Finite Group DatabasebetaFinite Group DatabasebetaOrder 4860.
118 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#1113⋊C3 | — | 5 | 1 | no | maximal, Hall |
| 2 | #11717694 | — | 6 | 1 | no | maximal |
| 3 | C3⋊#4174 | — | 10 | 1 | no | maximal |
| 4 | C34⋊C5 | — | 6 | 1 | no | — |
| 5 | C3×#1113 | — | 5 | 1 | no | — |
| 6 | #1113⋊C3 | — | 5 | 3 | no | — |
| 7 | C3×AΣL(1,𝔽27) | — | 10 | 1 | no | Sylow |
| 8 | C32×C3⋊D3 | — | 15 | 1 | no | — |
| 9 | C3⋊#272 | — | 10 | 1 | no | — |
| 10 | #4174 | — | 30 | 3 | no | — |
| 11 | #1113 | — | 5 | 1 | no | — |
| 12 | C3×D32 | — | 45 | 1 | no | — |
| 13 | C34 | A5 | 1 | 1 | yes | maximal normal, characteristic, complemented |
| 14 | C3×3−1+2 | — | 20 | 1 | no | — |
| 15 | C3×H(3,𝔽3) | — | 10 | 1 | no | — |
| 16 | AΣL(1,𝔽27) | — | 10 | 3 | no | — |
| 17 | AΣL(1,𝔽27) | — | 20 | 3 | no | — |
| 18 | A5 | — | 81 | 3 | no | maximal |
| 19 | C3×C3⋊D3 | — | 15 | 1 | no | — |
| 20 | C3×C3⋊D3 | — | 15 | 1 | no | — |
| 21 | C3×C3⋊D3 | — | 30 | 1 | no | — |
| 22 | C3×C3⋊D3 | — | 90 | 1 | no | — |
| 23 | C32×D3 | — | 45 | 2 | no | — |
| 24 | C32×D3 | — | 90 | 1 | no | — |
| 25 | #272 | — | 30 | 3 | no | — |
| 26 | #272 | — | 90 | 2 | no | — |
| 27 | C2×C3×D3 | — | 135 | 1 | no | — |
| 28 | C3×A4 | — | 135 | 1 | no | — |
| 29 | D32 | — | 45 | 1 | no | — |
| 30 | C33 | — | 5 | 1 | no | — |
| 31 | C33 | — | 10 | 1 | no | — |
| 32 | C33 | — | 10 | 1 | no | — |
| 33 | C33 | — | 15 | 1 | no | — |
| 34 | C33 | — | 30 | 1 | no | — |
| 35 | 3−1+2 | — | 20 | 3 | no | — |
| 36 | 3−1+2 | — | 60 | 2 | no | — |
| 37 | H(3,𝔽3) | — | 10 | 3 | no | — |
| 38 | H(3,𝔽3) | — | 30 | 2 | no | — |
| 39 | C3×C9 | — | 60 | 1 | no | — |
| 40 | C2×C32 | — | 135 | 1 | no | — |
| 41 | C3⋊D3 | — | 15 | 1 | no | — |
| 42 | C3⋊D3 | — | 90 | 1 | no | — |
| 43 | C3×D3 | — | 270 | 3 | no | — |
| 44 | C3×D3 | — | 45 | 2 | no | — |
| 45 | C3×D3 | — | 45 | 2 | no | — |
| 46 | C3×D3 | — | 90 | 2 | no | — |
| 47 | C3×D3 | — | 90 | 1 | no | — |
| 48 | C3×D3 | — | 90 | 1 | no | — |
| 49 | C3×D3 | — | 90 | 1 | no | — |
| 50 | C3×D3 | — | 90 | 1 | no | — |
| 51 | C22×C3 | — | 135 | 1 | no | — |
| 52 | C2×D3 | — | 135 | 1 | no | — |
| 53 | A4 | — | 135 | 3 | no | — |
| 54 | D5 | — | 486 | 1 | no | — |
| 55 | C32 | — | 10 | 1 | no | — |
| 56 | C32 | — | 10 | 1 | no | — |
| 57 | C32 | — | 10 | 2 | no | — |
| 58 | C32 | — | 15 | 1 | no | — |
| 59 | C32 | — | 15 | 1 | no | — |
| 60 | C32 | — | 30 | 1 | no | — |
| 61 | C32 | — | 30 | 1 | no | — |
| 62 | C32 | — | 30 | 3 | no | — |
| 63 | C32 | — | 90 | 1 | no | — |
| 64 | C32 | — | 180 | 1 | no | — |
| 65 | C9 | — | 60 | 3 | no | — |
| 66 | C2×C3 | — | 270 | 1 | no | — |
| 67 | C2×C3 | — | 135 | 1 | no | — |
| 68 | C2×C3 | — | 135 | 1 | no | — |
| 69 | D3 | — | 270 | 3 | no | — |
| 70 | D3 | — | 45 | 2 | no | — |
| 71 | D3 | — | 90 | 1 | no | — |
| 72 | C5 | — | 486 | 1 | no | Sylow |
| 73 | C22 | — | 135 | 1 | no | Sylow |
| 74 | C3 | — | 5 | 1 | no | — |
| 75 | C3 | — | 10 | 1 | no | — |
| 76 | C3 | — | 10 | 1 | no | — |
| 77 | C3 | — | 15 | 1 | no | — |
| 78 | C3 | — | 90 | 3 | no | — |
| 79 | C2 | — | 135 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| Fitting, socle, cosocle | C34 | A5 |
| LCS | G | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C34 | A5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1113⋊C3 | 5 |
| #11717694 | 6 |
| C3⋊#4174 | 10 |
| A5 | 81 |