Subgroups — C₁₉×(C₃⋊D₃)⋊D₁₃ #22580372

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₉×D₃₉	C₂	1	2	yes	maximal, complemented
3	D₃×C₁₉×D₁₃	—	3	2	no	maximal
4	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₉×D₃₉	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₁₉	—	3	2	no	—
7	D₃×C₁₃×C₁₉	—	6	1	no	—
8	C₃×C₁₉×D₁₃	—	3	2	no	—
9	C₂×C₁₉×D₁₃	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	—	2	1	no	—
11	C₃×C₁₃×C₁₉	C₂×D₃	1	2	yes	complemented
12	D₃²×C₁₉	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₁₉	—	9	1	no	—
14	C₁₉×D₁₃	—	3	2	no	—
15	(C₃⋊D₃)⋊D₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃⋊D₃×C₁₉	D₁₃	1	1	yes	characteristic, complemented
17	C₃×D₃×C₁₉	—	13	2	no	—
18	C₁₃×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
19	C₁₃×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
20	C₃×D₃₉	C₂×C₁₉	1	2	yes	complemented
21	C₂×D₃×C₁₉	—	39	2	no	—
22	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
23	D₃×D₁₃	—	3	2	no	—
24	C₃²×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₉	—	39	2	no	—
26	D₃×C₁₉	—	3	2	no	—
27	D₃×C₁₉	—	6	1	no	—
28	D₃×C₁₉	—	13	2	no	—
29	D₃₉	D₃×C₁₉	1	2	yes	complemented
30	C₃×D₁₃	—	3	2	no	—
31	D₃×C₁₃	—	3	2	no	—
32	D₃×C₁₃	—	6	1	no	—
33	C₂²×C₁₉	—	117	1	no	Hall
34	C₃×C₁₉	—	2	1	no	—
35	C₃×C₁₉	D₃×D₁₃	1	2	yes	complemented
36	C₂×D₁₃	—	9	1	no	Hall
37	C₃×C₁₃	—	2	1	no	—
38	C₃×C₁₃	C₂×D₃×C₁₉	1	2	yes	complemented
39	C₂×C₁₉	—	9	1	no	—
40	C₂×C₁₉	—	39	2	no	—
41	D₃²	—	13	1	no	Hall
42	C₂×C₁₃	—	9	1	no	—
43	D₁₃	—	3	2	no	—
44	C₁₉	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃⋊D₃	C₁₉×D₁₃	1	1	yes	characteristic, complemented
46	C₃×D₃	—	13	2	no	—
47	C₁₃	D₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₃	—	39	2	no	—
49	C₃²	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	39	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	13	2	no	—
54	C₂²	—	117	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₁₉×D₁₃	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	39	2	no	—

	subgroup	G/H
center, hypercenter	C₁₉	(C₃⋊D₃)⋊D₁₃
commutator, hypocenter	C₃²×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₁₉	C₂	semidirect
2. C₃×C₁₉×D₃₉	C₂	semidirect
4. C₃²×C₁₃×C₁₉	C₂²	semidirect
5. C₁₉×D₃₉	D₃	semidirect
11. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
15. (C₃⋊D₃)⋊D₁₃	C₁₉	direct (N × H)
16. C₃⋊D₃×C₁₉	D₁₃	semidirect
18. C₁₃×C₁₉	D₃²	semidirect
19. C₁₃×C₃⋊D₃	C₂×C₁₉	semidirect
20. C₃×D₃₉	C₂×C₁₉	semidirect
22. C₃²×C₁₉	C₂×D₁₃	semidirect
24. C₃²×C₁₃	C₂²×C₁₉	semidirect
29. D₃₉	D₃×C₁₉	semidirect
35. C₃×C₁₉	D₃×D₁₃	semidirect
38. C₃×C₁₃	C₂×D₃×C₁₉	semidirect
44. C₁₉	(C₃⋊D₃)⋊D₁₃	direct (N × H)
45. C₃⋊D₃	C₁₉×D₁₃	semidirect
47. C₁₃	D₃²×C₁₉	semidirect
49. C₃²	C₂×C₁₉×D₁₃	semidirect
56. C₃	D₃×C₁₉×D₁₃	semidirect

Subgroups — C19×(C3⋊D3)⋊D13 #22580372

Conjugacy classes of subgroups

Complements

Subgroups — C₁₉×(C₃⋊D₃)⋊D₁₃ #22580372