Subgroups — C₁₉×#829 #14268982

Order 1824.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₉×Q₃₂	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₉	—	2	1	no	—
6	C₁₉×Dic₆	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₁₉	—	3	1	no	—
9	Q₁₆×C₁₉	D₃	1	1	yes	characteristic
10	C₁₆×C₁₉	—	3	1	no	—
11	C₃×C₄×C₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
13	Dic₃×C₁₉	—	4	1	no	—
14	Q₈×C₁₉	—	2	1	no	—
15	Q₈×C₁₉	—	6	1	no	—
16	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
18	#829	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₄×C₁₉	—	4	1	no	—
20	C₄×C₁₉	—	12	1	no	—
21	C₄×C₁₉	#67	1	1	yes	characteristic
22	C₃×C₁₉	Q₃₂	1	1	yes	characteristic, complemented, Hall
23	C₃×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
24	Dic₁₂	C₂×C₁₉	1	1	yes	characteristic
25	C₃⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
26	C₂×C₁₉	#213	1	1	yes	characteristic
27	Q₃₂	—	3	1	no	Sylow
28	C₃×Q₈	—	2	1	no	—
29	Dic₆	—	2	1	no	—
30	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
31	C₁₉	#829	1	1	yes	characteristic, direct product factor, Sylow
32	Q₁₆	—	3	1	no	—
33	Q₁₆	D₃×C₁₉	1	1	yes	characteristic
34	C₁₆	—	3	1	no	—
35	C₃×C₄	—	4	1	no	—
36	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
37	Dic₃	—	4	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	6	1	no	—
40	C₈	C₂×D₃×C₁₉	1	1	yes	characteristic
41	C₂×C₃	D₈×C₁₉	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	—	12	1	no	—
44	C₄	C₁₉×#67	1	1	yes	characteristic
45	C₃	C₁₉×Q₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₁₉×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₉	#213
commutator, cosocle	C₃×C₈	C₂²×C₁₉
Frattini	C₈	C₂×D₃×C₁₉
Fitting	C₃×Q₁₆×C₁₉	C₂
socle, prime radical	C₂×C₃×C₁₉	D₈
hypercenter	Q₁₆×C₁₉	D₃
hypocenter	C₃	C₁₉×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ C₈×C₁₉ ◁ Q₁₆×C₁₉

Complements

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

N	H ≅ G/N	type
18. #829	C₁₉	direct (N × H)
22. C₃×C₁₉	Q₃₂	semidirect
31. C₁₉	#829	direct (N × H)
45. C₃	C₁₉×Q₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×Q₁₆×C₁₉	2
C₁₉×Dic₁₂	2
C₁₉×C₃⋊C₁₆	2
C₁₉×Q₃₂	3
#829	19

Subgroups — C19×#829 #14268982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#829 #14268982