Subgroups — #28355753

Order 13851.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095320	C₃	1	3	yes	maximal, complemented
2	#17987374	C₃	1	9	yes	maximal, complemented
3	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
5	#13095320	—	3	6	no	—
6	#13095320	C₃²	1	9	yes	complemented
7	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×C₉⋊C₉	—	3	2	no	—
9	C₁₉×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₁₉	C₃²	1	3	yes	complemented
11	#10624839	—	19	1	no	maximal, Sylow
12	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃²×C₁₉⋊C₃	—	9	3	no	—
14	C₃×C₉×C₁₉	—	3	3	no	—
15	C₃×C₉×C₁₉	—	3	3	no	—
16	C₃×C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
17	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
18	C₃²⋊(C₁₉⋊C₃)	—	3	9	no	—
19	C₃²⋊(C₁₉⋊C₃)	—	9	6	no	—
20	C₃×#732	—	19	3	no	—
21	#6887	C₁₉⋊C₃	1	1	yes	characteristic, complemented
22	#6879	—	19	9	no	—
23	C₃²×C₁₉	—	9	1	no	—
24	C₃²×C₁₉	#732	1	3	yes	—
25	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×C₁₉⋊C₃	—	9	9	no	—
27	C₃×C₁₉⋊C₃	—	27	9	no	—
28	C₉×C₁₉	—	3	2	no	—
29	C₉×C₁₉	—	3	1	no	—
30	C₉×C₁₉	—	9	3	no	—
31	C₃×H(3,𝔽₃)	—	57	3	no	—
32	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
33	#732	—	19	9	no	—
34	#732	—	57	6	no	—
35	C₉⋊C₉	—	3	2	no	—
36	C₃²⋊C₉	—	3	1	no	—
37	C₉²	C₃×C₁₉⋊C₃	1	3	yes	complemented
38	C₃×C₁₉	—	3	1	no	—
39	C₃×C₁₉	—	3	3	no	—
40	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
41	C₁₉⋊C₃	—	27	9	no	—
42	C₃³	—	171	3	no	—
43	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
44	H(3,𝔽₃)	—	57	9	no	—
45	H(3,𝔽₃)	—	171	6	no	—
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	2	yes	—
49	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
50	C₁₉	#10624839	1	1	yes	characteristic, complemented, Sylow
51	C₃²	—	513	9	no	—
52	C₃²	—	9	1	no	—
53	C₃²	—	171	9	no	—
54	C₃²	#13095320	1	3	yes	—
55	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
56	C₉	—	3	2	no	—
57	C₉	—	3	1	no	—
58	C₉	—	9	3	no	—
59	C₃	—	513	9	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	3	no	—
62	C₃	C₃×#13095320	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#13095320
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃×C₁₉	C₃×#732
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624839
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. C₃×#13095320	C₃	semidirect
2. #17987374	C₃	semidirect
3. C₁₉×#6887	C₃	semidirect
6. #13095320	C₃²	semidirect
10. C₉²×C₁₉	C₃²	semidirect
21. #6887	C₁₉⋊C₃	semidirect
37. C₉²	C₃×C₁₉⋊C₃	semidirect
50. C₁₉	#10624839	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
#17987374	3
C₁₉×#6887	3
#10624839	19