Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #10613444 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10599944 | C2 | 1 | 2 | yes | maximal |
| 3 | C5×#1412 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10598275 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598030 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #66050 | C22 | 1 | 1 | yes | characteristic |
| 7 | #66022 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C5×#490 | C22 | 1 | 1 | yes | characteristic |
| 9 | #65360 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65358 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #65061 | — | 2 | 2 | no | — |
| 12 | #65054 | — | 2 | 2 | no | — |
| 13 | #65029 | — | 2 | 2 | no | — |
| 14 | D5×#97 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #64992 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | C5×#353 | C22 | 1 | 2 | yes | — |
| 17 | #64765 | C22 | 1 | 2 | yes | — |
| 18 | #64693 | — | 2 | 2 | no | — |
| 19 | #13594 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C2×#711 | D4 | 1 | 2 | yes | — |
| 21 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 22 | C5×#125 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | #4084 | — | 4 | 1 | no | — |
| 24 | #4082 | D4 | 1 | 2 | yes | — |
| 25 | D4×Dic5 | — | 4 | 1 | no | — |
| 26 | C2×C8×D5 | — | 2 | 1 | no | — |
| 27 | #4042 | — | 4 | 1 | no | — |
| 28 | #4038 | — | 2 | 1 | no | — |
| 29 | #4034 | — | 2 | 1 | no | — |
| 30 | #4033 | — | 4 | 1 | no | — |
| 31 | #4023 | — | 4 | 2 | no | — |
| 32 | C42×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | #4016 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | #4015 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C5×#102 | — | 2 | 2 | no | — |
| 36 | C5×#99 | — | 2 | 2 | no | — |
| 37 | C5×#97 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | #3966 | — | 2 | 2 | no | — |
| 39 | #3964 | — | 2 | 2 | no | — |
| 40 | #3948 | — | 2 | 2 | no | — |
| 41 | #3947 | — | 2 | 1 | no | — |
| 42 | #3942 | — | 2 | 2 | no | — |
| 43 | #3938 | — | 4 | 2 | no | — |
| 44 | #3935 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #3135 | — | 5 | 1 | no | — |
| 46 | #2126 | — | 5 | 2 | no | — |
| 47 | #1412 | — | 5 | 1 | no | — |
| 48 | #1412 | — | 5 | 2 | no | — |
| 49 | #1412 | D5 | 1 | 1 | yes | characteristic, complemented |
| 50 | C2×C5×D4 | — | 4 | 1 | no | — |
| 51 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 52 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 53 | C22×Dic5 | — | 2 | 2 | no | — |
| 54 | #711 | — | 4 | 2 | no | — |
| 55 | #711 | — | 4 | 2 | no | — |
| 56 | C2×C4×D5 | — | 2 | 1 | no | — |
| 57 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 58 | C2×Dic10 | — | 4 | 1 | no | — |
| 59 | C2×Dic10 | C22⋊C4 | 1 | 2 | yes | — |
| 60 | C2×C5×C8 | — | 2 | 1 | no | — |
| 61 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 62 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 63 | C5×C22⋊C4 | — | 4 | 2 | no | — |
| 64 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 65 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 66 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 67 | #685 | — | 4 | 1 | no | — |
| 68 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 69 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 70 | #683 | — | 4 | 1 | no | — |
| 71 | #683 | — | 4 | 1 | no | — |
| 72 | #683 | — | 8 | 2 | no | — |
| 73 | C4×Dic5 | — | 2 | 1 | no | — |
| 74 | C4×Dic5 | — | 4 | 1 | no | — |
| 75 | C4×Dic5 | — | 8 | 2 | no | — |
| 76 | C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 77 | C2×#168 | — | 2 | 1 | no | — |
| 78 | C8×D5 | — | 4 | 1 | no | — |
| 79 | C8×D5 | — | 4 | 1 | no | — |
| 80 | #533 | — | 5 | 1 | no | — |
| 81 | #532 | — | 5 | 1 | no | — |
| 82 | #491 | — | 5 | 1 | no | — |
| 83 | #491 | — | 5 | 1 | no | — |
| 84 | #490 | — | 5 | 1 | no | — |
| 85 | #490 | C2×D5 | 1 | 1 | yes | characteristic |
| 86 | #489 | — | 10 | 2 | no | — |
| 87 | #416 | — | 10 | 2 | no | — |
| 88 | #410 | — | 10 | 2 | no | — |
| 89 | C2×#97 | — | 5 | 1 | no | — |
| 90 | #354 | — | 10 | 2 | no | — |
| 91 | #353 | — | 5 | 2 | no | — |
| 92 | #353 | C2×D5 | 1 | 2 | yes | — |
| 93 | C23×C5 | — | 2 | 2 | no | — |
| 94 | C22×D5 | #99 | 1 | 1 | yes | characteristic |
| 95 | C5×D4 | — | 4 | 2 | no | — |
| 96 | C5×D4 | — | 8 | 2 | no | — |
| 97 | C2×C4×C5 | — | 2 | 1 | no | — |
| 98 | C2×C4×C5 | — | 4 | 1 | no | — |
| 99 | C2×C4×C5 | — | 8 | 2 | no | — |
| 100 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C22⋊D5 | — | 8 | 2 | no | — |
| 102 | C2×Dic5 | — | 2 | 1 | no | — |
| 103 | C2×Dic5 | — | 2 | 2 | no | — |
| 104 | C2×Dic5 | — | 4 | 2 | no | — |
| 105 | C2×Dic5 | — | 4 | 2 | no | — |
| 106 | C2×Dic5 | — | 4 | 1 | no | — |
| 107 | C2×Dic5 | — | 8 | 2 | no | — |
| 108 | C2×Dic5 | #99 | 1 | 1 | yes | characteristic |
| 109 | C4×D5 | — | 2 | 1 | no | — |
| 110 | C4×D5 | — | 2 | 1 | no | — |
| 111 | C4×D5 | — | 8 | 1 | no | — |
| 112 | Dic10 | — | 4 | 2 | no | — |
| 113 | Dic10 | — | 8 | 2 | no | — |
| 114 | C5×C8 | — | 4 | 1 | no | — |
| 115 | #168 | — | 4 | 1 | no | — |
| 116 | C2×#41 | — | 5 | 2 | no | — |
| 117 | C22×C8 | — | 10 | 1 | no | — |
| 118 | C4⋊Q8 | — | 5 | 1 | no | — |
| 119 | C4⋊Q8 | — | 10 | 1 | no | — |
| 120 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 121 | #125 | — | 5 | 1 | no | — |
| 122 | #125 | C4×D5 | 1 | 1 | yes | characteristic |
| 123 | #124 | — | 5 | 2 | no | — |
| 124 | C22⋊Q8 | — | 20 | 1 | no | — |
| 125 | #121 | — | 20 | 1 | no | — |
| 126 | C4×Q8 | — | 20 | 1 | no | — |
| 127 | C4×D4 | — | 20 | 1 | no | — |
| 128 | #117 | — | 10 | 1 | no | — |
| 129 | #117 | — | 20 | 2 | no | — |
| 130 | C2×C42 | — | 5 | 1 | no | — |
| 131 | #103 | — | 10 | 2 | no | — |
| 132 | #103 | — | 10 | 2 | no | — |
| 133 | #102 | — | 2 | 2 | no | — |
| 134 | #102 | — | 10 | 2 | no | — |
| 135 | #99 | — | 2 | 2 | no | — |
| 136 | #99 | — | 10 | 2 | no | — |
| 137 | #99 | — | 20 | 2 | no | — |
| 138 | #97 | — | 5 | 1 | no | — |
| 139 | #97 | — | 10 | 1 | no | — |
| 140 | #97 | C4×D5 | 1 | 1 | yes | characteristic |
| 141 | C22×C5 | — | 4 | 2 | no | — |
| 142 | C22×C5 | — | 8 | 2 | no | — |
| 143 | C22×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 144 | C2×D5 | — | 2 | 1 | no | — |
| 145 | C2×D5 | — | 4 | 1 | no | — |
| 146 | C4×C5 | — | 2 | 1 | no | — |
| 147 | C4×C5 | — | 4 | 1 | no | — |
| 148 | C4×C5 | — | 8 | 1 | no | — |
| 149 | C4×C5 | — | 16 | 2 | no | — |
| 150 | Dic5 | — | 4 | 1 | no | — |
| 151 | Dic5 | — | 4 | 2 | no | — |
| 152 | Dic5 | — | 8 | 1 | no | — |
| 153 | Dic5 | — | 16 | 2 | no | — |
| 154 | Dic5 | #354 | 1 | 1 | yes | characteristic |
| 155 | Dic5 | #354 | 1 | 1 | yes | characteristic |
| 156 | #41 | — | 20 | 2 | no | — |
| 157 | #41 | — | 20 | 2 | no | — |
| 158 | C2×Q8 | — | 5 | 2 | no | — |
| 159 | C2×Q8 | — | 20 | 1 | no | — |
| 160 | C2×D4 | — | 4 | 1 | no | — |
| 161 | C2×D4 | — | 10 | 2 | no | — |
| 162 | C2×D4 | D4×D5 | 1 | 2 | yes | — |
| 163 | C22×C4 | — | 5 | 1 | no | — |
| 164 | C22×C4 | — | 10 | 1 | no | — |
| 165 | C22×C4 | — | 10 | 2 | no | — |
| 166 | C2×C8 | — | 2 | 1 | no | — |
| 167 | C2×C8 | — | 10 | 1 | no | — |
| 168 | C2×C8 | — | 20 | 1 | no | — |
| 169 | C2×C8 | — | 20 | 1 | no | — |
| 170 | C4⋊C4 | — | 2 | 1 | no | — |
| 171 | C4⋊C4 | — | 4 | 1 | no | — |
| 172 | C4⋊C4 | — | 10 | 1 | no | — |
| 173 | C4⋊C4 | — | 20 | 1 | no | — |
| 174 | C4⋊C4 | — | 20 | 1 | no | — |
| 175 | C4⋊C4 | — | 20 | 1 | no | — |
| 176 | C4⋊C4 | — | 40 | 2 | no | — |
| 177 | C22⋊C4 | — | 4 | 2 | no | — |
| 178 | C22⋊C4 | — | 20 | 1 | no | — |
| 179 | C22⋊C4 | — | 20 | 2 | no | — |
| 180 | C22⋊C4 | — | 20 | 2 | no | — |
| 181 | C42 | — | 5 | 1 | no | — |
| 182 | C42 | — | 10 | 1 | no | — |
| 183 | C42 | — | 20 | 1 | no | — |
| 184 | C42 | — | 40 | 2 | no | — |
| 185 | C42 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 186 | C2×C5 | — | 2 | 1 | no | — |
| 187 | C2×C5 | — | 8 | 2 | no | — |
| 188 | C2×C5 | C2×#354 | 1 | 1 | yes | characteristic |
| 189 | D5 | — | 4 | 1 | no | — |
| 190 | C23 | — | 2 | 2 | no | — |
| 191 | C23 | — | 5 | 1 | no | — |
| 192 | Q8 | — | 20 | 2 | no | — |
| 193 | Q8 | — | 40 | 2 | no | — |
| 194 | D4 | — | 4 | 2 | no | — |
| 195 | D4 | — | 8 | 2 | no | — |
| 196 | D4 | — | 40 | 2 | no | — |
| 197 | C2×C4 | — | 2 | 1 | no | — |
| 198 | C2×C4 | — | 4 | 1 | no | — |
| 199 | C2×C4 | — | 5 | 1 | no | — |
| 200 | C2×C4 | — | 8 | 2 | no | — |
| 201 | C2×C4 | — | 10 | 1 | no | — |
| 202 | C2×C4 | — | 10 | 1 | no | — |
| 203 | C2×C4 | — | 10 | 1 | no | — |
| 204 | C2×C4 | — | 10 | 2 | no | — |
| 205 | C2×C4 | — | 20 | 2 | no | — |
| 206 | C2×C4 | — | 20 | 2 | no | — |
| 207 | C2×C4 | — | 20 | 1 | no | — |
| 208 | C2×C4 | — | 40 | 1 | no | — |
| 209 | C2×C4 | — | 40 | 2 | no | — |
| 210 | C2×C4 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 211 | C8 | — | 4 | 1 | no | — |
| 212 | C8 | — | 20 | 1 | no | — |
| 213 | C5 | #13594 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 214 | C22 | — | 4 | 2 | no | — |
| 215 | C22 | — | 8 | 2 | no | — |
| 216 | C22 | — | 10 | 1 | no | — |
| 217 | C22 | — | 20 | 1 | no | — |
| 218 | C22 | D5×#99 | 1 | 1 | yes | characteristic |
| 219 | C4 | — | 2 | 1 | no | — |
| 220 | C4 | — | 4 | 1 | no | — |
| 221 | C4 | — | 5 | 1 | no | — |
| 222 | C4 | — | 5 | 1 | no | — |
| 223 | C4 | — | 8 | 1 | no | — |
| 224 | C4 | — | 16 | 2 | no | — |
| 225 | C4 | — | 20 | 1 | no | — |
| 226 | C4 | — | 20 | 2 | no | — |
| 227 | C4 | — | 40 | 1 | no | — |
| 228 | C4 | — | 80 | 2 | no | — |
| 229 | C2 | — | 2 | 1 | no | — |
| 230 | C2 | — | 8 | 2 | no | — |
| 231 | C2 | — | 20 | 1 | no | — |
| 232 | C2 | D5×#354 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1412 | C2 | semidirect |
| 4. #10598275 | C2 | semidirect |
| 5. #10598030 | C2 | semidirect |
| 7. #66022 | C4 | semidirect |
| 10. #65358 | C4 | semidirect |
| 14. D5×#97 | C4 | semidirect |
| 15. #64992 | C4 | semidirect |
| 49. #1412 | D5 | semidirect |
| 213. C5 | #13594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613444 | 2 |
| #10599944 | 2 |
| C5×#1412 | 2 |
| #10598275 | 2 |
| #10598030 | 2 |
| #13594 | 5 |