Subgroups — C₁₃×#10624723 #23744874

Order 9477.

250 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	C₉×C₁₃×3₋¹⁺²	C₃	1	3	yes	maximal
3	C₃×C₁₃×C₉⋊C₉	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	1	yes	characteristic
8	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₁₃×#733	C₉	1	9	yes	complemented
11	C₁₃×C₉⋊C₉	—	3	3	no	—
12	C₁₃×C₉⋊C₉	—	3	6	no	—
13	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	C₉²×C₁₃	—	3	3	no	—
15	#10624723	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×3₋¹⁺²	—	3	6	no	—
18	C₁₃×3₋¹⁺²	C₃×C₉	1	9	yes	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	1	no	—
21	C₃×C₉×C₁₃	—	3	2	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	3	2	no	—
24	C₃×C₉×C₁₃	—	9	1	no	—
25	C₃×C₉×C₁₃	—	9	2	no	—
26	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
27	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
28	C₃×#733	C₃×C₁₃	1	1	yes	characteristic
29	C₉×3₋¹⁺²	C₃×C₁₃	1	3	yes	—
30	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
31	3₋¹⁺²⋊C₉	C₃×C₁₃	1	6	yes	—
32	#6868	C₃×C₁₃	1	2	yes	—
33	C₃²×C₁₃	—	3	1	no	—
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
36	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₃²×C₁₃	#737	1	2	yes	—
38	C₉×C₁₃	—	3	3	no	—
39	C₉×C₁₃	—	3	3	no	—
40	C₉×C₁₃	—	3	9	no	—
41	C₉×C₁₃	—	9	6	no	—
42	C₉×C₁₃	—	9	2	no	—
43	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
44	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
45	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
46	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
47	#733	C₉×C₁₃	1	9	yes	complemented
48	C₉⋊C₉	—	3	3	no	—
49	C₉⋊C₉	—	3	6	no	—
50	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
51	C₉²	—	3	3	no	—
52	C₃×C₁₃	—	3	1	no	—
53	C₃×C₁₃	—	3	2	no	—
54	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
55	C₃×C₁₃	#6912	1	1	yes	characteristic
56	C₃×C₁₃	#6913	1	2	yes	—
57	C₃³	C₃³×C₁₃	1	1	yes	characteristic
58	3₋¹⁺²	—	3	6	no	—
59	3₋¹⁺²	C₃×C₉×C₁₃	1	9	yes	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	2	no	—
63	C₃×C₉	—	3	6	no	—
64	C₃×C₉	—	3	2	no	—
65	C₃×C₉	—	9	1	no	—
66	C₃×C₉	—	9	2	no	—
67	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
68	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
69	C₁₃	#10624723	1	1	yes	characteristic, direct product factor, Sylow
70	C₃²	—	3	1	no	—
71	C₃²	—	3	2	no	—
72	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
73	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
74	C₃²	C₁₃×#737	1	2	yes	—
75	C₉	—	3	3	no	—
76	C₉	—	3	9	no	—
77	C₉	—	3	3	no	—
78	C₉	—	9	2	no	—
79	C₉	—	9	6	no	—
80	C₃	—	3	1	no	—
81	C₃	—	3	2	no	—
82	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
83	C₃	C₁₃×#6912	1	1	yes	characteristic
84	C₃	C₁₃×#6913	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃³×C₁₃	C₃³
LCS	G ▷ C₃² ▷ 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
10. C₁₃×#733	C₉	semidirect
15. #10624723	C₁₃	direct (N × H)
47. #733	C₉×C₁₃	semidirect
69. C₁₃	#10624723	direct (N × H)

Subgroups — C13×#10624723 #23744874

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624723 #23744874