Subgroups — C₁₉×#940 #14269685

Order 1824.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#67	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#127	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₉	C₂²	1	2	yes	—
7	C₂²×D₃×C₁₉	C₂²	1	2	yes	—
8	C₃×D₄×C₁₉	—	2	2	no	—
9	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#67	—	2	8	no	—
11	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
12	C₁₉×D₁₂	—	2	2	no	—
13	C₂×D₄×C₁₉	—	3	4	no	—
14	C₂×D₄×C₁₉	—	3	1	no	—
15	C₂×D₄×C₁₉	D₃	1	1	yes	characteristic, complemented
16	C₄²×C₁₉	—	3	1	no	—
17	C₂²×C₃×C₁₉	—	2	4	no	—
18	C₂²×C₃×C₁₉	—	2	2	no	—
19	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×D₃×C₁₉	—	2	2	no	—
21	C₂×D₃×C₁₉	—	2	4	no	—
22	C₃×C₄×C₁₉	D₄	1	2	yes	complemented
23	Dic₃×C₁₉	D₄	1	4	yes	complemented
24	C₂³×C₁₉	—	3	2	no	—
25	C₂³×C₁₉	C₂×D₃	1	2	yes	—
26	D₄×C₁₉	—	2	2	no	—
27	D₄×C₁₉	—	6	8	no	—
28	D₄×C₁₉	—	6	2	no	—
29	C₂×C₄×C₁₉	—	3	2	no	—
30	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃×C₁₉	—	4	2	no	—
32	C₂×C₃×C₁₉	C₂×D₄	1	2	yes	—
33	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
34	D₃×C₁₉	—	4	2	no	—
35	#940	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂²×C₁₉	—	2	4	no	—
37	C₂²×C₁₉	—	2	2	no	—
38	C₂²×C₁₉	—	6	4	no	—
39	C₂²×C₁₉	—	6	2	no	—
40	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
41	C₄×C₁₉	—	3	4	no	—
42	C₄×C₁₉	#67	1	2	yes	complemented
43	C₃×C₁₉	#127	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
45	C₂×#67	C₂×C₁₉	1	4	yes	complemented
46	C₂×D₁₂	C₂×C₁₉	1	1	yes	characteristic, complemented
47	C₄×Dic₃	C₂×C₁₉	1	1	yes	characteristic, complemented
48	C₂×C₁₉	—	4	2	no	—
49	C₂×C₁₉	—	12	2	no	—
50	C₂×C₁₉	D₃×D₄	1	2	yes	—
51	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
52	#127	—	3	1	no	Sylow
53	C₂³×C₃	C₂²×C₁₉	1	2	yes	—
54	C₂²×D₃	C₂²×C₁₉	1	2	yes	—
55	C₃×D₄	—	2	2	no	—
56	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
57	#67	—	2	8	no	—
58	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
59	D₁₂	—	2	2	no	—
60	C₁₉	#940	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×D₄	—	3	4	no	—
62	C₂×D₄	—	3	1	no	—
63	C₂×D₄	D₃×C₁₉	1	1	yes	characteristic, complemented
64	C₄²	—	3	1	no	—
65	C₂²×C₃	—	2	4	no	—
66	C₂²×C₃	—	2	2	no	—
67	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
68	C₂×D₃	—	2	2	no	—
69	C₂×D₃	—	2	4	no	—
70	C₃×C₄	D₄×C₁₉	1	2	yes	complemented
71	Dic₃	D₄×C₁₉	1	4	yes	complemented
72	C₂³	—	3	2	no	—
73	C₂³	C₂×D₃×C₁₉	1	2	yes	—
74	D₄	—	2	2	no	—
75	D₄	—	6	8	no	—
76	D₄	—	6	2	no	—
77	C₂×C₄	—	3	2	no	—
78	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
79	C₂×C₃	—	4	2	no	—
80	C₂×C₃	C₂×D₄×C₁₉	1	2	yes	—
81	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
82	D₃	—	4	2	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	6	4	no	—
86	C₂²	—	6	2	no	—
87	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
88	C₄	—	3	4	no	—
89	C₄	C₁₉×#67	1	2	yes	complemented
90	C₃	C₁₉×#127	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	4	2	no	—
92	C₂	—	12	2	no	—
93	C₂	D₃×D₄×C₁₉	1	2	yes	—
94	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂×C₃×D₄×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
hypercenter	C₂×D₄×C₁₉	D₃
hypocenter	C₃	C₁₉×#127
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×D₄×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×C₁₉	C₂	semidirect
2. C₂×C₁₉×#67	C₂	semidirect
3. C₂×C₁₉×D₁₂	C₂	semidirect
4. C₄×Dic₃×C₁₉	C₂	semidirect
15. C₂×D₄×C₁₉	D₃	semidirect
22. C₃×C₄×C₁₉	D₄	semidirect
23. Dic₃×C₁₉	D₄	semidirect
35. #940	C₁₉	direct (N × H)
42. C₄×C₁₉	#67	semidirect
43. C₃×C₁₉	#127	semidirect
44. C₂×C₃×D₄	C₂×C₁₉	semidirect
45. C₂×#67	C₂×C₁₉	semidirect
46. C₂×D₁₂	C₂×C₁₉	semidirect
47. C₄×Dic₃	C₂×C₁₉	semidirect
60. C₁₉	#940	direct (N × H)
63. C₂×D₄	D₃×C₁₉	semidirect
70. C₃×C₄	D₄×C₁₉	semidirect
71. Dic₃	D₄×C₁₉	semidirect
89. C₄	C₁₉×#67	semidirect
90. C₃	C₁₉×#127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₉	2
C₂×C₁₉×#67	2
C₂×C₁₉×D₁₂	2
C₄×Dic₃×C₁₉	2
C₁₉×#127	3
#940	19

Subgroups — C19×#940 #14269685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#940 #14269685