Subgroups — C₁₃×#10624817 #23744968

Order 9477.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6895	C₃	1	2	yes	maximal, complemented
2	C₁₃×#6893	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₁₃×H(3,𝔽₃)⋊C₉	C₃	1	3	yes	maximal
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₁₃×C₉⋊C₉	—	3	3	no	—
11	C₁₃×C₉⋊C₉	—	3	6	no	—
12	C₁₃×C₃²⋊C₉	—	3	3	no	—
13	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	#10624817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	1	no	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×3₋¹⁺²	—	3	6	no	—
18	C₁₃×H(3,𝔽₃)	—	3	3	no	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	2	no	—
21	C₃×C₉×C₁₃	—	3	6	no	—
22	C₃×C₉×C₁₃	—	3	3	no	—
23	C₃×C₉×C₁₃	—	9	3	no	—
24	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
25	#6895	C₃×C₁₃	1	2	yes	complemented
26	#6893	C₃×C₁₃	1	1	yes	characteristic
27	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
28	3₋¹⁺²⋊C₉	C₃×C₁₃	1	6	yes	complemented
29	H(3,𝔽₃)⋊C₉	C₃×C₁₃	1	3	yes	—
30	C₃²×C₁₃	—	3	3	no	—
31	C₃²×C₁₃	—	9	3	no	—
32	C₃²×C₁₃	—	9	1	no	—
33	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₃²×C₁₃	#737	1	3	yes	—
35	C₉×C₁₃	—	3	3	no	—
36	C₉×C₁₃	—	9	6	no	—
37	C₉×C₁₃	—	9	3	no	—
38	C₉×C₁₃	—	9	2	no	—
39	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
40	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
41	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
42	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
43	C₉⋊C₉	—	3	3	no	—
44	C₉⋊C₉	—	3	6	no	—
45	C₃²⋊C₉	—	3	3	no	—
46	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
47	C₃×C₁₃	—	3	3	no	—
48	C₃×C₁₃	—	27	1	no	—
49	C₃×C₁₃	#6893	1	1	yes	characteristic
50	C₃×C₁₃	#6913	1	3	yes	—
51	C₃³	—	3	1	no	—
52	C₃³	C₃³×C₁₃	1	1	yes	characteristic
53	3₋¹⁺²	—	3	6	no	—
54	H(3,𝔽₃)	—	3	3	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	3	2	no	—
57	C₃×C₉	—	3	6	no	—
58	C₃×C₉	—	3	3	no	—
59	C₃×C₉	—	9	3	no	—
60	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
61	C₁₃	#10624817	1	1	yes	characteristic, direct product factor, Sylow
62	C₃²	—	3	3	no	—
63	C₃²	—	9	1	no	—
64	C₃²	—	9	3	no	—
65	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
66	C₃²	C₁₃×#737	1	3	yes	—
67	C₉	—	3	3	no	—
68	C₉	—	9	2	no	—
69	C₉	—	9	3	no	—
70	C₉	—	9	6	no	—
71	C₃	—	3	3	no	—
72	C₃	—	27	1	no	—
73	C₃	C₁₃×#6893	1	1	yes	characteristic
74	C₃	C₁₃×#6913	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#6895	C₃	semidirect
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
4. C₁₃×3₋¹⁺²⋊C₉	C₃	semidirect
14. #10624817	C₁₃	direct (N × H)
25. #6895	C₃×C₁₃	semidirect
27. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
28. 3₋¹⁺²⋊C₉	C₃×C₁₃	semidirect
61. C₁₃	#10624817	direct (N × H)

Subgroups — C13×#10624817 #23744968

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624817 #23744968