Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
230 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D52 |
| commutator, socle | C2×C52 | C22×C8 |
| Fitting | C2×C52×C8 | C22 |
| prime radical | #87900 | C4 |
| cosocle | C52×C8 | C23 |
| hypercenter | C2×C8 | D52 |
| hypocenter | C52 | #504 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3944 | C2 | semidirect |
| 3. C2×C5×#672 | C2 | semidirect |
| 4. #11716585 | C2 | semidirect |
| 5. #11716583 | C2 | semidirect |
| 29. #3944 | D5 | semidirect |
| 30. C2×#672 | D5 | semidirect |
| 94. C52 | #504 | semidirect |
| 136. C5 | #65190 | semidirect |
| 137. C5 | #65196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717221 | 2 |
| C5×#3944 | 2 |
| C2×C5×#672 | 2 |
| #11716585 | 2 |
| #11716583 | 2 |
| #65196 | 5 |
| #65190 | 5 |