Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
728 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×D4 | C22 |
| hypercenter | C2×D4 | D52 |
| hypocenter | C52 | #532 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#711 | C2 | semidirect |
| 2. C2×#87874 | C2 | semidirect |
| 3. #11717260 | C2 | semidirect |
| 4. C5×#4082 | C2 | semidirect |
| 5. #11717089 | C2 | semidirect |
| 6. #11717070 | C2 | semidirect |
| 7. C4×D5×Dic5 | C2 | semidirect |
| 8. #11716985 | C2 | semidirect |
| 9. #11716982 | C2 | semidirect |
| 45. C4×C5×D5 | D4 | semidirect |
| 53. C2×#711 | D5 | semidirect |
| 63. #4082 | D5 | semidirect |
| 78. #1039 | #41 | semidirect |
| 175. C4×D5 | C22⋊D5 | semidirect |
| 187. C52 | #532 | semidirect |
| 275. C5 | #66002 | semidirect |
| 276. C5 | #66166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C2×#87874 | 2 |
| #11717260 | 2 |
| C5×#4082 | 2 |
| #11717089 | 2 |
| #11717070 | 2 |
| C4×D5×Dic5 | 2 |
| #11716985 | 2 |
| #11716982 | 2 |
| #66166 | 5 |
| #66002 | 5 |