Subgroups — C₃×C₁₉×#104 #14269041

Order 1824.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#104	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
6	C₃×D₄×C₁₉	—	2	1	no	—
7	C₃×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃×C₄×C₁₉	—	2	1	no	—
9	C₂×C₃×C₄×C₁₉	—	2	1	no	—
10	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₃×C₈×C₁₉	—	2	1	no	—
12	#41×C₁₉	C₂×C₃	1	1	yes	characteristic
13	M₁₆×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₄²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₁₉	—	2	1	no	—
16	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
17	C₃×C₄×C₁₉	—	2	2	no	—
18	C₃×C₄×C₁₉	—	2	1	no	—
19	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
21	Q₈×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
22	D₄×C₁₉	—	2	1	no	—
23	D₄×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×C₁₉	—	2	1	no	—
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
27	C₈×C₁₉	—	2	1	no	—
28	C₂×C₃×C₁₉	—	2	1	no	—
29	C₂×C₃×C₁₉	—	4	1	no	—
30	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₃×#104	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₁₉	—	2	1	no	—
33	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
34	C₄×C₁₉	—	2	2	no	—
35	C₄×C₁₉	—	2	1	no	—
36	C₄×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
37	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
38	C₃×C₁₉	#104	1	1	yes	characteristic, direct product factor, Hall
39	C₃×#41	C₂×C₁₉	1	1	yes	characteristic
40	C₃×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
41	C₃×C₄²	C₂×C₁₉	1	1	yes	characteristic, complemented
42	C₂×C₁₉	—	2	1	no	—
43	C₂×C₁₉	—	4	1	no	—
44	C₂×C₁₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
45	#104	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₃×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
47	C₃×D₄	—	2	1	no	—
48	C₃×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
49	C₂×C₃×C₄	—	2	1	no	—
50	C₂×C₃×C₄	—	2	1	no	—
51	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
52	C₃×C₈	—	2	1	no	—
53	C₁₉	C₃×#104	1	1	yes	characteristic, direct product factor, Sylow
54	#41	C₂×C₃×C₁₉	1	1	yes	characteristic
55	M₁₆	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
56	C₄²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
57	C₂²×C₃	—	2	1	no	—
58	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	2	1	no	—
61	C₃×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
62	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
63	Q₈	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
64	D₄	—	2	1	no	—
65	D₄	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	—	4	1	no	—
72	C₂×C₃	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
73	C₂²	—	2	1	no	—
74	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
78	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
79	C₃	C₁₉×#104	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	C₃×C₂²⋊C₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₁₉	D₄
commutator	C₄	C₂×C₃×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₁₉
socle	C₂×C₃×C₁₉	C₂²⋊C₄
prime radical	C₃×#41×C₁₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₁₉ ◁ C₂×C₃×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×M₁₆×C₁₉	C₂	semidirect
3. C₃×C₄²×C₁₉	C₂	semidirect
4. C₁₉×#104	C₃	direct (N × H)
5. C₃×Q₈×C₁₉	C₄	semidirect
7. C₃×D₄×C₁₉	C₄	semidirect
13. M₁₆×C₁₉	C₂×C₃	semidirect
14. C₄²×C₁₉	C₂×C₃	semidirect
21. Q₈×C₁₉	C₃×C₄	semidirect
23. D₄×C₁₉	C₃×C₄	semidirect
31. C₃×#104	C₁₉	direct (N × H)
38. C₃×C₁₉	#104	direct (N × H)
40. C₃×M₁₆	C₂×C₁₉	semidirect
41. C₃×C₄²	C₂×C₁₉	semidirect
45. #104	C₃×C₁₉	direct (N × H)
46. C₃×Q₈	C₄×C₁₉	semidirect
48. C₃×D₄	C₄×C₁₉	semidirect
53. C₁₉	C₃×#104	direct (N × H)
55. M₁₆	C₂×C₃×C₁₉	semidirect
56. C₄²	C₂×C₃×C₁₉	semidirect
63. Q₈	C₃×C₄×C₁₉	semidirect
65. D₄	C₃×C₄×C₁₉	semidirect
79. C₃	C₁₉×#104	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#41×C₁₉	2
C₃×M₁₆×C₁₉	2
C₃×C₄²×C₁₉	2
C₁₉×#104	3
C₃×#104	19

Subgroups — C3×C19×#104 #14269041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#104 #14269041