Subgroups — C₂×D₃₅×C₂₅₇ #49112685

Order 35980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅×C₂₅₇	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×D₇×C₂₅₇	—	5	1	no	maximal, Hall
5	C₂×D₅×C₂₅₇	—	7	1	no	maximal, Hall
6	C₂×C₇×C₂₅₇	D₅	1	1	yes	characteristic, complemented
7	D₇×C₂₅₇	—	5	2	no	—
8	C₂×C₅×C₂₅₇	D₇	1	1	yes	characteristic, complemented
9	D₅×C₂₅₇	—	7	2	no	—
10	C₇×C₂₅₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂₅₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₂₅₇	—	35	1	no	Hall
13	C₂×C₂₅₇	—	35	2	no	—
14	C₂×C₂₅₇	D₃₅	1	1	yes	characteristic, direct product factor
15	C₂₅₇	C₂×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₃₅	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₇	C₂×C₂₅₇	1	1	yes	characteristic, complemented
18	D₃₅	C₂×C₂₅₇	1	2	yes	direct product factor
19	C₅×C₇	C₂²×C₂₅₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇	—	5	1	no	Hall
21	C₂×D₅	—	7	1	no	Hall
22	C₂×C₇	D₅×C₂₅₇	1	1	yes	characteristic, complemented
23	D₇	—	5	2	no	—
24	C₂×C₅	D₇×C₂₅₇	1	1	yes	characteristic, complemented
25	D₅	—	7	2	no	—
26	C₇	C₂×D₅×C₂₅₇	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₇×C₂₅₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	35	1	no	Sylow
29	C₂	—	35	2	no	—
30	C₂	D₃₅×C₂₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₅₇	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₂₅₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₅₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₂₅₇

Complements

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

N	H ≅ G/N	type
1. D₃₅×C₂₅₇	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₅₇	C₂	semidirect
3. C₅×C₇×C₂₅₇	C₂²	semidirect
6. C₂×C₇×C₂₅₇	D₅	semidirect
8. C₂×C₅×C₂₅₇	D₇	semidirect
10. C₇×C₂₅₇	C₂×D₅	semidirect
11. C₅×C₂₅₇	C₂×D₇	semidirect
14. C₂×C₂₅₇	D₃₅	direct (N × H)
15. C₂₅₇	C₂×D₃₅	direct (N × H)
16. C₂×D₃₅	C₂₅₇	direct (N × H)
17. C₂×C₅×C₇	C₂×C₂₅₇	semidirect
18. D₃₅	C₂×C₂₅₇	direct (N × H)
19. C₅×C₇	C₂²×C₂₅₇	semidirect
22. C₂×C₇	D₅×C₂₅₇	semidirect
24. C₂×C₅	D₇×C₂₅₇	semidirect
26. C₇	C₂×D₅×C₂₅₇	semidirect
27. C₅	C₂×D₇×C₂₅₇	semidirect
30. C₂	D₃₅×C₂₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₅×C₂₅₇	2
C₂×C₅×C₇×C₂₅₇	2
C₂×D₇×C₂₅₇	5
C₂×D₅×C₂₅₇	7
C₂×D₃₅	257

Subgroups — C2×D35×C257 #49112685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₅×C₂₅₇ #49112685