Subgroups — C₁₉×#11725075 #30660587

Order 16758.

52 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×C₇×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₉×C₇⋊C₉	—	7	1	no	maximal
5	C₁₉×D₇⋊C₉	—	7	1	no	maximal
6	C₇×D₇×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₇⋊C₉	—	7	1	no	—
8	C₁₉×C₇⋊C₉	—	7	1	no	—
9	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	#11725075	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₉	—	7	1	no	—
12	C₃×D₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	#89205	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇×C₁₉	—	6	1	no	—
15	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×C₉×C₁₉	—	49	1	no	Hall
18	C₃×C₇×D₇	C₃×C₁₉	1	1	yes	characteristic
19	C₂×C₇×C₁₉	—	7	1	no	—
20	D₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented
21	C₉×C₁₉	—	49	1	no	Hall
22	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
23	C₇×C₁₉	—	6	1	no	—
24	C₇×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented
25	C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
26	C₂×C₇⋊C₉	—	7	1	no	—
27	D₇⋊C₉	—	7	1	no	—
28	C₂×C₃×C₁₉	—	7	1	no	—
29	C₇×D₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₇⋊C₉	—	7	1	no	—
31	C₇⋊C₉	—	7	1	no	—
32	C₃×C₁₉	#64422	1	1	yes	characteristic
33	C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₇	—	7	1	no	—
35	C₃×D₇	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
36	C₂×C₁₉	—	7	1	no	Hall
37	C₃×C₇	—	6	1	no	—
38	C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	1	yes	characteristic
39	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
40	C₁₉	#11725075	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₉	—	49	1	no	Hall
42	C₂×C₇	—	7	1	no	—
43	D₇	C₁₉×C₇⋊C₉	1	1	yes	characteristic, complemented
44	C₉	—	49	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	C₁₉×D₇⋊C₉	1	1	yes	characteristic, complemented
47	C₇	C₂×C₁₉×C₇⋊C₉	1	1	yes	characteristic, complemented
48	C₂×C₃	—	7	1	no	—
49	C₃	C₁₉×#64422	1	1	yes	characteristic
50	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#64422
commutator, hypocenter	C₇²	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×#64422
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₇×D₇×C₁₉	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
6. C₇×D₇×C₁₉	C₉	semidirect
9. C₇²×C₁₉	C₂×C₉	semidirect
10. #11725075	C₁₉	direct (N × H)
13. #89205	C₂×C₁₉	semidirect
20. D₇×C₁₉	C₇⋊C₉	semidirect
24. C₇×C₁₉	D₇⋊C₉	semidirect
25. C₇×C₁₉	C₂×C₇⋊C₉	semidirect
29. C₇×D₇	C₉×C₁₉	semidirect
33. C₇²	C₂×C₉×C₁₉	semidirect
40. C₁₉	#11725075	direct (N × H)
43. D₇	C₁₉×C₇⋊C₉	semidirect
46. C₇	C₁₉×D₇⋊C₉	semidirect
47. C₇	C₂×C₁₉×C₇⋊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×C₇×D₇×C₁₉	3
C₂×C₁₉×C₇⋊C₉	7
C₁₉×D₇⋊C₉	7
#11725075	19

Subgroups — C19×#11725075 #30660587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11725075 #30660587