Subgroups — Dic₃×C₁₉×C₁₃⋊C₃ #22580211

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×C₁₃⋊C₃	—	3	1	no	maximal
4	C₃×C₁₉×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₉×C₁₃⋊C₃	—	2	1	no	—
7	C₂×C₁₉×C₁₃⋊C₃	D₃	1	1	yes	characteristic
8	C₄×C₁₃×C₁₉	—	3	1	no	Hall
9	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₉×C₁₃⋊C₃	—	2	1	no	—
11	C₁₉×C₁₃⋊C₃	Dic₃	1	1	yes	characteristic, direct product factor
12	C₃×Dic₃×C₁₉	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic
14	Dic₃×C₁₃⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃²×C₁₉	—	13	1	no	—
16	C₁₃×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic
18	C₃×C₄×C₁₉	—	39	1	no	—
19	Dic₃×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃²×C₁₉	—	13	1	no	Hall
21	Dic₃×C₁₃	C₃×C₁₉	1	1	yes	characteristic, complemented
22	C₄×C₁₃⋊C₃	—	3	1	no	—
23	C₃×C₁₃⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₉	—	13	1	no	—
25	C₂×C₃×C₁₉	—	26	1	no	—
26	C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
27	C₂×C₃×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
28	C₂×C₁₃⋊C₃	—	2	1	no	—
29	C₂×C₁₃⋊C₃	D₃×C₁₉	1	1	yes	characteristic
30	C₄×C₁₉	—	3	1	no	Hall
31	C₃×C₁₉	—	13	1	no	—
32	C₃×C₁₉	—	26	1	no	—
33	C₃×C₁₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
34	C₄×C₁₃	—	3	1	no	Hall
35	C₃×C₁₃	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
36	C₁₃⋊C₃	—	2	1	no	—
37	C₁₃⋊C₃	Dic₃×C₁₉	1	1	yes	characteristic, direct product factor
38	C₂×C₁₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic
39	C₃×Dic₃	—	13	1	no	Hall
40	C₂×C₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic
41	C₁₉	Dic₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃²	—	13	1	no	—
43	C₁₃	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	39	1	no	—
45	Dic₃	C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
46	C₃²	—	13	1	no	Sylow
47	C₂×C₃	—	13	1	no	—
48	C₂×C₃	—	26	1	no	—
49	C₂×C₃	C₂×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	13	1	no	—
52	C₃	—	26	1	no	—
53	C₃	C₄×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂	D₃×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₃×C₁₃⋊C₃
commutator, hypocenter	C₃×C₁₃	C₃×C₄×C₁₉
Frattini	C₂	D₃×C₁₉×C₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₁₃×C₁₉	C₃	semidirect
4. C₃×C₁₉×C₁₃⋊C₃	C₄	semidirect
9. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
11. C₁₉×C₁₃⋊C₃	Dic₃	direct (N × H)
14. Dic₃×C₁₃⋊C₃	C₁₉	direct (N × H)
16. C₁₃×C₁₉	C₃×Dic₃	semidirect
19. Dic₃×C₁₉	C₁₃⋊C₃	direct (N × H)
21. Dic₃×C₁₃	C₃×C₁₉	semidirect
23. C₃×C₁₃⋊C₃	C₄×C₁₉	semidirect
33. C₃×C₁₉	C₄×C₁₃⋊C₃	semidirect
35. C₃×C₁₃	C₃×C₄×C₁₉	semidirect
37. C₁₃⋊C₃	Dic₃×C₁₉	direct (N × H)
41. C₁₉	Dic₃×C₁₃⋊C₃	direct (N × H)
43. C₁₃	C₃×Dic₃×C₁₉	semidirect
45. Dic₃	C₁₉×C₁₃⋊C₃	direct (N × H)
53. C₃	C₄×C₁₉×C₁₃⋊C₃	semidirect

Subgroups — Dic3×C19×C13⋊C3 #22580211

Conjugacy classes of subgroups

Complements

Subgroups — Dic₃×C₁₉×C₁₃⋊C₃ #22580211