Subgroups — C₁₉×#877 #14269629

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#217	C₂	1	1	yes	maximal, characteristic
4	C₁₉×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₃×C₁₉	C₂	1	2	yes	maximal, complemented
6	C₁₉×#117	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×Dic₃×C₁₉	C₄	1	4	yes	complemented
10	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
11	C₂×Dic₃×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₃×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₁₉	—	3	1	no	—
14	C₄⋊C₄×C₁₉	—	3	2	no	—
15	C₂²⋊C₄×C₁₉	—	3	1	no	—
16	C₂²⋊C₄×C₁₉	D₃	1	1	yes	characteristic
17	C₄²×C₁₉	—	3	2	no	—
18	C₂²×C₃×C₁₉	—	2	2	no	—
19	C₂²×C₃×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
21	C₃×C₄×C₁₉	—	2	2	no	—
22	Dic₃×C₁₉	—	2	2	no	—
23	Dic₃×C₁₉	C₂×C₄	1	2	yes	—
24	Dic₃×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
26	C₂×C₄×C₁₉	—	3	4	no	—
27	C₂×C₄×C₁₉	—	3	1	no	—
28	C₂×C₄×C₁₉	—	3	1	no	—
29	C₂×C₄×C₁₉	—	3	2	no	—
30	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
31	C₂×C₃×C₁₉	—	2	2	no	—
32	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₃×C₁₉	#41	1	2	yes	—
34	#877	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₁₉	—	2	2	no	—
36	C₂²×C₁₉	C₄×D₃	1	2	yes	—
37	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
38	C₄×C₁₉	—	2	2	no	—
39	C₄×C₁₉	—	3	2	no	—
40	C₄×C₁₉	—	3	2	no	—
41	C₄×C₁₉	—	6	2	no	—
42	C₃×C₁₉	#117	1	1	yes	characteristic, complemented, Hall
43	C₂²×Dic₃	C₂×C₁₉	1	1	yes	characteristic
44	C₃×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
45	#217	C₂×C₁₉	1	1	yes	characteristic
46	Dic₃⋊C₄	C₂×C₁₉	1	2	yes	complemented
47	C₄×Dic₃	C₂×C₁₉	1	2	yes	complemented
48	C₂×C₁₉	—	2	2	no	—
49	C₂×C₁₉	C₂×C₄×D₃	1	1	yes	characteristic
50	C₂×C₁₉	#237	1	2	yes	—
51	#117	—	3	1	no	Sylow
52	C₂³×C₃	C₂²×C₁₉	1	1	yes	characteristic
53	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	—
54	C₂×Dic₃	C₄×C₁₉	1	4	yes	complemented
55	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
56	C₂×Dic₃	C₂²×C₁₉	1	1	yes	characteristic
57	C₂×Dic₃	C₂²×C₁₉	1	1	yes	characteristic
58	C₁₉	#877	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²×C₄	—	3	1	no	—
60	C₄⋊C₄	—	3	2	no	—
61	C₂²⋊C₄	—	3	1	no	—
62	C₂²⋊C₄	D₃×C₁₉	1	1	yes	characteristic
63	C₄²	—	3	2	no	—
64	C₂²×C₃	—	2	2	no	—
65	C₂²×C₃	C₂×C₄×C₁₉	1	2	yes	—
66	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
67	C₃×C₄	—	2	2	no	—
68	Dic₃	—	2	2	no	—
69	Dic₃	C₂×C₄×C₁₉	1	2	yes	—
70	Dic₃	C₂×C₄×C₁₉	1	2	yes	—
71	C₂³	C₂×D₃×C₁₉	1	1	yes	characteristic
72	C₂×C₄	—	3	4	no	—
73	C₂×C₄	—	3	1	no	—
74	C₂×C₄	—	3	1	no	—
75	C₂×C₄	—	3	2	no	—
76	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
79	C₂×C₃	#41×C₁₉	1	2	yes	—
80	C₂²	—	2	2	no	—
81	C₂²	C₄×D₃×C₁₉	1	2	yes	—
82	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	3	2	no	—
85	C₄	—	3	2	no	—
86	C₄	—	6	2	no	—
87	C₃	C₁₉×#117	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	2	2	no	—
89	C₂	C₂×C₄×D₃×C₁₉	1	1	yes	characteristic
90	C₂	C₁₉×#237	1	2	yes	—

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₂²⋊C₄×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂³×C₃×C₁₉	C₂²
cosocle	C₂²×C₃	C₂³×C₁₉
hypercenter	C₂²⋊C₄×C₁₉	D₃
hypocenter	C₃	C₁₉×#117
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²⋊C₄×C₁₉

Complements

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

N	H ≅ G/N	type
4. C₁₉×Dic₃⋊C₄	C₂	semidirect
5. C₄×Dic₃×C₁₉	C₂	semidirect
9. C₂×Dic₃×C₁₉	C₄	semidirect
34. #877	C₁₉	direct (N × H)
42. C₃×C₁₉	#117	semidirect
46. Dic₃⋊C₄	C₂×C₁₉	semidirect
47. C₄×Dic₃	C₂×C₁₉	semidirect
54. C₂×Dic₃	C₄×C₁₉	semidirect
58. C₁₉	#877	direct (N × H)
87. C₃	C₁₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₃×C₁₉	2
C₃×C₂²⋊C₄×C₁₉	2
C₁₉×#217	2
C₁₉×Dic₃⋊C₄	2
C₄×Dic₃×C₁₉	2
C₁₉×#117	3
#877	19

Subgroups — C19×#877 #14269629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#877 #14269629