Subgroups — C₁₃×#10624787 #23744938

Order 9477.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#733	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6894	C₃	1	3	yes	maximal
3	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
4	C₁₃×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal
5	C₁₃×#6868	C₃	1	2	yes	maximal
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
7	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₁₃×#733	—	3	3	no	—
11	C₁₃×C₉⋊C₉	—	3	6	no	—
12	C₁₃×C₉⋊C₉	—	3	3	no	—
13	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	C₉²×C₁₃	—	3	2	no	—
15	C₉²×C₁₃	—	3	1	no	—
16	#10624787	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₁₃×3₋¹⁺²	—	3	3	no	—
19	C₁₃×3₋¹⁺²	—	3	6	no	—
20	C₃×C₉×C₁₃	—	3	1	no	—
21	C₃×C₉×C₁₃	—	3	2	no	—
22	C₃×C₉×C₁₃	—	3	2	no	—
23	C₃×C₉×C₁₃	—	3	3	no	—
24	C₃×C₉×C₁₃	—	3	6	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	3	no	—
27	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
28	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
29	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
30	C₃×#733	C₃×C₁₃	1	1	yes	characteristic
31	#6894	C₃×C₁₃	1	3	yes	—
32	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
33	3₋¹⁺²⋊C₉	C₃×C₁₃	1	6	yes	—
34	#6868	C₃×C₁₃	1	2	yes	—
35	C₃²×C₁₃	—	3	1	no	—
36	C₃²×C₁₃	—	3	2	no	—
37	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
39	C₃²×C₁₃	#737	1	2	yes	—
40	C₉×C₁₃	—	3	3	no	—
41	C₉×C₁₃	—	3	2	no	—
42	C₉×C₁₃	—	3	6	no	—
43	C₉×C₁₃	—	9	3	no	—
44	C₉×C₁₃	—	9	6	no	—
45	C₉×C₁₃	#733	1	3	yes	complemented
46	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
47	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
48	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
49	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
50	#733	—	3	3	no	—
51	C₉⋊C₉	—	3	6	no	—
52	C₉⋊C₉	—	3	3	no	—
53	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
54	C₉²	—	3	2	no	—
55	C₉²	—	3	1	no	—
56	C₃×C₁₃	—	3	1	no	—
57	C₃×C₁₃	—	3	2	no	—
58	C₃×C₁₃	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
59	C₃×C₁₃	C₃×#733	1	1	yes	characteristic
60	C₃×C₁₃	#6908	1	2	yes	—
61	C₃³	C₃³×C₁₃	1	1	yes	characteristic
62	3₋¹⁺²	—	3	3	no	—
63	3₋¹⁺²	—	3	6	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	6	no	—
69	C₃×C₉	—	3	6	no	—
70	C₃×C₉	—	3	3	no	—
71	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
72	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
73	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
74	C₁₃	#10624787	1	1	yes	characteristic, direct product factor, Sylow
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
79	C₃²	C₁₃×#737	1	2	yes	—
80	C₉	—	3	3	no	—
81	C₉	—	3	2	no	—
82	C₉	—	3	6	no	—
83	C₉	—	9	3	no	—
84	C₉	—	9	6	no	—
85	C₉	C₁₃×#733	1	3	yes	complemented
86	C₃	—	3	1	no	—
87	C₃	—	3	2	no	—
88	C₃	C₁₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
89	C₃	C₃×C₁₃×#733	1	1	yes	characteristic
90	C₃	C₁₃×#6908	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃³×C₁₃	C₃³
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
16. #10624787	C₁₃	direct (N × H)
45. C₉×C₁₃	#733	semidirect
74. C₁₃	#10624787	direct (N × H)
85. C₉	C₁₃×#733	semidirect

Subgroups — C13×#10624787 #23744938

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624787 #23744938