Subgroups — C₃×C₉×#10587020 #28356870

Order 13851.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587020	C₃	1	3	yes	maximal
2	C₉×#10587020	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587020	C₉	1	27	yes	direct product factor
5	C₃×#10587020	C₃²	1	9	yes	—
6	C₃²×#4294	C₉	1	2	yes	—
7	C₃²×#4294	C₃²	1	1	yes	characteristic
8	C₉×#4294	C₉	1	6	yes	—
9	C₉×#4294	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
11	C₃×C₉×C₂₇	—	19	1	no	maximal, Sylow
12	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₁₉	C₂₇	1	9	yes	complemented
14	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
15	C₃×#4294	C₂₇	1	18	yes	complemented
16	C₃×#4294	C₃×C₉	1	2	yes	—
17	C₃×#4294	C₃×C₉	1	9	yes	—
18	C₃×#4294	C₃×C₉	1	6	yes	—
19	C₃×#4294	C₃³	1	1	yes	characteristic
20	#10587020	C₃×C₉	1	27	yes	direct product factor
21	C₃²×C₂₇	—	19	3	no	—
22	C₃×C₉²	—	19	1	no	—
23	C₉×C₂₇	—	19	9	no	—
24	C₃²×C₁₉	C₉²	1	3	yes	—
25	C₃²×C₁₉	C₃×C₂₇	1	3	yes	—
26	C₃²×C₁₉	C₃×C₂₇	1	6	yes	—
27	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
28	C₉×C₁₉	C₃×C₂₇	1	9	yes	complemented
29	#4294	C₉²	1	6	yes	—
30	#4294	C₃×C₂₇	1	18	yes	complemented
31	#4294	C₃²×C₉	1	3	yes	—
32	C₃²×C₉	—	19	2	no	—
33	C₃²×C₉	—	19	1	no	—
34	C₃²×C₉	#4296	1	1	yes	characteristic
35	C₃×C₂₇	—	19	27	no	—
36	C₃×C₂₇	—	19	9	no	—
37	C₉²	—	19	6	no	—
38	C₉²	—	19	3	no	—
39	C₃×C₁₉	C₉×C₂₇	1	9	yes	complemented
40	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
41	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
42	C₃×C₁₉	C₃²×C₂₇	1	2	yes	—
43	C₃³	C₃×#4296	1	1	yes	characteristic
44	C₃×C₉	—	19	9	no	—
45	C₃×C₉	—	19	18	no	—
46	C₃×C₉	—	19	2	no	—
47	C₃×C₉	—	19	6	no	—
48	C₃×C₉	—	19	1	no	—
49	C₃×C₉	#10587020	1	9	yes	direct product factor
50	C₃×C₉	C₃×#4296	1	3	yes	—
51	C₂₇	—	19	27	no	—
52	C₁₉	C₃×C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
53	C₃²	C₉×#4296	1	3	yes	—
54	C₃²	C₃×#10587020	1	3	yes	—
55	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	6	yes	—
56	C₃²	C₃²×#4296	1	1	yes	characteristic
57	C₉	—	19	3	no	—
58	C₉	—	19	6	no	—
59	C₉	—	19	18	no	—
60	C₉	C₃×#10587020	1	9	yes	direct product factor
61	C₃	C₉×#10587020	1	9	yes	direct product factor
62	C₃	C₃×C₉×#4296	1	1	yes	characteristic
63	C₃	C₃²×#10587020	1	1	yes	characteristic
64	C₃	C₃×(C₁₉⋊C₃)⋊C₂₇	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₃²×C₉	#4296
commutator, hypocenter	C₁₉	C₃×C₉×C₂₇
Frattini	C₃²	C₃²×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle, prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×#4294	C₃³
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. C₉×#10587020	C₃	direct (N × H)
4. C₃×#10587020	C₉	direct (N × H)
13. C₃×C₉×C₁₉	C₂₇	semidirect
15. C₃×#4294	C₂₇	semidirect
20. #10587020	C₃×C₉	direct (N × H)
28. C₉×C₁₉	C₃×C₂₇	semidirect
30. #4294	C₃×C₂₇	semidirect
39. C₃×C₁₉	C₉×C₂₇	semidirect
49. C₃×C₉	#10587020	direct (N × H)
52. C₁₉	C₃×C₉×C₂₇	semidirect
60. C₉	C₃×#10587020	direct (N × H)
61. C₃	C₉×#10587020	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#10587020	3
C₉×#10587020	3
C₃×C₉×#4294	3
C₃×C₉×C₂₇	19

Subgroups — C3×C9×#10587020 #28356870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#10587020 #28356870