Subgroups — C₂×C₃⋊C₈×D₁₉ #14269249

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃⋊C₈×D₁₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₈×D₁₉	—	3	1	no	maximal, Hall
6	C₂²×C₃×D₁₉	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₃×Dic₁₉	C₄	1	1	yes	characteristic
9	C₃×C₄×D₁₉	C₄	1	2	yes	—
10	C₃×C₄×D₁₉	C₂²	1	2	yes	—
11	C₃⋊(C₁₉⋊C₈)	C₂²	1	2	yes	complemented
12	C₁₉×C₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂×C₄×D₁₉	D₃	1	1	yes	characteristic
14	C₂×C₈×C₁₉	—	3	1	no	—
15	C₂×C₁₉⋊C₈	—	3	1	no	—
16	C₈×D₁₉	—	3	4	no	—
17	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×D₁₉	C₈	1	4	yes	complemented
19	C₂×C₃×D₁₉	C₂×C₄	1	2	yes	—
20	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₃×Dic₁₉	C₂×C₄	1	2	yes	—
23	C₂²×D₁₉	Dic₃	1	1	yes	characteristic
24	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₉	Dic₃	1	1	yes	characteristic
26	C₄×D₁₉	Dic₃	1	2	yes	—
27	C₄×D₁₉	C₂×D₃	1	2	yes	—
28	C₈×C₁₉	—	3	2	no	—
29	C₁₉⋊C₈	—	3	2	no	—
30	C₂×C₃×C₁₉	C₂×C₈	1	2	yes	complemented
31	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₃×D₁₉	C₂×C₈	1	4	yes	complemented
33	C₂²×C₃⋊C₈	—	19	1	no	maximal, Hall
34	C₂²×C₁₉	C₂×Dic₃	1	1	yes	characteristic
35	C₂×D₁₉	C₃⋊C₈	1	4	yes	direct product factor
36	C₂×D₁₉	C₂×Dic₃	1	2	yes	—
37	C₄×C₁₉	C₂×Dic₃	1	1	yes	characteristic
38	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
39	Dic₁₉	C₂×Dic₃	1	2	yes	—
40	C₃×C₁₉	C₂²×C₈	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₃×C₄	—	19	1	no	—
42	C₂×C₃⋊C₈	—	19	1	no	—
43	C₂×C₃⋊C₈	—	19	4	no	—
44	C₂×C₃⋊C₈	D₁₉	1	1	yes	characteristic, direct product factor
45	C₂×C₁₉	C₂×C₃⋊C₈	1	2	yes	complemented
46	C₂×C₁₉	C₂²×Dic₃	1	1	yes	characteristic
47	D₁₉	C₂×C₃⋊C₈	1	4	yes	direct product factor
48	C₂²×C₈	—	57	1	no	Sylow
49	C₂³×C₃	—	19	1	no	—
50	C₂×C₃×C₄	—	19	1	no	—
51	C₂×C₃×C₄	—	19	2	no	—
52	C₂×C₃×C₄	—	19	2	no	—
53	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
54	C₃⋊C₈	—	19	2	no	—
55	C₃⋊C₈	C₂×D₁₉	1	2	yes	direct product factor
56	C₁₉	C₂²×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	19	1	no	—
58	C₂×C₈	—	3	1	no	—
59	C₂×C₈	—	57	4	no	—
60	C₂×C₈	—	57	1	no	—
61	C₂²×C₃	—	19	4	no	—
62	C₂²×C₃	—	19	2	no	—
63	C₂²×C₃	C₄×D₁₉	1	1	yes	characteristic
64	C₃×C₄	—	19	2	no	—
65	C₃×C₄	C₄×D₁₉	1	1	yes	characteristic
66	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
67	C₂³	—	19	1	no	—
68	C₂×C₄	—	19	1	no	—
69	C₂×C₄	—	19	2	no	—
70	C₂×C₄	—	19	2	no	—
71	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
72	C₈	—	3	2	no	—
73	C₈	—	57	2	no	—
74	C₂×C₃	—	19	4	no	—
75	C₂×C₃	C₈×D₁₉	1	2	yes	complemented
76	C₂×C₃	C₂×C₄×D₁₉	1	1	yes	characteristic
77	C₂²	—	19	4	no	—
78	C₂²	—	19	2	no	—
79	C₂²	Dic₃×D₁₉	1	1	yes	characteristic
80	C₄	—	19	2	no	—
81	C₄	Dic₃×D₁₉	1	1	yes	characteristic
82	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
83	C₃	C₂×C₈×D₁₉	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	19	4	no	—
85	C₂	C₃⋊C₈×D₁₉	1	2	yes	direct product factor
86	C₂	C₂×Dic₃×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₁₉
commutator, hypocenter	C₃×C₁₉	C₂²×C₈
Frattini	C₄	C₂×D₃×D₁₉
Fitting	C₂×C₃×C₄×C₁₉	C₂²
socle	C₂²×C₃×C₁₉	C₂×C₄
prime radical	C₂²×C₃×D₁₉	C₄
cosocle	C₃×C₄×C₁₉	C₂³
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊(C₁₉⋊C₈)	C₂	semidirect
3. C₂×C₁₉×C₃⋊C₈	C₂	semidirect
4. C₃⋊C₈×D₁₉	C₂	direct (N × H)
11. C₃⋊(C₁₉⋊C₈)	C₂²	semidirect
12. C₁₉×C₃⋊C₈	C₂²	semidirect
18. C₂×C₃×D₁₉	C₈	semidirect
30. C₂×C₃×C₁₉	C₂×C₈	semidirect
32. C₃×D₁₉	C₂×C₈	semidirect
35. C₂×D₁₉	C₃⋊C₈	direct (N × H)
40. C₃×C₁₉	C₂²×C₈	semidirect
44. C₂×C₃⋊C₈	D₁₉	direct (N × H)
45. C₂×C₁₉	C₂×C₃⋊C₈	semidirect
47. D₁₉	C₂×C₃⋊C₈	direct (N × H)
55. C₃⋊C₈	C₂×D₁₉	direct (N × H)
56. C₁₉	C₂²×C₃⋊C₈	semidirect
75. C₂×C₃	C₈×D₁₉	semidirect
83. C₃	C₂×C₈×D₁₉	semidirect
85. C₂	C₃⋊C₈×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₁₉	2
C₂×C₃⋊(C₁₉⋊C₈)	2
C₂×C₁₉×C₃⋊C₈	2
C₃⋊C₈×D₁₉	2
C₂×C₈×D₁₉	3
C₂²×C₃⋊C₈	19

Subgroups — C2×C3⋊C8×D19 #14269249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊C₈×D₁₉ #14269249