Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D5 |
| commutator, socle | C22×C5 | C22×C4 |
| Fitting | C5×#97 | C2 |
| prime radical | C2×D20 | C4 |
| cosocle | C2×C4×C5 | C23 |
| hypercenter | #97 | D5 |
| hypocenter | C5 | #435 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#676 | C2 | semidirect |
| 2. C2×C8×D5 | C2 | semidirect |
| 4. C5×#97 | C2 | semidirect |
| 5. #3952 | C2 | semidirect |
| 6. #3952 | C2 | semidirect |
| 7. C4⋊#168 | C2 | semidirect |
| 35. C5×C8 | D4 | semidirect |
| 44. #97 | D5 | semidirect |
| 51. C2×D5 | M16 | semidirect |
| 91. C8 | D20 | semidirect |
| 92. C5 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#676 | 2 |
| C2×C8×D5 | 2 |
| C4×D20 | 2 |
| C5×#97 | 2 |
| #3952 | 2 |
| C4⋊#168 | 2 |
| #435 | 5 |