Subgroups — C₂×C₁₉×#204 #14269654

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#204	C₂	1	4	yes	maximal, direct product factor
5	C₂×SD₁₆×C₁₉	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₉	—	2	1	no	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×Dic₃×C₁₉	—	2	1	no	—
9	C₁₉×D₁₂	—	2	1	no	—
10	C₁₉×D₁₂	C₂²	1	2	yes	—
11	C₁₉×Dic₆	—	2	1	no	—
12	C₁₉×Dic₆	C₂²	1	2	yes	complemented
13	C₃×C₈×C₁₉	C₂²	1	2	yes	complemented
14	C₂×Q₈×C₁₉	—	3	1	no	—
15	C₂×D₄×C₁₉	—	3	1	no	—
16	SD₁₆×C₁₉	—	3	4	no	—
17	C₂×C₈×C₁₉	D₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
19	C₂×D₃×C₁₉	—	2	2	no	—
20	C₂×D₃×C₁₉	—	4	2	no	—
21	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	Dic₃×C₁₉	—	2	2	no	—
24	C₂³×C₁₉	—	6	1	no	—
25	Q₈×C₁₉	—	3	2	no	—
26	Q₈×C₁₉	—	6	1	no	—
27	D₄×C₁₉	—	3	2	no	—
28	D₄×C₁₉	—	6	1	no	—
29	C₂×C₄×C₁₉	—	6	1	no	—
30	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
31	C₈×C₁₉	C₂×D₃	1	2	yes	complemented
32	C₂×C₃×C₁₉	SD₁₆	1	2	yes	complemented
33	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
34	D₃×C₁₉	—	4	2	no	—
35	C₂×#204	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂²×C₁₉	—	6	2	no	—
37	C₂²×C₁₉	—	12	2	no	—
38	C₂²×C₁₉	D₁₂	1	1	yes	characteristic
39	C₄×C₁₉	—	6	2	no	—
40	C₄×C₁₉	D₁₂	1	1	yes	characteristic
41	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
42	C₃×C₁₉	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
43	C₂×D₁₂	C₂×C₁₉	1	1	yes	characteristic
44	C₂×Dic₆	C₂×C₁₉	1	1	yes	characteristic, complemented
45	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
46	#204	C₂×C₁₉	1	4	yes	direct product factor
47	C₂×C₁₉	—	12	2	no	—
48	C₂×C₁₉	#204	1	2	yes	direct product factor
49	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
50	C₂×SD₁₆	—	3	1	no	Sylow
51	C₂²×D₃	—	2	1	no	—
52	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
53	C₂×Dic₃	—	2	1	no	—
54	D₁₂	—	2	1	no	—
55	D₁₂	C₂²×C₁₉	1	2	yes	—
56	Dic₆	—	2	1	no	—
57	Dic₆	C₂²×C₁₉	1	2	yes	complemented
58	C₃×C₈	C₂²×C₁₉	1	2	yes	complemented
59	C₁₉	C₂×#204	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×Q₈	—	3	1	no	—
61	C₂×D₄	—	3	1	no	—
62	SD₁₆	—	3	4	no	—
63	C₂×C₈	D₃×C₁₉	1	1	yes	characteristic, complemented
64	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
65	C₂×D₃	—	2	2	no	—
66	C₂×D₃	—	4	2	no	—
67	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
68	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
69	Dic₃	—	2	2	no	—
70	C₂³	—	6	1	no	—
71	Q₈	—	3	2	no	—
72	Q₈	—	6	1	no	—
73	D₄	—	3	2	no	—
74	D₄	—	6	1	no	—
75	C₂×C₄	—	6	1	no	—
76	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
77	C₈	C₂×D₃×C₁₉	1	2	yes	complemented
78	C₂×C₃	SD₁₆×C₁₉	1	2	yes	complemented
79	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
80	D₃	—	4	2	no	—
81	C₂²	—	6	2	no	—
82	C₂²	—	12	2	no	—
83	C₂²	C₁₉×D₁₂	1	1	yes	characteristic
84	C₄	—	6	2	no	—
85	C₄	C₁₉×D₁₂	1	1	yes	characteristic
86	C₄	C₂²×D₃×C₁₉	1	1	yes	characteristic
87	C₃	C₂×SD₁₆×C₁₉	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	12	2	no	—
89	C₂	C₁₉×#204	1	2	yes	direct product factor
90	C₂	C₂×C₁₉×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×C₈×C₁₉	C₂
socle	C₂²×C₃×C₁₉	D₄
prime radical	C₂×C₁₉×D₁₂	C₂
hypercenter	C₂×C₈×C₁₉	D₃
hypocenter	C₃	C₂×SD₁₆×C₁₉
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×Dic₆	C₂	semidirect
3. C₂×C₃×C₈×C₁₉	C₂	semidirect
4. C₁₉×#204	C₂	direct (N × H)
12. C₁₉×Dic₆	C₂²	semidirect
13. C₃×C₈×C₁₉	C₂²	semidirect
17. C₂×C₈×C₁₉	D₃	semidirect
31. C₈×C₁₉	C₂×D₃	semidirect
32. C₂×C₃×C₁₉	SD₁₆	semidirect
35. C₂×#204	C₁₉	direct (N × H)
42. C₃×C₁₉	C₂×SD₁₆	semidirect
44. C₂×Dic₆	C₂×C₁₉	semidirect
45. C₂×C₃×C₈	C₂×C₁₉	semidirect
46. #204	C₂×C₁₉	direct (N × H)
48. C₂×C₁₉	#204	direct (N × H)
57. Dic₆	C₂²×C₁₉	semidirect
58. C₃×C₈	C₂²×C₁₉	semidirect
59. C₁₉	C₂×#204	direct (N × H)
63. C₂×C₈	D₃×C₁₉	semidirect
77. C₈	C₂×D₃×C₁₉	semidirect
78. C₂×C₃	SD₁₆×C₁₉	semidirect
87. C₃	C₂×SD₁₆×C₁₉	semidirect
89. C₂	C₁₉×#204	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×D₁₂	2
C₂×C₁₉×Dic₆	2
C₂×C₃×C₈×C₁₉	2
C₁₉×#204	2
C₂×SD₁₆×C₁₉	3
C₂×#204	19

Subgroups — C2×C19×#204 #14269654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#204 #14269654