Subgroups — C₁₉×#926 #14269678

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#217	C₂	1	2	yes	maximal
3	C₁₉×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
4	C₄×Dic₃×C₁₉	C₂	1	2	yes	maximal, complemented
5	C₁₉×#117	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₉	C₄	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃×C₁₉	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₉	D₃	1	1	yes	characteristic
12	C₄⋊C₄×C₁₉	—	3	2	no	—
13	C₂²⋊C₄×C₁₉	—	3	2	no	—
14	C₄²×C₁₉	—	3	2	no	—
15	C₂²×C₃×C₁₉	—	2	2	no	—
16	C₂²×C₃×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₃×C₄×C₁₉	C₂×C₄	1	2	yes	—
20	Dic₃×C₁₉	—	2	4	no	—
21	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
22	C₂×C₄×C₁₉	—	3	4	no	—
23	C₂×C₄×C₁₉	Dic₃	1	4	yes	complemented
24	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
26	C₂×C₃×C₁₉	—	2	2	no	—
27	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₃×C₁₉	#41	1	2	yes	—
29	#926	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₁₉	—	2	2	no	—
31	C₂²×C₁₉	C₂×Dic₃	1	2	yes	—
32	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₉	—	6	4	no	—
34	C₄×C₁₉	C₂×Dic₃	1	2	yes	—
35	C₄×C₁₉	C₂×Dic₃	1	2	yes	—
36	C₃×C₁₉	#117	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃×C₄	C₂×C₁₉	1	1	yes	characteristic
38	#217	C₂×C₁₉	1	2	yes	—
39	C₄⋊Dic₃	C₂×C₁₉	1	2	yes	complemented
40	C₄×Dic₃	C₂×C₁₉	1	2	yes	complemented
41	C₂×C₁₉	—	2	2	no	—
42	C₂×C₁₉	#235	1	2	yes	—
43	C₂×C₁₉	C₂²×Dic₃	1	1	yes	characteristic
44	#117	—	3	1	no	Sylow
45	C₂³×C₃	C₂²×C₁₉	1	1	yes	characteristic
46	C₂×C₃×C₄	C₄×C₁₉	1	4	yes	complemented
47	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
48	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
49	C₂×Dic₃	C₂²×C₁₉	1	4	yes	—
50	C₁₉	#926	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₄	D₃×C₁₉	1	1	yes	characteristic
52	C₄⋊C₄	—	3	2	no	—
53	C₂²⋊C₄	—	3	2	no	—
54	C₄²	—	3	2	no	—
55	C₂²×C₃	—	2	2	no	—
56	C₂²×C₃	C₂×C₄×C₁₉	1	2	yes	—
57	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
58	C₃×C₄	C₂×C₄×C₁₉	1	2	yes	—
59	C₃×C₄	C₂×C₄×C₁₉	1	2	yes	—
60	Dic₃	—	2	4	no	—
61	C₂³	C₂×D₃×C₁₉	1	1	yes	characteristic
62	C₂×C₄	—	3	4	no	—
63	C₂×C₄	Dic₃×C₁₉	1	4	yes	complemented
64	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
65	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
68	C₂×C₃	#41×C₁₉	1	2	yes	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂×Dic₃×C₁₉	1	2	yes	—
71	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
72	C₄	—	6	4	no	—
73	C₄	C₂×Dic₃×C₁₉	1	2	yes	—
74	C₄	C₂×Dic₃×C₁₉	1	2	yes	—
75	C₃	C₁₉×#117	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	2	2	no	—
77	C₂	C₁₉×#235	1	2	yes	—
78	C₂	C₂²×Dic₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂²×C₃×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 ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₁₉×C₄⋊Dic₃	C₂	semidirect
4. C₄×Dic₃×C₁₉	C₂	semidirect
7. C₂×C₃×C₄×C₁₉	C₄	semidirect
23. C₂×C₄×C₁₉	Dic₃	semidirect
29. #926	C₁₉	direct (N × H)
36. C₃×C₁₉	#117	semidirect
39. C₄⋊Dic₃	C₂×C₁₉	semidirect
40. C₄×Dic₃	C₂×C₁₉	semidirect
46. C₂×C₃×C₄	C₄×C₁₉	semidirect
50. C₁₉	#926	direct (N × H)
63. C₂×C₄	Dic₃×C₁₉	semidirect
75. 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×C₃×C₄×C₁₉	2
C₁₉×#217	2
C₁₉×C₄⋊Dic₃	2
C₄×Dic₃×C₁₉	2
C₁₉×#117	3
#926	19

Subgroups — C19×#926 #14269678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#926 #14269678