Subgroups — C₃×#13133352 #19099790

Order 5100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	#13133352	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#66774	—	5	1	no	maximal
5	C₃×Dic₈₅	—	5	1	no	maximal
6	C₅×D₅×C₁₇	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₁₇	—	5	1	no	—
8	C₃×D₅×C₁₇	D₅	1	1	yes	characteristic
9	C₅²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	#66774	—	5	1	no	—
11	Dic₈₅	—	5	1	no	—
12	C₃×#1042	—	17	1	no	maximal, Hall
13	C₃×C₅×C₁₇	—	4	1	no	—
14	C₃×C₅×C₁₇	Dic₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
16	C₃×Dic₁₇	—	25	1	no	Hall
17	C₂×C₅×C₁₇	—	5	1	no	—
18	D₅×C₁₇	C₃×D₅	1	1	yes	characteristic
19	C₃×C₅×D₅	D₁₇	1	1	yes	characteristic
20	C₂×C₃×C₁₇	—	5	1	no	—
21	#1042	—	17	1	no	Hall
22	C₅×C₁₇	—	4	1	no	—
23	C₅×C₁₇	C₃×Dic₅	1	1	yes	characteristic, complemented
24	C₅×C₁₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	C₃×C₅²	Dic₁₇	1	1	yes	characteristic, complemented, Hall
26	Dic₁₇	—	25	1	no	Hall
27	C₃×AGL(1,𝔽₅)	—	85	1	no	—
28	C₃×Dic₅	—	85	1	no	—
29	C₃×C₁₇	#1042	1	1	yes	characteristic, complemented, Hall
30	C₅×D₅	C₃×D₁₇	1	1	yes	characteristic
31	C₂×C₁₇	—	5	1	no	—
32	C₂×C₃×C₅	—	5	1	no	—
33	C₃×D₅	D₈₅	1	1	yes	characteristic
34	C₅²	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
35	AGL(1,𝔽₅)	—	85	1	no	—
36	Dic₅	—	85	1	no	—
37	C₁₇	C₃×#1042	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	—	4	1	no	—
39	C₃×C₅	Dic₈₅	1	1	yes	characteristic, complemented
40	C₃×C₅	#66774	1	1	yes	characteristic, complemented
41	C₃×C₄	—	425	1	no	Hall
42	C₂×C₅	—	5	1	no	—
43	D₅	C₃×D₈₅	1	1	yes	characteristic
44	C₂×C₃	—	5	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₃×Dic₈₅	1	1	yes	characteristic, complemented
47	C₅	C₃×#66774	1	1	yes	characteristic, complemented
48	C₄	—	425	1	no	Sylow
49	C₃	#13133352	1	1	yes	characteristic, direct product factor, Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#13133352
commutator, hypocenter	C₅²×C₁₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₇	C₄
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. #13133352	C₃	direct (N × H)
3. C₃×C₅²×C₁₇	C₄	semidirect
9. C₅²×C₁₇	C₃×C₄	semidirect
14. C₃×C₅×C₁₇	Dic₅	semidirect
15. C₃×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
23. C₅×C₁₇	C₃×Dic₅	semidirect
24. C₅×C₁₇	C₃×AGL(1,𝔽₅)	semidirect
25. C₃×C₅²	Dic₁₇	semidirect
29. C₃×C₁₇	#1042	semidirect
34. C₅²	C₃×Dic₁₇	semidirect
37. C₁₇	C₃×#1042	semidirect
39. C₃×C₅	Dic₈₅	semidirect
40. C₃×C₅	#66774	semidirect
46. C₅	C₃×Dic₈₅	semidirect
47. C₅	C₃×#66774	semidirect
49. C₃	#13133352	direct (N × H)

Subgroups — C3×#13133352 #19099790

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133352 #19099790