Subgroups — C₂×C₃×C₁₇×D₁₆₉ #46828166

Order 34476.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₆₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₁₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₇×C₁₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₁₆₉	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₇×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₇×C₁₆₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₇×D₁₃	—	13	1	no	maximal
9	C₂×C₃×D₁₆₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₁₃×C₁₇	D₁₃	1	1	yes	characteristic
11	C₃×C₁₇×D₁₃	—	13	2	no	—
12	C₂×C₃×C₁₆₉	C₂×C₁₇	1	1	yes	characteristic, complemented
13	C₃×D₁₆₉	C₂×C₁₇	1	2	yes	direct product factor
14	C₂×C₁₇×D₁₃	—	13	1	no	—
15	C₂×D₁₆₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃×C₁₇	C₂×D₁₃	1	1	yes	characteristic
17	C₃×C₁₆₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃×C₁₇	C₃×D₁₃	1	1	yes	characteristic
19	C₁₇×D₁₃	—	13	2	no	—
20	C₂×C₁₆₉	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
21	D₁₆₉	C₂×C₃×C₁₇	1	2	yes	direct product factor
22	C₁₃×C₁₇	C₂×C₃×D₁₃	1	1	yes	characteristic
23	C₂²×C₃×C₁₇	—	169	1	no	Hall
24	C₁₆₉	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×D₁₃	—	13	1	no	—
26	C₂×C₃×C₁₇	—	169	2	no	—
27	C₂×C₃×C₁₇	D₁₆₉	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₁₃	C₁₇×D₁₃	1	1	yes	characteristic
29	C₃×D₁₃	—	13	2	no	—
30	C₂²×C₁₇	—	169	1	no	Hall
31	C₂×D₁₃	—	13	1	no	—
32	C₃×C₁₇	C₂×D₁₆₉	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₁₃	C₂×C₁₇×D₁₃	1	1	yes	characteristic
34	C₂×C₁₇	—	169	2	no	—
35	C₂×C₁₇	C₃×D₁₆₉	1	1	yes	characteristic, direct product factor
36	C₂×C₁₃	C₃×C₁₇×D₁₃	1	1	yes	characteristic
37	D₁₃	—	13	2	no	—
38	C₁₇	C₂×C₃×D₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₃	C₂×C₃×C₁₇×D₁₃	1	1	yes	characteristic
40	C₂²×C₃	—	169	1	no	Hall
41	C₂×C₃	—	169	2	no	—
42	C₂×C₃	C₁₇×D₁₆₉	1	1	yes	characteristic, direct product factor
43	C₂²	—	169	1	no	Sylow
44	C₃	C₂×C₁₇×D₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	169	2	no	—
46	C₂	C₃×C₁₇×D₁₆₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₁₆₉
commutator, cosocle, hypocenter	C₁₆₉	C₂²×C₃×C₁₇
Frattini	C₁₃	C₂×C₃×C₁₇×D₁₃
Fitting	C₂×C₃×C₁₇×C₁₆₉	C₂
socle	C₂×C₃×C₁₃×C₁₇	D₁₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₁₆₉	C₂	direct (N × H)
2. C₂×C₃×C₁₇×C₁₆₉	C₂	semidirect
3. C₂×C₁₇×D₁₆₉	C₃	direct (N × H)
4. C₃×C₁₇×C₁₆₉	C₂²	semidirect
5. C₁₇×D₁₆₉	C₂×C₃	direct (N × H)
6. C₂×C₁₇×C₁₆₉	C₂×C₃	semidirect
7. C₁₇×C₁₆₉	C₂²×C₃	semidirect
9. C₂×C₃×D₁₆₉	C₁₇	direct (N × H)
12. C₂×C₃×C₁₆₉	C₂×C₁₇	semidirect
13. C₃×D₁₆₉	C₂×C₁₇	direct (N × H)
15. C₂×D₁₆₉	C₃×C₁₇	direct (N × H)
17. C₃×C₁₆₉	C₂²×C₁₇	semidirect
20. C₂×C₁₆₉	C₂×C₃×C₁₇	semidirect
21. D₁₆₉	C₂×C₃×C₁₇	direct (N × H)
24. C₁₆₉	C₂²×C₃×C₁₇	semidirect
27. C₂×C₃×C₁₇	D₁₆₉	direct (N × H)
32. C₃×C₁₇	C₂×D₁₆₉	direct (N × H)
35. C₂×C₁₇	C₃×D₁₆₉	direct (N × H)
38. C₁₇	C₂×C₃×D₁₆₉	direct (N × H)
42. C₂×C₃	C₁₇×D₁₆₉	direct (N × H)
44. C₃	C₂×C₁₇×D₁₆₉	direct (N × H)
46. C₂	C₃×C₁₇×D₁₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₇×D₁₆₉	2
C₂×C₃×C₁₇×C₁₆₉	2
C₂×C₁₇×D₁₆₉	3
C₂×C₃×C₁₇×D₁₃	13
C₂×C₃×D₁₆₉	17

Subgroups — C2×C3×C17×D169 #46828166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₇×D₁₆₉ #46828166