Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
380 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11717040 |
| commutator, cosocle | C2×C4×C52 | C23 |
| Frattini | C2×C4 | C2×D52 |
| Fitting | C52×M16 | C22 |
| socle | C2×C52 | #120 |
| hypercenter | M16 | D52 |
| hypocenter | C52 | #453 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717472 | C2 | semidirect |
| 2. C5×#4054 | C2 | semidirect |
| 3. #11717032 | C2 | semidirect |
| 4. #11716948 | C2 | semidirect |
| 5. #11716692 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. #11716609 | C2 | semidirect |
| 11. C2×C5×D20 | C22 | semidirect |
| 18. C52×M16 | C22 | semidirect |
| 19. C4×#1039 | C22 | semidirect |
| 20. C5×#681 | C22 | semidirect |
| 33. C4⋊(C5⋊D5) | D4 | semidirect |
| 35. #6045 | D4 | semidirect |
| 41. C5×D20 | D4 | semidirect |
| 43. C5×Dic10 | D4 | semidirect |
| 57. #4054 | D5 | semidirect |
| 64. #3955 | D5 | semidirect |
| 98. C2×D20 | C2×D5 | semidirect |
| 103. C5×M16 | C2×D5 | semidirect |
| 104. C5×M16 | C2×D5 | semidirect |
| 110. #681 | C2×D5 | semidirect |
| 160. D20 | C22⋊D5 | semidirect |
| 169. Dic10 | C22⋊D5 | semidirect |
| 182. C52 | #453 | semidirect |
| 230. M16 | D52 | semidirect |
| 271. C5 | #65036 | semidirect |
| 272. C5 | #65487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717472 | 2 |
| C5×#4054 | 2 |
| #11717032 | 2 |
| #11716948 | 2 |
| #11716692 | 2 |
| C5×#3955 | 2 |
| #11716609 | 2 |
| #65487 | 5 |
| #65036 | 5 |