Subgroups — C₅×C₃⋊#66772 #19099802

Order 5100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×#66772	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#66772	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₃⋊#595	—	5	1	no	maximal
6	C₅²×D₁₇	D₃	1	1	yes	characteristic
7	C₃×C₅×D₁₇	—	2	2	no	—
8	C₃×C₅×D₁₇	D₅	1	1	yes	characteristic
9	C₃×C₅×D₁₇	C₂×C₅	1	1	yes	characteristic
10	C₅²×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
11	#66772	—	3	1	no	—
12	C₅×#595	—	15	1	no	—
13	C₅×Dic₁₅	—	17	1	no	maximal, Hall
14	C₃×C₅×C₁₇	—	2	2	no	—
15	C₃×C₅×C₁₇	Dic₅	1	1	yes	characteristic, complemented
16	C₃×C₅×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented
17	C₃⋊#595	—	5	1	no	Hall
18	C₅×D₁₇	—	2	2	no	—
19	C₅×D₁₇	C₅×D₃	1	1	yes	characteristic
20	C₅×D₁₇	D₁₅	1	1	yes	characteristic
21	C₂×C₃×C₅²	—	17	1	no	—
22	C₃×D₁₇	C₅×D₅	1	1	yes	characteristic
23	C₅×Dic₅	—	51	1	no	Hall
24	C₅×C₁₇	—	2	2	no	—
25	C₅×C₁₇	C₅×Dic₃	1	1	yes	characteristic, complemented
26	C₅×C₁₇	Dic₁₅	1	1	yes	characteristic, complemented
27	C₃×C₅²	#595	1	1	yes	characteristic, complemented, Hall
28	#595	—	15	1	no	Hall
29	Dic₁₅	—	17	1	no	—
30	C₅×Dic₃	—	85	1	no	—
31	C₃×C₁₇	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅²	—	17	1	no	—
33	D₁₇	C₅×D₁₅	1	1	yes	characteristic
34	C₂×C₃×C₅	—	17	1	no	—
35	C₂×C₃×C₅	—	17	1	no	—
36	C₂×C₃×C₅	—	34	2	no	—
37	C₅²	C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
38	C₄×C₅	—	255	1	no	—
39	Dic₅	—	51	1	no	—
40	C₁₇	C₅×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₅	—	2	2	no	—
42	C₃×C₅	C₅×#595	1	1	yes	characteristic, complemented
43	C₃×C₅	#66772	1	1	yes	characteristic, complemented
44	Dic₃	—	85	1	no	Hall
45	C₂×C₅	—	17	1	no	—
46	C₂×C₅	—	17	1	no	—
47	C₂×C₅	—	34	2	no	—
48	C₂×C₃	—	17	1	no	—
49	C₅	—	2	2	no	—
50	C₅	C₅×C₃⋊#595	1	1	yes	characteristic, complemented
51	C₅	C₃⋊#66772	1	1	yes	characteristic, direct product factor
52	C₄	—	255	1	no	Sylow
53	C₃	C₅×#66772	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#66772
commutator, hypocenter	C₃×C₅×C₁₇	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₇	C₄
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₇	C₄	semidirect
4. C₃⋊#66772	C₅	direct (N × H)
10. C₅²×C₁₇	Dic₃	semidirect
15. C₃×C₅×C₁₇	Dic₅	semidirect
16. C₃×C₅×C₁₇	C₄×C₅	semidirect
25. C₅×C₁₇	C₅×Dic₃	semidirect
26. C₅×C₁₇	Dic₁₅	semidirect
27. C₃×C₅²	#595	semidirect
31. C₃×C₁₇	C₅×Dic₅	semidirect
37. C₅²	C₃⋊#595	semidirect
40. C₁₇	C₅×Dic₁₅	semidirect
42. C₃×C₅	C₅×#595	semidirect
43. C₃×C₅	#66772	semidirect
50. C₅	C₅×C₃⋊#595	semidirect
51. C₅	C₃⋊#66772	direct (N × H)
53. C₃	C₅×#66772	semidirect

Subgroups — C5×C3⋊#66772 #19099802

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊#66772 #19099802