Subgroups — C₂×C₅×D₇×C₂₅₇ #49112681

Order 35980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₅₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₅×C₂₅₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₅₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₅×C₂₅₇

Complements

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

N	H ≅ G/N	type
1. C₅×D₇×C₂₅₇	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₅₇	C₂	semidirect
3. C₅×C₇×C₂₅₇	C₂²	semidirect
4. C₂×D₇×C₂₅₇	C₅	direct (N × H)
6. C₂×C₇×C₂₅₇	C₂×C₅	semidirect
7. D₇×C₂₅₇	C₂×C₅	direct (N × H)
9. C₂×C₅×C₂₅₇	D₇	direct (N × H)
10. C₇×C₂₅₇	C₂²×C₅	semidirect
11. C₅×C₂₅₇	C₂×D₇	direct (N × H)
14. C₂×C₂₅₇	C₅×D₇	direct (N × H)
15. C₂₅₇	C₂×C₅×D₇	direct (N × H)
16. C₂×C₅×D₇	C₂₅₇	direct (N × H)
17. C₂×C₅×C₇	C₂×C₂₅₇	semidirect
18. C₅×D₇	C₂×C₂₅₇	direct (N × H)
19. C₅×C₇	C₂²×C₂₅₇	semidirect
20. C₂×D₇	C₅×C₂₅₇	direct (N × H)
22. C₂×C₇	C₂×C₅×C₂₅₇	semidirect
23. D₇	C₂×C₅×C₂₅₇	direct (N × H)
25. C₂×C₅	D₇×C₂₅₇	direct (N × H)
26. C₇	C₂²×C₅×C₂₅₇	semidirect
27. C₅	C₂×D₇×C₂₅₇	direct (N × H)
30. C₂	C₅×D₇×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
C₅×D₇×C₂₅₇	2
C₂×C₅×C₇×C₂₅₇	2
C₂×D₇×C₂₅₇	5
C₂²×C₅×C₂₅₇	7
C₂×C₅×D₇	257

Subgroups — C2×C5×D7×C257 #49112681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₇×C₂₅₇ #49112681