← C3×C4×C92×C25 #72201571
Subgroups — C3×C4×C92×C25 #72201571
Order 24300.
1134 conjugacy classes of subgroups.
The subgroup lattice has 108 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C3×C92×C25 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C32×C4×C9×C25 | C3 | 1 | 4 | yes | maximal |
| 3 | C4×C92×C25 | C3 | 1 | 9 | yes | maximal, direct product factor |
| 4 | C3×C92×C25 | C4 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 5 | C3×C4×C5×C92 | C5 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×C32×C9×C25 | C2×C3 | 1 | 4 | yes | — |
| 7 | C2×C92×C25 | C2×C3 | 1 | 9 | yes | — |
| 8 | C33×C4×C25 | C32 | 1 | 1 | yes | characteristic |
| 9 | C3×C4×C9×C25 | C9 | 1 | 36 | yes | direct product factor |
| 10 | C3×C4×C9×C25 | C32 | 1 | 12 | yes | — |
| 11 | C2×C3×C5×C92 | C2×C5 | 1 | 1 | yes | characteristic |
| 12 | C32×C9×C25 | C3×C4 | 1 | 4 | yes | — |
| 13 | C92×C25 | C3×C4 | 1 | 9 | yes | direct product factor |
| 14 | C32×C4×C5×C9 | C3×C5 | 1 | 4 | yes | — |
| 15 | C4×C5×C92 | C3×C5 | 1 | 9 | yes | — |
| 16 | C2×C33×C25 | C2×C32 | 1 | 1 | yes | characteristic |
| 17 | C2×C3×C9×C25 | C2×C9 | 1 | 36 | yes | — |
| 18 | C2×C3×C9×C25 | C2×C32 | 1 | 12 | yes | — |
| 19 | C3×C5×C92 | C4×C5 | 1 | 1 | yes | characteristic |
| 20 | C3×C4×C92 | C25 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 21 | C32×C4×C25 | C3×C9 | 1 | 12 | yes | — |
| 22 | C32×C4×C25 | C33 | 1 | 1 | yes | characteristic |
| 23 | C4×C9×C25 | C3×C9 | 1 | 36 | yes | direct product factor |
| 24 | C2×C32×C5×C9 | C2×C3×C5 | 1 | 4 | yes | — |
| 25 | C2×C5×C92 | C2×C3×C5 | 1 | 9 | yes | — |
| 26 | C33×C25 | C32×C4 | 1 | 1 | yes | characteristic |
| 27 | C3×C9×C25 | C4×C9 | 1 | 36 | yes | direct product factor |
| 28 | C3×C9×C25 | C32×C4 | 1 | 12 | yes | — |
| 29 | C33×C4×C5 | C32×C5 | 1 | 1 | yes | characteristic |
| 30 | C3×C4×C5×C9 | C5×C9 | 1 | 36 | yes | — |
| 31 | C3×C4×C5×C9 | C32×C5 | 1 | 12 | yes | — |
| 32 | C2×C3×C92 | C2×C25 | 1 | 1 | yes | characteristic |
| 33 | C2×C32×C25 | C2×C3×C9 | 1 | 12 | yes | — |
| 34 | C2×C32×C25 | C2×C33 | 1 | 1 | yes | characteristic |
| 35 | C2×C9×C25 | C2×C3×C9 | 1 | 36 | yes | — |
| 36 | C32×C5×C9 | C3×C4×C5 | 1 | 4 | yes | — |
| 37 | C5×C92 | C3×C4×C5 | 1 | 9 | yes | — |
| 38 | C32×C4×C9 | C3×C25 | 1 | 4 | yes | — |
| 39 | C4×C92 | C3×C25 | 1 | 9 | yes | direct product factor |
| 40 | C3×C4×C25 | C92 | 1 | 9 | yes | direct product factor |
| 41 | C3×C4×C25 | C32×C9 | 1 | 4 | yes | — |
| 42 | C2×C33×C5 | C2×C32×C5 | 1 | 1 | yes | characteristic |
| 43 | C2×C3×C5×C9 | C2×C5×C9 | 1 | 36 | yes | — |
| 44 | C2×C3×C5×C9 | C2×C32×C5 | 1 | 12 | yes | — |
| 45 | C3×C92 | C4×C25 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 46 | C32×C25 | C3×C4×C9 | 1 | 12 | yes | — |
| 47 | C32×C25 | C33×C4 | 1 | 1 | yes | characteristic |
| 48 | C9×C25 | C3×C4×C9 | 1 | 36 | yes | direct product factor |
| 49 | C32×C4×C5 | C3×C5×C9 | 1 | 12 | yes | — |
| 50 | C32×C4×C5 | C33×C5 | 1 | 1 | yes | characteristic |
| 51 | C4×C5×C9 | C3×C5×C9 | 1 | 36 | yes | — |
| 52 | C2×C32×C9 | C2×C3×C25 | 1 | 4 | yes | — |
| 53 | C2×C92 | C2×C3×C25 | 1 | 9 | yes | — |
| 54 | C2×C3×C25 | C2×C92 | 1 | 9 | yes | — |
| 55 | C2×C3×C25 | C2×C32×C9 | 1 | 4 | yes | — |
| 56 | C33×C5 | C32×C4×C5 | 1 | 1 | yes | characteristic |
| 57 | C3×C5×C9 | C4×C5×C9 | 1 | 36 | yes | — |
| 58 | C3×C5×C9 | C32×C4×C5 | 1 | 12 | yes | — |
| 59 | C33×C4 | C32×C25 | 1 | 1 | yes | characteristic |
| 60 | C3×C4×C9 | C9×C25 | 1 | 36 | yes | direct product factor |
| 61 | C3×C4×C9 | C32×C25 | 1 | 12 | yes | — |
| 62 | C4×C25 | C3×C92 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 63 | C2×C32×C5 | C2×C3×C5×C9 | 1 | 12 | yes | — |
| 64 | C2×C32×C5 | C2×C33×C5 | 1 | 1 | yes | characteristic |
| 65 | C2×C5×C9 | C2×C3×C5×C9 | 1 | 36 | yes | — |
| 66 | C32×C9 | C3×C4×C25 | 1 | 4 | yes | — |
| 67 | C92 | C3×C4×C25 | 1 | 9 | yes | direct product factor |
| 68 | C3×C25 | C4×C92 | 1 | 9 | yes | direct product factor |
| 69 | C3×C25 | C32×C4×C9 | 1 | 4 | yes | — |
| 70 | C3×C4×C5 | C5×C92 | 1 | 9 | yes | — |
| 71 | C3×C4×C5 | C32×C5×C9 | 1 | 4 | yes | — |
| 72 | C2×C33 | C2×C32×C25 | 1 | 1 | yes | characteristic |
| 73 | C2×C3×C9 | C2×C9×C25 | 1 | 36 | yes | — |
| 74 | C2×C3×C9 | C2×C32×C25 | 1 | 12 | yes | — |
| 75 | C2×C25 | C2×C3×C92 | 1 | 1 | yes | characteristic |
| 76 | C32×C5 | C3×C4×C5×C9 | 1 | 12 | yes | — |
| 77 | C32×C5 | C33×C4×C5 | 1 | 1 | yes | characteristic |
| 78 | C5×C9 | C3×C4×C5×C9 | 1 | 36 | yes | — |
| 79 | C32×C4 | C3×C9×C25 | 1 | 12 | yes | — |
| 80 | C32×C4 | C33×C25 | 1 | 1 | yes | characteristic |
| 81 | C4×C9 | C3×C9×C25 | 1 | 36 | yes | direct product factor |
| 82 | C2×C3×C5 | C2×C5×C92 | 1 | 9 | yes | — |
| 83 | C2×C3×C5 | C2×C32×C5×C9 | 1 | 4 | yes | — |
| 84 | C33 | C32×C4×C25 | 1 | 1 | yes | characteristic |
| 85 | C3×C9 | C4×C9×C25 | 1 | 36 | yes | direct product factor |
| 86 | C3×C9 | C32×C4×C25 | 1 | 12 | yes | — |
| 87 | C25 | C3×C4×C92 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 88 | C4×C5 | C3×C5×C92 | 1 | 1 | yes | characteristic |
| 89 | C2×C32 | C2×C3×C9×C25 | 1 | 12 | yes | — |
| 90 | C2×C32 | C2×C33×C25 | 1 | 1 | yes | characteristic |
| 91 | C2×C9 | C2×C3×C9×C25 | 1 | 36 | yes | — |
| 92 | C3×C5 | C4×C5×C92 | 1 | 9 | yes | — |
| 93 | C3×C5 | C32×C4×C5×C9 | 1 | 4 | yes | — |
| 94 | C3×C4 | C92×C25 | 1 | 9 | yes | direct product factor |
| 95 | C3×C4 | C32×C9×C25 | 1 | 4 | yes | — |
| 96 | C2×C5 | C2×C3×C5×C92 | 1 | 1 | yes | characteristic |
| 97 | C32 | C3×C4×C9×C25 | 1 | 12 | yes | — |
| 98 | C32 | C33×C4×C25 | 1 | 1 | yes | characteristic |
| 99 | C9 | C3×C4×C9×C25 | 1 | 36 | yes | direct product factor |
| 100 | C2×C3 | C2×C92×C25 | 1 | 9 | yes | — |
| 101 | C2×C3 | C2×C32×C9×C25 | 1 | 4 | yes | — |
| 102 | C5 | C3×C4×C5×C92 | 1 | 1 | yes | characteristic |
| 103 | C4 | C3×C92×C25 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 104 | C3 | C4×C92×C25 | 1 | 9 | yes | direct product factor |
| 105 | C3 | C32×C4×C9×C25 | 1 | 4 | yes | — |
| 106 | C2 | C2×C3×C92×C25 | 1 | 1 | yes | characteristic |
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