Subgroups — C₃×(C₁₉⋊C₃)⋊Dic₁₃ #22580201

Order 8892.

72 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	C₃×Dic₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₁₉⋊C₃)⋊Dic₁₃	C₃	1	3	yes	maximal, direct product factor
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	C₂×C₃	1	3	yes	—
7	Dic₂₄₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₃×C₁₉⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₃×(C₁₉⋊C₃)⋊C₄	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic
12	C₃²×Dic₁₃	—	19	1	no	maximal, Hall
13	C₂×C₃×C₁₉⋊C₃	D₁₃	1	1	yes	characteristic
14	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃²×C₁₃	—	19	1	no	—
16	C₃×Dic₁₉	—	13	1	no	—
17	(C₁₉⋊C₃)⋊C₄	—	13	3	no	—
18	C₃×C₁₉⋊C₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×Dic₁₃	—	19	3	no	—
20	C₃×Dic₁₃	—	19	1	no	—
21	C₃²×C₁₃	—	19	1	no	Hall
22	C₂×C₃×C₁₉	C₃×D₁₃	1	1	yes	characteristic
23	C₂×C₁₉⋊C₃	C₃×D₁₃	1	3	yes	—
24	C₂×C₃×C₁₃	—	19	3	no	—
25	C₂×C₃×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic
26	Dic₁₉	—	13	1	no	Hall
27	C₃×C₁₉	C₃×Dic₁₃	1	1	yes	characteristic, complemented
28	C₁₉⋊C₃	C₃×Dic₁₃	1	3	yes	complemented
29	Dic₁₃	—	19	1	no	Hall
30	C₃×C₁₃	—	19	3	no	—
31	C₃×C₁₃	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
32	C₂×C₁₉	C₃²×D₁₃	1	1	yes	characteristic
33	C₃²×C₄	—	247	1	no	Hall
34	C₂×C₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic
35	C₁₉	C₃²×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	19	1	no	—
37	C₁₃	C₃×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	247	3	no	—
39	C₃×C₄	—	247	1	no	—
40	C₃²	—	19	1	no	Sylow
41	C₂×C₃	—	19	3	no	—
42	C₂×C₃	(C₁₉⋊C₃)⋊D₁₃	1	1	yes	characteristic
43	C₄	—	247	1	no	Sylow
44	C₃	—	19	3	no	—
45	C₃	(C₁₉⋊C₃)⋊Dic₁₃	1	1	yes	characteristic, direct product factor
46	C₂	C₃×(C₁₉⋊C₃)⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₉⋊C₃)⋊D₁₃
commutator, hypocenter	C₁₃×C₁₉	C₃²×C₄
Frattini	C₂	C₃×(C₁₉⋊C₃)⋊D₁₃
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×Dic₂₄₇	C₃	semidirect
3. (C₁₉⋊C₃)⋊Dic₁₃	C₃	direct (N × H)
4. C₃×C₁₃×C₁₉⋊C₃	C₄	semidirect
7. Dic₂₄₇	C₃²	semidirect
8. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
9. C₁₃×C₁₉⋊C₃	C₃×C₄	semidirect
14. C₁₃×C₁₉	C₃²×C₄	semidirect
18. C₃×C₁₉⋊C₃	Dic₁₃	semidirect
27. C₃×C₁₉	C₃×Dic₁₃	semidirect
28. C₁₉⋊C₃	C₃×Dic₁₃	semidirect
31. C₃×C₁₃	(C₁₉⋊C₃)⋊C₄	semidirect
35. C₁₉	C₃²×Dic₁₃	semidirect
37. C₁₃	C₃×(C₁₉⋊C₃)⋊C₄	semidirect
45. C₃	(C₁₉⋊C₃)⋊Dic₁₃	direct (N × H)

Subgroups — C3×(C19⋊C3)⋊Dic13 #22580201

Conjugacy classes of subgroups

Complements

Subgroups — C₃×(C₁₉⋊C₃)⋊Dic₁₃ #22580201