Subgroups — D₁₃×AGL(1,𝔽₁₉) #22580246

Order 8892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	#4296⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×AGL(1,𝔽₁₉)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₁₃×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
6	(C₁₉⋊C₃)⋊D₁₃	C₂×C₃	1	1	yes	characteristic
7	D₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
8	C₁₃×D₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
9	D₁₃×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×AGL(1,𝔽₁₉)	—	13	1	no	maximal, Hall
12	D₂₄₇	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₃×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
14	C₁₉×D₁₃	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×C₉×D₁₃	—	19	1	no	maximal, Hall
16	C₂×#4296	—	13	1	no	—
17	AGL(1,𝔽₁₉)	—	13	1	no	—
18	AGL(1,𝔽₁₉)	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₉×C₁₃	—	19	1	no	—
21	C₉×D₁₃	—	19	1	no	—
22	C₉×D₁₃	—	19	1	no	—
23	C₂×D₁₉⋊C₃	—	13	1	no	—
24	#4296	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₃	—	19	1	no	—
26	C₉×C₁₃	—	19	1	no	Hall
27	C₂×C₁₉⋊C₃	—	13	1	no	—
28	D₁₉⋊C₃	—	13	1	no	—
29	D₁₉⋊C₃	C₃×D₁₃	1	1	yes	characteristic
30	C₂×C₃×C₁₃	—	19	1	no	—
31	C₃×D₁₃	—	19	1	no	—
32	C₃×D₁₃	—	19	1	no	—
33	C₂×D₁₉	—	13	1	no	Hall
34	C₁₉⋊C₃	C₂×C₃×D₁₃	1	1	yes	characteristic
35	C₂×D₁₃	—	19	1	no	Hall
36	C₃×C₁₃	—	19	1	no	—
37	C₂×C₁₉	—	13	1	no	—
38	D₁₉	—	13	1	no	—
39	D₁₉	C₉×D₁₃	1	1	yes	characteristic, complemented
40	C₂²×C₉	—	247	1	no	Hall
41	C₂×C₁₃	—	19	1	no	—
42	D₁₃	—	19	1	no	—
43	D₁₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor
44	C₁₉	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₉	—	19	1	no	—
46	C₂×C₉	—	247	1	no	—
47	C₂×C₉	—	247	1	no	—
48	C₁₃	C₂×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	247	1	no	—
50	C₉	—	19	1	no	Sylow
51	C₂×C₃	—	19	1	no	—
52	C₂×C₃	—	247	1	no	—
53	C₂×C₃	—	247	1	no	—
54	C₂²	—	247	1	no	Sylow
55	C₃	—	19	1	no	—
56	C₂	—	13	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	247	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₉	C₂²×C₉
LCS	G ▷ C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₁₃×#4296	C₂	semidirect
2. #4296⋊D₁₃	C₂	semidirect
3. C₁₃×AGL(1,𝔽₁₉)	C₂	semidirect
5. C₁₃×#4296	C₂²	semidirect
9. D₁₃×D₁₉	C₉	semidirect
12. D₂₄₇	C₂×C₉	semidirect
13. C₁₃×D₁₉	C₂×C₉	semidirect
14. C₁₉×D₁₃	C₂×C₉	semidirect
18. AGL(1,𝔽₁₉)	D₁₃	direct (N × H)
19. C₁₃×C₁₉	C₂²×C₉	semidirect
24. #4296	C₂×D₁₃	semidirect
39. D₁₉	C₉×D₁₃	semidirect
43. D₁₃	AGL(1,𝔽₁₉)	direct (N × H)
44. C₁₉	C₂×C₉×D₁₃	semidirect
48. C₁₃	C₂×AGL(1,𝔽₁₉)	semidirect

Subgroups — D13×AGL(1,𝔽19) #22580246

Conjugacy classes of subgroups

Complements

Subgroups — D₁₃×AGL(1,𝔽₁₉) #22580246