Subgroups — C₁₃×#14558801 #44527651

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#11924780	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×(C₁₉⋊C₃)⋊D₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₁₃×AGL(1,𝔽₁₉)	—	7	1	no	maximal, Hall
5	C₁₃×D₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
6	#14558801	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×#4296	—	7	1	no	Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₁₃×D₇⋊C₉	—	19	1	no	maximal, Hall
10	C₁₃×D₁₉⋊C₃	—	7	1	no	—
11	#11924780	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₇⋊C₉	—	19	1	no	Hall
13	(C₁₉⋊C₃)⋊D₇	C₃×C₁₃	1	1	yes	characteristic
14	C₁₃×C₁₉⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×C₁₃×D₇	—	19	1	no	—
16	C₁₃×D₁₉	—	7	1	no	Hall
17	C₇×C₁₉⋊C₃	C₂×C₃×C₁₃	1	1	yes	characteristic
18	AGL(1,𝔽₁₉)	—	7	1	no	Hall
19	C₃×C₇×C₁₃	—	19	1	no	—
20	D₁₃₃	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₉×C₁₃	—	133	1	no	Hall
23	C₁₃×D₇	—	19	1	no	Hall
24	#4296	—	7	1	no	Hall
25	C₇×C₁₉	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
26	D₇⋊C₉	—	19	1	no	Hall
27	C₉×C₁₃	—	133	1	no	Hall
28	D₁₉⋊C₃	—	7	1	no	—
29	C₇×C₁₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	133	1	no	—
31	C₇⋊C₉	—	19	1	no	Hall
32	C₁₉⋊C₃	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic
33	C₃×D₇	—	19	1	no	—
34	C₃×C₁₃	—	19	1	no	—
35	D₁₉	—	7	1	no	Hall
36	C₂×C₁₃	—	133	1	no	Hall
37	C₃×C₇	—	19	1	no	—
38	C₁₉	C₁₃×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	133	1	no	Hall
40	D₇	—	19	1	no	Hall
41	C₁₃	#14558801	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	—	133	1	no	Sylow
43	C₇	C₁₃×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	133	1	no	—
45	C₃	—	19	1	no	—
46	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	#14558801
commutator, hypocenter	C₇×C₁₉	C₂×C₉×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₉
prime radical	C₁₃×(C₁₉⋊C₃)⋊D₇	C₃
cosocle	C₇×C₁₉⋊C₃	C₂×C₃×C₁₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×#11924780	C₂	semidirect
5. C₁₃×D₁₃₃	C₉	semidirect
6. #14558801	C₁₃	direct (N × H)
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
11. #11924780	C₂×C₁₃	semidirect
20. D₁₃₃	C₉×C₁₃	semidirect
21. C₁₃×C₁₉	D₇⋊C₉	semidirect
25. C₇×C₁₉	C₂×C₉×C₁₃	semidirect
29. C₇×C₁₃	AGL(1,𝔽₁₉)	semidirect
38. C₁₉	C₁₃×D₇⋊C₉	semidirect
41. C₁₃	#14558801	direct (N × H)
43. C₇	C₁₃×AGL(1,𝔽₁₉)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#11924780	2
C₁₃×(C₁₉⋊C₃)⋊D₇	3
C₁₃×AGL(1,𝔽₁₉)	7
#14558801	13
C₁₃×D₇⋊C₉	19

Subgroups — C13×#14558801 #44527651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14558801 #44527651