Subgroups — C₃×#13133348 #19099786

Order 5100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	#13133348	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	2	no	maximal
5	C₁₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₁₇	—	5	2	no	—
7	C₃×D₅×C₁₇	—	10	2	no	—
8	C₅²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	#66774	—	5	2	no	—
10	C₃×#1044	—	17	1	no	maximal, Hall
11	C₃×C₅×C₁₇	—	2	2	no	—
12	C₃×C₅×C₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
13	C₃×Dic₁₇	—	25	1	no	Hall
14	D₅×C₁₇	—	5	2	no	—
15	D₅×C₁₇	—	10	2	no	—
16	C₃×C₅⋊D₅	D₁₇	1	1	yes	characteristic
17	C₂×C₃×C₁₇	—	25	1	no	—
18	#1044	—	17	1	no	Hall
19	C₅×C₁₇	—	2	2	no	—
20	C₅×C₁₇	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
21	C₃×C₅²	Dic₁₇	1	1	yes	characteristic, complemented, Hall
22	Dic₁₇	—	25	1	no	Hall
23	C₃×AGL(1,𝔽₅)	—	85	2	no	—
24	C₃×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
25	C₅⋊D₅	C₃×D₁₇	1	1	yes	characteristic
26	C₂×C₁₇	—	25	1	no	—
27	C₃×D₅	—	5	2	no	—
28	C₃×D₅	—	10	2	no	—
29	C₅²	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
30	AGL(1,𝔽₅)	—	85	2	no	—
31	C₁₇	C₃×#1044	1	1	yes	characteristic, complemented, Sylow
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	#66774	1	2	yes	complemented
34	C₃×C₄	—	425	1	no	Hall
35	D₅	—	5	2	no	—
36	D₅	—	10	2	no	—
37	C₂×C₃	—	25	1	no	—
38	C₅	—	2	2	no	—
39	C₅	C₃×#66774	1	2	yes	complemented
40	C₄	—	425	1	no	Sylow
41	C₃	#13133348	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#13133348
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. #13133348	C₃	direct (N × H)
3. C₃×C₅²×C₁₇	C₄	semidirect
8. C₅²×C₁₇	C₃×C₄	semidirect
12. C₃×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
20. C₅×C₁₇	C₃×AGL(1,𝔽₅)	semidirect
21. C₃×C₅²	Dic₁₇	semidirect
24. C₃×C₁₇	#1044	semidirect
29. C₅²	C₃×Dic₁₇	semidirect
31. C₁₇	C₃×#1044	semidirect
33. C₃×C₅	#66774	semidirect
39. C₅	C₃×#66774	semidirect
41. C₃	#13133348	direct (N × H)

Subgroups — C3×#13133348 #19099786

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133348 #19099786