Subgroups — C₁₃×#10624513 #23744664

Order 9477.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6867	C₃	1	3	yes	maximal
3	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
4	C₁₃×C₉⋊C₉	—	3	2	no	—
5	C₁₃×C₃²⋊C₉	—	3	1	no	—
6	C₁₃×C₃²⋊C₉	—	3	3	no	—
7	C₉²×C₁₃	C₉	1	3	yes	complemented
8	#10624513	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×C₉×C₁₃	—	3	3	no	—
11	C₃×C₉×C₁₃	—	3	3	no	—
12	C₃×C₉×C₁₃	—	9	3	no	—
13	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
15	#6887	C₃×C₁₃	1	1	yes	characteristic
16	#6867	C₃×C₁₃	1	3	yes	—
17	C₃²×C₁₃	—	9	1	no	—
18	C₃²×C₁₃	C₃²⋊C₉	1	1	yes	characteristic
19	C₃²×C₁₃	#731	1	3	yes	—
20	C₉×C₁₃	—	3	1	no	—
21	C₉×C₁₃	—	3	2	no	—
22	C₉×C₁₃	—	9	3	no	—
23	C₉×C₁₃	—	27	3	no	—
24	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
25	C₉⋊C₉	—	3	2	no	—
26	C₃²⋊C₉	—	3	1	no	—
27	C₃²⋊C₉	—	3	3	no	—
28	C₉²	C₉×C₁₃	1	3	yes	complemented
29	C₃×C₁₃	—	3	1	no	—
30	C₃×C₁₃	—	3	3	no	—
31	C₃×C₁₃	#6867	1	1	yes	characteristic
32	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	9	3	no	—
36	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
37	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
38	C₁₃	#10624513	1	1	yes	characteristic, direct product factor, Sylow
39	C₃²	—	9	1	no	—
40	C₃²	C₁₃×C₃²⋊C₉	1	1	yes	characteristic
41	C₃²	C₁₃×#731	1	3	yes	—
42	C₉	—	3	1	no	—
43	C₉	—	3	2	no	—
44	C₉	—	9	3	no	—
45	C₉	—	27	3	no	—
46	C₃	—	3	1	no	—
47	C₃	—	3	3	no	—
48	C₃	C₁₃×#6867	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	#6867
commutator	C₃×C₉	C₃×C₉×C₁₃
Frattini, cosocle	C₃²×C₉	C₃²×C₁₃
prime radical	C₃³×C₁₃	H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃³×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₉²×C₁₃	C₉	semidirect
8. #10624513	C₁₃	direct (N × H)
28. C₉²	C₉×C₁₃	semidirect
38. C₁₃	#10624513	direct (N × H)

Subgroups — C13×#10624513 #23744664

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624513 #23744664