Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×A5 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C4×A5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×A5 | — | 2 | 2 | no | — |
| 4 | C2×A5 | C22 | 1 | 1 | yes | characteristic |
| 5 | D4×A4 | — | 5 | 1 | no | maximal, Hall |
| 6 | D4×D5 | — | 6 | 1 | no | maximal |
| 7 | A5 | D4 | 1 | 1 | yes | characteristic, direct product factor |
| 8 | C22×A4 | — | 5 | 2 | no | — |
| 9 | D3×D4 | — | 10 | 1 | no | maximal |
| 10 | C4×A4 | — | 5 | 1 | no | — |
| 11 | C22×D5 | — | 6 | 2 | no | — |
| 12 | C5×D4 | — | 6 | 1 | no | — |
| 13 | C22⋊D5 | — | 6 | 2 | no | — |
| 14 | D20 | — | 6 | 1 | no | — |
| 15 | C4×D5 | — | 6 | 1 | no | — |
| 16 | C22×D4 | — | 5 | 1 | no | Sylow |
| 17 | C22×D3 | — | 10 | 2 | no | — |
| 18 | C2×A4 | — | 5 | 1 | no | — |
| 19 | C2×A4 | — | 10 | 2 | no | — |
| 20 | C3×D4 | — | 10 | 1 | no | — |
| 21 | #67 | — | 10 | 2 | no | — |
| 22 | D12 | — | 10 | 1 | no | — |
| 23 | C4×D3 | — | 10 | 1 | no | — |
| 24 | C22×C5 | — | 6 | 2 | no | — |
| 25 | C2×D5 | — | 6 | 1 | no | — |
| 26 | C2×D5 | — | 6 | 2 | no | — |
| 27 | C2×D5 | — | 12 | 2 | no | — |
| 28 | C2×D5 | — | 12 | 2 | no | — |
| 29 | C4×C5 | — | 6 | 1 | no | — |
| 30 | Dic5 | — | 6 | 1 | no | — |
| 31 | C24 | — | 5 | 2 | no | — |
| 32 | C2×D4 | — | 15 | 1 | no | — |
| 33 | C2×D4 | — | 15 | 1 | no | — |
| 34 | C2×D4 | — | 15 | 2 | no | — |
| 35 | C22×C4 | — | 5 | 1 | no | — |
| 36 | C22×C3 | — | 10 | 2 | no | — |
| 37 | C2×D3 | — | 10 | 1 | no | — |
| 38 | C2×D3 | — | 10 | 2 | no | — |
| 39 | C2×D3 | — | 20 | 2 | no | — |
| 40 | C2×D3 | — | 20 | 2 | no | — |
| 41 | A4 | — | 5 | 1 | no | — |
| 42 | C3×C4 | — | 10 | 1 | no | — |
| 43 | Dic3 | — | 10 | 1 | no | — |
| 44 | C2×C5 | — | 6 | 1 | no | — |
| 45 | C2×C5 | — | 12 | 2 | no | — |
| 46 | D5 | — | 6 | 1 | no | — |
| 47 | D5 | — | 6 | 1 | no | — |
| 48 | D5 | — | 12 | 2 | no | — |
| 49 | C23 | — | 5 | 1 | no | — |
| 50 | C23 | — | 10 | 2 | no | — |
| 51 | C23 | — | 15 | 2 | no | — |
| 52 | C23 | — | 15 | 2 | no | — |
| 53 | C23 | — | 30 | 2 | no | — |
| 54 | D4 | — | 15 | 2 | no | — |
| 55 | D4 | — | 15 | 2 | no | — |
| 56 | D4 | — | 15 | 1 | no | — |
| 57 | D4 | A5 | 1 | 1 | yes | maximal normal, characteristic, direct product factor |
| 58 | C2×C4 | — | 15 | 1 | no | — |
| 59 | C2×C4 | — | 15 | 1 | no | — |
| 60 | C2×C3 | — | 10 | 1 | no | — |
| 61 | C2×C3 | — | 20 | 2 | no | — |
| 62 | D3 | — | 10 | 1 | no | — |
| 63 | D3 | — | 10 | 1 | no | — |
| 64 | D3 | — | 20 | 2 | no | — |
| 65 | C5 | — | 6 | 1 | no | Sylow |
| 66 | C22 | — | 5 | 1 | no | — |
| 67 | C22 | — | 15 | 1 | no | — |
| 68 | C22 | — | 15 | 1 | no | — |
| 69 | C22 | — | 15 | 2 | no | — |
| 70 | C22 | — | 30 | 2 | no | — |
| 71 | C22 | — | 30 | 2 | no | — |
| 72 | C22 | — | 30 | 2 | no | — |
| 73 | C22 | — | 30 | 2 | no | — |
| 74 | C22 | C2×A5 | 1 | 2 | yes | complemented |
| 75 | C4 | — | 15 | 1 | no | — |
| 76 | C4 | C2×A5 | 1 | 1 | yes | characteristic, complemented |
| 77 | C3 | — | 10 | 1 | no | Sylow |
| 78 | C2 | — | 2 | 2 | no | — |
| 79 | C2 | — | 15 | 1 | no | — |
| 80 | C2 | — | 15 | 1 | no | — |
| 81 | C2 | — | 30 | 2 | no | — |
| 82 | C2 | C22×A5 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2 | C22×A5 |
| commutator, socle | C2×A5 | C22 |
| Fitting, hypercenter | D4 | A5 |
| hypocenter | A5 | D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×A5 | C2 | semidirect |
| 2. C4×A5 | C2 | semidirect |
| 7. A5 | D4 | direct (N × H) |
| 57. D4 | A5 | direct (N × H) |
| 74. C22 | C2×A5 | semidirect |
| 76. C4 | C2×A5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×A5 | 2 |
| C4×A5 | 2 |
| D4×A4 | 5 |
| D4×D5 | 6 |
| D3×D4 | 10 |