← C5×C82×C81 #72203081
Subgroups — C5×C82×C81 #72203081
Order 25920.
370 conjugacy classes of subgroups.
The subgroup lattice has 100 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C4×C5×C8×C81 | C2 | 1 | 3 | yes | maximal |
| 2 | C5×C82×C27 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C42×C5×C81 | C22 | 1 | 1 | yes | characteristic |
| 4 | C2×C5×C8×C81 | C4 | 1 | 6 | yes | — |
| 5 | C82×C81 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C4×C5×C8×C27 | C2×C3 | 1 | 3 | yes | — |
| 7 | C2×C4×C5×C81 | C2×C4 | 1 | 3 | yes | — |
| 8 | C5×C8×C81 | C8 | 1 | 12 | yes | direct product factor |
| 9 | C5×C82×C9 | C9 | 1 | 1 | yes | characteristic |
| 10 | C4×C8×C81 | C2×C5 | 1 | 3 | yes | — |
| 11 | C42×C5×C27 | C22×C3 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×C8×C27 | C3×C4 | 1 | 6 | yes | — |
| 13 | C82×C27 | C3×C5 | 1 | 1 | yes | characteristic |
| 14 | C22×C5×C81 | C42 | 1 | 1 | yes | characteristic |
| 15 | C4×C5×C81 | C2×C8 | 1 | 6 | yes | — |
| 16 | C4×C5×C8×C9 | C2×C9 | 1 | 3 | yes | — |
| 17 | C2×C8×C81 | C4×C5 | 1 | 6 | yes | — |
| 18 | C42×C81 | C22×C5 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×C5×C27 | C2×C3×C4 | 1 | 3 | yes | — |
| 20 | C5×C8×C27 | C3×C8 | 1 | 12 | yes | — |
| 21 | C3×C5×C82 | C27 | 1 | 1 | yes | characteristic |
| 22 | C4×C8×C27 | C2×C3×C5 | 1 | 3 | yes | — |
| 23 | C2×C5×C81 | C4×C8 | 1 | 3 | yes | — |
| 24 | C2×C5×C8×C9 | C4×C9 | 1 | 6 | yes | — |
| 25 | C42×C5×C9 | C22×C9 | 1 | 1 | yes | characteristic |
| 26 | C2×C4×C81 | C2×C4×C5 | 1 | 3 | yes | — |
| 27 | C8×C81 | C5×C8 | 1 | 12 | yes | direct product factor |
| 28 | C82×C9 | C5×C9 | 1 | 1 | yes | characteristic |
| 29 | C22×C5×C27 | C3×C42 | 1 | 1 | yes | characteristic |
| 30 | C4×C5×C27 | C2×C3×C8 | 1 | 6 | yes | — |
| 31 | C3×C4×C5×C8 | C2×C27 | 1 | 3 | yes | — |
| 32 | C2×C8×C27 | C3×C4×C5 | 1 | 6 | yes | — |
| 33 | C42×C27 | C22×C3×C5 | 1 | 1 | yes | characteristic |
| 34 | C5×C81 | C82 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 35 | C2×C4×C5×C9 | C2×C4×C9 | 1 | 3 | yes | — |
| 36 | C5×C8×C9 | C8×C9 | 1 | 12 | yes | — |
| 37 | C22×C81 | C42×C5 | 1 | 1 | yes | characteristic |
| 38 | C4×C81 | C2×C5×C8 | 1 | 6 | yes | — |
| 39 | C5×C82 | C81 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 40 | C4×C8×C9 | C2×C5×C9 | 1 | 3 | yes | — |
| 41 | C2×C5×C27 | C3×C4×C8 | 1 | 3 | yes | — |
| 42 | C2×C3×C5×C8 | C4×C27 | 1 | 6 | yes | — |
| 43 | C3×C42×C5 | C22×C27 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×C27 | C2×C3×C4×C5 | 1 | 3 | yes | — |
| 45 | C8×C27 | C3×C5×C8 | 1 | 12 | yes | — |
| 46 | C3×C82 | C5×C27 | 1 | 1 | yes | characteristic |
| 47 | C22×C5×C9 | C42×C9 | 1 | 1 | yes | characteristic |
| 48 | C4×C5×C9 | C2×C8×C9 | 1 | 6 | yes | — |
| 49 | C2×C81 | C4×C5×C8 | 1 | 3 | yes | — |
| 50 | C4×C5×C8 | C2×C81 | 1 | 3 | yes | — |
| 51 | C2×C8×C9 | C4×C5×C9 | 1 | 6 | yes | — |
| 52 | C42×C9 | C22×C5×C9 | 1 | 1 | yes | characteristic |
| 53 | C5×C27 | C3×C82 | 1 | 1 | yes | characteristic |
| 54 | C2×C3×C4×C5 | C2×C4×C27 | 1 | 3 | yes | — |
| 55 | C3×C5×C8 | C8×C27 | 1 | 12 | yes | — |
| 56 | C22×C27 | C3×C42×C5 | 1 | 1 | yes | characteristic |
| 57 | C4×C27 | C2×C3×C5×C8 | 1 | 6 | yes | — |
| 58 | C3×C4×C8 | C2×C5×C27 | 1 | 3 | yes | — |
| 59 | C2×C5×C9 | C4×C8×C9 | 1 | 3 | yes | — |
| 60 | C81 | C5×C82 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 61 | C2×C5×C8 | C4×C81 | 1 | 6 | yes | — |
| 62 | C42×C5 | C22×C81 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×C9 | C2×C4×C5×C9 | 1 | 3 | yes | — |
| 64 | C8×C9 | C5×C8×C9 | 1 | 12 | yes | — |
| 65 | C82 | C5×C81 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 66 | C22×C3×C5 | C42×C27 | 1 | 1 | yes | characteristic |
| 67 | C3×C4×C5 | C2×C8×C27 | 1 | 6 | yes | — |
| 68 | C2×C27 | C3×C4×C5×C8 | 1 | 3 | yes | — |
| 69 | C2×C3×C8 | C4×C5×C27 | 1 | 6 | yes | — |
| 70 | C3×C42 | C22×C5×C27 | 1 | 1 | yes | characteristic |
| 71 | C5×C9 | C82×C9 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×C5 | C2×C4×C81 | 1 | 3 | yes | — |
| 73 | C5×C8 | C8×C81 | 1 | 12 | yes | direct product factor |
| 74 | C22×C9 | C42×C5×C9 | 1 | 1 | yes | characteristic |
| 75 | C4×C9 | C2×C5×C8×C9 | 1 | 6 | yes | — |
| 76 | C4×C8 | C2×C5×C81 | 1 | 3 | yes | — |
| 77 | C2×C3×C5 | C4×C8×C27 | 1 | 3 | yes | — |
| 78 | C27 | C3×C5×C82 | 1 | 1 | yes | characteristic |
| 79 | C2×C3×C4 | C2×C4×C5×C27 | 1 | 3 | yes | — |
| 80 | C3×C8 | C5×C8×C27 | 1 | 12 | yes | — |
| 81 | C22×C5 | C42×C81 | 1 | 1 | yes | characteristic |
| 82 | C4×C5 | C2×C8×C81 | 1 | 6 | yes | — |
| 83 | C2×C9 | C4×C5×C8×C9 | 1 | 3 | yes | — |
| 84 | C2×C8 | C4×C5×C81 | 1 | 6 | yes | — |
| 85 | C42 | C22×C5×C81 | 1 | 1 | yes | characteristic |
| 86 | C3×C5 | C82×C27 | 1 | 1 | yes | characteristic |
| 87 | C22×C3 | C42×C5×C27 | 1 | 1 | yes | characteristic |
| 88 | C3×C4 | C2×C5×C8×C27 | 1 | 6 | yes | — |
| 89 | C2×C5 | C4×C8×C81 | 1 | 3 | yes | — |
| 90 | C9 | C5×C82×C9 | 1 | 1 | yes | characteristic |
| 91 | C2×C4 | C2×C4×C5×C81 | 1 | 3 | yes | — |
| 92 | C8 | C5×C8×C81 | 1 | 12 | yes | direct product factor |
| 93 | C2×C3 | C4×C5×C8×C27 | 1 | 3 | yes | — |
| 94 | C5 | C82×C81 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 95 | C22 | C42×C5×C81 | 1 | 1 | yes | characteristic |
| 96 | C4 | C2×C5×C8×C81 | 1 | 6 | yes | — |
| 97 | C3 | C5×C82×C27 | 1 | 1 | yes | characteristic |
| 98 | C2 | C4×C5×C8×C81 | 1 | 3 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta