Subgroups — C₂×C₁₉×#217 #14269704

Order 1824.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₁₉×#217	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₂²⋊C₄×C₁₉	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₉	—	2	4	no	—
6	C₂³×C₃×C₁₉	C₄	1	4	yes	complemented
7	C₂³×C₃×C₁₉	C₂²	1	2	yes	—
8	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₉	—	2	4	no	—
10	C₂×Dic₃×C₁₉	C₂²	1	4	yes	complemented
11	C₂⁴×C₁₉	D₃	1	1	yes	characteristic
12	C₂²×C₄×C₁₉	—	3	2	no	—
13	C₂²⋊C₄×C₁₉	—	3	4	no	—
14	C₂²×C₃×C₁₉	—	2	8	no	—
15	C₂²×C₃×C₁₉	—	2	4	no	—
16	C₂²×C₃×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₃×C₁₉	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃×C₁₉	D₄	1	4	yes	—
19	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
20	Dic₃×C₁₉	—	2	4	no	—
21	C₂³×C₁₉	—	2	4	no	—
22	C₂³×C₁₉	Dic₃	1	4	yes	complemented
23	C₂³×C₁₉	C₂×D₃	1	2	yes	—
24	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄×C₁₉	—	3	4	no	—
26	C₂×C₄×C₁₉	—	6	4	no	—
27	C₂×C₃×C₁₉	—	2	4	no	—
28	C₂×C₃×C₁₉	C₂²⋊C₄	1	4	yes	complemented
29	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₃×C₁₉	C₂×D₄	1	2	yes	—
31	C₂×#217	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₁₉	—	2	8	no	—
33	C₂²×C₁₉	—	2	4	no	—
34	C₂²×C₁₉	C₂×Dic₃	1	2	yes	—
35	C₂²×C₁₉	C₂×Dic₃	1	4	yes	complemented
36	C₂²×C₁₉	#67	1	4	yes	—
37	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
38	C₄×C₁₉	—	6	4	no	—
39	C₃×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
40	C₂⁴×C₃	C₂×C₁₉	1	1	yes	characteristic
41	C₂²×Dic₃	C₂×C₁₉	1	2	yes	complemented
42	#217	C₂×C₁₉	1	4	yes	direct product factor
43	C₂×C₁₉	—	2	4	no	—
44	C₂×C₁₉	#217	1	4	yes	direct product factor
45	C₂×C₁₉	C₂²×Dic₃	1	1	yes	characteristic
46	C₂×C₁₉	C₂×#67	1	2	yes	—
47	C₂×C₂²⋊C₄	—	3	1	no	Sylow
48	C₂³×C₃	—	2	4	no	—
49	C₂³×C₃	C₄×C₁₉	1	4	yes	complemented
50	C₂³×C₃	C₂²×C₁₉	1	2	yes	—
51	C₂³×C₃	C₂²×C₁₉	1	1	yes	characteristic
52	C₂×Dic₃	—	2	4	no	—
53	C₂×Dic₃	C₂²×C₁₉	1	4	yes	complemented
54	C₁₉	C₂×#217	1	1	yes	characteristic, direct product factor, Sylow
55	C₂⁴	D₃×C₁₉	1	1	yes	characteristic
56	C₂²×C₄	—	3	2	no	—
57	C₂²⋊C₄	—	3	4	no	—
58	C₂²×C₃	—	2	8	no	—
59	C₂²×C₃	—	2	4	no	—
60	C₂²×C₃	C₂×C₄×C₁₉	1	2	yes	—
61	C₂²×C₃	C₂×C₄×C₁₉	1	4	yes	complemented
62	C₂²×C₃	D₄×C₁₉	1	4	yes	—
63	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
64	Dic₃	—	2	4	no	—
65	C₂³	—	2	4	no	—
66	C₂³	Dic₃×C₁₉	1	4	yes	complemented
67	C₂³	C₂×D₃×C₁₉	1	2	yes	—
68	C₂³	C₂×D₃×C₁₉	1	1	yes	characteristic
69	C₂×C₄	—	3	4	no	—
70	C₂×C₄	—	6	4	no	—
71	C₂×C₃	—	2	4	no	—
72	C₂×C₃	C₂²⋊C₄×C₁₉	1	4	yes	complemented
73	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
74	C₂×C₃	C₂×D₄×C₁₉	1	2	yes	—
75	C₂²	—	2	8	no	—
76	C₂²	—	2	4	no	—
77	C₂²	C₂×Dic₃×C₁₉	1	2	yes	—
78	C₂²	C₂×Dic₃×C₁₉	1	4	yes	complemented
79	C₂²	C₁₉×#67	1	4	yes	—
80	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
81	C₄	—	6	4	no	—
82	C₃	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
83	C₂	—	2	4	no	—
84	C₂	C₁₉×#217	1	4	yes	direct product factor
85	C₂	C₂²×Dic₃×C₁₉	1	1	yes	characteristic
86	C₂	C₂×C₁₉×#67	1	2	yes	—

	subgroup	G/H
center	C₂³×C₁₉	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting, prime radical	C₂⁴×C₃×C₁₉	C₂
socle	C₂³×C₃×C₁₉	C₂²
cosocle	C₂²×C₃	C₂³×C₁₉
hypercenter	C₂⁴×C₁₉	D₃
hypocenter	C₃	C₂×C₂²⋊C₄×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₃×C₁₉	C₂	semidirect
3. C₁₉×#217	C₂	direct (N × H)
6. C₂³×C₃×C₁₉	C₄	semidirect
10. C₂×Dic₃×C₁₉	C₂²	semidirect
17. C₂²×C₃×C₁₉	C₂×C₄	semidirect
22. C₂³×C₁₉	Dic₃	semidirect
28. C₂×C₃×C₁₉	C₂²⋊C₄	semidirect
31. C₂×#217	C₁₉	direct (N × H)
35. C₂²×C₁₉	C₂×Dic₃	semidirect
39. C₃×C₁₉	C₂×C₂²⋊C₄	semidirect
41. C₂²×Dic₃	C₂×C₁₉	semidirect
42. #217	C₂×C₁₉	direct (N × H)
44. C₂×C₁₉	#217	direct (N × H)
49. C₂³×C₃	C₄×C₁₉	semidirect
53. C₂×Dic₃	C₂²×C₁₉	semidirect
54. C₁₉	C₂×#217	direct (N × H)
61. C₂²×C₃	C₂×C₄×C₁₉	semidirect
66. C₂³	Dic₃×C₁₉	semidirect
72. C₂×C₃	C₂²⋊C₄×C₁₉	semidirect
78. C₂²	C₂×Dic₃×C₁₉	semidirect
82. C₃	C₂×C₂²⋊C₄×C₁₉	semidirect
84. C₂	C₁₉×#217	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₉	2
C₂²×Dic₃×C₁₉	2
C₁₉×#217	2
C₂×C₂²⋊C₄×C₁₉	3
C₂×#217	19

Subgroups — C2×C19×#217 #14269704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#217 #14269704