Finite Group DatabasebetaFinite Group DatabasebetaOrder 7200.
2244 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 2244 conjugacy classes of subgroups — too many to draw. Only its 247 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72222577 |
| commutator, hypocenter | C32×C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C22×C4 |
| prime radical | C2×#14268487 | C2 |
| cosocle | C32×C5⋊D5 | C24 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14268437 | 2 |
| C2×C3×#10597183 | 2 |
| C2×#14268434 | 2 |
| C2×C3⋊D3×#1044 | 2 |
| C2×D3×D5⋊AGL(1,𝔽5) | 3 |
| #72222577 | 2 |
| C2×#14268487 | 2 |
| C2×D32×AGL(1,𝔽5) | 5 |