Subgroups — C₁₉×C₃⋊#64424 #30660818

Order 16758.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₃⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#64424	—	3	1	no	maximal
4	C₁₉×#3861	—	2	1	no	—
5	C₁₉×#3861	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×C₃⋊AGL(1,𝔽₇)	—	7	8	no	maximal
8	C₁₉×C₇⋊D₇	—	3	1	no	Hall
9	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
10	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#64424	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₉×D₂₁	—	7	8	no	—
13	C₁₉×AGL(1,𝔽₇)	—	21	8	no	—
14	C₃×#3861	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	8	yes	complemented
16	C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
17	C₁₉×ΓL(1,𝔽₈)	—	14	8	no	—
18	C₃×D₃×C₁₉	—	49	1	no	Hall
19	C₃⋊(C₇⋊D₇)	C₃×C₁₉	1	1	yes	characteristic, complemented
20	#64424	—	3	1	no	—
21	D₇×C₁₉	—	21	8	no	—
22	C₃²×C₁₉	—	49	1	no	Hall
23	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
24	#3861	—	2	1	no	—
25	#3861	D₃×C₁₉	1	1	yes	characteristic, complemented
26	C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	1	8	yes	complemented
27	C₃⋊AGL(1,𝔽₇)	—	7	8	no	—
28	C₂×C₃×C₁₉	—	147	1	no	—
29	D₃×C₁₉	—	49	1	no	—
30	C₇⋊D₇	—	3	1	no	Hall
31	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
32	C₃×C₁₉	—	49	1	no	—
33	C₃×C₁₉	—	98	1	no	—
34	C₃×C₁₉	#64424	1	1	yes	characteristic, complemented
35	C₇²	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
36	D₂₁	—	7	8	no	—
37	AGL(1,𝔽₇)	—	21	8	no	—
38	C₂×C₁₉	—	147	1	no	Hall
39	C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	8	yes	complemented
40	ΓL(1,𝔽₈)	—	7	8	no	—
41	ΓL(1,𝔽₈)	—	14	8	no	—
42	C₁₉	C₃⋊#64424	1	1	yes	characteristic, direct product factor, Sylow
43	C₃×D₃	—	49	1	no	Hall
44	D₇	—	21	8	no	—
45	C₃²	—	49	1	no	Sylow
46	C₇	C₁₉×C₃⋊AGL(1,𝔽₇)	1	8	yes	complemented
47	C₂×C₃	—	147	1	no	—
48	D₃	—	49	1	no	—
49	C₃	—	49	1	no	—
50	C₃	—	98	1	no	—
51	C₃	C₁₉×#64424	1	1	yes	characteristic, complemented
52	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊#64424
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3861	C₂	semidirect
2. C₁₉×C₃⋊(C₇⋊D₇)	C₃	semidirect
5. C₁₉×#3861	D₃	semidirect
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
10. C₇²×C₁₉	C₃×D₃	semidirect
11. C₃⋊#64424	C₁₉	direct (N × H)
14. C₃×#3861	C₂×C₁₉	semidirect
15. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
19. C₃⋊(C₇⋊D₇)	C₃×C₁₉	semidirect
23. C₃×C₇²	C₂×C₃×C₁₉	semidirect
25. #3861	D₃×C₁₉	semidirect
26. C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
34. C₃×C₁₉	#64424	semidirect
35. C₇²	C₃×D₃×C₁₉	semidirect
39. C₃×C₇	C₁₉×AGL(1,𝔽₇)	semidirect
42. C₁₉	C₃⋊#64424	direct (N × H)
46. C₇	C₁₉×C₃⋊AGL(1,𝔽₇)	semidirect
51. C₃	C₁₉×#64424	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₉×#3861	2
C₁₉×C₃⋊(C₇⋊D₇)	3
C₁₉×#64424	3
C₁₉×C₃⋊AGL(1,𝔽₇)	7
C₃⋊#64424	19

Subgroups — C19×C3⋊#64424 #30660818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#64424 #30660818