Subgroups — C₂×C₇×D₁₂₈₅ #49112684

Order 35980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₂₈₅	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	—	5	1	no	maximal, Hall
5	C₂×D₁₂₈₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇×C₂₅₇	D₅	1	1	yes	characteristic, complemented
7	C₇×D₂₅₇	—	5	2	no	—
8	C₂×C₅×C₂₅₇	C₂×C₇	1	1	yes	characteristic, complemented
9	D₁₂₈₅	C₂×C₇	1	2	yes	direct product factor
10	C₇×C₂₅₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂₅₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₂₅₇	—	5	1	no	Hall
13	C₂×C₂₅₇	C₇×D₅	1	1	yes	characteristic, complemented
14	D₂₅₇	—	5	2	no	—
15	C₂₅₇	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₇×D₅	—	257	1	no	maximal, Hall
17	C₂×C₅×C₇	D₂₅₇	1	1	yes	characteristic, complemented
18	C₇×D₅	—	257	2	no	—
19	C₅×C₇	C₂×D₂₅₇	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₇	—	1285	1	no	Hall
21	C₂×D₅	—	257	1	no	Hall
22	C₂×C₇	—	1285	2	no	—
23	C₂×C₇	D₁₂₈₅	1	1	yes	characteristic, direct product factor
24	C₂×C₅	C₇×D₂₅₇	1	1	yes	characteristic, complemented
25	D₅	—	257	2	no	—
26	C₇	C₂×D₁₂₈₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₅	C₂×C₇×D₂₅₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	1285	1	no	Sylow
29	C₂	—	1285	2	no	—
30	C₂	C₇×D₁₂₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₂₈₅
commutator, cosocle, hypocenter	C₅×C₂₅₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₅₇	C₂
LCS	G ▷ C₅×C₂₅₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₂₈₅	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₅₇	C₂	semidirect
3. C₅×C₇×C₂₅₇	C₂²	semidirect
5. C₂×D₁₂₈₅	C₇	direct (N × H)
6. C₂×C₇×C₂₅₇	D₅	semidirect
8. C₂×C₅×C₂₅₇	C₂×C₇	semidirect
9. D₁₂₈₅	C₂×C₇	direct (N × H)
10. C₇×C₂₅₇	C₂×D₅	semidirect
11. C₅×C₂₅₇	C₂²×C₇	semidirect
13. C₂×C₂₅₇	C₇×D₅	semidirect
15. C₂₅₇	C₂×C₇×D₅	semidirect
17. C₂×C₅×C₇	D₂₅₇	semidirect
19. C₅×C₇	C₂×D₂₅₇	semidirect
23. C₂×C₇	D₁₂₈₅	direct (N × H)
24. C₂×C₅	C₇×D₂₅₇	semidirect
26. C₇	C₂×D₁₂₈₅	direct (N × H)
27. C₅	C₂×C₇×D₂₅₇	semidirect
30. C₂	C₇×D₁₂₈₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₁₂₈₅	2
C₂×C₅×C₇×C₂₅₇	2
C₂×C₇×D₂₅₇	5
C₂×D₁₂₈₅	7
C₂×C₇×D₅	257

Subgroups — C2×C7×D1285 #49112684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₂₈₅ #49112684