Subgroups — C₁₆₉×Dic₅₁ #46828129

Order 34476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₇×C₁₆₉	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₁₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₁₆₉	D₃	1	1	yes	characteristic
5	C₁₇×C₁₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₁₃×Dic₅₁	C₁₃	1	1	yes	maximal, characteristic
7	Dic₃×C₁₆₉	—	17	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₁₇	C₂×C₁₃	1	1	yes	characteristic
9	C₂×C₃×C₁₆₉	D₁₇	1	1	yes	characteristic
10	C₁₃×Dic₁₇	—	3	1	no	—
11	C₄×C₁₆₉	—	51	1	no	Hall
12	C₃×C₁₃×C₁₇	C₄×C₁₃	1	1	yes	characteristic
13	C₃×C₁₆₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₁₇	D₃×C₁₃	1	1	yes	characteristic
15	C₂×C₁₆₉	D₅₁	1	1	yes	characteristic
16	C₁₃×C₁₇	Dic₃×C₁₃	1	1	yes	characteristic
17	Dic₅₁	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₆₉	Dic₅₁	1	1	yes	characteristic, direct product factor, Sylow
19	Dic₃×C₁₃	—	17	1	no	—
20	C₂×C₃×C₁₇	C₂×C₁₆₉	1	1	yes	characteristic
21	C₂×C₃×C₁₃	C₁₃×D₁₇	1	1	yes	characteristic
22	Dic₁₇	—	3	1	no	Hall
23	C₄×C₁₃	—	51	1	no	—
24	C₃×C₁₇	C₄×C₁₆₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₃	C₁₃×Dic₁₇	1	1	yes	characteristic
26	C₂×C₁₇	D₃×C₁₆₉	1	1	yes	characteristic
27	C₂×C₁₃	C₁₃×D₅₁	1	1	yes	characteristic
28	C₁₇	Dic₃×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	C₁₃×Dic₅₁	1	1	yes	characteristic
30	Dic₃	—	17	1	no	Hall
31	C₂×C₃	D₁₇×C₁₆₉	1	1	yes	characteristic
32	C₄	—	51	1	no	Sylow
33	C₃	Dic₁₇×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₅₁×C₁₆₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆₉	D₅₁
commutator, hypocenter	C₃×C₁₇	C₄×C₁₆₉
Frattini	C₂×C₁₃	C₁₃×D₅₁
Fitting	C₂×C₃×C₁₇×C₁₆₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₁₃×C₁₇	C₂×C₁₃
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂×C₁₆₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₇×C₁₆₉	C₄	semidirect
5. C₁₇×C₁₆₉	Dic₃	semidirect
13. C₃×C₁₆₉	Dic₁₇	semidirect
17. Dic₅₁	C₁₆₉	direct (N × H)
18. C₁₆₉	Dic₅₁	direct (N × H)
24. C₃×C₁₇	C₄×C₁₆₉	semidirect
28. C₁₇	Dic₃×C₁₆₉	semidirect
33. C₃	Dic₁₇×C₁₆₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₇×C₁₆₉	2
Dic₁₇×C₁₆₉	3
C₁₃×Dic₅₁	13
Dic₃×C₁₆₉	17

Subgroups — C169×Dic51 #46828129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆₉×Dic₅₁ #46828129