Subgroups — C₃×C₁₃⋊C₃×Dic₁₉ #22580200

Order 8892.

72 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	C₃×C₁₃×Dic₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃⋊C₃×Dic₁₉	C₃	1	3	yes	maximal, direct product factor
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	C₂×C₃	1	3	yes	—
7	C₁₃×Dic₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₉×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₃²×Dic₁₉	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic
12	C₃×C₄×C₁₃⋊C₃	—	19	1	no	maximal, Hall
13	C₂×C₃²×C₁₉	—	13	1	no	—
14	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic
16	C₃×Dic₁₉	—	13	3	no	—
17	C₃×Dic₁₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₃²×C₁₉	—	13	1	no	Hall
19	C₃×C₄×C₁₃	—	19	1	no	—
20	C₄×C₁₃⋊C₃	—	19	3	no	—
21	C₃×C₁₃⋊C₃	Dic₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₁₉	—	13	3	no	—
23	C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
24	C₂×C₃×C₁₃	C₃×D₁₉	1	1	yes	characteristic
25	C₂×C₁₃⋊C₃	C₃×D₁₉	1	3	yes	—
26	Dic₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₁₉	—	13	3	no	—
28	C₃×C₁₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₄×C₁₃	—	19	1	no	Hall
30	C₃×C₁₃	C₃×Dic₁₉	1	1	yes	characteristic, complemented
31	C₁₃⋊C₃	C₃×Dic₁₉	1	3	yes	direct product factor
32	C₂×C₁₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic
33	C₃²×C₄	—	247	1	no	Hall
34	C₂×C₁₃	C₃²×D₁₉	1	1	yes	characteristic
35	C₁₉	C₃×C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	13	1	no	—
37	C₁₃	C₃²×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	19	1	no	—
39	C₃×C₄	—	247	3	no	—
40	C₃²	—	13	1	no	Sylow
41	C₂×C₃	—	13	3	no	—
42	C₂×C₃	D₁₉×C₁₃⋊C₃	1	1	yes	characteristic
43	C₄	—	19	1	no	Sylow
44	C₃	—	13	3	no	—
45	C₃	C₁₃⋊C₃×Dic₁₉	1	1	yes	characteristic, direct product factor
46	C₂	C₃×D₁₉×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₉×C₁₃⋊C₃
commutator, hypocenter	C₁₃×C₁₉	C₃²×C₄
Frattini	C₂	C₃×D₁₉×C₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×Dic₁₉	C₃	semidirect
3. C₁₃⋊C₃×Dic₁₉	C₃	direct (N × H)
4. C₃×C₁₉×C₁₃⋊C₃	C₄	semidirect
7. C₁₃×Dic₁₉	C₃²	semidirect
8. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
9. C₁₉×C₁₃⋊C₃	C₃×C₄	semidirect
14. C₁₃×C₁₉	C₃²×C₄	semidirect
17. C₃×Dic₁₉	C₁₃⋊C₃	direct (N × H)
21. C₃×C₁₃⋊C₃	Dic₁₉	direct (N × H)
26. Dic₁₉	C₃×C₁₃⋊C₃	direct (N × H)
28. C₃×C₁₉	C₄×C₁₃⋊C₃	semidirect
30. C₃×C₁₃	C₃×Dic₁₉	semidirect
31. C₁₃⋊C₃	C₃×Dic₁₉	direct (N × H)
35. C₁₉	C₃×C₄×C₁₃⋊C₃	semidirect
37. C₁₃	C₃²×Dic₁₉	semidirect
45. C₃	C₁₃⋊C₃×Dic₁₉	direct (N × H)

Subgroups — C3×C13⋊C3×Dic19 #22580200

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃⋊C₃×Dic₁₉ #22580200