← C3×#66264 #11756972
Subgroups — C3×#66264 #11756972
Order 960.
516 conjugacy classes of subgroups.
The subgroup lattice has 184 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×D5×#41 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#4133 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#4131 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C3×D5⋊M16 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×C3×#700 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #66264 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 7 | C3×C5×#41 | C4 | 1 | 1 | yes | characteristic |
| 8 | C3×#713 | C22 | 1 | 1 | yes | characteristic |
| 9 | C3×Q8×D5 | C4 | 1 | 1 | yes | characteristic |
| 10 | C3×#711 | C22 | 1 | 3 | yes | — |
| 11 | C3×D4×D5 | C4 | 1 | 3 | yes | — |
| 12 | C3×#709 | C4 | 1 | 3 | yes | — |
| 13 | C2×C3×C4×D5 | C22 | 1 | 3 | yes | — |
| 14 | C3×#704 | C22 | 1 | 6 | yes | complemented |
| 15 | C2×C3×#170 | C22 | 1 | 6 | yes | complemented |
| 16 | C3×#700 | C22 | 1 | 3 | yes | — |
| 17 | C3×#700 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#700 | C22 | 1 | 6 | yes | complemented |
| 19 | C3×D5⋊C8 | C22 | 1 | 6 | yes | complemented |
| 20 | C3×#568 | — | 5 | 1 | no | maximal, Hall |
| 21 | D5×#41 | C2×C3 | 1 | 1 | yes | characteristic |
| 22 | #4133 | C2×C3 | 1 | 2 | yes | complemented |
| 23 | #4131 | C2×C3 | 1 | 6 | yes | complemented |
| 24 | D5⋊M16 | C2×C3 | 1 | 3 | yes | complemented |
| 25 | C2×#700 | C2×C3 | 1 | 3 | yes | complemented |
| 26 | C22×C3×D5 | C2×C4 | 1 | 3 | yes | — |
| 27 | C3×C5×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C3×C5×D4 | C2×C4 | 1 | 3 | yes | — |
| 29 | C2×C3×C4×C5 | C2×C4 | 1 | 3 | yes | — |
| 30 | C3×C22⋊D5 | C2×C4 | 1 | 6 | yes | — |
| 31 | C2×C3×Dic5 | C23 | 1 | 3 | yes | — |
| 32 | C3×D20 | C2×C4 | 1 | 3 | yes | — |
| 33 | C3×C4×D5 | C2×C4 | 1 | 3 | yes | — |
| 34 | C3×C4×D5 | C2×C4 | 1 | 3 | yes | — |
| 35 | C3×C4×D5 | C23 | 1 | 3 | yes | — |
| 36 | C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 37 | C3×Dic10 | C2×C4 | 1 | 3 | yes | — |
| 38 | C3×#170 | C23 | 1 | 2 | yes | — |
| 39 | C3×#170 | C23 | 1 | 6 | yes | — |
| 40 | C2×C3×#41 | — | 5 | 1 | no | — |
| 41 | C3×#131 | — | 5 | 6 | no | — |
| 42 | C3×#131 | — | 5 | 2 | no | — |
| 43 | C2×C3×M16 | — | 5 | 3 | no | — |
| 44 | C2×C3×M16 | — | 5 | 3 | no | — |
| 45 | C5×#41 | C3×C4 | 1 | 1 | yes | characteristic |
| 46 | #713 | C22×C3 | 1 | 1 | yes | characteristic |
| 47 | Q8×D5 | C3×C4 | 1 | 1 | yes | characteristic |
| 48 | #711 | C22×C3 | 1 | 3 | yes | — |
| 49 | D4×D5 | C3×C4 | 1 | 3 | yes | — |
| 50 | #709 | C3×C4 | 1 | 3 | yes | — |
| 51 | C2×C4×D5 | C22×C3 | 1 | 3 | yes | — |
| 52 | #704 | C22×C3 | 1 | 6 | yes | complemented |
| 53 | C2×#170 | C22×C3 | 1 | 6 | yes | complemented |
| 54 | #700 | C22×C3 | 1 | 3 | yes | — |
| 55 | #700 | C22×C3 | 1 | 1 | yes | characteristic |
| 56 | #700 | C22×C3 | 1 | 6 | yes | complemented |
| 57 | D5⋊C8 | C22×C3 | 1 | 6 | yes | complemented |
| 58 | #568 | — | 5 | 1 | no | Sylow |
| 59 | C22×C3×C5 | C22×C4 | 1 | 3 | yes | — |
| 60 | C2×C3×D5 | — | 4 | 3 | no | — |
| 61 | C2×C3×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×D5 | C22×C4 | 1 | 3 | yes | — |
| 63 | C3×C4×C5 | C22×C4 | 1 | 3 | yes | — |
| 64 | C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 65 | C3×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 66 | C3×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 67 | C3×#41 | — | 5 | 1 | no | — |
| 68 | C3×#41 | — | 5 | 3 | no | — |
| 69 | C3×#41 | — | 5 | 3 | no | — |
| 70 | C3×#41 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 71 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 72 | C2×C3×D4 | — | 5 | 3 | no | — |
| 73 | C22×C3×C4 | — | 5 | 3 | no | — |
| 74 | C3×M16 | — | 5 | 3 | no | — |
| 75 | C3×M16 | — | 5 | 1 | no | — |
| 76 | C3×M16 | — | 5 | 6 | no | — |
| 77 | C3×M16 | — | 5 | 6 | no | — |
| 78 | C2×C3×C8 | — | 5 | 6 | no | — |
| 79 | C2×C3×C8 | — | 5 | 6 | no | — |
| 80 | C22×D5 | C2×C3×C4 | 1 | 3 | yes | — |
| 81 | C5×Q8 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 82 | C5×D4 | C2×C3×C4 | 1 | 3 | yes | — |
| 83 | C2×C4×C5 | C2×C3×C4 | 1 | 3 | yes | — |
| 84 | C22⋊D5 | C2×C3×C4 | 1 | 6 | yes | — |
| 85 | C2×Dic5 | C23×C3 | 1 | 3 | yes | — |
| 86 | D20 | C2×C3×C4 | 1 | 3 | yes | — |
| 87 | C4×D5 | C2×C3×C4 | 1 | 3 | yes | — |
| 88 | C4×D5 | C2×C3×C4 | 1 | 3 | yes | — |
| 89 | C4×D5 | C23×C3 | 1 | 3 | yes | — |
| 90 | C4×D5 | C23×C3 | 1 | 1 | yes | characteristic |
| 91 | Dic10 | C2×C3×C4 | 1 | 3 | yes | — |
| 92 | #170 | C23×C3 | 1 | 2 | yes | — |
| 93 | #170 | C23×C3 | 1 | 6 | yes | — |
| 94 | C2×#41 | — | 5 | 1 | no | — |
| 95 | #131 | — | 5 | 6 | no | — |
| 96 | #131 | — | 5 | 2 | no | — |
| 97 | C2×M16 | — | 5 | 3 | no | — |
| 98 | C2×M16 | — | 5 | 3 | no | — |
| 99 | C2×C3×C5 | — | 2 | 3 | no | — |
| 100 | C2×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 101 | C3×D5 | — | 2 | 1 | no | — |
| 102 | C3×D5 | — | 2 | 3 | no | — |
| 103 | C23×C3 | — | 5 | 3 | no | — |
| 104 | C3×Q8 | — | 5 | 3 | no | — |
| 105 | C3×Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 106 | C3×D4 | — | 5 | 6 | no | — |
| 107 | C3×D4 | — | 5 | 3 | no | — |
| 108 | C3×D4 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 109 | C2×C3×C4 | — | 5 | 3 | no | — |
| 110 | C2×C3×C4 | — | 5 | 3 | no | — |
| 111 | C2×C3×C4 | — | 5 | 3 | no | — |
| 112 | C2×C3×C4 | — | 5 | 3 | no | — |
| 113 | C2×C3×C4 | — | 5 | 1 | no | — |
| 114 | C2×C3×C4 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 115 | C3×C8 | — | 5 | 2 | no | — |
| 116 | C3×C8 | — | 5 | 6 | no | — |
| 117 | C22×C5 | C22×C3×C4 | 1 | 3 | yes | — |
| 118 | C2×D5 | — | 4 | 3 | no | — |
| 119 | C2×D5 | C22×C3×C4 | 1 | 1 | yes | characteristic |
| 120 | C2×D5 | C22×C3×C4 | 1 | 3 | yes | — |
| 121 | C4×C5 | C22×C3×C4 | 1 | 3 | yes | — |
| 122 | C4×C5 | C22×C3×C4 | 1 | 1 | yes | characteristic |
| 123 | Dic5 | C22×C3×C4 | 1 | 3 | yes | — |
| 124 | Dic5 | C24×C3 | 1 | 1 | yes | characteristic |
| 125 | #41 | — | 5 | 1 | no | — |
| 126 | #41 | — | 5 | 3 | no | — |
| 127 | #41 | — | 5 | 3 | no | — |
| 128 | #41 | C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 129 | C2×Q8 | — | 5 | 1 | no | — |
| 130 | C2×D4 | — | 5 | 3 | no | — |
| 131 | C22×C4 | — | 5 | 3 | no | — |
| 132 | M16 | — | 5 | 3 | no | — |
| 133 | M16 | — | 5 | 1 | no | — |
| 134 | M16 | — | 5 | 6 | no | — |
| 135 | M16 | — | 5 | 6 | no | — |
| 136 | C2×C8 | — | 5 | 6 | no | — |
| 137 | C2×C8 | — | 5 | 6 | no | — |
| 138 | C3×C5 | #568 | 1 | 1 | yes | characteristic, complemented, Hall |
| 139 | C22×C3 | — | 5 | 1 | no | — |
| 140 | C22×C3 | — | 5 | 3 | no | — |
| 141 | C22×C3 | — | 20 | 3 | no | — |
| 142 | C22×C3 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 143 | C3×C4 | — | 5 | 3 | no | — |
| 144 | C3×C4 | — | 5 | 1 | no | — |
| 145 | C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 146 | C3×C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 147 | C2×C5 | — | 2 | 3 | no | — |
| 148 | C2×C5 | C23×C3×C4 | 1 | 1 | yes | characteristic |
| 149 | D5 | — | 2 | 1 | no | — |
| 150 | D5 | — | 2 | 3 | no | — |
| 151 | C23 | — | 5 | 3 | no | — |
| 152 | Q8 | — | 5 | 3 | no | — |
| 153 | Q8 | C2×C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 154 | D4 | — | 5 | 6 | no | — |
| 155 | D4 | — | 5 | 3 | no | — |
| 156 | D4 | C2×C3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 157 | C2×C4 | — | 5 | 3 | no | — |
| 158 | C2×C4 | — | 5 | 3 | no | — |
| 159 | C2×C4 | — | 5 | 1 | no | — |
| 160 | C2×C4 | — | 5 | 3 | no | — |
| 161 | C2×C4 | — | 5 | 3 | no | — |
| 162 | C2×C4 | C2×C3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 163 | C8 | — | 5 | 2 | no | — |
| 164 | C8 | — | 5 | 6 | no | — |
| 165 | C2×C3 | — | 2 | 3 | no | — |
| 166 | C2×C3 | — | 10 | 1 | no | — |
| 167 | C2×C3 | — | 10 | 3 | no | — |
| 168 | C2×C3 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 169 | C5 | C3×#568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 170 | C22 | — | 5 | 1 | no | — |
| 171 | C22 | — | 5 | 3 | no | — |
| 172 | C22 | — | 20 | 3 | no | — |
| 173 | C22 | C22×C3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 174 | C4 | — | 5 | 1 | no | — |
| 175 | C4 | — | 5 | 3 | no | — |
| 176 | C4 | C22×C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 177 | C4 | C22×C3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 178 | C3 | #66264 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 179 | C2 | — | 2 | 3 | no | — |
| 180 | C2 | — | 10 | 1 | no | — |
| 181 | C2 | — | 10 | 3 | no | — |
| 182 | C2 | C23×C3×AGL(1,𝔽5) | 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