Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
48 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | 2−1+4⋊C5 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #456 | — | 5 | 1 | no | maximal, Sylow |
| 3 | 2−1+4 | D5 | 1 | 1 | yes | characteristic |
| 4 | #137 | — | 5 | 2 | no | — |
| 5 | C4⋊Q8 | — | 5 | 1 | no | — |
| 6 | #104 | — | 5 | 2 | no | — |
| 7 | #101 | — | 5 | 1 | no | — |
| 8 | Dic5 | — | 16 | 1 | no | maximal |
| 9 | #41 | — | 5 | 2 | no | — |
| 10 | C2×Q8 | — | 5 | 1 | no | — |
| 11 | C2×Q8 | — | 5 | 1 | no | — |
| 12 | Q16 | — | 10 | 2 | no | — |
| 13 | SD16 | — | 10 | 2 | no | — |
| 14 | M16 | — | 5 | 2 | no | — |
| 15 | C4⋊C4 | — | 10 | 2 | no | — |
| 16 | C42 | — | 5 | 1 | no | — |
| 17 | C2×C5 | — | 16 | 1 | no | — |
| 18 | Q8 | — | 5 | 2 | no | — |
| 19 | Q8 | — | 10 | 2 | no | — |
| 20 | D4 | — | 5 | 2 | no | — |
| 21 | C2×C4 | — | 5 | 1 | no | — |
| 22 | C2×C4 | — | 5 | 2 | no | — |
| 23 | C2×C4 | — | 10 | 1 | no | — |
| 24 | C2×C4 | — | 10 | 1 | no | — |
| 25 | C8 | — | 10 | 2 | no | — |
| 26 | C5 | — | 16 | 1 | no | Sylow |
| 27 | C22 | — | 5 | 1 | no | — |
| 28 | C4 | — | 5 | 2 | no | — |
| 29 | C4 | — | 10 | 2 | no | — |
| 30 | C4 | — | 20 | 1 | no | — |
| 31 | C2 | — | 10 | 1 | no | — |
| 32 | C2 | (C24⋊C5)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | (C24⋊C5)⋊C2 |
| commutator, prime radical, cosocle, hypocenter | 2−1+4⋊C5 | C2 |
| Fitting | 2−1+4 | D5 |
| LCS | G ▷ 2−1+4⋊C5 | |
| UCS | C1 ◁ C2 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 2−1+4⋊C5 | 2 |
| #456 | 5 |
| Dic5 | 16 |