Subgroups — C₉×C₁₃×C₂₇⋊C₃ #23744831

Order 9477.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₇⋊C₃	C₃	1	3	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6864	C₃	1	6	yes	maximal, complemented
4	C₉×C₁₃×C₂₇	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₁₃	C₉	1	3	yes	—
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₁₃×C₂₇⋊C₃	C₉	1	27	yes	direct product factor
8	C₃×C₁₃×C₂₇	C₃²	1	9	yes	—
9	C₉²×C₁₃	C₉	1	6	yes	—
10	C₉²×C₁₃	C₃²	1	2	yes	—
11	C₉²×C₁₃	C₃²	1	1	yes	characteristic
12	C₉×C₂₇⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₁₃	—	3	9	no	—
15	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
16	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
17	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
18	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
19	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×C₂₇	C₃×C₉	1	27	yes	complemented
21	C₃×C₂₇⋊C₃	C₃×C₁₃	1	3	yes	—
22	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
23	#6864	C₃×C₁₃	1	6	yes	complemented
24	C₉×C₂₇	C₃×C₁₃	1	3	yes	complemented
25	C₃²×C₁₃	—	3	3	no	—
26	C₃²×C₁₃	C₉²	1	3	yes	—
27	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
28	C₉×C₁₃	—	3	6	no	—
29	C₉×C₁₃	C₉²	1	6	yes	—
30	C₉×C₁₃	C₂₇⋊C₃	1	9	yes	direct product factor
31	C₉×C₁₃	C₃²×C₉	1	3	yes	—
32	C₃²×C₉	C₉×C₁₃	1	3	yes	—
33	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
34	C₂₇⋊C₃	C₉×C₁₃	1	27	yes	direct product factor
35	C₃×C₂₇	C₃²×C₁₃	1	9	yes	—
36	C₉²	C₉×C₁₃	1	6	yes	—
37	C₉²	C₃²×C₁₃	1	2	yes	—
38	C₉²	C₃²×C₁₃	1	1	yes	characteristic
39	C₃×C₁₃	—	3	3	no	—
40	C₃×C₁₃	C₃×C₉²	1	1	yes	characteristic
41	C₃×C₁₃	C₃×C₂₇⋊C₃	1	3	yes	—
42	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
43	C₃×C₉	—	3	9	no	—
44	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
45	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
46	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
47	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
48	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
49	C₂₇	C₃×C₉×C₁₃	1	27	yes	complemented
50	C₁₃	C₉×C₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₃²	—	3	3	no	—
52	C₃²	C₉²×C₁₃	1	3	yes	—
53	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
54	C₉	—	3	6	no	—
55	C₉	C₉²×C₁₃	1	6	yes	—
56	C₉	C₁₃×C₂₇⋊C₃	1	9	yes	direct product factor
57	C₉	C₃²×C₉×C₁₃	1	3	yes	—
58	C₃	—	3	3	no	—
59	C₃	C₃×C₉²×C₁₃	1	1	yes	characteristic
60	C₃	C₃×C₁₃×C₂₇⋊C₃	1	3	yes	—

	subgroup	G/H
center	C₉²×C₁₃	C₃²
commutator	C₃	C₃×C₉²×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃²×C₁₃	C₃²×C₉
prime radical	C₃³×C₁₃	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6864	C₃	semidirect
4. C₉×C₁₃×C₂₇	C₃	semidirect
7. C₁₃×C₂₇⋊C₃	C₉	direct (N × H)
12. C₉×C₂₇⋊C₃	C₁₃	direct (N × H)
20. C₁₃×C₂₇	C₃×C₉	semidirect
23. #6864	C₃×C₁₃	semidirect
24. C₉×C₂₇	C₃×C₁₃	semidirect
30. C₉×C₁₃	C₂₇⋊C₃	direct (N × H)
34. C₂₇⋊C₃	C₉×C₁₃	direct (N × H)
49. C₂₇	C₃×C₉×C₁₃	semidirect
50. C₁₃	C₉×C₂₇⋊C₃	direct (N × H)
56. C₉	C₁₃×C₂₇⋊C₃	direct (N × H)

Subgroups — C9×C13×C27⋊C3 #23744831

Conjugacy classes of subgroups

Complements

Subgroups — C₉×C₁₃×C₂₇⋊C₃ #23744831