Subgroups — C₂×C₅×C₇×D₂₅₇ #49112680

Order 35980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₂₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₂₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₂₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₂₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇×C₂₅₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×D₂₅₇	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₂₅₇	C₂×C₇	1	1	yes	characteristic, complemented
9	C₅×D₂₅₇	C₂×C₇	1	2	yes	direct product factor
10	C₇×C₂₅₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂₅₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₂₅₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₂₅₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented
14	D₂₅₇	C₂×C₅×C₇	1	2	yes	direct product factor
15	C₂₅₇	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅×C₇	—	257	1	no	maximal, Hall
17	C₂×C₅×C₇	—	257	2	no	—
18	C₂×C₅×C₇	D₂₅₇	1	1	yes	characteristic, direct product factor
19	C₅×C₇	C₂×D₂₅₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₇	—	257	1	no	Hall
21	C₂²×C₅	—	257	1	no	Hall
22	C₂×C₇	—	257	2	no	—
23	C₂×C₇	C₅×D₂₅₇	1	1	yes	characteristic, direct product factor
24	C₂×C₅	—	257	2	no	—
25	C₂×C₅	C₇×D₂₅₇	1	1	yes	characteristic, direct product factor
26	C₇	C₂×C₅×D₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₅	C₂×C₇×D₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	257	1	no	Sylow
29	C₂	—	257	2	no	—
30	C₂	C₅×C₇×D₂₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₂₅₇
commutator, cosocle, hypocenter	C₂₅₇	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₅₇	C₂
LCS	G ▷ C₂₅₇
UCS	C₁ ◁ C₂×C₅×C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×C₇×D₂₅₇	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₅₇	C₂	semidirect
3. C₅×C₇×C₂₅₇	C₂²	semidirect
4. C₂×C₇×D₂₅₇	C₅	direct (N × H)
5. C₂×C₅×D₂₅₇	C₇	direct (N × H)
6. C₂×C₇×C₂₅₇	C₂×C₅	semidirect
7. C₇×D₂₅₇	C₂×C₅	direct (N × H)
8. C₂×C₅×C₂₅₇	C₂×C₇	semidirect
9. C₅×D₂₅₇	C₂×C₇	direct (N × H)
10. C₇×C₂₅₇	C₂²×C₅	semidirect
11. C₅×C₂₅₇	C₂²×C₇	semidirect
12. C₂×D₂₅₇	C₅×C₇	direct (N × H)
13. C₂×C₂₅₇	C₂×C₅×C₇	semidirect
14. D₂₅₇	C₂×C₅×C₇	direct (N × H)
15. C₂₅₇	C₂²×C₅×C₇	semidirect
18. C₂×C₅×C₇	D₂₅₇	direct (N × H)
19. C₅×C₇	C₂×D₂₅₇	direct (N × H)
23. C₂×C₇	C₅×D₂₅₇	direct (N × H)
25. C₂×C₅	C₇×D₂₅₇	direct (N × H)
26. C₇	C₂×C₅×D₂₅₇	direct (N × H)
27. C₅	C₂×C₇×D₂₅₇	direct (N × H)
30. C₂	C₅×C₇×D₂₅₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₇×D₂₅₇	2
C₂×C₅×C₇×C₂₅₇	2
C₂×C₇×D₂₅₇	5
C₂×C₅×D₂₅₇	7
C₂²×C₅×C₇	257

Subgroups — C2×C5×C7×D257 #49112680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×D₂₅₇ #49112680