← C3×#10600556 #14298840
Subgroups — C3×#10600556 #14298840
Order 1920.
432 conjugacy classes of subgroups.
The subgroup lattice has 148 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C3×C4×C5×C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#65225 | C2 | 1 | 2 | yes | maximal |
| 3 | C3×#64771 | C2 | 1 | 4 | yes | maximal |
| 4 | #10600556 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C22×C3×C5×C8 | C22 | 1 | 2 | yes | — |
| 6 | C2×C3×C42×C5 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C3×C4⋊Dic5 | C22 | 1 | 4 | yes | — |
| 8 | C3×C4×C5×C8 | C4 | 1 | 4 | yes | complemented |
| 9 | C3×#3963 | — | 2 | 4 | no | — |
| 10 | C3×#1835 | — | 5 | 1 | no | maximal, Hall |
| 11 | C2×C4×C5×C8 | C2×C3 | 1 | 1 | yes | characteristic |
| 12 | #65225 | C2×C3 | 1 | 2 | yes | — |
| 13 | #64771 | C2×C3 | 1 | 4 | yes | — |
| 14 | C22×C3×C4×C5 | D4 | 1 | 2 | yes | — |
| 15 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 16 | C22×C3×Dic5 | — | 2 | 4 | no | — |
| 17 | C2×C3×C5×C8 | — | 2 | 4 | no | — |
| 18 | C2×C3×C5×C8 | C2×C4 | 1 | 4 | yes | — |
| 19 | C3×C42×C5 | C2×C4 | 1 | 2 | yes | — |
| 20 | C3×C42×C5 | Q8 | 1 | 2 | yes | — |
| 21 | C3×C4⋊Dic5 | — | 2 | 8 | no | — |
| 22 | C2×C3×C4×C8 | D5 | 1 | 1 | yes | characteristic |
| 23 | C3×#382 | — | 5 | 2 | no | — |
| 24 | C3×#340 | — | 5 | 4 | no | — |
| 25 | C22×C5×C8 | C22×C3 | 1 | 2 | yes | — |
| 26 | C2×C42×C5 | C22×C3 | 1 | 1 | yes | characteristic |
| 27 | C2×C4⋊Dic5 | C22×C3 | 1 | 4 | yes | — |
| 28 | C4×C5×C8 | C3×C4 | 1 | 4 | yes | complemented |
| 29 | #3963 | — | 2 | 4 | no | — |
| 30 | #1835 | — | 5 | 1 | no | Sylow |
| 31 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 32 | C2×C3×C4×C5 | — | 2 | 4 | no | — |
| 33 | C2×C3×C4×C5 | C4⋊C4 | 1 | 4 | yes | — |
| 34 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×C4×C5 | C2×Q8 | 1 | 1 | yes | characteristic |
| 36 | C2×C3×C4×C5 | #41 | 1 | 4 | yes | — |
| 37 | C2×C3×Dic5 | — | 4 | 4 | no | — |
| 38 | C2×C3×Dic5 | — | 4 | 8 | no | — |
| 39 | C3×C5×C8 | — | 2 | 4 | no | — |
| 40 | C22×C3×C8 | C2×D5 | 1 | 2 | yes | — |
| 41 | C2×C3×C4⋊C4 | — | 5 | 4 | no | — |
| 42 | C2×C3×C42 | C2×D5 | 1 | 1 | yes | characteristic |
| 43 | C3×C4×C8 | Dic5 | 1 | 4 | yes | complemented |
| 44 | C3×#95 | — | 10 | 4 | no | — |
| 45 | C22×C4×C5 | C3×D4 | 1 | 2 | yes | — |
| 46 | C22×C4×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 47 | C22×Dic5 | — | 2 | 4 | no | — |
| 48 | C2×C5×C8 | — | 2 | 4 | no | — |
| 49 | C2×C5×C8 | C2×C3×C4 | 1 | 4 | yes | — |
| 50 | C42×C5 | C2×C3×C4 | 1 | 2 | yes | — |
| 51 | C42×C5 | C3×Q8 | 1 | 2 | yes | — |
| 52 | C4⋊Dic5 | — | 2 | 8 | no | — |
| 53 | C2×C4×C8 | C3×D5 | 1 | 1 | yes | characteristic |
| 54 | #382 | — | 5 | 2 | no | — |
| 55 | #340 | — | 5 | 4 | no | — |
| 56 | C22×C3×C5 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 57 | C22×C3×C5 | #124 | 1 | 2 | yes | — |
| 58 | C22×C3×C5 | #135 | 1 | 4 | yes | — |
| 59 | C3×C4×C5 | — | 2 | 4 | no | — |
| 60 | C3×C4×C5 | #117 | 1 | 2 | yes | — |
| 61 | C3×C4×C5 | #125 | 1 | 2 | yes | — |
| 62 | C3×Dic5 | — | 8 | 4 | no | — |
| 63 | C22×C3×C4 | — | 10 | 4 | no | — |
| 64 | C22×C3×C4 | D20 | 1 | 2 | yes | — |
| 65 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 66 | C2×C3×C8 | — | 2 | 4 | no | — |
| 67 | C2×C3×C8 | C2×Dic5 | 1 | 4 | yes | — |
| 68 | C3×C4⋊C4 | — | 10 | 8 | no | — |
| 69 | C3×C42 | Dic10 | 1 | 2 | yes | — |
| 70 | C3×C42 | C2×Dic5 | 1 | 2 | yes | — |
| 71 | C23×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×C5 | — | 2 | 4 | no | — |
| 73 | C2×C4×C5 | C3×C4⋊C4 | 1 | 4 | yes | — |
| 74 | C2×C4×C5 | C22×C3×C4 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C5 | C2×C3×Q8 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×C5 | C3×#41 | 1 | 4 | yes | — |
| 77 | C2×Dic5 | — | 4 | 4 | no | — |
| 78 | C2×Dic5 | — | 4 | 8 | no | — |
| 79 | C5×C8 | — | 2 | 4 | no | — |
| 80 | C22×C8 | C2×C3×D5 | 1 | 2 | yes | — |
| 81 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 82 | C2×C42 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 83 | C4×C8 | C3×Dic5 | 1 | 4 | yes | complemented |
| 84 | #95 | — | 10 | 4 | no | — |
| 85 | C2×C3×C5 | #382 | 1 | 1 | yes | characteristic |
| 86 | C2×C3×C5 | #427 | 1 | 2 | yes | — |
| 87 | C2×C3×C5 | #488 | 1 | 4 | yes | — |
| 88 | C23×C3 | C2×D20 | 1 | 1 | yes | characteristic |
| 89 | C2×C3×C4 | — | 2 | 4 | no | — |
| 90 | C2×C3×C4 | — | 20 | 4 | no | — |
| 91 | C2×C3×C4 | — | 20 | 8 | no | — |
| 92 | C2×C3×C4 | C4⋊Dic5 | 1 | 4 | yes | — |
| 93 | C2×C3×C4 | C2×Dic10 | 1 | 1 | yes | characteristic |
| 94 | C2×C3×C4 | #709 | 1 | 4 | yes | — |
| 95 | C2×C3×C4 | C22×Dic5 | 1 | 1 | yes | characteristic |
| 96 | C3×C8 | — | 2 | 4 | no | — |
| 97 | C22×C5 | C2×C3×C4⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C22×C5 | C3×#124 | 1 | 2 | yes | — |
| 99 | C22×C5 | C3×#135 | 1 | 4 | yes | — |
| 100 | C4×C5 | — | 2 | 4 | no | — |
| 101 | C4×C5 | C3×#117 | 1 | 2 | yes | — |
| 102 | C4×C5 | C3×#125 | 1 | 2 | yes | — |
| 103 | Dic5 | — | 8 | 4 | no | — |
| 104 | C22×C4 | — | 10 | 4 | no | — |
| 105 | C22×C4 | C3×D20 | 1 | 2 | yes | — |
| 106 | C22×C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 107 | C2×C8 | — | 2 | 4 | no | — |
| 108 | C2×C8 | C2×C3×Dic5 | 1 | 4 | yes | — |
| 109 | C4⋊C4 | — | 10 | 8 | no | — |
| 110 | C42 | C3×Dic10 | 1 | 2 | yes | — |
| 111 | C42 | C2×C3×Dic5 | 1 | 2 | yes | — |
| 112 | C3×C5 | #1835 | 1 | 1 | yes | characteristic, complemented, Hall |
| 113 | C22×C3 | #4021 | 1 | 2 | yes | — |
| 114 | C22×C3 | #4050 | 1 | 4 | yes | — |
| 115 | C22×C3 | C2×C4⋊Dic5 | 1 | 1 | yes | characteristic |
| 116 | C3×C4 | — | 2 | 4 | no | — |
| 117 | C3×C4 | — | 40 | 4 | no | — |
| 118 | C3×C4 | #4016 | 1 | 2 | yes | — |
| 119 | C3×C4 | #4072 | 1 | 2 | yes | — |
| 120 | C2×C5 | C3×#382 | 1 | 1 | yes | characteristic |
| 121 | C2×C5 | C3×#427 | 1 | 2 | yes | — |
| 122 | C2×C5 | C3×#488 | 1 | 4 | yes | — |
| 123 | C23 | C2×C3×D20 | 1 | 1 | yes | characteristic |
| 124 | C2×C4 | — | 2 | 4 | no | — |
| 125 | C2×C4 | — | 20 | 4 | no | — |
| 126 | C2×C4 | — | 20 | 8 | no | — |
| 127 | C2×C4 | C3×C4⋊Dic5 | 1 | 4 | yes | — |
| 128 | C2×C4 | C2×C3×Dic10 | 1 | 1 | yes | characteristic |
| 129 | C2×C4 | C3×#709 | 1 | 4 | yes | — |
| 130 | C2×C4 | C22×C3×Dic5 | 1 | 1 | yes | characteristic |
| 131 | C8 | — | 2 | 4 | no | — |
| 132 | C2×C3 | #64986 | 1 | 4 | yes | — |
| 133 | C2×C3 | #65225 | 1 | 1 | yes | characteristic |
| 134 | C2×C3 | #65395 | 1 | 2 | yes | — |
| 135 | C5 | C3×#1835 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 136 | C22 | C3×#4021 | 1 | 2 | yes | — |
| 137 | C22 | C3×#4050 | 1 | 4 | yes | — |
| 138 | C22 | C2×C3×C4⋊Dic5 | 1 | 1 | yes | characteristic |
| 139 | C4 | — | 2 | 4 | no | — |
| 140 | C4 | — | 40 | 4 | no | — |
| 141 | C4 | C3×#4016 | 1 | 2 | yes | — |
| 142 | C4 | C3×#4072 | 1 | 2 | yes | — |
| 143 | C3 | #10600556 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 144 | C2 | C3×#64986 | 1 | 4 | yes | — |
| 145 | C2 | C3×#65225 | 1 | 1 | yes | characteristic |
| 146 | C2 | C3×#65395 | 1 | 2 | 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