Subgroups — C₁₃×#10624837 #23744988

Order 9477.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6908	C₃	1	3	yes	maximal, complemented
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6880	C₃	1	2	yes	maximal, complemented
4	C₁₃×#6879	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#6878	C₃	1	6	yes	maximal, complemented
6	C₁₃×#737	—	3	3	no	—
7	C₃²×C₉×C₁₃	—	3	1	no	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×#733	C₃²	1	6	yes	—
10	C₁₃×#732	C₃²	1	3	yes	—
11	C₁₃×#731	—	3	3	no	—
12	C₁₃×AΣL(1,𝔽₂₇)	—	3	3	no	—
13	C₉²×C₁₃	—	3	1	no	—
14	C₉²×C₁₃	—	3	1	no	—
15	C₉²×C₁₃	C₃²	1	2	yes	—
16	C₉²×C₁₃	C₃²	1	1	yes	characteristic
17	#10624837	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₁₃×3₋¹⁺²	—	3	6	no	—
20	C₁₃×3₋¹⁺²	—	9	6	no	—
21	C₁₃×H(3,𝔽₃)	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	9	no	—
23	C₃×C₉×C₁₃	—	3	2	no	—
24	C₃×C₉×C₁₃	—	3	1	no	—
25	C₃×C₉×C₁₃	—	3	2	no	—
26	C₃×C₉×C₁₃	—	3	1	no	—
27	C₃×C₉×C₁₃	—	9	3	no	—
28	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
29	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
31	#6908	C₃×C₁₃	1	3	yes	complemented
32	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
33	#6880	C₃×C₁₃	1	2	yes	complemented
34	#6879	C₃×C₁₃	1	1	yes	characteristic, complemented
35	#6878	C₃×C₁₃	1	6	yes	complemented
36	C₃²×C₁₃	—	3	3	no	—
37	C₃²×C₁₃	—	3	1	no	—
38	C₃²×C₁₃	—	9	3	no	—
39	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₉×C₁₃	—	3	6	no	—
41	C₉×C₁₃	—	3	3	no	—
42	C₉×C₁₃	—	3	1	no	—
43	C₉×C₁₃	—	3	1	no	—
44	C₉×C₁₃	—	9	6	no	—
45	C₉×C₁₃	#732	1	2	yes	—
46	C₉×C₁₃	#732	1	1	yes	characteristic
47	#737	—	3	3	no	—
48	C₃²×C₉	—	3	1	no	—
49	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
50	#733	C₃²×C₁₃	1	6	yes	—
51	#732	C₃²×C₁₃	1	3	yes	—
52	#731	—	3	3	no	—
53	AΣL(1,𝔽₂₇)	—	3	3	no	—
54	C₉²	—	3	1	no	—
55	C₉²	—	3	1	no	—
56	C₉²	C₃²×C₁₃	1	2	yes	—
57	C₉²	C₃²×C₁₃	1	1	yes	characteristic
58	C₃×C₁₃	—	3	1	no	—
59	C₃×C₁₃	—	3	3	no	—
60	C₃×C₁₃	—	27	3	no	—
61	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
62	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
63	3₋¹⁺²	—	3	6	no	—
64	3₋¹⁺²	—	9	6	no	—
65	H(3,𝔽₃)	—	3	3	no	—
66	C₃×C₉	—	3	9	no	—
67	C₃×C₉	—	3	2	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	3	2	no	—
71	C₃×C₉	—	9	3	no	—
72	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
73	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
74	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
75	C₁₃	#10624837	1	1	yes	characteristic, direct product factor, Sylow
76	C₃²	—	3	3	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	9	3	no	—
79	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
80	C₉	—	3	6	no	—
81	C₉	—	3	3	no	—
82	C₉	—	3	1	no	—
83	C₉	—	3	1	no	—
84	C₉	—	9	6	no	—
85	C₉	C₁₃×#732	1	1	yes	characteristic
86	C₉	C₁₃×#732	1	2	yes	—
87	C₃	—	3	1	no	—
88	C₃	—	3	3	no	—
89	C₃	—	27	3	no	—
90	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₁₃	#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃×C₁₃	C₃×#732
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₃ ◁ C₃×C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#6908	C₃	semidirect
2. C₃×C₉²×C₁₃	C₃	semidirect
3. C₁₃×#6880	C₃	semidirect
4. C₁₃×#6879	C₃	semidirect
5. C₁₃×#6878	C₃	semidirect
17. #10624837	C₁₃	direct (N × H)
31. #6908	C₃×C₁₃	semidirect
32. C₃×C₉²	C₃×C₁₃	semidirect
33. #6880	C₃×C₁₃	semidirect
34. #6879	C₃×C₁₃	semidirect
35. #6878	C₃×C₁₃	semidirect
75. C₁₃	#10624837	direct (N × H)

Subgroups — C13×#10624837 #23744988

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624837 #23744988