Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 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 | C2 | #4028 |
| commutator, cosocle | C2×C4×C5 | C23 |
| Frattini | C2×C4 | C22×D5 |
| Fitting | C5×#104 | C2 |
| socle | C2×C5 | #120 |
| hypercenter | #104 | D5 |
| hypocenter | C5 | #454 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #104 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #4150 | C2 | semidirect |
| 2. #4095 | C2 | semidirect |
| 3. #4054 | C2 | semidirect |
| 4. #4021 | C2 | semidirect |
| 5. C5×#104 | C2 | semidirect |
| 6. #3956 | C2 | semidirect |
| 7. #3937 | C2 | semidirect |
| 53. #104 | D5 | semidirect |
| 110. C5 | #454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4150 | 2 |
| #4095 | 2 |
| #4054 | 2 |
| #4021 | 2 |
| C5×#104 | 2 |
| #3956 | 2 |
| #3937 | 2 |
| #454 | 5 |