Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
218 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C5 |
| prime radical | C5×#121 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#126 | C2 | semidirect |
| 2. C5×#125 | C2 | semidirect |
| 3. C5×#123 | C2 | semidirect |
| 4. C5×#123 | C2 | semidirect |
| 5. C5×C22⋊Q8 | C2 | semidirect |
| 6. C5×C22⋊Q8 | C2 | semidirect |
| 8. C4×C5×D4 | C2 | semidirect |
| 9. C2×C5×C4⋊C4 | C2 | semidirect |
| 31. #539 | C5 | direct (N × H) |
| 48. #126 | C2×C5 | semidirect |
| 49. #125 | C2×C5 | semidirect |
| 50. #123 | C2×C5 | semidirect |
| 51. #123 | C2×C5 | semidirect |
| 52. C22⋊Q8 | C2×C5 | semidirect |
| 53. C22⋊Q8 | C2×C5 | semidirect |
| 55. C4×D4 | C2×C5 | semidirect |
| 56. C2×C4⋊C4 | C2×C5 | semidirect |
| 113. C5 | #539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#126 | 2 |
| C5×#125 | 2 |
| C5×#123 | 2 |
| C5×C22⋊Q8 | 2 |
| C5×#121 | 2 |
| C4×C5×D4 | 2 |
| C2×C5×C4⋊C4 | 2 |
| #539 | 5 |