Subgroups — C₁₉×#13109903 #44527622

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#11717942	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₉₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₁₉×D₁₃⋊C₉	—	7	1	no	maximal, Hall
5	C₁₉×D₉₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₇⋊C₉	—	13	1	no	maximal, Hall
7	C₁₉×C₁₃⋊C₉	—	7	1	no	Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	#13109903	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₉×D₁₃	—	7	1	no	—
11	C₁₉×C₇⋊C₉	—	13	1	no	Hall
12	#11717942	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₇×C₁₉	—	13	1	no	—
14	C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×D₉₁	C₃×C₁₉	1	1	yes	characteristic
16	C₁₉×D₁₃	—	7	1	no	Hall
17	C₃×C₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic
18	C₂×C₉×C₁₉	—	91	1	no	Hall
19	C₃×C₇×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
20	D₇×C₁₉	—	13	1	no	Hall
21	C₁₃×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	D₁₃⋊C₉	—	7	1	no	Hall
23	D₉₁	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
24	C₉×C₁₉	—	91	1	no	Hall
25	C₇×C₁₉	D₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
26	D₇⋊C₉	—	13	1	no	Hall
27	C₁₃⋊C₉	—	7	1	no	Hall
28	C₂×C₃×C₁₉	—	91	1	no	—
29	C₇×C₁₃	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	—	7	1	no	—
31	C₇⋊C₉	—	13	1	no	Hall
32	C₃×C₁₉	#10587723	1	1	yes	characteristic
33	C₃×D₇	—	13	1	no	—
34	C₃×C₁₃	C₁₉×AGL(1,𝔽₇)	1	1	yes	characteristic
35	C₂×C₁₉	—	91	1	no	Hall
36	D₁₃	—	7	1	no	Hall
37	C₃×C₇	C₁₉×D₁₃⋊C₃	1	1	yes	characteristic
38	C₁₉	#13109903	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₉	—	91	1	no	Hall
40	D₇	—	13	1	no	Hall
41	C₁₃	C₁₉×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	91	1	no	Sylow
43	C₇	C₁₉×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	91	1	no	—
45	C₃	C₁₉×#10587723	1	1	yes	characteristic
46	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#10587723
commutator, hypocenter	C₇×C₁₃	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×#10587723
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×D₉₁	C₃
cosocle	C₃×C₇×C₁₃	C₂×C₃×C₁₉
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×#11717942	C₂	semidirect
5. C₁₉×D₉₁	C₉	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
9. #13109903	C₁₉	direct (N × H)
12. #11717942	C₂×C₁₉	semidirect
21. C₁₃×C₁₉	D₇⋊C₉	semidirect
23. D₉₁	C₉×C₁₉	semidirect
25. C₇×C₁₉	D₁₃⋊C₉	semidirect
29. C₇×C₁₃	C₂×C₉×C₁₉	semidirect
38. C₁₉	#13109903	direct (N × H)
41. C₁₃	C₁₉×D₇⋊C₉	semidirect
43. C₇	C₁₉×D₁₃⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#11717942	2
C₃×C₁₉×D₉₁	3
C₁₉×D₁₃⋊C₉	7
C₁₉×D₇⋊C₉	13
#13109903	19

Subgroups — C19×#13109903 #44527622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13109903 #44527622