Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
656 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 98 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×#564 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10604591 | C2 | 1 | 3 | yes | maximal |
| 3 | D5⋊#330 | C2 | 1 | 3 | yes | maximal |
| 4 | C5×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 5 | D5×#125 | — | 2 | 6 | no | — |
| 6 | D5×#125 | C22 | 1 | 3 | yes | — |
| 7 | C5⋊#564 | — | 2 | 6 | no | — |
| 8 | C5⋊#564 | C4 | 1 | 3 | yes | complemented |
| 9 | #65688 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65676 | C22 | 1 | 3 | yes | — |
| 11 | #64874 | — | 2 | 6 | no | — |
| 12 | #64870 | — | 2 | 6 | no | — |
| 13 | #8509 | — | 5 | 1 | no | maximal, Sylow |
| 14 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 15 | C2×D5⋊C8 | — | 2 | 3 | no | — |
| 16 | C5×#125 | — | 2 | 6 | no | — |
| 17 | C5×#125 | C2×C4 | 1 | 3 | yes | — |
| 18 | D5×C4⋊C4 | — | 2 | 6 | no | — |
| 19 | D5×C4⋊C4 | — | 2 | 6 | no | — |
| 20 | D5×C4⋊C4 | D4 | 1 | 6 | yes | — |
| 21 | #4036 | — | 2 | 6 | no | — |
| 22 | #4036 | — | 2 | 6 | no | — |
| 23 | #4036 | D4 | 1 | 6 | yes | — |
| 24 | #4035 | — | 2 | 6 | no | — |
| 25 | #4035 | — | 2 | 6 | no | — |
| 26 | #4035 | — | 2 | 6 | no | — |
| 27 | #4035 | — | 2 | 6 | no | — |
| 28 | #4035 | — | 2 | 6 | no | — |
| 29 | C42×D5 | — | 2 | 2 | no | — |
| 30 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 31 | #4016 | — | 2 | 6 | no | — |
| 32 | #4016 | C2×C4 | 1 | 3 | yes | — |
| 33 | #4002 | — | 2 | 6 | no | — |
| 34 | C2×#564 | — | 5 | 1 | no | — |
| 35 | #1992 | — | 5 | 3 | no | — |
| 36 | C2×#330 | — | 5 | 3 | no | — |
| 37 | C22×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 38 | C2×C4×D5 | — | 2 | 6 | no | — |
| 39 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 40 | C2×#170 | — | 4 | 3 | no | — |
| 41 | C4⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 42 | D5⋊C8 | — | 2 | 6 | no | — |
| 43 | D5⋊C8 | — | 4 | 3 | no | — |
| 44 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 45 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 46 | C5×C4⋊C4 | C22⋊C4 | 1 | 6 | yes | — |
| 47 | C42×C5 | — | 2 | 2 | no | — |
| 48 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 49 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 50 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 51 | C4⋊Dic5 | C22⋊C4 | 1 | 6 | yes | — |
| 52 | #683 | — | 2 | 6 | no | — |
| 53 | #683 | — | 2 | 6 | no | — |
| 54 | #683 | — | 2 | 6 | no | — |
| 55 | #683 | — | 2 | 6 | no | — |
| 56 | #683 | — | 2 | 6 | no | — |
| 57 | C4×Dic5 | — | 2 | 6 | no | — |
| 58 | C4×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 59 | #564 | — | 5 | 3 | no | — |
| 60 | #564 | — | 10 | 6 | no | — |
| 61 | #564 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 62 | C2×#125 | — | 5 | 3 | no | — |
| 63 | C2×#125 | — | 10 | 6 | no | — |
| 64 | C2×#97 | — | 5 | 3 | no | — |
| 65 | #384 | — | 5 | 1 | no | — |
| 66 | #340 | — | 10 | 6 | no | — |
| 67 | #330 | — | 10 | 6 | no | — |
| 68 | C22×D5 | #120 | 1 | 1 | yes | characteristic |
| 69 | C2×AGL(1,𝔽5) | — | 8 | 3 | no | — |
| 70 | C2×C4×C5 | — | 2 | 6 | no | — |
| 71 | C2×C4×C5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 72 | C2×Dic5 | — | 2 | 6 | no | — |
| 73 | C2×Dic5 | #120 | 1 | 3 | yes | — |
| 74 | C4×D5 | — | 2 | 3 | no | — |
| 75 | C4×D5 | — | 2 | 3 | no | — |
| 76 | C4×D5 | — | 4 | 6 | no | — |
| 77 | C4×D5 | — | 4 | 6 | no | — |
| 78 | #170 | — | 4 | 6 | no | — |
| 79 | C22×C8 | — | 10 | 3 | no | — |
| 80 | #125 | — | 2 | 6 | no | — |
| 81 | #125 | — | 5 | 6 | no | — |
| 82 | #125 | — | 5 | 3 | no | — |
| 83 | #125 | — | 10 | 6 | no | — |
| 84 | #125 | — | 10 | 6 | no | — |
| 85 | #125 | — | 10 | 6 | no | — |
| 86 | #125 | — | 10 | 6 | no | — |
| 87 | #125 | — | 10 | 6 | no | — |
| 88 | #125 | — | 10 | 6 | no | — |
| 89 | #125 | — | 10 | 6 | no | — |
| 90 | #125 | — | 10 | 6 | no | — |
| 91 | #125 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 92 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 93 | C2×C4⋊C4 | — | 10 | 6 | no | — |
| 94 | C2×C4⋊C4 | — | 10 | 6 | no | — |
| 95 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 96 | C2×C42 | — | 5 | 1 | no | — |
| 97 | C2×C42 | — | 10 | 2 | no | — |
| 98 | #97 | — | 10 | 6 | no | — |
| 99 | C22×C5 | #379 | 1 | 1 | yes | characteristic |
| 100 | C2×D5 | #454 | 1 | 3 | yes | — |
| 101 | C2×D5 | #456 | 1 | 3 | yes | — |
| 102 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 103 | C4×C5 | — | 2 | 3 | no | — |
| 104 | C4×C5 | — | 4 | 6 | no | — |
| 105 | Dic5 | — | 2 | 3 | no | — |
| 106 | Dic5 | — | 4 | 6 | no | — |
| 107 | C22×C4 | — | 5 | 3 | no | — |
| 108 | C22×C4 | — | 10 | 6 | no | — |
| 109 | C22×C4 | — | 20 | 1 | no | — |
| 110 | C2×C8 | — | 10 | 6 | no | — |
| 111 | C2×C8 | — | 20 | 3 | no | — |
| 112 | C2×C8 | — | 20 | 3 | no | — |
| 113 | C4⋊C4 | — | 2 | 6 | no | — |
| 114 | C4⋊C4 | — | 2 | 6 | no | — |
| 115 | C4⋊C4 | — | 5 | 6 | no | — |
| 116 | C4⋊C4 | — | 10 | 6 | no | — |
| 117 | C4⋊C4 | — | 10 | 6 | no | — |
| 118 | C4⋊C4 | — | 10 | 6 | no | — |
| 119 | C4⋊C4 | — | 10 | 6 | no | — |
| 120 | C4⋊C4 | — | 10 | 6 | no | — |
| 121 | C4⋊C4 | — | 10 | 6 | no | — |
| 122 | C4⋊C4 | — | 10 | 6 | no | — |
| 123 | C4⋊C4 | — | 20 | 6 | no | — |
| 124 | C4⋊C4 | C22⋊AGL(1,𝔽5) | 1 | 6 | yes | — |
| 125 | C42 | — | 2 | 2 | no | — |
| 126 | C42 | — | 5 | 3 | no | — |
| 127 | C42 | — | 10 | 6 | no | — |
| 128 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 129 | C2×C5 | #1793 | 1 | 3 | yes | — |
| 130 | D5 | #1658 | 1 | 1 | yes | characteristic |
| 131 | D5 | #1663 | 1 | 3 | yes | — |
| 132 | C23 | — | 5 | 1 | no | — |
| 133 | C2×C4 | — | 2 | 6 | no | — |
| 134 | C2×C4 | — | 5 | 3 | no | — |
| 135 | C2×C4 | — | 10 | 3 | no | — |
| 136 | C2×C4 | — | 10 | 3 | no | — |
| 137 | C2×C4 | — | 10 | 6 | no | — |
| 138 | C2×C4 | — | 20 | 6 | no | — |
| 139 | C2×C4 | — | 20 | 6 | no | — |
| 140 | C2×C4 | — | 40 | 3 | no | — |
| 141 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 142 | C8 | — | 20 | 6 | no | — |
| 143 | C5 | #8509 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 144 | C22 | — | 5 | 3 | no | — |
| 145 | C22 | — | 5 | 3 | no | — |
| 146 | C22 | #65800 | 1 | 1 | yes | characteristic |
| 147 | C4 | — | 2 | 3 | no | — |
| 148 | C4 | — | 4 | 6 | no | — |
| 149 | C4 | — | 10 | 3 | no | — |
| 150 | C4 | — | 20 | 6 | no | — |
| 151 | C4 | — | 80 | 1 | no | — |
| 152 | C2 | — | 5 | 1 | no | — |
| 153 | C2 | — | 5 | 3 | no | — |
| 154 | C2 | #10605019 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#564 | C4 | semidirect |
| 8. C5⋊#564 | C4 | semidirect |
| 61. #564 | AGL(1,𝔽5) | semidirect |
| 143. C5 | #8509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#564 | 2 |
| #10604591 | 2 |
| D5⋊#330 | 2 |
| #8509 | 5 |