Subgroups — C₁₉×#11760386 #34093063

Order 19950.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₇⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₅⋊D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₉×(C₅⋊D₅)⋊C₃	—	7	1	no	maximal, Hall
5	C₁₉×C₅²⋊C₃	—	7	1	no	Hall
6	C₁₉×D₃₅	—	15	2	no	—
7	#11760386	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₅⋊D₅	—	7	1	no	Hall
9	C₁₉×AGL(1,𝔽₇)	—	25	1	no	maximal, Hall
10	C₅×C₇×C₁₉	—	3	2	no	—
11	C₇⋊(C₅²⋊C₃)	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	C₁₉×ΓL(1,𝔽₈)	—	25	1	no	Hall
14	C₅⋊D₃₅	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
15	D₇×C₁₉	—	25	1	no	Hall
16	D₅×C₁₉	—	105	2	no	—
17	C₅²×C₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
18	(C₅⋊D₅)⋊C₃	—	7	1	no	Hall
19	C₇×C₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₉	—	175	1	no	Hall
21	C₅×C₁₉	—	3	2	no	—
22	C₅²⋊C₃	—	7	1	no	Hall
23	D₃₅	—	15	2	no	—
24	C₃×C₁₉	—	175	1	no	Hall
25	C₅⋊D₅	—	7	1	no	Hall
26	AGL(1,𝔽₇)	—	25	1	no	Hall
27	C₂×C₁₉	—	175	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	C₁₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₈)	—	25	1	no	Hall
31	C₁₉	#11760386	1	1	yes	characteristic, direct product factor, Sylow
32	D₇	—	25	1	no	Hall
33	D₅	—	105	2	no	—
34	C₇	C₁₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	175	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	175	1	no	Sylow
38	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	#11760386
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₇⋊(C₅²⋊C₃)	C₂	semidirect
2. C₁₉×C₅⋊D₃₅	C₃	semidirect
3. C₅²×C₇×C₁₉	C₂×C₃	semidirect
7. #11760386	C₁₉	direct (N × H)
11. C₇⋊(C₅²⋊C₃)	C₂×C₁₉	semidirect
12. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
14. C₅⋊D₃₅	C₃×C₁₉	semidirect
17. C₅²×C₇	C₂×C₃×C₁₉	semidirect
19. C₇×C₁₉	(C₅⋊D₅)⋊C₃	semidirect
29. C₅²	C₁₉×AGL(1,𝔽₇)	semidirect
31. C₁₉	#11760386	direct (N × H)
34. C₇	C₁₉×(C₅⋊D₅)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₇⋊(C₅²⋊C₃)	2
C₁₉×C₅⋊D₃₅	3
C₁₉×(C₅⋊D₅)⋊C₃	7
#11760386	19
C₁₉×AGL(1,𝔽₇)	25

Subgroups — C19×#11760386 #34093063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11760386 #34093063