Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 83 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×#1042 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting, prime radical | C2×C52×D4 | C4 |
| cosocle | C2×C5×Dic5 | C23 |
| hypercenter | C2×D4 | #1042 |
| hypocenter | C52 | #436 |
| 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×#87853 | C2 | semidirect |
| 3. C22⋊#6032 | C2 | semidirect |
| 4. C4⋊#6032 | C2 | semidirect |
| 5. C4×#6032 | C2 | semidirect |
| 27. #6032 | D4 | semidirect |
| 42. C4×C52 | M16 | semidirect |
| 101. C52 | #436 | semidirect |
| 119. C4×C5 | #681 | semidirect |
| 120. C4×C5 | #704 | semidirect |
| 158. C5 | #65301 | semidirect |
| 159. C5 | #65774 | semidirect |
| 168. C4 | #87853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87853 | 2 |
| C5×D4×Dic5 | 2 |
| C22⋊#6032 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #65774 | 5 |
| #65301 | 5 |