Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
728 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #532 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#709 | C2 | semidirect |
| 2. C2×C4×#1039 | C2 | semidirect |
| 3. #11717098 | C2 | semidirect |
| 4. #11717032 | C2 | semidirect |
| 5. C4×#6037 | C2 | semidirect |
| 6. #11716985 | C2 | semidirect |
| 7. #11716981 | C2 | semidirect |
| 24. C2×C4×C52 | D4 | semidirect |
| 37. C2×#709 | D5 | semidirect |
| 54. #1039 | #41 | semidirect |
| 97. C2×C4×C5 | C22⋊D5 | semidirect |
| 119. C52 | #532 | semidirect |
| 172. C2×C4 | #6037 | semidirect |
| 176. C5 | #66166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×C4×#1039 | 2 |
| #11717098 | 2 |
| #11717032 | 2 |
| C4×#6037 | 2 |
| #11716985 | 2 |
| #11716981 | 2 |
| #66166 | 5 |