Subgroups — C₁₉×#827 #14268980

Order 1824.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×SD₃₂	—	3	1	no	maximal, Hall
5	C₃×D₄×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	D₈×C₁₉	D₃	1	1	yes	characteristic
10	C₁₆×C₁₉	—	3	1	no	—
11	C₂²×C₃×C₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
13	Dic₃×C₁₉	—	4	1	no	—
14	Q₈×C₁₉	—	6	1	no	—
15	D₄×C₁₉	—	2	1	no	—
16	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	—	8	1	no	—
18	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
19	#827	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₁₉	—	4	1	no	—
21	C₄×C₁₉	—	12	1	no	—
22	C₄×C₁₉	#67	1	1	yes	characteristic
23	C₃×C₁₉	SD₃₂	1	1	yes	characteristic, complemented, Hall
24	C₃×D₈	C₂×C₁₉	1	1	yes	characteristic
25	Dic₁₂	C₂×C₁₉	1	1	yes	characteristic, complemented
26	C₃⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₂×C₁₉	—	8	1	no	—
28	C₂×C₁₉	#213	1	1	yes	characteristic
29	SD₃₂	—	3	1	no	Sylow
30	C₃×D₄	—	2	1	no	—
31	Dic₆	—	2	1	no	—
32	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
33	C₁₉	#827	1	1	yes	characteristic, direct product factor, Sylow
34	Q₁₆	—	3	1	no	—
35	D₈	D₃×C₁₉	1	1	yes	characteristic
36	C₁₆	—	3	1	no	—
37	C₂²×C₃	—	4	1	no	—
38	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
39	Dic₃	—	4	1	no	—
40	Q₈	—	6	1	no	—
41	D₄	—	2	1	no	—
42	C₈	C₂×D₃×C₁₉	1	1	yes	characteristic
43	C₂×C₃	—	8	1	no	—
44	C₂×C₃	D₈×C₁₉	1	1	yes	characteristic
45	C₂²	—	4	1	no	—
46	C₄	—	12	1	no	—
47	C₄	C₁₉×#67	1	1	yes	characteristic
48	C₃	C₁₉×SD₃₂	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	8	1	no	—
50	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, prime radical	C₃×D₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	D₈
hypercenter	D₈×C₁₉	D₃
hypocenter	C₃	C₁₉×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ C₈×C₁₉ ◁ D₈×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×Dic₁₂	C₂	semidirect
3. C₁₉×C₃⋊C₁₆	C₂	semidirect
19. #827	C₁₉	direct (N × H)
23. C₃×C₁₉	SD₃₂	semidirect
25. Dic₁₂	C₂×C₁₉	semidirect
26. C₃⋊C₁₆	C₂×C₁₉	semidirect
33. C₁₉	#827	direct (N × H)
48. C₃	C₁₉×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₈×C₁₉	2
C₁₉×Dic₁₂	2
C₁₉×C₃⋊C₁₆	2
C₁₉×SD₃₂	3
#827	19

Subgroups — C19×#827 #14268980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#827 #14268980