Subgroups — C₂×C₁₉×#215 #14269695

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#215	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×SD₁₆×C₁₉	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₉	—	2	1	no	—
7	C₃×Q₈×C₁₉	—	2	1	no	—
8	C₃×Q₈×C₁₉	C₂²	1	2	yes	complemented
9	C₂×C₃×C₄×C₁₉	—	2	1	no	—
10	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×D₁₂	—	2	1	no	—
12	C₁₉×D₁₂	C₂²	1	2	yes	—
13	C₁₉×C₃⋊C₈	C₂²	1	2	yes	complemented
14	C₂×Q₈×C₁₉	D₃	1	1	yes	characteristic, complemented
15	C₂×D₄×C₁₉	—	3	1	no	—
16	SD₁₆×C₁₉	—	3	4	no	—
17	C₂×C₈×C₁₉	—	3	1	no	—
18	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
19	C₂×D₃×C₁₉	—	2	2	no	—
20	C₂×D₃×C₁₉	—	4	2	no	—
21	C₃×C₄×C₁₉	—	2	2	no	—
22	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×C₁₉	—	6	1	no	—
25	Q₈×C₁₉	—	2	1	no	—
26	Q₈×C₁₉	C₂×D₃	1	2	yes	complemented
27	D₄×C₁₉	—	3	2	no	—
28	D₄×C₁₉	—	6	1	no	—
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
31	C₈×C₁₉	—	3	2	no	—
32	C₂×C₃×C₁₉	SD₁₆	1	2	yes	complemented
33	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
34	D₃×C₁₉	—	4	2	no	—
35	C₂×#215	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂²×C₁₉	—	6	2	no	—
37	C₂²×C₁₉	—	12	2	no	—
38	C₂²×C₁₉	#67	1	1	yes	characteristic
39	C₄×C₁₉	—	2	2	no	—
40	C₄×C₁₉	#67	1	1	yes	characteristic
41	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
42	C₃×C₁₉	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
44	C₂×D₁₂	C₂×C₁₉	1	1	yes	characteristic
45	#215	C₂×C₁₉	1	4	yes	direct product factor
46	C₂×C₃⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
47	C₂×C₁₉	—	12	2	no	—
48	C₂×C₁₉	#215	1	2	yes	direct product factor
49	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
50	C₂×SD₁₆	—	3	1	no	Sylow
51	C₂²×D₃	—	2	1	no	—
52	C₃×Q₈	—	2	1	no	—
53	C₃×Q₈	C₂²×C₁₉	1	2	yes	complemented
54	C₂×C₃×C₄	—	2	1	no	—
55	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
56	D₁₂	—	2	1	no	—
57	D₁₂	C₂²×C₁₉	1	2	yes	—
58	C₃⋊C₈	C₂²×C₁₉	1	2	yes	complemented
59	C₁₉	C₂×#215	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×Q₈	D₃×C₁₉	1	1	yes	characteristic, complemented
61	C₂×D₄	—	3	1	no	—
62	SD₁₆	—	3	4	no	—
63	C₂×C₈	—	3	1	no	—
64	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
65	C₂×D₃	—	2	2	no	—
66	C₂×D₃	—	4	2	no	—
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
69	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
70	C₂³	—	6	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	C₂×D₃×C₁₉	1	2	yes	complemented
73	D₄	—	3	2	no	—
74	D₄	—	6	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
77	C₈	—	3	2	no	—
78	C₂×C₃	SD₁₆×C₁₉	1	2	yes	complemented
79	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
80	D₃	—	4	2	no	—
81	C₂²	—	6	2	no	—
82	C₂²	—	12	2	no	—
83	C₂²	C₁₉×#67	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	C₁₉×#67	1	1	yes	characteristic
86	C₄	C₂²×D₃×C₁₉	1	1	yes	characteristic
87	C₃	C₂×SD₁₆×C₁₉	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	12	2	no	—
89	C₂	C₁₉×#215	1	2	yes	direct product factor
90	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	#67
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle	C₂²×C₃×C₁₉	D₄
prime radical	C₂×C₁₉×D₁₂	C₂
hypercenter	C₂×Q₈×C₁₉	D₃
hypocenter	C₃	C₂×SD₁₆×C₁₉
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×Q₈×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₉	C₂	semidirect
3. C₁₉×#215	C₂	direct (N × H)
4. C₂×C₁₉×C₃⋊C₈	C₂	semidirect
8. C₃×Q₈×C₁₉	C₂²	semidirect
13. C₁₉×C₃⋊C₈	C₂²	semidirect
14. C₂×Q₈×C₁₉	D₃	semidirect
26. Q₈×C₁₉	C₂×D₃	semidirect
32. C₂×C₃×C₁₉	SD₁₆	semidirect
35. C₂×#215	C₁₉	direct (N × H)
42. C₃×C₁₉	C₂×SD₁₆	semidirect
43. C₂×C₃×Q₈	C₂×C₁₉	semidirect
45. #215	C₂×C₁₉	direct (N × H)
46. C₂×C₃⋊C₈	C₂×C₁₉	semidirect
48. C₂×C₁₉	#215	direct (N × H)
53. C₃×Q₈	C₂²×C₁₉	semidirect
58. C₃⋊C₈	C₂²×C₁₉	semidirect
59. C₁₉	C₂×#215	direct (N × H)
60. C₂×Q₈	D₃×C₁₉	semidirect
72. Q₈	C₂×D₃×C₁₉	semidirect
78. C₂×C₃	SD₁₆×C₁₉	semidirect
87. C₃	C₂×SD₁₆×C₁₉	semidirect
89. C₂	C₁₉×#215	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×Q₈×C₁₉	2
C₂×C₁₉×D₁₂	2
C₁₉×#215	2
C₂×C₁₉×C₃⋊C₈	2
C₂×SD₁₆×C₁₉	3
C₂×#215	19

Subgroups — C2×C19×#215 #14269695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#215 #14269695