Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
138 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 23 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 | C5×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #91954 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #91185 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #65535 | — | 3 | 1 | no | maximal, Hall |
| 5 | C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×C5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 7 | C5⋊#226 | — | 2 | 1 | no | — |
| 8 | #6716 | — | 4 | 1 | no | maximal |
| 9 | #5430 | — | 5 | 1 | no | maximal, Hall |
| 10 | C5×2−1+4 | D3 | 1 | 1 | yes | characteristic |
| 11 | #4097 | — | 3 | 1 | no | — |
| 12 | #4097 | — | 3 | 1 | no | — |
| 13 | #4090 | — | 3 | 1 | no | — |
| 14 | #3969 | — | 3 | 1 | no | — |
| 15 | #3969 | — | 3 | 1 | no | — |
| 16 | #3968 | — | 3 | 1 | no | — |
| 17 | C3×C5×D4 | — | 4 | 1 | no | — |
| 18 | Dic30 | — | 4 | 1 | no | — |
| 19 | C5×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 20 | C3⋊#168 | — | 4 | 1 | no | — |
| 21 | 2−1+4⋊C3 | D5 | 1 | 1 | yes | characteristic |
| 22 | #984 | — | 5 | 1 | no | — |
| 23 | GU(2,𝔽3) | — | 5 | 1 | no | — |
| 24 | C5×#41 | — | 3 | 1 | no | — |
| 25 | C5×#41 | — | 6 | 1 | no | — |
| 26 | C5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 27 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 28 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 29 | C2×Dic10 | — | 3 | 1 | no | — |
| 30 | #689 | — | 6 | 1 | no | — |
| 31 | #689 | — | 6 | 1 | no | — |
| 32 | #687 | — | 6 | 1 | no | — |
| 33 | #687 | — | 6 | 1 | no | — |
| 34 | #683 | — | 6 | 2 | no | — |
| 35 | C4×Dic5 | — | 3 | 1 | no | — |
| 36 | #681 | — | 3 | 1 | no | — |
| 37 | #681 | — | 3 | 1 | no | — |
| 38 | #456 | — | 15 | 1 | no | Sylow |
| 39 | C22×C3×C5 | — | 8 | 1 | no | — |
| 40 | C3×C4×C5 | — | 4 | 1 | no | — |
| 41 | Dic15 | — | 8 | 1 | no | — |
| 42 | #41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 43 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 44 | #226 | — | 10 | 1 | no | — |
| 45 | #214 | — | 20 | 1 | no | — |
| 46 | C5×Q8 | — | 3 | 1 | no | — |
| 47 | C5×Q8 | — | 6 | 1 | no | — |
| 48 | C5×Q8 | #67 | 1 | 1 | yes | characteristic |
| 49 | C5×D4 | — | 3 | 1 | no | — |
| 50 | C5×D4 | — | 6 | 1 | no | — |
| 51 | C5×D4 | S4 | 1 | 1 | yes | characteristic |
| 52 | C2×C4×C5 | — | 3 | 1 | no | — |
| 53 | C2×C4×C5 | — | 3 | 2 | no | — |
| 54 | C2×C4×C5 | — | 6 | 1 | no | — |
| 55 | C2×Dic5 | — | 6 | 1 | no | — |
| 56 | C2×Dic5 | — | 6 | 1 | no | — |
| 57 | Dic10 | — | 6 | 1 | no | — |
| 58 | Dic10 | — | 6 | 1 | no | — |
| 59 | #168 | — | 6 | 1 | no | — |
| 60 | #168 | — | 6 | 1 | no | — |
| 61 | 2−1+4 | D15 | 1 | 1 | yes | characteristic |
| 62 | #137 | — | 15 | 1 | no | — |
| 63 | #137 | — | 15 | 1 | no | — |
| 64 | C4⋊Q8 | — | 15 | 1 | no | — |
| 65 | #104 | — | 15 | 1 | no | — |
| 66 | #104 | — | 15 | 1 | no | — |
| 67 | #101 | — | 15 | 1 | no | — |
| 68 | C2×C3×C5 | — | 4 | 1 | no | — |
| 69 | C2×C3×C5 | — | 16 | 1 | no | — |
| 70 | C3×D4 | — | 4 | 1 | no | — |
| 71 | Dic6 | — | 20 | 1 | no | — |
| 72 | SL(2,𝔽3) | C22⋊D5 | 1 | 1 | yes | characteristic |
| 73 | C3⋊C8 | — | 20 | 1 | no | — |
| 74 | C22×C5 | — | 2 | 1 | no | — |
| 75 | C22×C5 | — | 3 | 1 | no | — |
| 76 | C4×C5 | — | 3 | 1 | no | — |
| 77 | C4×C5 | — | 6 | 1 | no | — |
| 78 | C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 79 | Dic5 | — | 6 | 2 | no | — |
| 80 | Dic5 | — | 12 | 1 | no | — |
| 81 | #41 | — | 3 | 1 | no | — |
| 82 | #41 | — | 6 | 1 | no | — |
| 83 | #41 | C2×D15 | 1 | 1 | yes | characteristic |
| 84 | C2×Q8 | — | 2 | 1 | no | — |
| 85 | C2×Q8 | — | 3 | 1 | no | — |
| 86 | C2×Q8 | — | 15 | 1 | no | — |
| 87 | Q16 | — | 30 | 1 | no | — |
| 88 | Q16 | — | 30 | 1 | no | — |
| 89 | SD16 | — | 30 | 1 | no | — |
| 90 | SD16 | — | 30 | 1 | no | — |
| 91 | M16 | — | 15 | 1 | no | — |
| 92 | M16 | — | 15 | 1 | no | — |
| 93 | C4⋊C4 | — | 30 | 2 | no | — |
| 94 | C42 | — | 15 | 1 | no | — |
| 95 | C3×C5 | — | 4 | 1 | no | Hall |
| 96 | C22×C3 | — | 8 | 1 | no | — |
| 97 | C3×C4 | — | 4 | 1 | no | — |
| 98 | Dic3 | — | 40 | 1 | no | — |
| 99 | C2×C5 | — | 4 | 1 | no | — |
| 100 | C2×C5 | — | 6 | 1 | no | — |
| 101 | C2×C5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 102 | Q8 | — | 3 | 1 | no | — |
| 103 | Q8 | — | 6 | 1 | no | — |
| 104 | Q8 | — | 30 | 1 | no | — |
| 105 | Q8 | — | 30 | 1 | no | — |
| 106 | Q8 | #1220 | 1 | 1 | yes | characteristic |
| 107 | D4 | — | 3 | 1 | no | — |
| 108 | D4 | — | 6 | 1 | no | — |
| 109 | D4 | C5⋊S4 | 1 | 1 | yes | characteristic |
| 110 | C2×C4 | — | 3 | 1 | no | — |
| 111 | C2×C4 | — | 3 | 2 | no | — |
| 112 | C2×C4 | — | 6 | 1 | no | — |
| 113 | C2×C4 | — | 30 | 1 | no | — |
| 114 | C2×C4 | — | 30 | 1 | no | — |
| 115 | C8 | — | 30 | 1 | no | — |
| 116 | C8 | — | 30 | 1 | no | — |
| 117 | C2×C3 | — | 4 | 1 | no | — |
| 118 | C2×C3 | — | 16 | 1 | no | — |
| 119 | C5 | #5430 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 120 | C22 | — | 2 | 1 | no | — |
| 121 | C22 | — | 3 | 1 | no | — |
| 122 | C4 | — | 3 | 1 | no | — |
| 123 | C4 | — | 6 | 1 | no | — |
| 124 | C4 | — | 30 | 2 | no | — |
| 125 | C4 | — | 60 | 1 | no | — |
| 126 | C4 | C2×C5⋊S4 | 1 | 1 | yes | characteristic |
| 127 | C3 | — | 4 | 1 | no | Sylow |
| 128 | C2 | — | 4 | 1 | no | — |
| 129 | C2 | — | 6 | 1 | no | — |
| 130 | C2 | #91958 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #91954 | C2 | semidirect |
| 3. #91185 | C2 | semidirect |
| 119. C5 | #5430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×2−1+4⋊C3 | 2 |
| #91954 | 2 |
| #91185 | 2 |
| #65535 | 3 |
| #6716 | 4 |
| #5430 | 5 |