Subgroups — C₁₉×#10624848 #28353044

Order 13851.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#733	C₃	1	2	yes	maximal, complemented
2	C₃×C₁₉×#732	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#6883	C₃	1	9	yes	maximal, complemented
5	C₃×C₁₉×3₋¹⁺²	—	3	2	no	—
6	C₃×C₁₉×H(3,𝔽₃)	—	3	1	no	—
7	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×#733	—	3	2	no	—
9	C₁₉×#733	—	3	2	no	—
10	C₁₉×#733	C₃²	1	6	yes	complemented
11	C₁₉×#732	—	3	1	no	—
12	C₁₉×#732	—	3	1	no	—
13	C₁₉×#732	C₃²	1	3	yes	—
14	C₁₉×C₉⋊C₉	—	3	1	no	—
15	C₁₉×C₉⋊C₉	C₃²	1	3	yes	complemented
16	C₁₉×C₃²⋊C₉	—	3	1	no	—
17	C₉²×C₁₉	—	3	1	no	—
18	#10624848	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃³×C₁₉	—	9	1	no	—
20	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
21	C₁₉×3₋¹⁺²	—	3	6	no	—
22	C₁₉×3₋¹⁺²	—	9	2	no	—
23	C₁₉×3₋¹⁺²	—	9	2	no	—
24	C₁₉×H(3,𝔽₃)	—	3	3	no	—
25	C₁₉×H(3,𝔽₃)	—	9	2	no	—
26	C₃×C₉×C₁₉	—	3	2	no	—
27	C₃×C₉×C₁₉	—	3	1	no	—
28	C₃×C₉×C₁₉	—	3	3	no	—
29	C₃×C₉×C₁₉	—	9	2	no	—
30	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
32	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
33	C₃×#733	C₃×C₁₉	1	2	yes	complemented
34	C₃×#732	C₃×C₁₉	1	1	yes	characteristic
35	#6887	C₃×C₁₉	1	1	yes	characteristic, complemented
36	#6883	C₃×C₁₉	1	9	yes	complemented
37	C₃²×C₁₉	—	9	1	no	—
38	C₃²×C₁₉	—	9	3	no	—
39	C₃²×C₁₉	—	27	3	no	—
40	C₃²×C₁₉	#732	1	2	yes	—
41	C₃²×C₁₉	#732	1	1	yes	characteristic
42	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₉×C₁₉	—	3	1	no	—
44	C₉×C₁₉	—	3	1	no	—
45	C₉×C₁₉	—	3	1	no	—
46	C₉×C₁₉	—	9	3	no	—
47	C₉×C₁₉	—	9	6	no	—
48	C₃×3₋¹⁺²	—	3	2	no	—
49	C₃×H(3,𝔽₃)	—	3	1	no	—
50	C₃²×C₉	C₃²×C₁₉	1	1	yes	characteristic
51	#733	—	3	2	no	—
52	#733	—	3	2	no	—
53	#733	C₃²×C₁₉	1	6	yes	complemented
54	#732	—	3	1	no	—
55	#732	—	3	1	no	—
56	#732	C₃²×C₁₉	1	3	yes	—
57	C₉⋊C₉	—	3	1	no	—
58	C₉⋊C₉	C₃²×C₁₉	1	3	yes	complemented
59	C₃²⋊C₉	—	3	1	no	—
60	C₉²	—	3	1	no	—
61	C₃×C₁₉	—	3	1	no	—
62	C₃×C₁₉	—	3	1	no	—
63	C₃×C₁₉	—	3	2	no	—
64	C₃×C₁₉	—	27	3	no	—
65	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
66	C₃³	—	9	1	no	—
67	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
68	3₋¹⁺²	—	3	6	no	—
69	3₋¹⁺²	—	9	2	no	—
70	3₋¹⁺²	—	9	2	no	—
71	H(3,𝔽₃)	—	3	3	no	—
72	H(3,𝔽₃)	—	9	2	no	—
73	C₃×C₉	—	3	2	no	—
74	C₃×C₉	—	3	1	no	—
75	C₃×C₉	—	3	3	no	—
76	C₃×C₉	—	9	2	no	—
77	C₃×C₉	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
78	C₃×C₉	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
79	C₃×C₉	C₃³×C₁₉	1	1	yes	characteristic
80	C₁₉	#10624848	1	1	yes	characteristic, direct product factor, Sylow
81	C₃²	—	9	1	no	—
82	C₃²	—	9	3	no	—
83	C₃²	—	27	3	no	—
84	C₃²	C₁₉×#732	1	2	yes	—
85	C₃²	C₁₉×#732	1	1	yes	characteristic
86	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	3	1	no	—
90	C₉	—	9	3	no	—
91	C₉	—	9	6	no	—
92	C₃	—	3	1	no	—
93	C₃	—	3	1	no	—
94	C₃	—	3	2	no	—
95	C₃	—	27	3	no	—
96	C₃	C₃×C₁₉×#732	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#733	C₃	semidirect
3. C₁₉×#6887	C₃	semidirect
4. C₁₉×#6883	C₃	semidirect
10. C₁₉×#733	C₃²	semidirect
15. C₁₉×C₉⋊C₉	C₃²	semidirect
18. #10624848	C₁₉	direct (N × H)
33. C₃×#733	C₃×C₁₉	semidirect
35. #6887	C₃×C₁₉	semidirect
36. #6883	C₃×C₁₉	semidirect
53. #733	C₃²×C₁₉	semidirect
58. C₉⋊C₉	C₃²×C₁₉	semidirect
80. C₁₉	#10624848	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×C₁₉×#733	3
C₃×C₁₉×#732	3
C₁₉×#6887	3
C₁₉×#6883	3
#10624848	19

Subgroups — C19×#10624848 #28353044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624848 #28353044