Subgroups — C₃×C₁₉×#5997⋊C₃ #45692200

Order 33516.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#64424	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#5997	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#5997⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₉×#3861	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₁₉×#64424	C₂×C₃	1	3	yes	—
7	C₁₉×#5997	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₁₉×#3861	C₃×C₄	1	3	yes	complemented
9	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃×C₁₉×AGL(1,𝔽₇)	—	14	4	no	—
11	C₁₉×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
12	C₃×#5997⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₉×ΓL(1,𝔽₈)	—	14	4	no	—
14	C₇²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×#64424	C₂×C₁₉	1	1	yes	characteristic
16	C₃×D₇×C₁₉	—	14	4	no	—
17	C₁₉×AGL(1,𝔽₇)	—	14	12	no	—
18	C₃²×C₄×C₁₉	—	49	1	no	maximal, Hall
19	C₃×#5997	C₃×C₁₉	1	1	yes	characteristic, complemented
20	#5997⋊C₃	C₃×C₁₉	1	3	yes	direct product factor
21	C₃×#3861	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇×C₁₉	—	2	4	no	—
23	C₁₉×ΓL(1,𝔽₈)	—	14	12	no	—
24	C₂×C₃²×C₁₉	—	49	1	no	—
25	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	1	yes	characteristic
26	#64424	C₂×C₃×C₁₉	1	3	yes	—
27	D₇×C₁₉	—	14	4	no	—
28	C₃×C₄×C₁₉	—	49	1	no	—
29	C₃×C₄×C₁₉	—	49	3	no	—
30	#5997	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃²×C₁₉	—	49	1	no	Hall
32	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
33	#3861	C₃×C₄×C₁₉	1	3	yes	complemented
34	C₇×C₁₉	—	2	4	no	—
35	C₃×AGL(1,𝔽₇)	—	14	4	no	—
36	C₂×C₃×C₁₉	—	49	3	no	—
37	C₂×C₃×C₁₉	—	49	1	no	—
38	C₇⋊D₇	C₂×C₃²×C₁₉	1	1	yes	characteristic
39	C₄×C₁₉	—	49	1	no	Hall
40	C₃×ΓL(1,𝔽₈)	—	14	4	no	—
41	C₃×C₁₉	—	49	3	no	—
42	C₃×C₁₉	#5997⋊C₃	1	1	yes	characteristic, direct product factor
43	C₇²	C₃²×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
44	C₃×D₇	—	14	4	no	—
45	AGL(1,𝔽₇)	—	14	12	no	—
46	C₂×C₁₉	—	49	1	no	—
47	C₃²×C₄	—	49	1	no	Hall
48	C₃×C₇	—	2	4	no	—
49	ΓL(1,𝔽₈)	—	14	12	no	—
50	C₁₉	C₃×#5997⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃²	—	49	1	no	—
52	D₇	—	14	4	no	—
53	C₃×C₄	—	49	3	no	—
54	C₃×C₄	—	49	1	no	—
55	C₃²	—	49	1	no	Sylow
56	C₇	—	2	4	no	—
57	C₂×C₃	—	49	3	no	—
58	C₂×C₃	—	49	1	no	—
59	C₄	—	49	1	no	Sylow
60	C₃	—	49	3	no	—
61	C₃	C₁₉×#5997⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#5997⋊C₃
commutator, hypocenter	C₇²	C₃²×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₃×C₄
prime radical	C₃×C₁₉×#64424	C₂
cosocle	C₇⋊D₇	C₂×C₃²×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×#5997	C₃	semidirect
3. C₁₉×#5997⋊C₃	C₃	direct (N × H)
4. C₃×C₁₉×#3861	C₄	semidirect
7. C₁₉×#5997	C₃²	semidirect
8. C₁₉×#3861	C₃×C₄	semidirect
9. C₃×C₇²×C₁₉	C₃×C₄	semidirect
12. C₃×#5997⋊C₃	C₁₉	direct (N × H)
14. C₇²×C₁₉	C₃²×C₄	semidirect
19. C₃×#5997	C₃×C₁₉	semidirect
20. #5997⋊C₃	C₃×C₁₉	direct (N × H)
21. C₃×#3861	C₄×C₁₉	semidirect
30. #5997	C₃²×C₁₉	semidirect
32. C₃×C₇²	C₃×C₄×C₁₉	semidirect
33. #3861	C₃×C₄×C₁₉	semidirect
42. C₃×C₁₉	#5997⋊C₃	direct (N × H)
43. C₇²	C₃²×C₄×C₁₉	semidirect
50. C₁₉	C₃×#5997⋊C₃	direct (N × H)
61. C₃	C₁₉×#5997⋊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×#64424	2
C₃×C₁₉×#5997	3
C₁₉×#5997⋊C₃	3
C₃×#5997⋊C₃	19
C₃²×C₄×C₁₉	49

Subgroups — C3×C19×#5997⋊C3 #45692200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#5997⋊C₃ #45692200