |
| 65 | C5×SD16 | — | 4 | 2 | no | — |
| 66 | C5×SD16 | — | 4 | 2 | no | — |
| 67 | C5×D8 | — | 4 | 2 | no | — |
| 68 | C5×D8 | SD16 | 1 | 2 | yes | complemented |
| 69 | C5×M16 | — | 2 | 2 | no | — |
| 70 | C5×M16 | — | 4 | 2 | no | — |
| 71 | C2×C5×C8 | — | 4 | 2 | no | — |
| 72 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 73 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 74 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | #687 | — | 8 | 4 | no | — |
| 76 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 77 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 78 | C2×#168 | — | 2 | 2 | no | — |
| 79 | #672 | — | 4 | 2 | no | — |
| 80 | #577 | — | 2 | 2 | no | — |
| 81 | #498 | — | 5 | 1 | no | — |
| 82 | #498 | — | 10 | 1 | no | — |
| 83 | #492 | — | 10 | 1 | no | — |
| 84 | #492 | C2×D5 | 1 | 1 | yes | characteristic |
| 85 | #471 | — | 2 | 2 | no | — |
| 86 | #456 | — | 2 | 1 | no | — |
| 87 | #453 | — | 2 | 1 | no | — |
| 88 | #443 | C2×D5 | 1 | 2 | yes | — |
| 89 | #365 | — | 10 | 2 | no | — |
| 90 | #364 | — | 5 | 2 | no | — |
| 91 | #360 | — | 10 | 2 | no | — |
| 92 | C82 | — | 5 | 1 | no | — |
| 93 | C23×C5 | — | 4 | 1 | no | — |
| 94 | C23×C5 | — | 8 | 1 | no | — |
| 95 | C5×Q8 | — | 2 | 2 | no | — |
| 96 | C5×Q8 | — | 4 | 2 | no | — |
| 97 | C5×Q8 | — | 8 | 1 | no | — |
| 98 | C5×D4 | — | 2 | 2 | no | — |
| 99 | C5×D4 | — | 4 | 2 | no | — |
| 100 | C5×D4 | — | 4 | 2 | no | — |
| 101 | C5×D4 | — | 8 | 2 | no | — |
| 102 | C5×D4 | — | 8 | 2 | no | — |
| 103 | C5×D4 | — | 8 | 1 | no | — |
| 104 | C2×C4×C5 | — | 2 | 1 | no | — |
| 105 | C2×C4×C5 | — | 4 | 2 | no | — |
| 106 | C2×C4×C5 | — | 4 | 1 | no | — |
| 107 | C2×C4×C5 | — | 8 | 1 | no | — |
| 108 | C2×C4×C5 | — | 8 | 2 | no | — |
| 109 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 110 | C2×Dic5 | — | 8 | 1 | no | — |
| 111 | Dic10 | — | 8 | 2 | no | — |
| 112 | C5×C8 | — | 4 | 2 | no | — |
| 113 | C5×C8 | C2×SD16 | 1 | 2 | yes | — |
| 114 | C5×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 115 | #168 | — | 2 | 4 | no | — |
| 116 | 2−1+4 | — | 2 | 1 | no | — |
| 117 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 118 | #137 | — | 2 | 2 | no | — |
| 119 | #137 | — | 4 | 2 | no | — |
| 120 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 121 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 122 | #135 | — | 4 | 2 | no | — |
| 123 | #135 | C22⋊D5 | 1 | 2 | yes | — |
| 124 | C2×SD16 | — | 2 | 2 | no | — |
| 125 | C2×SD16 | — | 4 | 2 | no | — |
| 126 | C2×SD16 | — | 20 | 2 | no | — |
| 127 | #131 | — | 2 | 2 | no | — |
| 128 | C4⋊Q8 | — | 10 | 1 | no | — |
| 129 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 130 | #127 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 131 | M32 | — | 10 | 2 | no | — |
| 132 | #108 | C22⋊D5 | 1 | 2 | yes | — |
| 133 | #106 | — | 10 | 2 | no | — |
| 134 | #106 | — | 20 | 2 | no | — |
| 135 | #104 | — | 2 | 2 | no | — |
| 136 | #101 | — | 2 | 1 | no | — |
| 137 | #100 | — | 2 | 1 | no | — |
| 138 | C4×C8 | — | 10 | 1 | no | — |
| 139 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 140 | C22×C5 | — | 4 | 2 | no | — |
| 141 | C22×C5 | — | 8 | 1 | no | — |
| 142 | C22×C5 | — | 16 | 1 | no | — |
| 143 | C22×C5 | — | 32 | 1 | no | — |
| 144 | C22×C5 | #453 | 1 | 1 | yes | characteristic |
| 145 | C4×C5 | — | 2 | 2 | no | — |
| 146 | C4×C5 | — | 4 | 2 | no | — |
| 147 | C4×C5 | — | 8 | 1 | no | — |
| 148 | C4×C5 | #450 | 1 | 2 | yes | — |
| 149 | Dic5 | — | 16 | 1 | no | — |
| 150 | #41 | — | 2 | 2 | no | — |
| 151 | #41 | — | 4 | 2 | no | — |
| 152 | #41 | — | 4 | 2 | no | — |
| 153 | #41 | — | 8 | 1 | no | — |
| 154 | C2×Q8 | — | 2 | 1 | no | — |
| 155 | C2×Q8 | — | 4 | 2 | no | — |
| 156 | C2×Q8 | — | 20 | 1 | no | — |
| 157 | C2×D4 | — | 2 | 1 | no | — |
| 158 | C2×D4 | — | 4 | 1 | no | — |
| 159 | C2×D4 | — | 4 | 2 | no | — |
| 160 | C2×D4 | — | 8 | 1 | no | — |
| 161 | Q16 | — | 4 | 2 | no | — |
| 162 | Q16 | #687 | 1 | 2 | yes | complemented |
| 163 | SD16 | — | 2 | 2 | no | — |
| 164 | SD16 | — | 4 | 2 | no | — |
| 165 | SD16 | — | 4 | 2 | no | — |
| 166 | SD16 | — | 4 | 2 | no | — |
| 167 | SD16 | — | 4 | 2 | no | — |
| 168 | SD16 | — | 40 | 4 | no | — |
| 169 | D8 | — | 4 | 2 | no | — |
| 170 | D8 | #687 | 1 | 2 | yes | complemented |
| 171 | M16 | — | 2 | 2 | no | — |
| 172 | M16 | — | 4 | 2 | no | — |
| 173 | C2×C8 | — | 4 | 2 | no | — |
| 174 | C2×C8 | — | 10 | 2 | no | — |
| 175 | C2×C8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 176 | C4⋊C4 | — | 4 | 1 | no | — |
| 177 | C4⋊C4 | — | 20 | 1 | no | — |
| 178 | C4⋊C4 | — | 20 | 1 | no | — |
| 179 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 180 | C16 | — | 20 | 2 | no | — |
| 181 | C2×C5 | — | 2 | 1 | no | — |
| 182 | C2×C5 | — | 8 | 2 | no | — |
| 183 | C2×C5 | — | 16 | 1 | no | — |
| 184 | C2×C5 | #1629 | 1 | 1 | yes | characteristic |
| 185 | C23 | — | 4 | 1 | no | — |
| 186 | C23 | — | 8 | 1 | no | — |
| 187 | Q8 | — | 2 | 2 | no | — |
| 188 | Q8 | — | 4 | 2 | no | — |
| 189 | Q8 | — | 8 | 1 | no | — |
| 190 | Q8 | — | 40 | 2 | no | — |
| 191 | D4 | — | 2 | 2 | no | — |
| 192 | D4 | — | 4 | 2 | no | — |
| 193 | D4 | — | 4 | 2 | no | — |
| 194 | D4 | — | 8 | 2 | no | — |
| 195 | D4 | — | 8 | 2 | no | — |
| 196 | D4 | — | 8 | 1 | no | — |
| 197 | C2×C4 | — | 2 | 1 | no | — |
| 198 | C2×C4 | — | 4 | 2 | no | — |
| 199 | C2×C4 | — | 4 | 1 | no | — |
| 200 | C2×C4 | — | 8 | 1 | no | — |
| 201 | C2×C4 | — | 8 | 2 | no | — |
| 202 | C2×C4 | — | 40 | 1 | no | — |
| 203 | C2×C4 | #4099 | 1 | 1 | yes | characteristic |
| 204 | C8 | — | 4 | 2 | no | — |
| 205 | C8 | — | 10 | 4 | no | — |
| 206 | C8 | #4078 | 1 | 2 | yes | — |
| 207 | C8 | C2×#687 | 1 | 2 | yes | — |
| 208 | C5 | #12364 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 209 | C22 | — | 4 | 2 | no | — |
| 210 | C22 | — | 8 | 1 | no | — |
| 211 | C22 | — | 16 | 1 | no | — |
| 212 | C22 | — | 32 | 1 | no | — |
| 213 | C22 | #65530 | 1 | 1 | yes | characteristic |
| 214 | C4 | — | 2 | 2 | no | — |
| 215 | C4 | — | 4 | 2 | no | — |
| 216 | C4 | — | 8 | 1 | no | — |
| 217 | C4 | — | 80 | 1 | no | — |
| 218 | C4 | #65507 | 1 | 2 | yes | — |
| 219 | C2 | — | 2 | 1 | no | — |
| 220 | C2 | — | 8 | 2 | no | — |
| 221 | C2 | — | 16 | 1 | no | — |
| 222 | C2 | #10602700 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10602047 | C2 | semidirect |
| 3. #10601712 | C2 | semidirect |
| 4. #10598278 | C2 | semidirect |
| 5. #10598257 | C2 | semidirect |
| 14. #64969 | C22 | semidirect |
| 17. #64683 | C22 | semidirect |
| 18. C8×#168 | C22 | semidirect |
| 61. C5×Q16 | SD16 | semidirect |
| 68. C5×D8 | SD16 | semidirect |
| 162. Q16 | #687 | semidirect |
| 170. D8 | #687 | semidirect |
| 208. C5 | #12364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3291 | 2 |
| #10602047 | 2 |
| #10601712 | 2 |
| #10598278 | 2 |
| #10598257 | 2 |
| #12364 | 5 |