Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 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 | #10613740 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10602236 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10600166 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5×#1400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598097 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#4050 | — | 2 | 1 | no | — |
| 7 | C2×C5×M32 | C22 | 1 | 1 | yes | characteristic |
| 8 | #65404 | — | 2 | 1 | no | — |
| 9 | #65198 | — | 2 | 2 | no | — |
| 10 | #65197 | — | 2 | 2 | no | — |
| 11 | #65193 | — | 2 | 1 | no | — |
| 12 | #65193 | C22 | 1 | 2 | yes | — |
| 13 | C2×D80 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C5×M64 | C22 | 1 | 2 | yes | complemented |
| 15 | #64729 | — | 2 | 1 | no | — |
| 16 | #64725 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #64669 | — | 2 | 2 | no | — |
| 18 | D160 | — | 2 | 2 | no | — |
| 19 | #13667 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C2×#709 | — | 4 | 1 | no | — |
| 21 | C22×C5×C8 | D4 | 1 | 1 | yes | characteristic |
| 22 | #4076 | — | 4 | 1 | no | — |
| 23 | C2×Dic20 | — | 2 | 1 | no | — |
| 24 | #4050 | — | 2 | 2 | no | — |
| 25 | #4050 | — | 2 | 2 | no | — |
| 26 | #4050 | — | 4 | 1 | no | — |
| 27 | #4050 | — | 4 | 1 | no | — |
| 28 | C2×D40 | — | 2 | 1 | no | — |
| 29 | C2×D40 | — | 2 | 1 | no | — |
| 30 | C2×#677 | — | 4 | 1 | no | — |
| 31 | C5×M32 | — | 2 | 2 | no | — |
| 32 | C2×C5×C16 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C5×C16 | C23 | 1 | 1 | yes | characteristic |
| 34 | #3953 | — | 4 | 1 | no | — |
| 35 | #3950 | — | 2 | 1 | no | — |
| 36 | Dic40 | — | 2 | 1 | no | — |
| 37 | Dic40 | D4 | 1 | 2 | yes | complemented |
| 38 | #3932 | — | 2 | 2 | no | — |
| 39 | #3932 | — | 2 | 2 | no | — |
| 40 | D80 | — | 2 | 1 | no | — |
| 41 | D80 | — | 2 | 2 | no | — |
| 42 | D80 | D4 | 1 | 2 | yes | complemented |
| 43 | C5×C32 | — | 2 | 2 | no | — |
| 44 | #3414 | — | 5 | 1 | no | — |
| 45 | #2263 | — | 5 | 2 | no | — |
| 46 | #2218 | — | 5 | 1 | no | — |
| 47 | #1418 | — | 5 | 2 | no | — |
| 48 | #1400 | D5 | 1 | 1 | yes | characteristic, complemented |
| 49 | C22×C4×C5 | D8 | 1 | 1 | yes | characteristic |
| 50 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 51 | C2×C22⋊D5 | — | 8 | 1 | no | — |
| 52 | #709 | — | 4 | 2 | no | — |
| 53 | #709 | — | 4 | 2 | no | — |
| 54 | #709 | — | 8 | 1 | no | — |
| 55 | #709 | — | 8 | 1 | no | — |
| 56 | C2×D20 | — | 4 | 1 | no | — |
| 57 | C2×D20 | — | 4 | 1 | no | — |
| 58 | C2×C4×D5 | — | 8 | 1 | no | — |
| 59 | C2×Dic10 | — | 4 | 1 | no | — |
| 60 | C2×C5×C8 | — | 2 | 1 | no | — |
| 61 | C2×C5×C8 | — | 2 | 1 | no | — |
| 62 | C2×C5×C8 | D8 | 1 | 1 | yes | characteristic |
| 63 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 64 | #685 | — | 8 | 1 | no | — |
| 65 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 66 | Dic20 | — | 2 | 2 | no | — |
| 67 | Dic20 | — | 4 | 1 | no | — |
| 68 | D40 | — | 2 | 2 | no | — |
| 69 | D40 | — | 4 | 1 | no | — |
| 70 | D40 | — | 4 | 1 | no | — |
| 71 | D40 | — | 4 | 1 | no | — |
| 72 | #677 | — | 4 | 2 | no | — |
| 73 | #677 | — | 4 | 2 | no | — |
| 74 | C5×C16 | — | 2 | 1 | no | — |
| 75 | C5×C16 | C2×D4 | 1 | 2 | yes | — |
| 76 | C2×#135 | — | 10 | 1 | no | — |
| 77 | #510 | — | 10 | 2 | no | — |
| 78 | #509 | — | 10 | 2 | no | — |
| 79 | #508 | — | 5 | 2 | no | — |
| 80 | #508 | — | 10 | 1 | no | — |
| 81 | C2×D16 | — | 5 | 1 | no | — |
| 82 | C2×M32 | C2×D5 | 1 | 1 | yes | characteristic |
| 83 | #466 | — | 10 | 1 | no | — |
| 84 | SD64 | — | 10 | 2 | no | — |
| 85 | D32 | — | 10 | 2 | no | — |
| 86 | M64 | C2×D5 | 1 | 2 | yes | complemented |
| 87 | #367 | — | 5 | 1 | no | — |
| 88 | #357 | — | 10 | 1 | no | — |
| 89 | C23×C5 | D16 | 1 | 1 | yes | characteristic |
| 90 | C22×D5 | — | 8 | 1 | no | — |
| 91 | C22×D5 | — | 8 | 1 | no | — |
| 92 | C2×C4×C5 | — | 2 | 1 | no | — |
| 93 | C2×C4×C5 | — | 2 | 1 | no | — |
| 94 | C2×C4×C5 | D16 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 96 | C22⋊D5 | — | 8 | 2 | no | — |
| 97 | C22⋊D5 | — | 8 | 2 | no | — |
| 98 | C22⋊D5 | — | 16 | 2 | no | — |
| 99 | C2×Dic5 | — | 8 | 1 | no | — |
| 100 | C2×Dic5 | — | 8 | 1 | no | — |
| 101 | D20 | — | 4 | 2 | no | — |
| 102 | D20 | — | 8 | 1 | no | — |
| 103 | D20 | — | 8 | 1 | no | — |
| 104 | D20 | — | 8 | 1 | no | — |
| 105 | C4×D5 | — | 8 | 2 | no | — |
| 106 | C4×D5 | — | 8 | 2 | no | — |
| 107 | Dic10 | — | 4 | 2 | no | — |
| 108 | Dic10 | — | 8 | 1 | no | — |
| 109 | C5×C8 | — | 2 | 1 | no | — |
| 110 | C5×C8 | #120 | 1 | 1 | yes | characteristic |
| 111 | C5×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 112 | C2×#41 | — | 20 | 1 | no | — |
| 113 | #135 | — | 10 | 2 | no | — |
| 114 | #135 | — | 10 | 2 | no | — |
| 115 | #135 | — | 20 | 1 | no | — |
| 116 | #135 | — | 20 | 1 | no | — |
| 117 | C2×Q16 | — | 10 | 1 | no | — |
| 118 | C2×SD16 | — | 20 | 1 | no | — |
| 119 | C2×D8 | — | 10 | 1 | no | — |
| 120 | C2×D8 | — | 10 | 1 | no | — |
| 121 | C22×C8 | D20 | 1 | 1 | yes | characteristic |
| 122 | #121 | — | 20 | 1 | no | — |
| 123 | Q32 | — | 5 | 2 | no | — |
| 124 | Q32 | — | 10 | 1 | no | — |
| 125 | SD32 | — | 10 | 2 | no | — |
| 126 | SD32 | — | 10 | 2 | no | — |
| 127 | D16 | — | 5 | 2 | no | — |
| 128 | D16 | — | 10 | 1 | no | — |
| 129 | D16 | — | 10 | 2 | no | — |
| 130 | M32 | — | 2 | 2 | no | — |
| 131 | C2×C16 | D20 | 1 | 1 | yes | characteristic |
| 132 | C2×C16 | C22×D5 | 1 | 1 | yes | characteristic |
| 133 | #107 | — | 10 | 1 | no | — |
| 134 | #102 | — | 20 | 1 | no | — |
| 135 | C32 | — | 2 | 2 | no | — |
| 136 | C22×C5 | — | 2 | 1 | no | — |
| 137 | C22×C5 | — | 4 | 1 | no | — |
| 138 | C22×C5 | C2×D16 | 1 | 1 | yes | characteristic |
| 139 | C2×D5 | — | 8 | 2 | no | — |
| 140 | C2×D5 | — | 16 | 2 | no | — |
| 141 | C2×D5 | — | 16 | 1 | no | — |
| 142 | C2×D5 | — | 16 | 1 | no | — |
| 143 | C2×D5 | — | 16 | 1 | no | — |
| 144 | C4×C5 | — | 2 | 1 | no | — |
| 145 | C4×C5 | #447 | 1 | 1 | yes | characteristic |
| 146 | C4×C5 | #509 | 1 | 1 | yes | characteristic |
| 147 | Dic5 | — | 8 | 2 | no | — |
| 148 | Dic5 | — | 16 | 1 | no | — |
| 149 | #41 | — | 20 | 2 | no | — |
| 150 | #41 | — | 20 | 2 | no | — |
| 151 | #41 | — | 40 | 1 | no | — |
| 152 | #41 | — | 40 | 1 | no | — |
| 153 | C2×Q8 | — | 20 | 1 | no | — |
| 154 | C2×D4 | — | 20 | 1 | no | — |
| 155 | C2×D4 | — | 20 | 1 | no | — |
| 156 | C2×D4 | — | 40 | 1 | no | — |
| 157 | C2×D4 | — | 40 | 1 | no | — |
| 158 | C22×C4 | — | 40 | 1 | no | — |
| 159 | C22×C4 | D40 | 1 | 1 | yes | characteristic |
| 160 | Q16 | — | 10 | 2 | no | — |
| 161 | Q16 | — | 20 | 1 | no | — |
| 162 | SD16 | — | 20 | 2 | no | — |
| 163 | SD16 | — | 20 | 2 | no | — |
| 164 | D8 | — | 10 | 2 | no | — |
| 165 | D8 | — | 20 | 1 | no | — |
| 166 | D8 | — | 20 | 1 | no | — |
| 167 | D8 | — | 20 | 1 | no | — |
| 168 | C2×C8 | — | 2 | 1 | no | — |
| 169 | C2×C8 | — | 2 | 1 | no | — |
| 170 | C2×C8 | D40 | 1 | 1 | yes | characteristic |
| 171 | C2×C8 | C2×D20 | 1 | 1 | yes | characteristic |
| 172 | C4⋊C4 | — | 20 | 1 | no | — |
| 173 | C22⋊C4 | — | 40 | 1 | no | — |
| 174 | C16 | — | 2 | 1 | no | — |
| 175 | C16 | D4×D5 | 1 | 2 | yes | — |
| 176 | C2×C5 | — | 2 | 1 | no | — |
| 177 | C2×C5 | — | 4 | 1 | no | — |
| 178 | C2×C5 | #2184 | 1 | 1 | yes | characteristic |
| 179 | D5 | — | 16 | 2 | no | — |
| 180 | D5 | — | 32 | 1 | no | — |
| 181 | C23 | — | 40 | 1 | no | — |
| 182 | C23 | — | 40 | 1 | no | — |
| 183 | C23 | D80 | 1 | 1 | yes | characteristic |
| 184 | Q8 | — | 20 | 2 | no | — |
| 185 | Q8 | — | 40 | 1 | no | — |
| 186 | D4 | — | 20 | 2 | no | — |
| 187 | D4 | — | 40 | 1 | no | — |
| 188 | D4 | — | 40 | 2 | no | — |
| 189 | D4 | — | 40 | 2 | no | — |
| 190 | D4 | — | 40 | 1 | no | — |
| 191 | D4 | — | 40 | 1 | no | — |
| 192 | D4 | — | 80 | 2 | no | — |
| 193 | C2×C4 | — | 2 | 1 | no | — |
| 194 | C2×C4 | — | 2 | 1 | no | — |
| 195 | C2×C4 | — | 40 | 2 | no | — |
| 196 | C2×C4 | — | 40 | 1 | no | — |
| 197 | C2×C4 | — | 40 | 2 | no | — |
| 198 | C2×C4 | — | 40 | 1 | no | — |
| 199 | C2×C4 | D80 | 1 | 1 | yes | characteristic |
| 200 | C2×C4 | C2×D40 | 1 | 1 | yes | characteristic |
| 201 | C8 | — | 2 | 1 | no | — |
| 202 | C8 | #4028 | 1 | 1 | yes | characteristic |
| 203 | C8 | #4054 | 1 | 1 | yes | characteristic |
| 204 | C5 | #13667 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 205 | C22 | — | 2 | 1 | no | — |
| 206 | C22 | — | 4 | 1 | no | — |
| 207 | C22 | — | 40 | 2 | no | — |
| 208 | C22 | — | 80 | 1 | no | — |
| 209 | C22 | — | 80 | 1 | no | — |
| 210 | C22 | — | 80 | 2 | no | — |
| 211 | C22 | — | 80 | 1 | no | — |
| 212 | C22 | C2×D80 | 1 | 1 | yes | characteristic |
| 213 | C4 | — | 2 | 1 | no | — |
| 214 | C4 | — | 40 | 2 | no | — |
| 215 | C4 | — | 80 | 1 | no | — |
| 216 | C4 | #65021 | 1 | 1 | yes | characteristic |
| 217 | C4 | #65197 | 1 | 1 | yes | characteristic |
| 218 | C2 | — | 2 | 1 | no | — |
| 219 | C2 | — | 4 | 1 | no | — |
| 220 | C2 | — | 80 | 2 | no | — |
| 221 | C2 | — | 160 | 1 | no | — |
| 222 | C2 | #10599901 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10613740 | C2 | semidirect |
| 2. #10602236 | C2 | semidirect |
| 3. #10600166 | C2 | semidirect |
| 4. C5×#1400 | C2 | semidirect |
| 5. #10598097 | C2 | semidirect |
| 13. C2×D80 | C22 | semidirect |
| 14. C5×M64 | C22 | semidirect |
| 16. #64725 | C22 | semidirect |
| 37. Dic40 | D4 | semidirect |
| 42. D80 | D4 | semidirect |
| 48. #1400 | D5 | semidirect |
| 86. M64 | C2×D5 | semidirect |
| 204. C5 | #13667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613740 | 2 |
| #10602236 | 2 |
| #10600166 | 2 |
| C5×#1400 | 2 |
| #10598097 | 2 |
| #13667 | 5 |