Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 61 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 | D5×#490 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D5×#353 | 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 | D5×#127 | C22 | 1 | 1 | yes | characteristic |
| 7 | D5×#125 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C5×#490 | C22 | 1 | 1 | yes | characteristic |
| 9 | #65360 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65356 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | D5×#102 | — | 2 | 2 | no | — |
| 12 | #65053 | — | 2 | 2 | no | — |
| 13 | D5×#99 | — | 2 | 2 | no | — |
| 14 | #65002 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | D5×#97 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | C5×#353 | C22 | 1 | 2 | yes | — |
| 17 | #64765 | C22 | 1 | 2 | yes | — |
| 18 | #64694 | — | 2 | 2 | no | — |
| 19 | C2×#1412 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C2×D4×D5 | — | 4 | 1 | no | — |
| 21 | C2×D4×D5 | D4 | 1 | 2 | yes | — |
| 22 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 23 | C5×#125 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #4086 | — | 4 | 1 | no | — |
| 25 | #4086 | D4 | 1 | 2 | yes | — |
| 26 | C2×C8×D5 | — | 2 | 1 | no | — |
| 27 | D5×C4⋊C4 | — | 2 | 1 | no | — |
| 28 | D5×C4⋊C4 | — | 4 | 1 | no | — |
| 29 | #4036 | — | 2 | 1 | no | — |
| 30 | #4035 | — | 4 | 1 | no | — |
| 31 | D5×C22⋊C4 | — | 4 | 2 | no | — |
| 32 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C42×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | #4016 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C5×#102 | — | 2 | 2 | no | — |
| 36 | C5×#99 | — | 2 | 2 | no | — |
| 37 | C5×#97 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | #3966 | — | 2 | 2 | no | — |
| 39 | #3964 | — | 2 | 2 | no | — |
| 40 | #3953 | — | 2 | 2 | no | — |
| 41 | #3947 | — | 2 | 1 | no | — |
| 42 | #3941 | — | 2 | 2 | no | — |
| 43 | #3938 | — | 4 | 2 | no | — |
| 44 | #3935 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×#490 | — | 5 | 1 | no | — |
| 46 | C2×#353 | — | 5 | 2 | no | — |
| 47 | #1412 | — | 5 | 1 | no | — |
| 48 | #1412 | — | 5 | 2 | no | — |
| 49 | #1412 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 50 | C23×D5 | — | 2 | 2 | no | — |
| 51 | C2×C5×D4 | — | 4 | 1 | no | — |
| 52 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 53 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 54 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 55 | D4×D5 | — | 4 | 2 | no | — |
| 56 | D4×D5 | — | 4 | 2 | no | — |
| 57 | D4×D5 | — | 8 | 4 | no | — |
| 58 | C2×D20 | — | 4 | 1 | no | — |
| 59 | C2×D20 | C22⋊C4 | 1 | 2 | yes | — |
| 60 | C2×C4×D5 | — | 2 | 1 | no | — |
| 61 | C2×C4×D5 | — | 4 | 1 | no | — |
| 62 | C2×C4×D5 | — | 8 | 2 | no | — |
| 63 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C2×C5×C8 | — | 2 | 1 | no | — |
| 65 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 66 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 67 | C5×C22⋊C4 | — | 4 | 2 | no | — |
| 68 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 69 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 70 | #685 | — | 8 | 2 | no | — |
| 71 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 72 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 73 | #683 | — | 4 | 1 | no | — |
| 74 | #683 | — | 4 | 1 | no | — |
| 75 | #683 | — | 4 | 1 | no | — |
| 76 | C4×Dic5 | — | 2 | 1 | no | — |
| 77 | C4×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 78 | C2×#168 | — | 2 | 1 | no | — |
| 79 | C8×D5 | — | 4 | 1 | no | — |
| 80 | C8×D5 | — | 4 | 1 | no | — |
| 81 | C2×#127 | — | 5 | 1 | no | — |
| 82 | C2×#125 | — | 5 | 1 | no | — |
| 83 | #490 | — | 5 | 1 | no | — |
| 84 | #490 | — | 5 | 1 | no | — |
| 85 | #490 | — | 5 | 1 | no | — |
| 86 | #490 | — | 10 | 2 | no | — |
| 87 | #490 | C2×D5 | 1 | 1 | yes | characteristic |
| 88 | C2×#102 | — | 10 | 2 | no | — |
| 89 | C2×#99 | — | 10 | 2 | no | — |
| 90 | C2×#97 | — | 5 | 1 | no | — |
| 91 | #353 | — | 5 | 2 | no | — |
| 92 | #353 | — | 10 | 2 | no | — |
| 93 | #353 | C2×D5 | 1 | 2 | yes | — |
| 94 | C23×C5 | — | 2 | 2 | no | — |
| 95 | C22×D5 | — | 2 | 2 | no | — |
| 96 | C22×D5 | — | 4 | 2 | no | — |
| 97 | C22×D5 | — | 4 | 2 | no | — |
| 98 | C22×D5 | — | 8 | 4 | no | — |
| 99 | C22×D5 | #99 | 1 | 1 | yes | characteristic |
| 100 | C5×D4 | — | 4 | 2 | no | — |
| 101 | C5×D4 | — | 8 | 2 | no | — |
| 102 | C2×C4×C5 | — | 2 | 1 | no | — |
| 103 | C2×C4×C5 | — | 4 | 1 | no | — |
| 104 | C2×C4×C5 | — | 8 | 2 | no | — |
| 105 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 106 | C22⋊D5 | — | 8 | 2 | no | — |
| 107 | C22⋊D5 | — | 8 | 4 | no | — |
| 108 | C2×Dic5 | — | 2 | 1 | no | — |
| 109 | C2×Dic5 | — | 4 | 1 | no | — |
| 110 | C2×Dic5 | — | 8 | 2 | no | — |
| 111 | C2×Dic5 | #99 | 1 | 1 | yes | characteristic |
| 112 | D20 | — | 4 | 2 | no | — |
| 113 | D20 | — | 8 | 2 | no | — |
| 114 | C4×D5 | — | 2 | 1 | no | — |
| 115 | C4×D5 | — | 2 | 1 | no | — |
| 116 | C4×D5 | — | 4 | 2 | no | — |
| 117 | C4×D5 | — | 8 | 2 | no | — |
| 118 | C4×D5 | — | 16 | 4 | no | — |
| 119 | C5×C8 | — | 4 | 1 | no | — |
| 120 | #168 | — | 4 | 1 | no | — |
| 121 | C22×D4 | — | 5 | 2 | no | — |
| 122 | C22×D4 | — | 20 | 1 | no | — |
| 123 | C22×C8 | — | 10 | 1 | no | — |
| 124 | #127 | — | 5 | 2 | no | — |
| 125 | #127 | — | 5 | 1 | no | — |
| 126 | #127 | — | 20 | 1 | no | — |
| 127 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 128 | #125 | — | 5 | 1 | no | — |
| 129 | #125 | — | 10 | 1 | no | — |
| 130 | #125 | — | 20 | 1 | no | — |
| 131 | #125 | C4×D5 | 1 | 1 | yes | characteristic, complemented |
| 132 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 133 | C2×C4⋊C4 | — | 20 | 1 | no | — |
| 134 | C2×C22⋊C4 | — | 20 | 2 | no | — |
| 135 | C2×C42 | — | 5 | 1 | no | — |
| 136 | #102 | — | 2 | 2 | no | — |
| 137 | #102 | — | 10 | 2 | no | — |
| 138 | #102 | — | 10 | 2 | no | — |
| 139 | #102 | — | 10 | 2 | no | — |
| 140 | #99 | — | 2 | 2 | no | — |
| 141 | #99 | — | 10 | 2 | no | — |
| 142 | #99 | — | 20 | 2 | no | — |
| 143 | #97 | — | 5 | 1 | no | — |
| 144 | #97 | — | 10 | 1 | no | — |
| 145 | #97 | C4×D5 | 1 | 1 | yes | characteristic, complemented |
| 146 | C22×C5 | — | 4 | 2 | no | — |
| 147 | C22×C5 | — | 8 | 2 | no | — |
| 148 | C22×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 149 | C2×D5 | — | 2 | 2 | no | — |
| 150 | C2×D5 | — | 4 | 2 | no | — |
| 151 | C2×D5 | — | 8 | 4 | no | — |
| 152 | C2×D5 | — | 8 | 2 | no | — |
| 153 | C2×D5 | — | 16 | 2 | no | — |
| 154 | C2×D5 | #354 | 1 | 1 | yes | characteristic |
| 155 | C2×D5 | #354 | 1 | 1 | yes | characteristic |
| 156 | C4×C5 | — | 2 | 1 | no | — |
| 157 | C4×C5 | — | 4 | 1 | no | — |
| 158 | C4×C5 | — | 8 | 1 | no | — |
| 159 | C4×C5 | — | 16 | 2 | no | — |
| 160 | Dic5 | — | 2 | 1 | no | — |
| 161 | Dic5 | — | 4 | 1 | no | — |
| 162 | Dic5 | — | 8 | 1 | no | — |
| 163 | Dic5 | — | 16 | 2 | no | — |
| 164 | C24 | — | 10 | 2 | no | — |
| 165 | C2×D4 | — | 4 | 1 | no | — |
| 166 | C2×D4 | — | 5 | 2 | no | — |
| 167 | C2×D4 | — | 10 | 2 | no | — |
| 168 | C2×D4 | — | 20 | 1 | no | — |
| 169 | C2×D4 | — | 20 | 2 | no | — |
| 170 | C2×D4 | — | 20 | 2 | no | — |
| 171 | C2×D4 | — | 20 | 2 | no | — |
| 172 | C2×D4 | — | 40 | 4 | no | — |
| 173 | C2×D4 | D4×D5 | 1 | 2 | yes | — |
| 174 | C22×C4 | — | 5 | 1 | no | — |
| 175 | C22×C4 | — | 10 | 1 | no | — |
| 176 | C22×C4 | — | 20 | 1 | no | — |
| 177 | C22×C4 | — | 40 | 2 | no | — |
| 178 | C2×C8 | — | 2 | 1 | no | — |
| 179 | C2×C8 | — | 10 | 1 | no | — |
| 180 | C2×C8 | — | 20 | 1 | no | — |
| 181 | C2×C8 | — | 20 | 1 | no | — |
| 182 | C4⋊C4 | — | 2 | 1 | no | — |
| 183 | C4⋊C4 | — | 4 | 1 | no | — |
| 184 | C4⋊C4 | — | 10 | 1 | no | — |
| 185 | C4⋊C4 | — | 20 | 1 | no | — |
| 186 | C4⋊C4 | — | 20 | 1 | no | — |
| 187 | C4⋊C4 | — | 20 | 1 | no | — |
| 188 | C4⋊C4 | — | 20 | 1 | no | — |
| 189 | C22⋊C4 | — | 4 | 2 | no | — |
| 190 | C22⋊C4 | — | 20 | 2 | no | — |
| 191 | C22⋊C4 | — | 40 | 2 | no | — |
| 192 | C42 | — | 5 | 1 | no | — |
| 193 | C42 | — | 10 | 1 | no | — |
| 194 | C42 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 195 | C2×C5 | — | 2 | 1 | no | — |
| 196 | C2×C5 | — | 8 | 2 | no | — |
| 197 | C2×C5 | C2×#354 | 1 | 1 | yes | characteristic |
| 198 | D5 | — | 2 | 1 | no | — |
| 199 | D5 | — | 8 | 2 | no | — |
| 200 | D5 | #1412 | 1 | 2 | yes | direct product factor |
| 201 | C23 | — | 2 | 2 | no | — |
| 202 | C23 | — | 5 | 1 | no | — |
| 203 | C23 | — | 10 | 2 | no | — |
| 204 | C23 | — | 20 | 2 | no | — |
| 205 | C23 | — | 20 | 2 | no | — |
| 206 | C23 | — | 40 | 4 | no | — |
| 207 | D4 | — | 4 | 2 | no | — |
| 208 | D4 | — | 8 | 2 | no | — |
| 209 | D4 | — | 20 | 2 | no | — |
| 210 | D4 | — | 40 | 2 | no | — |
| 211 | D4 | — | 40 | 2 | no | — |
| 212 | D4 | — | 40 | 4 | no | — |
| 213 | C2×C4 | — | 2 | 1 | no | — |
| 214 | C2×C4 | — | 4 | 1 | no | — |
| 215 | C2×C4 | — | 5 | 1 | no | — |
| 216 | C2×C4 | — | 8 | 2 | no | — |
| 217 | C2×C4 | — | 10 | 1 | no | — |
| 218 | C2×C4 | — | 10 | 1 | no | — |
| 219 | C2×C4 | — | 10 | 1 | no | — |
| 220 | C2×C4 | — | 20 | 2 | no | — |
| 221 | C2×C4 | — | 20 | 1 | no | — |
| 222 | C2×C4 | — | 40 | 2 | no | — |
| 223 | C2×C4 | — | 40 | 2 | no | — |
| 224 | C2×C4 | — | 80 | 4 | no | — |
| 225 | C2×C4 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 226 | C8 | — | 4 | 1 | no | — |
| 227 | C8 | — | 20 | 1 | no | — |
| 228 | C5 | C2×#1412 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | C22 | — | 4 | 2 | no | — |
| 230 | C22 | — | 5 | 1 | no | — |
| 231 | C22 | — | 5 | 1 | no | — |
| 232 | C22 | — | 8 | 2 | no | — |
| 233 | C22 | — | 10 | 2 | no | — |
| 234 | C22 | — | 20 | 2 | no | — |
| 235 | C22 | — | 40 | 2 | no | — |
| 236 | C22 | — | 40 | 4 | no | — |
| 237 | C22 | — | 80 | 2 | no | — |
| 238 | C22 | D5×#99 | 1 | 1 | yes | characteristic |
| 239 | C4 | — | 2 | 1 | no | — |
| 240 | C4 | — | 4 | 1 | no | — |
| 241 | C4 | — | 8 | 1 | no | — |
| 242 | C4 | — | 10 | 1 | no | — |
| 243 | C4 | — | 16 | 2 | no | — |
| 244 | C4 | — | 20 | 1 | no | — |
| 245 | C4 | — | 40 | 1 | no | — |
| 246 | C4 | — | 80 | 2 | no | — |
| 247 | C2 | — | 2 | 1 | no | — |
| 248 | C2 | — | 5 | 2 | no | — |
| 249 | C2 | — | 8 | 2 | no | — |
| 250 | C2 | — | 10 | 1 | no | — |
| 251 | C2 | — | 40 | 2 | no | — |
| 252 | 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. D5×#125 | C4 | semidirect |
| 10. #65356 | C4 | semidirect |
| 14. #65002 | C4 | semidirect |
| 15. D5×#97 | C4 | semidirect |
| 23. C5×#125 | C2×C4 | semidirect |
| 34. #4016 | C2×C4 | semidirect |
| 37. C5×#97 | C2×C4 | semidirect |
| 44. #3935 | C2×C4 | semidirect |
| 49. #1412 | D5 | direct (N × H) |
| 131. #125 | C4×D5 | semidirect |
| 145. #97 | C4×D5 | semidirect |
| 200. D5 | #1412 | direct (N × H) |
| 228. C5 | C2×#1412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#490 | 2 |
| D5×#353 | 2 |
| C5×#1412 | 2 |
| #10598275 | 2 |
| #10598030 | 2 |
| C2×#1412 | 5 |