Subgroups — C₃×C₁₇×C₁₉×D₁₇ #45681981

Order 32946.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₁₉×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₇×C₁₉	—	17	1	no	maximal
5	C₃×C₁₉×D₁₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor
6	C₃×C₁₇×D₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₇×C₁₉	—	2	8	no	—
8	C₃×C₁₇×C₁₉	D₁₇	1	1	yes	characteristic, direct product factor
9	C₃×C₁₇×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented
10	C₃×C₁₇²	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×C₁₉	—	17	1	no	—
12	C₁₉×D₁₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor
13	C₁₇×D₁₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₁₇×C₁₉	—	2	8	no	—
15	C₁₇×C₁₉	C₃×D₁₇	1	1	yes	characteristic, direct product factor
16	C₁₇×C₁₉	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
17	C₁₇²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₁₉	—	17	1	no	Hall
19	C₂×C₃×C₁₇	—	17	1	no	—
20	C₃×D₁₇	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor
21	C₃×C₁₉	C₁₇×D₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₇	—	2	8	no	—
23	C₃×C₁₇	C₁₉×D₁₇	1	1	yes	characteristic, direct product factor
24	C₃×C₁₇	C₂×C₁₇×C₁₉	1	1	yes	characteristic, complemented
25	C₂×C₁₉	—	17	1	no	Hall
26	C₂×C₁₇	—	17	1	no	—
27	D₁₇	C₃×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor
28	C₁₉	C₃×C₁₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₁₇	—	2	8	no	—
30	C₁₇	C₃×C₁₉×D₁₇	1	1	yes	characteristic, direct product factor
31	C₁₇	C₂×C₃×C₁₇×C₁₉	1	1	yes	characteristic, complemented
32	C₂×C₃	—	17	1	no	Hall
33	C₃	C₁₇×C₁₉×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇×C₁₉	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₇²×C₁₉	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₁₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇²×C₁₉	C₂	semidirect
2. C₁₇×C₁₉×D₁₇	C₃	direct (N × H)
3. C₁₇²×C₁₉	C₂×C₃	semidirect
5. C₃×C₁₉×D₁₇	C₁₇	direct (N × H)
6. C₃×C₁₇×D₁₇	C₁₉	direct (N × H)
8. C₃×C₁₇×C₁₉	D₁₇	direct (N × H)
9. C₃×C₁₇×C₁₉	C₂×C₁₇	semidirect
10. C₃×C₁₇²	C₂×C₁₉	semidirect
12. C₁₉×D₁₇	C₃×C₁₇	direct (N × H)
13. C₁₇×D₁₇	C₃×C₁₉	direct (N × H)
15. C₁₇×C₁₉	C₃×D₁₇	direct (N × H)
16. C₁₇×C₁₉	C₂×C₃×C₁₇	semidirect
17. C₁₇²	C₂×C₃×C₁₉	semidirect
20. C₃×D₁₇	C₁₇×C₁₉	direct (N × H)
21. C₃×C₁₉	C₁₇×D₁₇	direct (N × H)
23. C₃×C₁₇	C₁₉×D₁₇	direct (N × H)
24. C₃×C₁₇	C₂×C₁₇×C₁₉	semidirect
27. D₁₇	C₃×C₁₇×C₁₉	direct (N × H)
28. C₁₉	C₃×C₁₇×D₁₇	direct (N × H)
30. C₁₇	C₃×C₁₉×D₁₇	direct (N × H)
31. C₁₇	C₂×C₃×C₁₇×C₁₉	semidirect
33. C₃	C₁₇×C₁₉×D₁₇	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×C₁₇²×C₁₉	2
C₁₇×C₁₉×D₁₇	3
C₂×C₃×C₁₇×C₁₉	17
C₃×C₁₉×D₁₇	17
C₃×C₁₇×D₁₇	19

Subgroups — C3×C17×C19×D17 #45681981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×C₁₉×D₁₇ #45681981