Subgroups — C₃⋊#13133347 #19099813

Order 5100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₈₅	C₂	1	1	yes	maximal, characteristic
2	#13133347	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#66776	—	5	1	no	maximal
5	C₃⋊#66775	—	5	1	no	maximal
6	C₅⋊D₈₅	D₃	1	1	yes	characteristic
7	C₃×D₈₅	—	5	1	no	—
8	C₃×D₈₅	—	5	1	no	—
9	C₃×D₈₅	—	10	2	no	—
10	C₅²×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
11	#66776	—	15	1	no	—
12	#66775	—	15	1	no	—
13	C₃⋊#1044	—	17	1	no	maximal, Hall
14	C₃×C₅×C₁₇	—	2	2	no	—
15	C₃×C₅×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
16	C₃×C₅×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₃⋊#595	—	25	1	no	Hall
18	D₈₅	—	5	1	no	—
19	D₈₅	—	5	1	no	—
20	D₈₅	—	10	2	no	—
21	C₃×C₅⋊D₅	—	17	1	no	—
22	C₃×D₁₇	—	25	1	no	—
23	#1044	—	51	1	no	Hall
24	C₅×C₁₇	—	2	2	no	—
25	C₅×C₁₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
26	C₅×C₁₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
27	C₃×C₅²	#595	1	1	yes	characteristic, complemented, Hall
28	#595	—	75	1	no	Hall
29	ΓL(1,𝔽₁₆)	—	85	1	no	—
30	ΓL(1,𝔽₁₆)	—	85	1	no	—
31	C₃×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
32	C₅⋊D₅	—	17	1	no	—
33	D₁₇	—	25	1	no	—
34	C₃×D₅	—	85	1	no	—
35	C₃×D₅	—	85	1	no	—
36	C₃×D₅	—	170	2	no	—
37	C₅²	C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
38	AGL(1,𝔽₅)	—	255	1	no	—
39	AGL(1,𝔽₅)	—	255	1	no	—
40	C₁₇	C₃⋊#1044	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₅	—	2	2	no	—
42	C₃×C₅	#66775	1	1	yes	characteristic, complemented
43	C₃×C₅	#66776	1	1	yes	characteristic, complemented
44	Dic₃	—	425	1	no	Hall
45	D₅	—	85	1	no	—
46	D₅	—	85	1	no	—
47	D₅	—	170	2	no	—
48	C₂×C₃	—	425	1	no	—
49	C₅	—	2	2	no	—
50	C₅	C₃⋊#66775	1	1	yes	characteristic, complemented
51	C₅	C₃⋊#66776	1	1	yes	characteristic, complemented
52	C₄	—	1275	1	no	Sylow
53	C₃	#13133347	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	425	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₇	C₄	semidirect
10. C₅²×C₁₇	Dic₃	semidirect
15. C₃×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
16. C₃×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
25. C₅×C₁₇	ΓL(1,𝔽₁₆)	semidirect
26. C₅×C₁₇	ΓL(1,𝔽₁₆)	semidirect
27. C₃×C₅²	#595	semidirect
31. C₃×C₁₇	#1044	semidirect
37. C₅²	C₃⋊#595	semidirect
40. C₁₇	C₃⋊#1044	semidirect
42. C₃×C₅	#66775	semidirect
43. C₃×C₅	#66776	semidirect
50. C₅	C₃⋊#66775	semidirect
51. C₅	C₃⋊#66776	semidirect
53. C₃	#13133347	semidirect

Subgroups — C3⋊#13133347 #19099813

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊#13133347 #19099813