Subgroups — C₁₉×#875 #14269627

Order 1824.

152 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	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₁₉×#124	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₉	C₂²	1	2	yes	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
10	C₁₉×D₁₂	—	2	2	no	—
11	C₁₉×Dic₆	—	2	2	no	—
12	C₂×Q₈×C₁₉	—	3	1	no	—
13	C₂×D₄×C₁₉	—	3	1	no	—
14	C₂²⋊C₄×C₁₉	—	3	4	no	—
15	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₉	—	2	2	no	—
18	C₂×D₃×C₁₉	—	2	4	no	—
19	C₃×C₄×C₁₉	—	2	2	no	—
20	C₃×C₄×C₁₉	D₄	1	2	yes	—
21	Dic₃×C₁₉	—	2	2	no	—
22	C₂³×C₁₉	—	3	2	no	—
23	Q₈×C₁₉	—	6	2	no	—
24	D₄×C₁₉	—	6	2	no	—
25	C₂×C₄×C₁₉	—	3	2	no	—
26	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₃×C₁₉	#41	1	2	yes	—
30	D₃×C₁₉	—	4	2	no	—
31	#875	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₁₉	—	6	2	no	—
33	C₂²×C₁₉	—	6	4	no	—
34	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₉	—	2	2	no	—
36	C₄×C₁₉	—	6	2	no	—
37	C₄×C₁₉	D₁₂	1	2	yes	—
38	C₃×C₁₉	#124	1	1	yes	characteristic, complemented, Hall
39	C₂×D₁₂	C₂×C₁₉	1	1	yes	characteristic
40	C₂×Dic₆	C₂×C₁₉	1	1	yes	characteristic, complemented
41	C₃×C₄²	C₂×C₁₉	1	1	yes	characteristic, complemented
42	(C₂×D₃)⋊C₄	C₂×C₁₉	1	4	yes	complemented
43	C₂×C₁₉	—	12	2	no	—
44	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
45	C₂×C₁₉	#235	1	2	yes	—
46	#124	—	3	1	no	Sylow
47	C₂²×D₃	C₂²×C₁₉	1	2	yes	—
48	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	—
49	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
50	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
51	D₁₂	—	2	2	no	—
52	Dic₆	—	2	2	no	—
53	C₁₉	#875	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×Q₈	—	3	1	no	—
55	C₂×D₄	—	3	1	no	—
56	C₂²⋊C₄	—	3	4	no	—
57	C₄²	D₃×C₁₉	1	1	yes	characteristic, complemented
58	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
59	C₂×D₃	—	2	2	no	—
60	C₂×D₃	—	2	4	no	—
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	D₄×C₁₉	1	2	yes	—
63	Dic₃	—	2	2	no	—
64	C₂³	—	3	2	no	—
65	Q₈	—	6	2	no	—
66	D₄	—	6	2	no	—
67	C₂×C₄	—	3	2	no	—
68	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	—
69	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
70	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
71	C₂×C₃	#41×C₁₉	1	2	yes	—
72	D₃	—	4	2	no	—
73	C₂²	—	6	2	no	—
74	C₂²	—	6	4	no	—
75	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	6	2	no	—
78	C₄	C₁₉×D₁₂	1	2	yes	—
79	C₃	C₁₉×#124	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	12	2	no	—
81	C₂	C₂×C₁₉×D₁₂	1	1	yes	characteristic
82	C₂	C₁₉×#235	1	2	yes	—

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₄²×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂×C₁₉×D₁₂	C₂
hypercenter	C₄²×C₁₉	D₃
hypocenter	C₃	C₁₉×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×Dic₆	C₂	semidirect
3. C₃×C₄²×C₁₉	C₂	semidirect
4. C₁₉×(C₂×D₃)⋊C₄	C₂	semidirect
15. C₄²×C₁₉	D₃	semidirect
31. #875	C₁₉	direct (N × H)
38. C₃×C₁₉	#124	semidirect
40. C₂×Dic₆	C₂×C₁₉	semidirect
41. C₃×C₄²	C₂×C₁₉	semidirect
42. (C₂×D₃)⋊C₄	C₂×C₁₉	semidirect
53. C₁₉	#875	direct (N × H)
57. C₄²	D₃×C₁₉	semidirect
79. C₃	C₁₉×#124	semidirect

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
C₃×C₄²×C₁₉	2
C₁₉×(C₂×D₃)⋊C₄	2
C₁₉×#124	3
#875	19

Subgroups — C19×#875 #14269627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#875 #14269627