Subgroups — C₉×#13095342 #28356877

Order 13851.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	3	yes	maximal
2	#17987555	C₃	1	6	yes	maximal, complemented
3	C₉×#10587020	C₃	1	3	yes	maximal, complemented
4	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
5	#13095342	C₉	1	27	yes	direct product factor
6	C₃×#10587020	C₃²	1	9	yes	—
7	C₃²×#4294	C₉	1	2	yes	—
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₉×#4294	C₉	1	2	yes	—
10	C₉×#4294	C₉	1	4	yes	—
11	C₉×#4294	C₃²	1	1	yes	characteristic
12	C₉×#4294	C₃²	1	2	yes	—
13	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
14	C₉×C₂₇⋊C₃	—	19	1	no	maximal, Sylow
15	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₁₉	—	3	3	no	—
17	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
18	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
19	C₃×#4294	—	3	6	no	—
20	C₃×#4294	C₃×C₉	1	4	yes	—
21	C₃×#4294	C₃×C₉	1	2	yes	—
22	C₃×#4294	C₃×C₉	1	9	yes	—
23	C₃×#4294	C₃×C₉	1	2	yes	—
24	C₃×#4294	C₃³	1	1	yes	characteristic
25	#10587020	C₃×C₉	1	27	yes	complemented
26	C₃×C₂₇⋊C₃	—	19	3	no	—
27	C₃×C₉²	—	19	1	no	—
28	#6864	—	19	6	no	—
29	C₉×C₂₇	—	19	3	no	—
30	C₃²×C₁₉	—	3	2	no	—
31	C₃²×C₁₉	—	3	1	no	—
32	C₃²×C₁₉	C₉²	1	3	yes	—
33	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
34	C₉×C₁₉	—	3	2	no	—
35	C₉×C₁₉	C₂₇⋊C₃	1	3	yes	complemented
36	#4294	—	3	4	no	—
37	#4294	C₉²	1	6	yes	—
38	#4294	C₂₇⋊C₃	1	6	yes	complemented
39	#4294	C₃²×C₉	1	3	yes	—
40	C₃²×C₉	—	19	1	no	—
41	C₃²×C₉	—	19	2	no	—
42	C₃²×C₉	#4296	1	1	yes	characteristic
43	C₂₇⋊C₃	—	19	27	no	—
44	C₃×C₂₇	—	19	9	no	—
45	C₉²	—	19	4	no	—
46	C₉²	—	19	2	no	—
47	C₉²	—	19	2	no	—
48	C₉²	—	19	1	no	—
49	C₃×C₁₉	—	3	3	no	—
50	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
51	C₃×C₁₉	C₃×C₂₇⋊C₃	1	1	yes	characteristic
52	C₃×C₁₉	C₃×C₂₇⋊C₃	1	2	yes	—
53	C₃³	C₃×#4296	1	1	yes	characteristic
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	19	9	no	—
56	C₃×C₉	—	19	2	no	—
57	C₃×C₉	—	19	2	no	—
58	C₃×C₉	—	19	1	no	—
59	C₃×C₉	—	19	4	no	—
60	C₃×C₉	—	57	6	no	—
61	C₃×C₉	C₃×#4296	1	2	yes	—
62	C₃×C₉	C₃×#4296	1	1	yes	characteristic
63	C₂₇	—	19	27	no	—
64	C₁₉	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₃²	—	3	1	no	—
66	C₃²	—	3	2	no	—
67	C₃²	C₉×#4296	1	3	yes	—
68	C₃²	C₃²×#4296	1	1	yes	characteristic
69	C₉	—	3	2	no	—
70	C₉	—	19	3	no	—
71	C₉	—	19	6	no	—
72	C₉	—	19	6	no	—
73	C₉	—	57	4	no	—
74	C₉	#13095342	1	3	yes	direct product factor
75	C₃	—	3	3	no	—
76	C₃	C₃×C₉×#4296	1	1	yes	characteristic
77	C₃	C₃×#13095342	1	1	yes	characteristic
78	C₃	(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×#4296
commutator	C₃×C₁₉	C₃×C₉²
Frattini	C₃²	C₃²×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #17987555	C₃	semidirect
3. C₉×#10587020	C₃	semidirect
5. #13095342	C₉	direct (N × H)
25. #10587020	C₃×C₉	semidirect
35. C₉×C₁₉	C₂₇⋊C₃	semidirect
38. #4294	C₂₇⋊C₃	semidirect
64. C₁₉	C₉×C₂₇⋊C₃	semidirect
74. C₉	#13095342	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×#13095342	3
#17987555	3
C₉×#10587020	3
C₃×C₉×#4294	3
C₉×C₂₇⋊C₃	19

Subgroups — C9×#13095342 #28356877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#13095342 #28356877