Subgroups — C₁₉⋊C₃×AGL(1,𝔽₁₃) #22580240

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#261×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688303	C₃	1	1	yes	maximal, characteristic, complemented
4	#15688302	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉×AGL(1,𝔽₁₃)	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₃⋊C₃×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
7	#13093365	C₂×C₃	1	1	yes	characteristic
8	#13093364	C₂×C₃	1	1	yes	characteristic
9	C₁₉×D₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic
10	D₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
11	C₁₉×#261	C₃²	1	1	yes	characteristic, complemented, Hall
12	#10625203	C₃×C₄	1	1	yes	characteristic, complemented
13	#10625202	C₃×C₄	1	1	yes	characteristic, complemented
14	C₁₃×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic, complemented
15	C₁₉×C₁₃⋊C₃	C₃×C₄	1	1	yes	characteristic, complemented
16	C₃×C₄×C₁₉⋊C₃	—	13	1	no	maximal, Hall
17	C₁₉×D₁₃	C₂×C₃²	1	1	yes	characteristic
18	C₃×AGL(1,𝔽₁₃)	—	19	1	no	maximal, Hall
19	C₂×C₃×C₁₉⋊C₃	—	13	1	no	—
20	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
21	C₃×D₁₃⋊C₃	—	19	1	no	—
22	C₃×C₄×C₁₉	—	13	1	no	—
23	C₄×C₁₉⋊C₃	—	13	1	no	—
24	C₄×C₁₉⋊C₃	—	13	1	no	—
25	C₄×C₁₉⋊C₃	—	13	1	no	—
26	C₃×C₁₉⋊C₃	—	13	1	no	Hall
27	C₃×#261	—	19	1	no	—
28	AGL(1,𝔽₁₃)	—	19	1	no	—
29	AGL(1,𝔽₁₃)	—	19	1	no	—
30	AGL(1,𝔽₁₃)	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃×C₁₃⋊C₃	—	19	1	no	Hall
32	C₂×C₃×C₁₉	—	13	1	no	—
33	C₂×C₁₉⋊C₃	—	13	1	no	—
34	C₂×C₁₉⋊C₃	—	13	1	no	—
35	C₂×C₁₉⋊C₃	—	13	1	no	—
36	C₃×D₁₃	—	19	1	no	—
37	D₁₃⋊C₃	—	19	1	no	—
38	D₁₃⋊C₃	—	19	1	no	—
39	D₁₃⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
40	C₄×C₁₉	—	13	1	no	Hall
41	C₃×C₁₉	—	13	1	no	—
42	C₁₉⋊C₃	—	13	1	no	—
43	C₁₉⋊C₃	—	13	1	no	—
44	C₁₉⋊C₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
45	#261	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₃×C₁₃	—	19	1	no	—
47	C₁₃⋊C₃	—	19	1	no	—
48	C₁₃⋊C₃	—	19	1	no	—
49	C₁₃⋊C₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
50	C₂×C₁₉	—	13	1	no	—
51	C₃²×C₄	—	247	1	no	Hall
52	D₁₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic
53	C₁₉	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃²	—	247	1	no	—
55	C₁₃	C₃×C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₄	—	13	1	no	—
57	C₃×C₄	—	247	1	no	—
58	C₃×C₄	—	247	1	no	—
59	C₃×C₄	—	247	1	no	—
60	C₃²	—	247	1	no	Sylow
61	C₂×C₃	—	13	1	no	—
62	C₂×C₃	—	247	1	no	—
63	C₂×C₃	—	247	1	no	—
64	C₂×C₃	—	247	1	no	—
65	C₄	—	13	1	no	Sylow
66	C₃	—	13	1	no	—
67	C₃	—	19	1	no	—
68	C₃	—	247	1	no	—
69	C₃	—	247	1	no	—
70	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₉	C₃²×C₄
LCS	G ▷ C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #261×C₁₉⋊C₃	C₃	semidirect
3. #15688303	C₃	semidirect
4. #15688302	C₃	semidirect
5. C₁₉×AGL(1,𝔽₁₃)	C₃	semidirect
6. C₁₃⋊C₃×C₁₉⋊C₃	C₄	semidirect
11. C₁₉×#261	C₃²	semidirect
12. #10625203	C₃×C₄	semidirect
13. #10625202	C₃×C₄	semidirect
14. C₁₃×C₁₉⋊C₃	C₃×C₄	semidirect
15. C₁₉×C₁₃⋊C₃	C₃×C₄	semidirect
20. C₁₃×C₁₉	C₃²×C₄	semidirect
30. AGL(1,𝔽₁₃)	C₁₉⋊C₃	direct (N × H)
44. C₁₉⋊C₃	AGL(1,𝔽₁₃)	direct (N × H)
45. #261	C₃×C₁₉⋊C₃	semidirect
49. C₁₃⋊C₃	C₄×C₁₉⋊C₃	semidirect
53. C₁₉	C₃×AGL(1,𝔽₁₃)	semidirect
55. C₁₃	C₃×C₄×C₁₉⋊C₃	semidirect

Subgroups — C19⋊C3×AGL(1,𝔽13) #22580240

Conjugacy classes of subgroups

Complements

Subgroups — C₁₉⋊C₃×AGL(1,𝔽₁₃) #22580240