Subgroups — C₃×Q₁₆×D₁₉ #14269583

Order 1824.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×D₁₉	C₂	1	2	yes	maximal
2	C₃×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64528	C₂	1	2	yes	maximal, complemented
4	C₃×Dic₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
6	Q₁₆×D₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×Q₈×C₁₉	C₂²	1	2	yes	—
8	C₃×C₄×D₁₉	—	2	2	no	—
9	C₃×C₄×D₁₉	C₂²	1	1	yes	characteristic
10	C₃×Dic₃₈	—	2	2	no	—
11	C₃×Dic₃₈	C₂²	1	2	yes	—
12	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₃×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	Q₈×D₁₉	C₂×C₃	1	2	yes	—
15	Q₁₆×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
16	#64528	C₂×C₃	1	2	yes	complemented
17	Dic₇₆	C₂×C₃	1	1	yes	characteristic, complemented
18	C₈×D₁₉	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×D₁₉	D₄	1	1	yes	characteristic
20	C₃×C₄×C₁₉	—	2	2	no	—
21	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₃×Dic₁₉	—	2	2	no	—
23	C₃×Dic₁₉	D₄	1	1	yes	characteristic
24	Q₈×C₁₉	C₂²×C₃	1	2	yes	—
25	C₄×D₁₉	—	2	2	no	—
26	C₄×D₁₉	C₂²×C₃	1	1	yes	characteristic
27	Dic₃₈	—	2	2	no	—
28	Dic₃₈	C₂²×C₃	1	2	yes	—
29	C₈×C₁₉	C₂²×C₃	1	1	yes	characteristic
30	C₁₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₃×D₁₉	Q₁₆	1	2	yes	direct product factor
33	C₂×C₃×Q₁₆	—	19	1	no	maximal, Hall
34	C₂×D₁₉	C₃×D₄	1	1	yes	characteristic
35	C₄×C₁₉	—	2	2	no	—
36	C₄×C₁₉	C₂³×C₃	1	1	yes	characteristic
37	Dic₁₉	—	2	2	no	—
38	Dic₁₉	C₃×D₄	1	1	yes	characteristic
39	C₃×C₁₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×Q₈	—	19	2	no	—
41	C₃×Q₁₆	—	19	2	no	—
42	C₃×Q₁₆	—	19	1	no	—
43	C₃×Q₁₆	D₁₉	1	1	yes	characteristic, direct product factor
44	C₂×C₃×C₈	—	19	1	no	—
45	C₂×C₁₉	C₂×C₃×D₄	1	1	yes	characteristic
46	D₁₉	C₃×Q₁₆	1	2	yes	direct product factor
47	C₂×Q₁₆	—	19	1	no	Sylow
48	C₃×Q₈	—	19	2	no	—
49	C₃×Q₈	—	38	2	no	—
50	C₃×Q₈	C₂×D₁₉	1	2	yes	—
51	C₂×C₃×C₄	—	19	1	no	—
52	C₂×C₃×C₄	—	38	2	no	—
53	C₃×C₈	—	19	1	no	—
54	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
55	C₁₉	C₂×C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	19	2	no	—
57	Q₁₆	—	19	2	no	—
58	Q₁₆	—	19	1	no	—
59	Q₁₆	C₃×D₁₉	1	1	yes	characteristic, direct product factor
60	C₂×C₈	—	19	1	no	—
61	C₂²×C₃	—	19	1	no	—
62	C₃×C₄	—	2	2	no	—
63	C₃×C₄	—	19	1	no	—
64	C₃×C₄	—	38	2	no	—
65	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
66	Q₈	—	19	2	no	—
67	Q₈	—	38	2	no	—
68	Q₈	C₂×C₃×D₁₉	1	2	yes	—
69	C₂×C₄	—	19	1	no	—
70	C₂×C₄	—	38	2	no	—
71	C₈	—	19	1	no	—
72	C₈	C₂×C₃×D₁₉	1	1	yes	characteristic
73	C₂×C₃	—	19	2	no	—
74	C₂×C₃	D₄×D₁₉	1	1	yes	characteristic
75	C₂²	—	19	1	no	—
76	C₄	—	2	2	no	—
77	C₄	—	19	1	no	—
78	C₄	—	38	2	no	—
79	C₄	C₂²×C₃×D₁₉	1	1	yes	characteristic
80	C₃	Q₁₆×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	—	19	2	no	—
82	C₂	C₃×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₁₉
Fitting	C₃×Q₁₆×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂×D₄
prime radical	C₂×C₃×D₁₉	D₄
hypercenter	C₃×Q₁₆	D₁₉
hypocenter	C₁₉	C₂×C₃×Q₁₆
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×Q₁₆×C₁₉	C₂	semidirect
3. C₃×#64528	C₂	semidirect
4. C₃×Dic₇₆	C₂	semidirect
6. Q₁₆×D₁₉	C₃	direct (N × H)
15. Q₁₆×C₁₉	C₂×C₃	semidirect
16. #64528	C₂×C₃	semidirect
17. Dic₇₆	C₂×C₃	semidirect
32. C₃×D₁₉	Q₁₆	direct (N × H)
39. C₃×C₁₉	C₂×Q₁₆	semidirect
43. C₃×Q₁₆	D₁₉	direct (N × H)
46. D₁₉	C₃×Q₁₆	direct (N × H)
55. C₁₉	C₂×C₃×Q₁₆	semidirect
59. Q₁₆	C₃×D₁₉	direct (N × H)
80. C₃	Q₁₆×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×D₁₉	2
C₃×Q₁₆×C₁₉	2
C₃×#64528	2
C₃×Dic₇₆	2
C₃×C₈×D₁₉	2
Q₁₆×D₁₉	3
C₂×C₃×Q₁₆	19

Subgroups — C3×Q16×D19 #14269583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₁₆×D₁₉ #14269583