Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
148 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 25 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 | #10602063 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#1410 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10598278 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #66047 | C4 | 1 | 1 | yes | characteristic |
| 5 | C5×#492 | C22 | 1 | 1 | yes | characteristic |
| 6 | #65380 | — | 2 | 1 | no | — |
| 7 | C5×#356 | — | 2 | 1 | no | — |
| 8 | #64764 | C4 | 1 | 1 | yes | characteristic |
| 9 | #64683 | — | 2 | 1 | no | — |
| 10 | #64676 | — | 2 | 1 | no | — |
| 11 | #7518 | — | 5 | 1 | no | maximal, Sylow |
| 12 | C2×C5×SD16 | — | 4 | 1 | no | — |
| 13 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 14 | C5×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 15 | #4082 | — | 4 | 1 | no | — |
| 16 | #4081 | — | 4 | 1 | no | — |
| 17 | D4×Dic5 | — | 4 | 1 | no | — |
| 18 | C4×Dic10 | — | 2 | 1 | no | — |
| 19 | C5×#101 | — | 4 | 1 | no | — |
| 20 | C4×C5×C8 | D4 | 1 | 1 | yes | characteristic |
| 21 | #3944 | — | 4 | 1 | no | — |
| 22 | #3942 | — | 4 | 1 | no | — |
| 23 | #3939 | — | 4 | 1 | no | — |
| 24 | C4⋊#168 | — | 2 | 1 | no | — |
| 25 | #1630 | — | 5 | 1 | no | — |
| 26 | #1410 | D5 | 1 | 1 | yes | characteristic |
| 27 | #1359 | — | 5 | 1 | no | — |
| 28 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 29 | C2×C5×D4 | — | 2 | 1 | no | — |
| 30 | C2×C5×D4 | — | 4 | 1 | no | — |
| 31 | C22×Dic5 | — | 4 | 1 | no | — |
| 32 | C2×Dic10 | — | 2 | 1 | no | — |
| 33 | C5×SD16 | — | 8 | 1 | no | — |
| 34 | C5×SD16 | — | 8 | 1 | no | — |
| 35 | C5×M16 | — | 8 | 1 | no | — |
| 36 | C2×C5×C8 | — | 2 | 1 | no | — |
| 37 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 38 | C42×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 39 | C22⋊Dic5 | — | 4 | 2 | no | — |
| 40 | C22⋊Dic5 | — | 4 | 1 | no | — |
| 41 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 42 | #683 | — | 4 | 1 | no | — |
| 43 | C4×Dic5 | — | 4 | 1 | no | — |
| 44 | C2×#168 | — | 4 | 1 | no | — |
| 45 | #672 | — | 8 | 1 | no | — |
| 46 | #559 | — | 5 | 1 | no | — |
| 47 | #492 | C2×D5 | 1 | 1 | yes | characteristic |
| 48 | #477 | — | 10 | 1 | no | — |
| 49 | #364 | — | 10 | 1 | no | — |
| 50 | #356 | — | 2 | 1 | no | — |
| 51 | #331 | — | 5 | 1 | no | — |
| 52 | Q8⋊C8 | — | 10 | 1 | no | — |
| 53 | C23×C5 | — | 4 | 1 | no | — |
| 54 | C5×Q8 | — | 8 | 1 | no | — |
| 55 | C5×D4 | — | 8 | 1 | no | — |
| 56 | C5×D4 | — | 8 | 1 | no | — |
| 57 | C5×D4 | — | 8 | 1 | no | — |
| 58 | C2×C4×C5 | — | 2 | 1 | no | — |
| 59 | C2×C4×C5 | — | 4 | 1 | no | — |
| 60 | C2×C4×C5 | #99 | 1 | 1 | yes | characteristic |
| 61 | C2×Dic5 | — | 4 | 1 | no | — |
| 62 | C2×Dic5 | — | 4 | 1 | no | — |
| 63 | C2×Dic5 | — | 16 | 1 | no | — |
| 64 | Dic10 | — | 4 | 1 | no | — |
| 65 | Dic10 | — | 4 | 1 | no | — |
| 66 | C5×C8 | — | 2 | 1 | no | — |
| 67 | C5×C8 | — | 2 | 1 | no | — |
| 68 | C5×C8 | — | 16 | 1 | no | — |
| 69 | #168 | — | 8 | 1 | no | — |
| 70 | C2×SD16 | — | 4 | 1 | no | — |
| 71 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 72 | #127 | C4×D5 | 1 | 1 | yes | characteristic |
| 73 | #124 | — | 20 | 1 | no | — |
| 74 | #123 | — | 20 | 1 | no | — |
| 75 | C4×Q8 | — | 10 | 1 | no | — |
| 76 | C4×D4 | — | 20 | 1 | no | — |
| 77 | M32 | — | 20 | 1 | no | — |
| 78 | #107 | — | 20 | 1 | no | — |
| 79 | C4⋊C8 | — | 10 | 1 | no | — |
| 80 | #103 | — | 20 | 1 | no | — |
| 81 | #101 | — | 4 | 1 | no | — |
| 82 | C4×C8 | D20 | 1 | 1 | yes | characteristic |
| 83 | C22×C5 | — | 8 | 2 | no | — |
| 84 | C22×C5 | — | 8 | 1 | no | — |
| 85 | C22×C5 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 86 | C4×C5 | — | 2 | 1 | no | — |
| 87 | C4×C5 | — | 2 | 1 | no | — |
| 88 | C4×C5 | — | 2 | 1 | no | — |
| 89 | C4×C5 | — | 8 | 1 | no | — |
| 90 | Dic5 | — | 8 | 1 | no | — |
| 91 | Dic5 | — | 8 | 1 | no | — |
| 92 | C2×Q8 | — | 2 | 1 | no | — |
| 93 | C2×Q8 | — | 10 | 1 | no | — |
| 94 | C2×D4 | — | 2 | 1 | no | — |
| 95 | C2×D4 | — | 4 | 1 | no | — |
| 96 | C22×C4 | — | 20 | 1 | no | — |
| 97 | SD16 | — | 8 | 1 | no | — |
| 98 | SD16 | — | 8 | 1 | no | — |
| 99 | M16 | — | 8 | 1 | no | — |
| 100 | C2×C8 | — | 2 | 1 | no | — |
| 101 | C2×C8 | — | 20 | 1 | no | — |
| 102 | C4⋊C4 | — | 4 | 1 | no | — |
| 103 | C4⋊C4 | — | 10 | 1 | no | — |
| 104 | C4⋊C4 | — | 20 | 1 | no | — |
| 105 | C22⋊C4 | — | 20 | 2 | no | — |
| 106 | C22⋊C4 | — | 20 | 1 | no | — |
| 107 | C42 | — | 20 | 1 | no | — |
| 108 | C42 | #685 | 1 | 1 | yes | characteristic |
| 109 | C16 | — | 40 | 1 | no | — |
| 110 | C2×C5 | — | 2 | 1 | no | — |
| 111 | C2×C5 | — | 16 | 1 | no | — |
| 112 | C2×C5 | #1402 | 1 | 1 | yes | characteristic |
| 113 | C23 | — | 4 | 1 | no | — |
| 114 | Q8 | — | 8 | 1 | no | — |
| 115 | Q8 | — | 20 | 1 | no | — |
| 116 | Q8 | — | 20 | 1 | no | — |
| 117 | D4 | — | 8 | 1 | no | — |
| 118 | D4 | — | 8 | 1 | no | — |
| 119 | D4 | — | 8 | 1 | no | — |
| 120 | C2×C4 | — | 2 | 1 | no | — |
| 121 | C2×C4 | — | 4 | 1 | no | — |
| 122 | C2×C4 | — | 20 | 1 | no | — |
| 123 | C2×C4 | — | 20 | 1 | no | — |
| 124 | C2×C4 | — | 80 | 1 | no | — |
| 125 | C2×C4 | #3938 | 1 | 1 | yes | characteristic |
| 126 | C8 | — | 2 | 1 | no | — |
| 127 | C8 | — | 2 | 1 | no | — |
| 128 | C8 | — | 16 | 1 | no | — |
| 129 | C8 | — | 40 | 1 | no | — |
| 130 | C5 | #7518 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 131 | C22 | — | 8 | 2 | no | — |
| 132 | C22 | — | 8 | 1 | no | — |
| 133 | C22 | #64691 | 1 | 1 | yes | characteristic |
| 134 | C4 | — | 2 | 1 | no | — |
| 135 | C4 | — | 2 | 1 | no | — |
| 136 | C4 | — | 2 | 1 | no | — |
| 137 | C4 | — | 8 | 1 | no | — |
| 138 | C4 | — | 40 | 1 | no | — |
| 139 | C4 | — | 40 | 1 | no | — |
| 140 | C2 | — | 2 | 1 | no | — |
| 141 | C2 | — | 16 | 1 | no | — |
| 142 | C2 | #10598029 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 130. C5 | #7518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602063 | 2 |
| C5×#1410 | 2 |
| #10598278 | 2 |
| #7518 | 5 |