Subgroups — C₁₃×#10624549 #23744700

Order 9477.

512 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal
3	C₁₃×#6855	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	3	no	—
6	C₃²×C₉×C₁₃	—	3	6	no	—
7	C₃²×C₉×C₁₃	C₉	1	9	yes	complemented
8	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₁₃×C₃²⋊C₉	—	3	9	no	—
11	#10624549	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	9	no	—
13	C₃³×C₁₃	C₃×C₉	1	3	yes	—
14	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
15	C₃³×C₁₃	3₋¹⁺²	1	6	yes	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₁₃	—	3	27	no	—
18	C₃×C₉×C₁₃	—	3	3	no	—
19	C₃×C₉×C₁₃	—	3	6	no	—
20	C₃×C₉×C₁₃	—	3	9	no	—
21	C₃×C₉×C₁₃	—	3	27	no	—
22	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
23	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
24	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
25	#6855	C₃×C₁₃	1	9	yes	complemented
26	C₃²×C₁₃	—	3	9	no	—
27	C₃²×C₁₃	—	3	9	no	—
28	C₃²×C₁₃	—	3	18	no	—
29	C₃²×C₁₃	C₃²⋊C₉	1	9	yes	—
30	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
31	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
32	C₃²×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
33	C₃²×C₁₃	#737	1	9	yes	—
34	C₉×C₁₃	—	3	9	no	—
35	C₉×C₁₃	—	9	9	no	—
36	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
37	C₃²×C₉	—	3	3	no	—
38	C₃²×C₉	—	3	6	no	—
39	C₃²×C₉	C₉×C₁₃	1	9	yes	complemented
40	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
41	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
42	C₃²⋊C₉	—	3	9	no	—
43	C₃×C₁₃	—	3	9	no	—
44	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
45	C₃×C₁₃	#6887	1	3	yes	—
46	C₃×C₁₃	#6893	1	3	yes	—
47	C₃×C₁₃	#6895	1	6	yes	—
48	C₃³	—	3	9	no	—
49	C₃³	C₃×C₉×C₁₃	1	3	yes	—
50	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
51	C₃³	C₁₃×3₋¹⁺²	1	6	yes	—
52	C₃³	C₃³×C₁₃	1	1	yes	characteristic
53	C₃×C₉	—	3	27	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	3	6	no	—
56	C₃×C₉	—	3	9	no	—
57	C₃×C₉	—	3	27	no	—
58	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
59	C₁₃	#10624549	1	1	yes	characteristic, direct product factor, Sylow
60	C₃²	—	3	9	no	—
61	C₃²	—	3	9	no	—
62	C₃²	—	3	18	no	—
63	C₃²	C₁₃×C₃²⋊C₉	1	9	yes	—
64	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
65	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
66	C₃²	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
67	C₃²	C₁₃×#737	1	9	yes	—
68	C₉	—	3	9	no	—
69	C₉	—	9	9	no	—
70	C₃	—	3	9	no	—
71	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic
72	C₃	C₁₃×#6887	1	3	yes	—
73	C₃	C₁₃×#6893	1	3	yes	—
74	C₃	C₁₃×#6895	1	6	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6855	C₃	semidirect
7. C₃²×C₉×C₁₃	C₉	semidirect
11. #10624549	C₁₃	direct (N × H)
25. #6855	C₃×C₁₃	semidirect
39. C₃²×C₉	C₉×C₁₃	semidirect
59. C₁₃	#10624549	direct (N × H)

Subgroups — C13×#10624549 #23744700

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624549 #23744700