Subgroups — C₁₉×#14523157 #50310329

Order 38532.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#10621730	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₉×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₉×#261	—	13	1	no	maximal
7	C₁₉×Dic₁₃⋊C₃	—	13	1	no	maximal
8	#14523157	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₉×D₁₃	—	13	1	no	—
10	C₂×C₁₉×C₁₃⋊C₃	—	13	1	no	—
11	D₁₃×C₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic
12	C₁₉×#261	—	13	1	no	—
13	C₁₉×Dic₁₃	—	13	1	no	—
14	C₃×C₁₃×C₁₉	—	13	1	no	—
15	C₁₉×C₁₃⋊C₃	#261	1	1	yes	characteristic, complemented
16	#10621730	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₃×C₁₃⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃×C₁₉	—	13	1	no	—
19	C₁₉×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic
20	C₁₃×D₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
21	C₁₃×C₁₉	—	12	1	no	—
22	C₁₃×C₁₉	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₁₃×C₁₉	C₃×#261	1	1	yes	characteristic, complemented
24	C₃×C₄×C₁₉	—	169	1	no	Hall
25	C₁₃²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₃×#261	—	13	1	no	—
27	Dic₁₃⋊C₃	—	13	1	no	—
28	C₂×C₃×C₁₉	—	169	1	no	—
29	C₃×D₁₃	—	13	1	no	—
30	C₂×C₁₃⋊C₃	—	13	1	no	—
31	C₄×C₁₉	—	169	1	no	Hall
32	C₃×C₁₉	—	13	1	no	Hall
33	#261	—	13	1	no	—
34	Dic₁₃	—	13	1	no	—
35	C₃×C₁₃	—	13	1	no	—
36	C₁₃⋊C₃	C₁₉×#261	1	1	yes	characteristic, complemented
37	C₂×C₁₉	—	13	1	no	—
38	C₂×C₁₃	—	13	1	no	—
39	D₁₃	C₁₉×D₁₃⋊C₃	1	1	yes	characteristic
40	C₁₉	#14523157	1	1	yes	characteristic, direct product factor, Sylow
41	C₁₃	—	12	1	no	—
42	C₁₃	C₁₉×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
43	C₁₃	C₃×C₁₉×#261	1	1	yes	characteristic, complemented
44	C₃×C₄	—	169	1	no	Hall
45	C₂×C₃	—	169	1	no	—
46	C₄	—	169	1	no	Sylow
47	C₃	—	13	1	no	Sylow
48	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#14523157
commutator, hypocenter	C₁₃²	C₃×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₃²×C₁₉	C₃×C₄
prime radical	C₁₉×D₁₃×C₁₃⋊C₃	C₂
cosocle	C₁₃×D₁₃	C₂×C₃×C₁₉
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×#10621730	C₃	semidirect
3. C₁₃×C₁₉×C₁₃⋊C₃	C₄	semidirect
5. C₁₃²×C₁₉	C₃×C₄	semidirect
8. #14523157	C₁₉	direct (N × H)
15. C₁₉×C₁₃⋊C₃	#261	semidirect
16. #10621730	C₃×C₁₉	semidirect
17. C₁₃×C₁₃⋊C₃	C₄×C₁₉	semidirect
22. C₁₃×C₁₉	Dic₁₃⋊C₃	semidirect
23. C₁₃×C₁₉	C₃×#261	semidirect
25. C₁₃²	C₃×C₄×C₁₉	semidirect
36. C₁₃⋊C₃	C₁₉×#261	semidirect
40. C₁₉	#14523157	direct (N × H)
42. C₁₃	C₁₉×Dic₁₃⋊C₃	semidirect
43. C₁₃	C₃×C₁₉×#261	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₁₃×C₁₃⋊C₃	2
C₁₉×#10621730	3
C₃×C₁₉×#261	13
C₁₉×Dic₁₃⋊C₃	13
#14523157	19

Subgroups — C19×#14523157 #50310329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14523157 #50310329