Subgroups — C₂×D₃₅×C₁₆₉ #37556804

Order 23660.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅×C₁₆₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₁₆₉	—	5	1	no	maximal, Hall
5	C₂×D₅×C₁₆₉	—	7	1	no	maximal, Hall
6	D₇×C₁₆₉	—	5	2	no	—
7	C₂×C₇×C₁₆₉	D₅	1	1	yes	characteristic, complemented
8	C₂×C₁₃×D₃₅	C₁₃	1	1	yes	maximal, characteristic
9	C₂×C₅×C₁₆₉	D₇	1	1	yes	characteristic, complemented
10	D₅×C₁₆₉	—	7	2	no	—
11	C₇×C₁₆₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇×C₁₃	C₂×C₁₃	1	1	yes	characteristic
13	C₁₃×D₃₅	C₂×C₁₃	1	2	yes	—
14	C₅×C₁₆₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₁₆₉	—	35	1	no	Hall
16	C₅×C₇×C₁₃	C₂²×C₁₃	1	1	yes	characteristic
17	C₂×C₁₃×D₇	—	5	1	no	—
18	C₂×C₁₆₉	—	35	2	no	—
19	C₂×C₁₆₉	D₃₅	1	1	yes	characteristic, direct product factor
20	C₂×D₅×C₁₃	—	7	1	no	—
21	C₂×C₇×C₁₃	D₅×C₁₃	1	1	yes	characteristic
22	C₁₃×D₇	—	5	2	no	—
23	C₁₆₉	C₂×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃₅	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅×C₁₃	C₁₃×D₇	1	1	yes	characteristic
26	D₅×C₁₃	—	7	2	no	—
27	C₇×C₁₃	C₂×D₅×C₁₃	1	1	yes	characteristic
28	C₂×C₅×C₇	C₂×C₁₆₉	1	1	yes	characteristic, complemented
29	D₃₅	C₂×C₁₆₉	1	2	yes	direct product factor
30	C₅×C₁₃	C₂×C₁₃×D₇	1	1	yes	characteristic
31	C₂²×C₁₃	—	35	1	no	—
32	C₅×C₇	C₂²×C₁₆₉	1	1	yes	characteristic, complemented, Hall
33	C₂×D₇	—	5	1	no	Hall
34	C₂×C₁₃	—	35	2	no	—
35	C₂×C₁₃	C₁₃×D₃₅	1	1	yes	characteristic
36	C₂×D₅	—	7	1	no	Hall
37	C₂×C₇	D₅×C₁₆₉	1	1	yes	characteristic, complemented
38	D₇	—	5	2	no	—
39	C₁₃	C₂×C₁₃×D₃₅	1	1	yes	characteristic
40	C₂×C₅	D₇×C₁₆₉	1	1	yes	characteristic, complemented
41	D₅	—	7	2	no	—
42	C₇	C₂×D₅×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
43	C₅	C₂×D₇×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	35	1	no	Sylow
45	C₂	—	35	2	no	—
46	C₂	D₃₅×C₁₆₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₆₉	D₃₅
commutator, hypocenter	C₅×C₇	C₂²×C₁₆₉
Frattini	C₁₃	C₂×C₁₃×D₃₅
Fitting	C₂×C₅×C₇×C₁₆₉	C₂
socle	C₂×C₅×C₇×C₁₃	C₂×C₁₃
prime radical	C₂×C₁₃×D₃₅	C₁₃
cosocle	C₅×C₇×C₁₃	C₂²×C₁₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₁₆₉

Complements

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

N	H ≅ G/N	type
1. D₃₅×C₁₆₉	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₆₉	C₂	semidirect
3. C₅×C₇×C₁₆₉	C₂²	semidirect
7. C₂×C₇×C₁₆₉	D₅	semidirect
9. C₂×C₅×C₁₆₉	D₇	semidirect
11. C₇×C₁₆₉	C₂×D₅	semidirect
14. C₅×C₁₆₉	C₂×D₇	semidirect
19. C₂×C₁₆₉	D₃₅	direct (N × H)
23. C₁₆₉	C₂×D₃₅	direct (N × H)
24. C₂×D₃₅	C₁₆₉	direct (N × H)
28. C₂×C₅×C₇	C₂×C₁₆₉	semidirect
29. D₃₅	C₂×C₁₆₉	direct (N × H)
32. C₅×C₇	C₂²×C₁₆₉	semidirect
37. C₂×C₇	D₅×C₁₆₉	semidirect
40. C₂×C₅	D₇×C₁₆₉	semidirect
42. C₇	C₂×D₅×C₁₆₉	semidirect
43. C₅	C₂×D₇×C₁₆₉	semidirect
46. C₂	D₃₅×C₁₆₉	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×C₁₆₉	2
C₂×C₅×C₇×C₁₆₉	2
C₂×D₇×C₁₆₉	5
C₂×D₅×C₁₆₉	7
C₂×C₁₃×D₃₅	13

Subgroups — C2×D35×C169 #37556804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₅×C₁₆₉ #37556804