Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D5 |
| commutator, cosocle | C2×C4×C5 | C23 |
| Frattini | C2×C4 | C22×D5 |
| Fitting | C5×#102 | C2 |
| socle | C22×C5 | C2×D4 |
| hypercenter | #102 | D5 |
| hypocenter | C5 | #469 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #4084 | C2 | semidirect |
| 2. C2×#686 | C2 | semidirect |
| 3. C2×#676 | C2 | semidirect |
| 4. #4041 | C2 | semidirect |
| 5. C5×#102 | C2 | semidirect |
| 6. #3953 | C2 | semidirect |
| 7. #3940 | C2 | semidirect |
| 38. #168 | D4 | semidirect |
| 45. #102 | D5 | semidirect |
| 97. C5 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4084 | 2 |
| C2×#686 | 2 |
| C2×#676 | 2 |
| #4041 | 2 |
| C5×#102 | 2 |
| #3953 | 2 |
| #3940 | 2 |
| #469 | 5 |