Subgroups — #28353281

Order 13851.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095320	C₃	1	1	yes	maximal, characteristic
2	#17987445	C₃	1	2	yes	maximal, complemented
3	C₁₉×#6867	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₁₉⋊C₃)	—	3	1	no	—
5	#13095320	—	3	3	no	—
6	#13095305	—	3	6	no	—
7	C₃²⋊#4294	—	3	2	no	—
8	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
9	C₁₉×C₃²⋊C₉	—	3	1	no	—
10	#10624485	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃²×C₁₉⋊C₃	—	9	1	no	—
13	C₃×C₉×C₁₉	—	3	2	no	—
14	C₃×C₉×C₁₉	—	3	1	no	—
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	—	9	1	no	—
17	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
18	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
19	C₃×#4294	—	3	6	no	—
20	C₃×#732	—	19	1	no	—
21	#6895	—	19	2	no	—
22	#6867	C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₃²×C₁₉	—	9	1	no	—
24	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
25	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	2	yes	—
26	C₃²×C₁₉	#731	1	1	yes	characteristic
27	C₃×C₁₉⋊C₃	—	9	3	no	—
28	C₃×C₁₉⋊C₃	—	27	3	no	—
29	C₉×C₁₉	—	9	1	no	—
30	C₉×C₁₉	—	27	1	no	—
31	#4294	—	9	6	no	—
32	C₃×H(3,𝔽₃)	—	57	1	no	—
33	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
34	#732	—	57	3	no	—
35	C₉⋊C₉	—	57	6	no	—
36	C₃²⋊C₉	—	3	1	no	—
37	C₃²⋊C₉	—	57	2	no	—
38	C₃×C₁₉	—	3	2	no	—
39	C₃×C₁₉	—	3	1	no	—
40	C₃×C₁₉	—	3	1	no	—
41	C₃×C₁₉	#6857	1	1	yes	characteristic
42	C₁₉⋊C₃	—	27	3	no	—
43	C₃³	—	171	1	no	—
44	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
45	H(3,𝔽₃)	—	57	3	no	—
46	H(3,𝔽₃)	—	171	2	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	3	2	no	—
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	9	1	no	—
51	C₃×C₉	—	57	6	no	—
52	C₁₉	#10624485	1	1	yes	characteristic, complemented, Sylow
53	C₃²	—	513	3	no	—
54	C₃²	—	9	1	no	—
55	C₃²	—	171	3	no	—
56	C₃²	#13095313	1	1	yes	characteristic
57	C₃²	#13095315	1	2	yes	—
58	C₃²	#13095317	1	1	yes	characteristic
59	C₉	—	9	1	no	—
60	C₉	—	27	1	no	—
61	C₉	—	171	6	no	—
62	C₃	—	513	3	no	—
63	C₃	—	3	1	no	—
64	C₃	—	3	2	no	—
65	C₃	—	3	1	no	—
66	C₃	#17987313	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987313
commutator, cosocle	C₃²×C₉×C₁₉	C₃²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6867	C₃
socle	C₃×C₁₉	#6857
prime radical	C₃×#13095320	C₃
hypercenter	#6867	C₁₉⋊C₃
hypocenter	C₁₉	#10624485
LCS	G ▷ C₃²×C₉×C₁₉ ▷ C₃³×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6867

Complements

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

N	H ≅ G/N	type
2. #17987445	C₃	semidirect
3. C₁₉×#6867	C₃	semidirect
22. #6867	C₁₉⋊C₃	semidirect
52. C₁₉	#10624485	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095320	3
#17987445	3
C₁₉×#6867	3
#10624485	19