Subgroups — C₇×C₁₃×AGL(1,𝔽₁₉) #44527639

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×#4296	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₁₃×AGL(1,𝔽₁₉)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇×AGL(1,𝔽₁₉)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×#4296	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₉×C₁₃	—	19	1	no	maximal, Hall
10	C₁₃×D₁₉⋊C₃	C₃×C₇	1	1	yes	characteristic
11	C₇×#4296	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉×C₁₃	—	19	1	no	Hall
13	C₇×D₁₉⋊C₃	C₃×C₁₃	1	1	yes	characteristic
14	C₁₃×C₁₉⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₃	—	19	1	no	—
16	C₁₃×D₁₉	C₇×C₉	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₉⋊C₃	C₂×C₃×C₁₃	1	1	yes	characteristic
18	AGL(1,𝔽₁₉)	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇×C₁₃	—	19	1	no	—
20	C₇×D₁₉	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₁₉	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₉×C₁₃	—	19	1	no	Hall
23	C₂×C₇×C₁₃	—	19	1	no	Hall
24	#4296	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₇×C₁₉	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×C₉	—	19	1	no	Hall
27	C₉×C₁₃	—	19	1	no	Hall
28	D₁₉⋊C₃	C₃×C₇×C₁₃	1	1	yes	characteristic
29	C₇×C₁₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₃	—	19	1	no	—
31	C₇×C₉	—	19	1	no	Hall
32	C₁₉⋊C₃	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic
33	C₂×C₃×C₇	—	19	1	no	—
34	C₃×C₁₃	—	19	1	no	—
35	D₁₉	C₇×C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₃	—	19	1	no	Hall
37	C₃×C₇	—	19	1	no	—
38	C₁₉	C₂×C₇×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	19	1	no	Hall
40	C₂×C₇	—	19	1	no	Hall
41	C₁₃	C₇×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	—	19	1	no	Sylow
43	C₇	C₁₃×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	—	19	1	no	—
45	C₃	—	19	1	no	—
46	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₃	AGL(1,𝔽₁₉)
commutator, hypocenter	C₁₉	C₂×C₇×C₉×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₉
prime radical	C₇×C₁₃×D₁₉⋊C₃	C₃
cosocle	C₁₉⋊C₃	C₂×C₃×C₇×C₁₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×#4296	C₂	semidirect
4. C₁₃×AGL(1,𝔽₁₉)	C₇	direct (N × H)
5. C₇×C₁₃×D₁₉	C₉	semidirect
6. C₇×AGL(1,𝔽₁₉)	C₁₃	direct (N × H)
7. C₁₃×#4296	C₂×C₇	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
11. C₇×#4296	C₂×C₁₃	semidirect
16. C₁₃×D₁₉	C₇×C₉	semidirect
18. AGL(1,𝔽₁₉)	C₇×C₁₃	direct (N × H)
20. C₇×D₁₉	C₉×C₁₃	semidirect
21. C₁₃×C₁₉	C₂×C₇×C₉	semidirect
24. #4296	C₂×C₇×C₁₃	semidirect
25. C₇×C₁₉	C₂×C₉×C₁₃	semidirect
29. C₇×C₁₃	AGL(1,𝔽₁₉)	direct (N × H)
35. D₁₉	C₇×C₉×C₁₃	semidirect
38. C₁₉	C₂×C₇×C₉×C₁₃	semidirect
41. C₁₃	C₇×AGL(1,𝔽₁₉)	direct (N × H)
43. C₇	C₁₃×AGL(1,𝔽₁₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃×#4296	2
C₇×C₁₃×D₁₉⋊C₃	3
C₁₃×AGL(1,𝔽₁₉)	7
C₇×AGL(1,𝔽₁₉)	13
C₂×C₇×C₉×C₁₃	19

Subgroups — C7×C13×AGL(1,𝔽19) #44527639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×AGL(1,𝔽₁₉) #44527639