Subgroups — Dic₃×C₁₃×C₁₉⋊C₃ #22580204

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×C₁₉⋊C₃	—	3	1	no	maximal
4	C₃×C₁₃×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₃×C₁₉⋊C₃	—	2	1	no	—
7	C₂×C₁₃×C₁₉⋊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	C₁₃×C₁₉⋊C₃	—	2	1	no	—
11	C₁₃×C₁₉⋊C₃	Dic₃	1	1	yes	characteristic, direct product factor
12	Dic₃×C₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic
14	C₃×Dic₃×C₁₃	—	19	1	no	maximal, Hall
15	C₂×C₃×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic
16	C₁₃×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₁₃	—	19	1	no	—
18	Dic₃×C₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
19	C₄×C₁₉⋊C₃	—	3	1	no	—
20	C₃×C₁₉⋊C₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄×C₁₃	—	57	1	no	—
22	Dic₃×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
23	C₃²×C₁₃	—	19	1	no	Hall
24	C₂×C₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
25	C₂×C₁₉⋊C₃	—	2	1	no	—
26	C₂×C₁₉⋊C₃	D₃×C₁₃	1	1	yes	characteristic
27	C₂×C₃×C₁₃	—	19	1	no	—
28	C₂×C₃×C₁₃	—	38	1	no	—
29	C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
30	C₄×C₁₉	—	3	1	no	Hall
31	C₃×C₁₉	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented
32	C₁₉⋊C₃	—	2	1	no	—
33	C₁₉⋊C₃	Dic₃×C₁₃	1	1	yes	characteristic, direct product factor
34	C₄×C₁₃	—	3	1	no	Hall
35	C₃×C₁₃	—	19	1	no	—
36	C₃×C₁₃	—	38	1	no	—
37	C₃×C₁₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
38	C₂×C₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic
39	C₃×Dic₃	—	19	1	no	Hall
40	C₂×C₁₃	D₃×C₁₉⋊C₃	1	1	yes	characteristic
41	C₁₉	C₃×Dic₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃²	—	19	1	no	—
43	C₁₃	Dic₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃×C₄	—	57	1	no	—
45	Dic₃	C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
46	C₃²	—	19	1	no	Sylow
47	C₂×C₃	—	19	1	no	—
48	C₂×C₃	—	38	1	no	—
49	C₂×C₃	C₂×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	19	1	no	—
52	C₃	—	38	1	no	—
53	C₃	C₄×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
54	C₂	D₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₁₃×C₁₉	C₃	semidirect
4. C₃×C₁₃×C₁₉⋊C₃	C₄	semidirect
9. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
11. C₁₃×C₁₉⋊C₃	Dic₃	direct (N × H)
12. Dic₃×C₁₉⋊C₃	C₁₃	direct (N × H)
16. C₁₃×C₁₉	C₃×Dic₃	semidirect
18. Dic₃×C₁₉	C₃×C₁₃	semidirect
20. C₃×C₁₉⋊C₃	C₄×C₁₃	semidirect
22. Dic₃×C₁₃	C₁₉⋊C₃	direct (N × H)
31. C₃×C₁₉	C₃×C₄×C₁₃	semidirect
33. C₁₉⋊C₃	Dic₃×C₁₃	direct (N × H)
37. C₃×C₁₃	C₄×C₁₉⋊C₃	semidirect
41. C₁₉	C₃×Dic₃×C₁₃	semidirect
43. C₁₃	Dic₃×C₁₉⋊C₃	direct (N × H)
45. Dic₃	C₁₃×C₁₉⋊C₃	direct (N × H)
53. C₃	C₄×C₁₃×C₁₉⋊C₃	semidirect

Subgroups — Dic3×C13×C19⋊C3 #22580204

Conjugacy classes of subgroups

Complements

Subgroups — Dic₃×C₁₃×C₁₉⋊C₃ #22580204