Subgroups — C₃×C₁₉×#102 #14269039

Order 1824.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#102	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₁₉	—	2	1	no	—
6	C₃×D₄×C₁₉	—	2	1	no	—
7	C₃×D₄×C₁₉	C₄	1	2	yes	complemented
8	C₂×C₃×C₄×C₁₉	—	2	1	no	—
9	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₃×C₈×C₁₉	—	2	1	no	—
11	C₂×D₄×C₁₉	C₂×C₃	1	1	yes	characteristic
12	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
13	C₄⋊C₄×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₁₉	—	2	2	no	—
15	C₂²×C₃×C₁₉	—	4	1	no	—
16	C₂²×C₃×C₁₉	—	4	1	no	—
17	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
18	C₃×C₄×C₁₉	—	4	1	no	—
19	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₁₉	—	2	1	no	—
22	D₄×C₁₉	—	2	1	no	—
23	D₄×C₁₉	C₃×C₄	1	2	yes	complemented
24	C₂×C₄×C₁₉	—	2	1	no	—
25	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
26	C₈×C₁₉	—	2	1	no	—
27	C₂×C₃×C₁₉	—	4	2	no	—
28	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₃×C₁₉	SD₁₆	1	1	yes	characteristic
31	C₃×#102	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₁₉	—	2	2	no	—
33	C₂²×C₁₉	—	4	1	no	—
34	C₂²×C₁₉	—	4	1	no	—
35	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
36	C₄×C₁₉	—	4	1	no	—
37	C₄×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
38	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
39	C₃×C₁₉	#102	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₃×D₄	C₂×C₁₉	1	1	yes	characteristic
41	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
42	C₃×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
43	C₂×C₁₉	—	4	2	no	—
44	C₂×C₁₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₁₉	C₃×D₈	1	1	yes	characteristic
46	C₂×C₁₉	C₃×SD₁₆	1	1	yes	characteristic
47	#102	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂³×C₃	—	2	1	no	—
49	C₃×D₄	—	2	1	no	—
50	C₃×D₄	C₄×C₁₉	1	2	yes	complemented
51	C₂×C₃×C₄	—	2	1	no	—
52	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
53	C₃×C₈	—	2	1	no	—
54	C₁₉	C₃×#102	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×D₄	C₂×C₃×C₁₉	1	1	yes	characteristic
56	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
57	C₄⋊C₄	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
58	C₂²×C₃	—	2	2	no	—
59	C₂²×C₃	—	4	1	no	—
60	C₂²×C₃	—	4	1	no	—
61	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
62	C₃×C₄	—	4	1	no	—
63	C₃×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
64	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
65	C₂³	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	C₃×C₄×C₁₉	1	2	yes	complemented
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₂×C₃	—	4	2	no	—
72	C₂×C₃	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
73	C₂×C₃	D₈×C₁₉	1	1	yes	characteristic
74	C₂×C₃	SD₁₆×C₁₉	1	1	yes	characteristic
75	C₂²	—	2	2	no	—
76	C₂²	—	4	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
81	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
82	C₃	C₁₉×#102	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	4	2	no	—
84	C₂	C₃×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
85	C₂	C₃×D₈×C₁₉	1	1	yes	characteristic
86	C₂	C₃×SD₁₆×C₁₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₈×C₁₉	C₂	semidirect
3. C₃×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#102	C₃	direct (N × H)
7. C₃×D₄×C₁₉	C₄	semidirect
12. C₂×C₈×C₁₉	C₂×C₃	semidirect
13. C₄⋊C₄×C₁₉	C₂×C₃	semidirect
23. D₄×C₁₉	C₃×C₄	semidirect
31. C₃×#102	C₁₉	direct (N × H)
39. C₃×C₁₉	#102	direct (N × H)
41. C₂×C₃×C₈	C₂×C₁₉	semidirect
42. C₃×C₄⋊C₄	C₂×C₁₉	semidirect
47. #102	C₃×C₁₉	direct (N × H)
50. C₃×D₄	C₄×C₁₉	semidirect
54. C₁₉	C₃×#102	direct (N × H)
56. C₂×C₈	C₂×C₃×C₁₉	semidirect
57. C₄⋊C₄	C₂×C₃×C₁₉	semidirect
67. D₄	C₃×C₄×C₁₉	semidirect
82. C₃	C₁₉×#102	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×D₄×C₁₉	2
C₂×C₃×C₈×C₁₉	2
C₃×C₄⋊C₄×C₁₉	2
C₁₉×#102	3
C₃×#102	19

Subgroups — C3×C19×#102 #14269039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#102 #14269039