Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
110 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 16 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⋊(#395⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10598830 | — | 3 | 1 | no | maximal, Hall |
| 3 | C5×C22⋊SL(2,𝔽3) | C4 | 1 | 1 | yes | characteristic |
| 4 | A4⋊#170 | — | 4 | 1 | no | maximal |
| 5 | #68002 | — | 5 | 1 | no | maximal, Hall |
| 6 | #65518 | D3 | 1 | 1 | yes | characteristic |
| 7 | #64919 | — | 3 | 1 | no | — |
| 8 | #64914 | — | 3 | 1 | no | — |
| 9 | A4×Dic5 | — | 4 | 1 | no | — |
| 10 | #395⋊C3 | — | 5 | 1 | no | — |
| 11 | C22×C5×Q8 | Dic3 | 1 | 1 | yes | characteristic |
| 12 | C2×#704 | — | 6 | 1 | no | — |
| 13 | C2×#683 | — | 3 | 1 | no | — |
| 14 | C22⋊#170 | — | 6 | 1 | no | — |
| 15 | #3963 | — | 3 | 1 | no | — |
| 16 | #1354 | — | 15 | 1 | no | Sylow |
| 17 | C2×C5×A4 | — | 4 | 1 | no | — |
| 18 | C5×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 19 | C3⋊#170 | — | 16 | 1 | no | — |
| 20 | C22⋊SL(2,𝔽3) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 21 | A4⋊C8 | — | 20 | 1 | no | — |
| 22 | C2×C5×Q8 | — | 12 | 1 | no | — |
| 23 | C22×C4×C5 | — | 3 | 1 | no | — |
| 24 | C22×Dic5 | — | 3 | 1 | no | — |
| 25 | C22×Dic5 | S4 | 1 | 1 | yes | characteristic |
| 26 | #704 | — | 6 | 2 | no | — |
| 27 | #704 | — | 12 | 1 | no | — |
| 28 | C2×#170 | — | 12 | 1 | no | — |
| 29 | C2×#170 | — | 12 | 1 | no | — |
| 30 | #683 | — | 12 | 1 | no | — |
| 31 | #395 | — | 5 | 1 | no | — |
| 32 | #343 | — | 15 | 1 | no | — |
| 33 | #324 | — | 15 | 1 | no | — |
| 34 | C5×A4 | — | 4 | 1 | no | — |
| 35 | C3×Dic5 | — | 16 | 1 | no | — |
| 36 | C4×A4 | — | 20 | 1 | no | — |
| 37 | C23×C5 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 38 | C5×Q8 | — | 4 | 1 | no | — |
| 39 | C5×Q8 | — | 12 | 1 | no | — |
| 40 | C2×C4×C5 | — | 6 | 1 | no | — |
| 41 | C2×C4×C5 | — | 12 | 1 | no | — |
| 42 | C2×Dic5 | — | 3 | 1 | no | — |
| 43 | C2×Dic5 | — | 3 | 1 | no | — |
| 44 | C2×Dic5 | — | 6 | 1 | no | — |
| 45 | C2×Dic5 | — | 6 | 1 | no | — |
| 46 | C2×Dic5 | — | 6 | 1 | no | — |
| 47 | #170 | — | 12 | 2 | no | — |
| 48 | #170 | — | 24 | 1 | no | — |
| 49 | C22×Q8 | ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 50 | C2×M16 | — | 30 | 1 | no | — |
| 51 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 52 | C22⋊C8 | — | 30 | 1 | no | — |
| 53 | #95 | — | 15 | 1 | no | — |
| 54 | C2×C3×C5 | — | 16 | 1 | no | — |
| 55 | C2×A4 | — | 4 | 1 | no | — |
| 56 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 57 | C3⋊C8 | — | 80 | 1 | no | — |
| 58 | C22×C5 | — | 3 | 1 | no | — |
| 59 | C22×C5 | — | 3 | 1 | no | — |
| 60 | C22×C5 | GU(2,𝔽3) | 1 | 1 | yes | characteristic |
| 61 | C4×C5 | — | 12 | 1 | no | — |
| 62 | Dic5 | — | 4 | 1 | no | — |
| 63 | Dic5 | — | 6 | 1 | no | — |
| 64 | Dic5 | — | 6 | 1 | no | — |
| 65 | C2×Q8 | — | 12 | 1 | no | — |
| 66 | C22×C4 | — | 3 | 1 | no | — |
| 67 | C22×C4 | — | 5 | 1 | no | — |
| 68 | C22×C4 | — | 15 | 1 | no | — |
| 69 | M16 | — | 30 | 2 | no | — |
| 70 | M16 | — | 60 | 1 | no | — |
| 71 | C2×C8 | — | 60 | 1 | no | — |
| 72 | C2×C8 | — | 60 | 1 | no | — |
| 73 | C4⋊C4 | — | 60 | 1 | no | — |
| 74 | C3×C5 | — | 16 | 1 | no | Hall |
| 75 | A4 | — | 4 | 1 | no | — |
| 76 | C3×C4 | — | 80 | 1 | no | — |
| 77 | C2×C5 | — | 3 | 1 | no | — |
| 78 | C2×C5 | — | 3 | 1 | no | — |
| 79 | C2×C5 | #4625 | 1 | 1 | yes | characteristic |
| 80 | C23 | A4⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 81 | Q8 | — | 4 | 1 | no | — |
| 82 | Q8 | — | 12 | 1 | no | — |
| 83 | C2×C4 | — | 6 | 1 | no | — |
| 84 | C2×C4 | — | 12 | 1 | no | — |
| 85 | C2×C4 | — | 15 | 1 | no | — |
| 86 | C2×C4 | — | 15 | 1 | no | — |
| 87 | C2×C4 | — | 30 | 1 | no | — |
| 88 | C2×C4 | — | 30 | 1 | no | — |
| 89 | C2×C4 | — | 30 | 1 | no | — |
| 90 | C8 | — | 60 | 2 | no | — |
| 91 | C8 | — | 120 | 1 | no | — |
| 92 | C2×C3 | — | 16 | 1 | no | — |
| 93 | C5 | #68002 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 94 | C22 | — | 3 | 1 | no | — |
| 95 | C22 | — | 3 | 1 | no | — |
| 96 | C22 | #91885 | 1 | 1 | yes | characteristic |
| 97 | C4 | — | 12 | 1 | no | — |
| 98 | C4 | — | 20 | 1 | no | — |
| 99 | C4 | — | 30 | 1 | no | — |
| 100 | C4 | — | 30 | 1 | no | — |
| 101 | C3 | — | 16 | 1 | no | Sylow |
| 102 | C2 | — | 3 | 1 | no | — |
| 103 | C2 | — | 3 | 1 | no | — |
| 104 | C2 | #11751559 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 93. C5 | #68002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊(#395⋊C3) | 2 |
| #10598830 | 3 |
| A4⋊#170 | 4 |
| #68002 | 5 |