Subgroups — C₂×C₁₉×C₄⋊Dic₃ #14269677

Order 1824.

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

	subgroup	G/H
center	C₂³×C₁₉	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂²×C₃×C₄×C₁₉	C₂
socle, prime radical	C₂³×C₃×C₁₉	C₂²
cosocle	C₂²×C₃	C₂³×C₁₉
hypercenter	C₂²×C₄×C₁₉	D₃
hypocenter	C₃	C₂×C₄⋊C₄×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×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	direct (N × H)
6. C₂×C₃×C₄×C₁₉	C₄	semidirect
17. C₃×C₄×C₁₉	C₂×C₄	semidirect
22. C₂×C₄×C₁₉	Dic₃	semidirect
24. C₂×C₃×C₁₉	C₄⋊C₄	semidirect
28. C₂×C₄⋊Dic₃	C₁₉	direct (N × H)
34. C₄×C₁₉	C₂×Dic₃	semidirect
35. C₃×C₁₉	C₂×C₄⋊C₄	semidirect
38. C₄⋊Dic₃	C₂×C₁₉	direct (N × H)
39. C₂×C₁₉	C₄⋊Dic₃	direct (N × H)
45. C₂×C₃×C₄	C₄×C₁₉	semidirect
49. C₁₉	C₂×C₄⋊Dic₃	direct (N × H)
57. C₃×C₄	C₂×C₄×C₁₉	semidirect
62. C₂×C₄	Dic₃×C₁₉	semidirect
64. C₂×C₃	C₄⋊C₄×C₁₉	semidirect
73. C₄	C₂×Dic₃×C₁₉	semidirect
74. C₃	C₂×C₄⋊C₄×C₁₉	semidirect
75. C₂	C₁₉×C₄⋊Dic₃	direct (N × H)

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
C₂²×Dic₃×C₁₉	2
C₁₉×C₄⋊Dic₃	2
C₂×C₄⋊C₄×C₁₉	3
C₂×C₄⋊Dic₃	19

Subgroups — C2×C19×C4⋊Dic3 #14269677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×C₄⋊Dic₃ #14269677