Subgroups — C₁₉×#828 #14268981

Order 1824.

52 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, complemented
2	C₁₉×D₂₄	C₂	1	1	yes	maximal, characteristic
3	C₁₉×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×SD₃₂	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₉	—	2	1	no	—
6	C₁₉×D₁₂	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₁₉	D₃	1	1	yes	characteristic, complemented
9	D₈×C₁₉	—	3	1	no	—
10	C₁₆×C₁₉	—	3	1	no	—
11	C₂×D₃×C₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	—	4	1	no	—
13	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
14	Q₈×C₁₉	—	2	1	no	—
15	D₄×C₁₉	—	6	1	no	—
16	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
18	D₃×C₁₉	—	8	1	no	—
19	#828	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₁₉	—	12	1	no	—
21	C₄×C₁₉	—	4	1	no	—
22	C₄×C₁₉	#67	1	1	yes	characteristic
23	C₃×C₁₉	SD₃₂	1	1	yes	characteristic, complemented, Hall
24	C₃×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
25	D₂₄	C₂×C₁₉	1	1	yes	characteristic
26	C₃⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₂×C₁₉	—	24	1	no	—
28	C₂×C₁₉	#213	1	1	yes	characteristic
29	SD₃₂	—	3	1	no	Sylow
30	C₃×Q₈	—	2	1	no	—
31	D₁₂	—	2	1	no	—
32	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
33	C₁₉	#828	1	1	yes	characteristic, direct product factor, Sylow
34	Q₁₆	D₃×C₁₉	1	1	yes	characteristic, complemented
35	D₈	—	3	1	no	—
36	C₁₆	—	3	1	no	—
37	C₂×D₃	—	4	1	no	—
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
40	Q₈	—	2	1	no	—
41	D₄	—	6	1	no	—
42	C₈	C₂×D₃×C₁₉	1	1	yes	characteristic
43	C₂×C₃	D₈×C₁₉	1	1	yes	characteristic
44	D₃	—	8	1	no	—
45	C₂²	—	12	1	no	—
46	C₄	—	4	1	no	—
47	C₄	C₁₉×#67	1	1	yes	characteristic
48	C₃	C₁₉×SD₃₂	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	24	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	C₃×Q₁₆×C₁₉	C₂
socle	C₂×C₃×C₁₉	D₈
prime radical	C₁₉×D₂₄	C₂
hypercenter	Q₁₆×C₁₉	D₃
hypocenter	C₃	C₁₉×SD₃₂
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
1. C₃×Q₁₆×C₁₉	C₂	semidirect
3. C₁₉×C₃⋊C₁₆	C₂	semidirect
8. Q₁₆×C₁₉	D₃	semidirect
19. #828	C₁₉	direct (N × H)
23. C₃×C₁₉	SD₃₂	semidirect
24. C₃×Q₁₆	C₂×C₁₉	semidirect
26. C₃⋊C₁₆	C₂×C₁₉	semidirect
33. C₁₉	#828	direct (N × H)
34. Q₁₆	D₃×C₁₉	semidirect
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×Q₁₆×C₁₉	2
C₁₉×D₂₄	2
C₁₉×C₃⋊C₁₆	2
C₁₉×SD₃₂	3
#828	19

Subgroups — C19×#828 #14268981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#828 #14268981