Subgroups — C₁₉×#10624849 #28353045

Order 13851.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#6908	C₃	1	3	yes	maximal, complemented
2	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#6883	C₃	1	3	yes	maximal, complemented
4	C₁₉×#6882	C₃	1	3	yes	maximal, complemented
5	C₁₉×#6881	C₃	1	3	yes	maximal, complemented
6	C₁₉×#737	—	3	3	no	—
7	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×#733	C₃²	1	3	yes	—
9	C₁₉×#733	C₃²	1	3	yes	—
10	C₁₉×#732	C₃²	1	3	yes	—
11	C₁₉×#731	—	3	3	no	—
12	C₁₉×AΣL(1,𝔽₂₇)	—	3	3	no	—
13	C₁₉×C₉⋊C₉	—	3	1	no	—
14	C₁₉×C₉⋊C₉	C₃²	1	3	yes	—
15	C₁₉×C₃²⋊C₉	—	3	1	no	—
16	C₉²×C₁₉	—	3	1	no	—
17	#10624849	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
19	C₁₉×3₋¹⁺²	—	3	3	no	—
20	C₁₉×3₋¹⁺²	—	3	3	no	—
21	C₁₉×3₋¹⁺²	—	9	6	no	—
22	C₁₉×H(3,𝔽₃)	—	3	3	no	—
23	C₃×C₉×C₁₉	—	3	3	no	—
24	C₃×C₉×C₁₉	—	3	3	no	—
25	C₃×C₉×C₁₉	—	9	3	no	—
26	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
29	#6908	C₃×C₁₉	1	3	yes	complemented
30	#6887	C₃×C₁₉	1	1	yes	characteristic, complemented
31	#6883	C₃×C₁₉	1	3	yes	complemented
32	#6882	C₃×C₁₉	1	3	yes	complemented
33	#6881	C₃×C₁₉	1	3	yes	complemented
34	C₃²×C₁₉	—	3	1	no	—
35	C₃²×C₁₉	—	9	1	no	—
36	C₃²×C₁₉	—	9	3	no	—
37	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₉×C₁₉	—	3	1	no	—
39	C₉×C₁₉	—	3	1	no	—
40	C₉×C₁₉	—	9	3	no	—
41	C₉×C₁₉	—	9	3	no	—
42	C₉×C₁₉	—	9	3	no	—
43	C₉×C₁₉	#732	1	3	yes	—
44	#737	—	3	3	no	—
45	C₃²×C₉	C₃²×C₁₉	1	1	yes	characteristic
46	#733	C₃²×C₁₉	1	3	yes	—
47	#733	C₃²×C₁₉	1	3	yes	—
48	#732	C₃²×C₁₉	1	3	yes	—
49	#731	—	3	3	no	—
50	AΣL(1,𝔽₂₇)	—	3	3	no	—
51	C₉⋊C₉	—	3	1	no	—
52	C₉⋊C₉	C₃²×C₁₉	1	3	yes	—
53	C₃²⋊C₉	—	3	1	no	—
54	C₉²	—	3	1	no	—
55	C₃×C₁₉	—	3	1	no	—
56	C₃×C₁₉	—	9	1	no	—
57	C₃×C₁₉	—	27	3	no	—
58	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
59	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
60	3₋¹⁺²	—	3	3	no	—
61	3₋¹⁺²	—	3	3	no	—
62	3₋¹⁺²	—	9	6	no	—
63	H(3,𝔽₃)	—	3	3	no	—
64	C₃×C₉	—	3	3	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	9	3	no	—
67	C₃×C₉	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
68	C₃×C₉	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
69	C₃×C₉	C₃³×C₁₉	1	1	yes	characteristic
70	C₁₉	#10624849	1	1	yes	characteristic, direct product factor, Sylow
71	C₃²	—	3	1	no	—
72	C₃²	—	9	1	no	—
73	C₃²	—	9	3	no	—
74	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
75	C₉	—	3	1	no	—
76	C₉	—	3	1	no	—
77	C₉	—	9	3	no	—
78	C₉	—	9	3	no	—
79	C₉	—	9	3	no	—
80	C₉	C₁₉×#732	1	3	yes	—
81	C₃	—	3	1	no	—
82	C₃	—	9	1	no	—
83	C₃	—	27	3	no	—
84	C₃	C₃×C₁₉×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₉	C₃×#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₉
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₉ ◁ C₃×C₉×C₁₉ ◁ C₃²×C₉×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#6908	C₃	semidirect
2. C₁₉×#6887	C₃	semidirect
3. C₁₉×#6883	C₃	semidirect
4. C₁₉×#6882	C₃	semidirect
5. C₁₉×#6881	C₃	semidirect
17. #10624849	C₁₉	direct (N × H)
29. #6908	C₃×C₁₉	semidirect
30. #6887	C₃×C₁₉	semidirect
31. #6883	C₃×C₁₉	semidirect
32. #6882	C₃×C₁₉	semidirect
33. #6881	C₃×C₁₉	semidirect
70. C₁₉	#10624849	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#6908	3
C₁₉×#6887	3
C₁₉×#6883	3
C₁₉×#6882	3
C₁₉×#6881	3
#10624849	19

Subgroups — C19×#10624849 #28353045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624849 #28353045