Subgroups — C₁₉×#11725078 #30660577

Order 16758.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#89205	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₁₉×D₇⋊C₉	—	7	2	no	maximal
5	C₁₉×C₇⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×C₇⋊C₉	—	7	2	no	—
7	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	#11725078	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×D₇×C₁₉	—	7	2	no	—
10	C₃×D₇×C₁₉	—	21	2	no	—
11	#89205	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×C₁₉	—	3	2	no	—
13	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	—
14	C₂×C₉×C₁₉	—	49	1	no	Hall
15	C₃×C₇⋊D₇	C₃×C₁₉	1	1	yes	characteristic
16	D₇×C₁₉	—	7	2	no	—
17	D₇×C₁₉	—	21	2	no	—
18	C₉×C₁₉	—	49	1	no	Hall
19	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
20	C₇×C₁₉	—	3	2	no	—
21	C₇×C₁₉	D₇⋊C₉	1	2	yes	complemented
22	D₇⋊C₉	—	7	2	no	—
23	C₂×C₃×C₁₉	—	49	1	no	—
24	C₇⋊D₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₇⋊C₉	—	7	2	no	—
26	C₃×C₁₉	#64425	1	1	yes	characteristic
27	C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₃×D₇	—	7	2	no	—
29	C₃×D₇	—	21	2	no	—
30	C₂×C₁₉	—	49	1	no	Hall
31	C₃×C₇	—	3	2	no	—
32	C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	2	yes	—
33	C₁₉	#11725078	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₉	—	49	1	no	Hall
35	D₇	—	7	2	no	—
36	D₇	—	21	2	no	—
37	C₉	—	49	1	no	Sylow
38	C₇	—	3	2	no	—
39	C₇	C₁₉×D₇⋊C₉	1	2	yes	complemented
40	C₂×C₃	—	49	1	no	—
41	C₃	C₁₉×#64425	1	1	yes	characteristic
42	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#64425
commutator, hypocenter	C₇²	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×#64425
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×#89205	C₂	semidirect
5. C₁₉×C₇⋊D₇	C₉	semidirect
7. C₇²×C₁₉	C₂×C₉	semidirect
8. #11725078	C₁₉	direct (N × H)
11. #89205	C₂×C₁₉	semidirect
21. C₇×C₁₉	D₇⋊C₉	semidirect
24. C₇⋊D₇	C₉×C₁₉	semidirect
27. C₇²	C₂×C₉×C₁₉	semidirect
33. C₁₉	#11725078	direct (N × H)
39. C₇	C₁₉×D₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#89205	2
C₃×C₁₉×C₇⋊D₇	3
C₁₉×D₇⋊C₉	7
#11725078	19

Subgroups — C19×#11725078 #30660577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11725078 #30660577