Subgroups — C₁₉×#904 #14269656

Order 1824.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#235	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#204	C₂	1	2	yes	maximal, complemented
6	C₁₉×#135	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#67	—	2	2	no	—
9	C₁₉×D₁₂	C₂²	1	2	yes	—
10	C₄×D₃×C₁₉	—	2	2	no	—
11	C₁₉×Dic₆	C₂²	1	2	yes	—
12	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#41×C₁₉	—	3	2	no	—
15	Q₁₆×C₁₉	—	3	1	no	—
16	SD₁₆×C₁₉	—	3	2	no	—
17	D₈×C₁₉	—	3	1	no	—
18	C₂×C₈×C₁₉	D₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
20	C₂×D₃×C₁₉	—	2	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	Q₈×C₁₉	—	3	2	no	—
25	D₄×C₁₉	—	3	2	no	—
26	D₄×C₁₉	—	6	2	no	—
27	C₂×C₄×C₁₉	—	6	2	no	—
28	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
29	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
30	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃×C₁₉	—	2	1	no	—
32	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
33	D₃×C₁₉	—	4	2	no	—
34	#904	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₁₉	—	6	2	no	—
36	C₂²×C₁₉	D₁₂	1	1	yes	characteristic
37	C₄×C₁₉	—	6	2	no	—
38	C₄×C₁₉	D₁₂	1	1	yes	characteristic
39	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
40	C₃×C₁₉	#135	1	1	yes	characteristic, complemented, Hall
41	#235	C₂×C₁₉	1	2	yes	complemented
42	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
43	Dic₁₂	C₂×C₁₉	1	1	yes	characteristic, complemented
44	D₂₄	C₂×C₁₉	1	1	yes	characteristic, complemented
45	#204	C₂×C₁₉	1	2	yes	complemented
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	—	12	2	no	—
48	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
49	#135	—	3	1	no	Sylow
50	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
51	#67	—	2	2	no	—
52	D₁₂	C₂²×C₁₉	1	2	yes	—
53	C₄×D₃	—	2	2	no	—
54	Dic₆	C₂²×C₁₉	1	2	yes	—
55	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
56	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
57	C₁₉	#904	1	1	yes	characteristic, direct product factor, Sylow
58	#41	—	3	2	no	—
59	Q₁₆	—	3	1	no	—
60	SD₁₆	—	3	2	no	—
61	D₈	—	3	1	no	—
62	C₂×C₈	D₃×C₁₉	1	1	yes	characteristic, complemented
63	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
64	C₂×D₃	—	2	2	no	—
65	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
66	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
67	Dic₃	—	2	2	no	—
68	Q₈	—	3	2	no	—
69	D₄	—	3	2	no	—
70	D₄	—	6	2	no	—
71	C₂×C₄	—	6	2	no	—
72	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
73	C₈	C₂×D₃×C₁₉	1	1	yes	characteristic
74	C₈	C₂×D₃×C₁₉	1	1	yes	characteristic
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
77	D₃	—	4	2	no	—
78	C₂²	—	6	2	no	—
79	C₂²	C₁₉×D₁₂	1	1	yes	characteristic
80	C₄	—	6	2	no	—
81	C₄	C₁₉×D₁₂	1	1	yes	characteristic
82	C₄	C₂²×D₃×C₁₉	1	1	yes	characteristic
83	C₃	C₁₉×#135	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	2	1	no	—
85	C₂	—	12	2	no	—
86	C₂	C₂×C₁₉×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×C₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂×D₄
hypercenter	C₂×C₈×C₁₉	D₃
hypocenter	C₃	C₁₉×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×#235	C₂	semidirect
2. C₂×C₃×C₈×C₁₉	C₂	semidirect
3. C₁₉×Dic₁₂	C₂	semidirect
4. C₁₉×D₂₄	C₂	semidirect
5. C₁₉×#204	C₂	semidirect
18. C₂×C₈×C₁₉	D₃	semidirect
34. #904	C₁₉	direct (N × H)
40. C₃×C₁₉	#135	semidirect
41. #235	C₂×C₁₉	semidirect
42. C₂×C₃×C₈	C₂×C₁₉	semidirect
43. Dic₁₂	C₂×C₁₉	semidirect
44. D₂₄	C₂×C₁₉	semidirect
45. #204	C₂×C₁₉	semidirect
57. C₁₉	#904	direct (N × H)
62. C₂×C₈	D₃×C₁₉	semidirect
83. C₃	C₁₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#235	2
C₂×C₃×C₈×C₁₉	2
C₁₉×Dic₁₂	2
C₁₉×D₂₄	2
C₁₉×#204	2
C₁₉×#135	3
#904	19

Subgroups — C19×#904 #14269656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#904 #14269656