Subgroups — C₃×C₁₉×#1043⋊C₃ #30685751

Order 17100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#1043	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1043⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₁₉×(C₅⋊D₅)⋊C₃	C₂×C₃	1	3	yes	—
7	C₁₉×#1043	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₉×C₅²⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₃×C₁₉×AGL(1,𝔽₅)	—	15	2	no	—
11	C₁₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
12	C₃×#1043⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₄×C₁₉	—	25	1	no	maximal, Hall
14	C₃×D₅×C₁₉	—	15	2	no	—
15	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
16	C₃×(C₅⋊D₅)⋊C₃	C₂×C₁₉	1	1	yes	characteristic
17	C₁₉×AGL(1,𝔽₅)	—	15	2	no	—
18	C₂×C₃²×C₁₉	—	25	1	no	—
19	C₃×#1043	C₃×C₁₉	1	1	yes	characteristic, complemented
20	#1043⋊C₃	C₃×C₁₉	1	3	yes	direct product factor
21	C₃×C₅×C₁₉	—	3	2	no	—
22	C₃×C₄×C₁₉	—	25	1	no	—
23	C₃×C₄×C₁₉	—	25	3	no	—
24	C₃×C₅²⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
25	D₅×C₁₉	—	15	2	no	—
26	C₃²×C₁₉	—	25	1	no	Hall
27	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	1	yes	characteristic
28	(C₅⋊D₅)⋊C₃	C₂×C₃×C₁₉	1	3	yes	—
29	C₂×C₃×C₁₉	—	25	3	no	—
30	C₂×C₃×C₁₉	—	25	1	no	—
31	#1043	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
32	C₅×C₁₉	—	3	2	no	—
33	C₄×C₁₉	—	25	1	no	Hall
34	C₃×C₅²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
35	C₅²⋊C₃	C₃×C₄×C₁₉	1	3	yes	complemented
36	C₃×AGL(1,𝔽₅)	—	15	2	no	—
37	C₃×C₁₉	—	25	3	no	—
38	C₃×C₁₉	#1043⋊C₃	1	1	yes	characteristic, direct product factor
39	C₅⋊D₅	C₂×C₃²×C₁₉	1	1	yes	characteristic
40	C₂×C₁₉	—	25	1	no	—
41	C₃²×C₄	—	25	1	no	Hall
42	C₃×D₅	—	15	2	no	—
43	C₅²	C₃²×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
44	AGL(1,𝔽₅)	—	15	2	no	—
45	C₁₉	C₃×#1043⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₃²	—	25	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	25	1	no	—
49	C₃×C₄	—	25	3	no	—
50	D₅	—	15	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	25	3	no	—
53	C₂×C₃	—	25	1	no	—
54	C₅	—	3	2	no	—
55	C₄	—	25	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	C₁₉×#1043⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#1043⋊C₃
commutator, hypocenter	C₅²	C₃²×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₃×C₄
prime radical	C₃×C₁₉×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₅⋊D₅	C₂×C₃²×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×#1043	C₃	semidirect
3. C₁₉×#1043⋊C₃	C₃	direct (N × H)
4. C₃×C₁₉×C₅²⋊C₃	C₄	semidirect
7. C₁₉×#1043	C₃²	semidirect
8. C₃×C₅²×C₁₉	C₃×C₄	semidirect
9. C₁₉×C₅²⋊C₃	C₃×C₄	semidirect
12. C₃×#1043⋊C₃	C₁₉	direct (N × H)
15. C₅²×C₁₉	C₃²×C₄	semidirect
19. C₃×#1043	C₃×C₁₉	semidirect
20. #1043⋊C₃	C₃×C₁₉	direct (N × H)
24. C₃×C₅²⋊C₃	C₄×C₁₉	semidirect
31. #1043	C₃²×C₁₉	semidirect
34. C₃×C₅²	C₃×C₄×C₁₉	semidirect
35. C₅²⋊C₃	C₃×C₄×C₁₉	semidirect
38. C₃×C₁₉	#1043⋊C₃	direct (N × H)
43. C₅²	C₃²×C₄×C₁₉	semidirect
45. C₁₉	C₃×#1043⋊C₃	direct (N × H)
57. C₃	C₁₉×#1043⋊C₃	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×C₁₉×(C₅⋊D₅)⋊C₃	2
C₃×C₁₉×#1043	3
C₁₉×#1043⋊C₃	3
C₃×#1043⋊C₃	19
C₃²×C₄×C₁₉	25

Subgroups — C3×C19×#1043⋊C3 #30685751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#1043⋊C₃ #30685751