Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
720 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D52 |
| commutator, socle, cosocle | C23×C52 | C23 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #392 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×D20 | C2 | semidirect |
| 2. C22×#6037 | C2 | semidirect |
| 3. C2×C5×#685 | C2 | semidirect |
| 4. C2×#87778 | C2 | semidirect |
| 5. #11716698 | C2 | semidirect |
| 31. C22×C5×D5 | D4 | semidirect |
| 32. C22×C5×D5 | D4 | semidirect |
| 34. C2×C4×C52 | D4 | semidirect |
| 37. C2×#1039 | D4 | semidirect |
| 45. C22×D20 | D5 | semidirect |
| 49. C2×#685 | D5 | semidirect |
| 132. C22×D5 | D20 | semidirect |
| 133. C22×D5 | C22⋊D5 | semidirect |
| 141. C2×C4×C5 | C22⋊D5 | semidirect |
| 142. C2×C4×C5 | C22⋊D5 | semidirect |
| 162. C52 | #392 | semidirect |
| 262. C2×C4 | #6037 | semidirect |
| 264. C5 | #65249 | semidirect |
| 265. C5 | #65512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×#6037 | 2 |
| C2×C5×#685 | 2 |
| C2×#87778 | 2 |
| #11716698 | 2 |
| #65512 | 5 |
| #65249 | 5 |