Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
70 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#124 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #3935 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C5×Q8 | C4 | 1 | 1 | yes | characteristic |
| 4 | C2×C5×D4 | C4 | 1 | 1 | yes | characteristic |
| 5 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 6 | C42×C5 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#168 | — | 2 | 2 | no | — |
| 8 | #329 | — | 5 | 1 | no | maximal, Sylow |
| 9 | C23×C5 | — | 2 | 1 | no | — |
| 10 | C5×Q8 | — | 4 | 1 | no | — |
| 11 | C5×D4 | — | 4 | 1 | no | — |
| 12 | C2×C4×C5 | — | 2 | 1 | no | — |
| 13 | C2×C4×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 14 | C2×C4×C5 | D4 | 1 | 2 | yes | — |
| 15 | #168 | — | 2 | 4 | no | — |
| 16 | #124 | D5 | 1 | 1 | yes | characteristic |
| 17 | #97 | — | 5 | 2 | no | — |
| 18 | C22×C5 | — | 4 | 1 | no | — |
| 19 | C22×C5 | — | 4 | 2 | no | — |
| 20 | C22×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 21 | C4×C5 | — | 2 | 1 | no | — |
| 22 | C4×C5 | — | 2 | 2 | no | — |
| 23 | C4×C5 | — | 4 | 1 | no | — |
| 24 | C2×Q8 | Dic5 | 1 | 1 | yes | characteristic |
| 25 | C2×D4 | Dic5 | 1 | 1 | yes | characteristic |
| 26 | C2×C8 | — | 10 | 2 | no | — |
| 27 | C22⋊C4 | — | 2 | 2 | no | — |
| 28 | C42 | C2×D5 | 1 | 1 | yes | characteristic |
| 29 | C2×C5 | — | 8 | 1 | no | — |
| 30 | C2×C5 | #100 | 1 | 1 | yes | characteristic |
| 31 | C2×C5 | #104 | 1 | 2 | yes | — |
| 32 | C23 | — | 2 | 1 | no | — |
| 33 | Q8 | — | 4 | 1 | no | — |
| 34 | D4 | — | 4 | 1 | no | — |
| 35 | C2×C4 | — | 2 | 1 | no | — |
| 36 | C2×C4 | C2×Dic5 | 1 | 1 | yes | characteristic |
| 37 | C2×C4 | C22⋊D5 | 1 | 2 | yes | — |
| 38 | C8 | — | 10 | 4 | no | — |
| 39 | C5 | #329 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 40 | C22 | — | 4 | 1 | no | — |
| 41 | C22 | — | 4 | 2 | no | — |
| 42 | C22 | C22⋊Dic5 | 1 | 1 | yes | characteristic |
| 43 | C4 | — | 2 | 1 | no | — |
| 44 | C4 | — | 2 | 2 | no | — |
| 45 | C4 | — | 4 | 1 | no | — |
| 46 | C2 | — | 8 | 1 | no | — |
| 47 | C2 | #3965 | 1 | 1 | yes | characteristic |
| 48 | C2 | #3969 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3935 | C2 | semidirect |
| 39. C5 | #329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#124 | 2 |
| #3935 | 2 |
| #329 | 5 |