Subgroups — C₁₃×#10624735 #23744886

Order 9477.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×AΣL(1,𝔽₂₇)	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	2	yes	maximal, complemented
4	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃⁴×C₁₃	C₃²	1	3	yes	—
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
8	C₃×C₁₃×H(3,𝔽₃)	—	3	3	no	—
9	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
10	C₃×C₁₃×H(3,𝔽₃)	—	3	3	no	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
12	C₁₃×AΣL(1,𝔽₂₇)	—	3	27	no	—
13	C₁₃×C₃²⋊C₉	—	3	6	no	—
14	#10624735	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	6	no	—
16	C₃³×C₁₃	—	3	3	no	—
17	C₃³×C₁₃	—	3	3	no	—
18	C₃³×C₁₃	—	3	3	no	—
19	C₃³×C₁₃	—	9	3	no	—
20	C₃³×C₁₃	—	9	9	no	—
21	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
22	C₃³×C₁₃	H(3,𝔽₃)	1	9	yes	complemented
23	C₃³×C₁₃	C₃³	1	1	yes	characteristic
24	C₁₃×3₋¹⁺²	—	3	18	no	—
25	C₁₃×H(3,𝔽₃)	—	3	27	no	—
26	C₁₃×H(3,𝔽₃)	—	3	9	no	—
27	C₁₃×H(3,𝔽₃)	—	9	9	no	—
28	C₃×C₉×C₁₃	—	3	6	no	—
29	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic, complemented
30	C₃×AΣL(1,𝔽₂₇)	C₃×C₁₃	1	9	yes	complemented
31	#6891	C₃×C₁₃	1	2	yes	complemented
32	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic, complemented
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	3	3	no	—
35	C₃²×C₁₃	—	3	9	no	—
36	C₃²×C₁₃	—	3	3	no	—
37	C₃²×C₁₃	—	3	6	no	—
38	C₃²×C₁₃	—	9	9	no	—
39	C₃²×C₁₃	—	9	9	no	—
40	C₃²×C₁₃	—	9	18	no	—
41	C₃²×C₁₃	—	9	9	no	—
42	C₃²×C₁₃	—	9	3	no	—
43	C₃²×C₁₃	—	9	9	no	—
44	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
45	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
46	C₉×C₁₃	—	9	6	no	—
47	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
48	C₃⁴	C₃²×C₁₃	1	3	yes	—
49	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
50	C₃×H(3,𝔽₃)	—	3	3	no	—
51	C₃×H(3,𝔽₃)	—	3	9	no	—
52	C₃×H(3,𝔽₃)	—	3	3	no	—
53	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
54	AΣL(1,𝔽₂₇)	—	3	27	no	—
55	C₃²⋊C₉	—	3	6	no	—
56	C₃×C₁₃	—	3	3	no	—
57	C₃×C₁₃	—	9	3	no	—
58	C₃×C₁₃	—	9	9	no	—
59	C₃×C₁₃	—	27	3	no	—
60	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
61	C₃×C₁₃	#6909	1	3	yes	—
62	C₃³	—	3	3	no	—
63	C₃³	—	3	6	no	—
64	C₃³	—	3	3	no	—
65	C₃³	—	3	3	no	—
66	C₃³	—	9	3	no	—
67	C₃³	—	9	9	no	—
68	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
69	C₃³	C₁₃×H(3,𝔽₃)	1	9	yes	complemented
70	C₃³	C₃³×C₁₃	1	1	yes	characteristic
71	3₋¹⁺²	—	3	18	no	—
72	H(3,𝔽₃)	—	3	27	no	—
73	H(3,𝔽₃)	—	3	9	no	—
74	H(3,𝔽₃)	—	9	9	no	—
75	C₃×C₉	—	3	6	no	—
76	C₁₃	#10624735	1	1	yes	characteristic, direct product factor, Sylow
77	C₃²	—	3	3	no	—
78	C₃²	—	3	3	no	—
79	C₃²	—	3	9	no	—
80	C₃²	—	3	3	no	—
81	C₃²	—	3	6	no	—
82	C₃²	—	9	9	no	—
83	C₃²	—	9	9	no	—
84	C₃²	—	9	18	no	—
85	C₃²	—	9	9	no	—
86	C₃²	—	9	3	no	—
87	C₃²	—	9	9	no	—
88	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
89	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
90	C₉	—	9	6	no	—
91	C₃	—	3	3	no	—
92	C₃	—	9	3	no	—
93	C₃	—	9	9	no	—
94	C₃	—	27	3	no	—
95	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
96	C₃	C₁₃×#6909	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×H(3,𝔽₃)	C₃	semidirect
2. C₃×C₁₃×AΣL(1,𝔽₂₇)	C₃	semidirect
3. C₁₃×#6891	C₃	semidirect
4. C₁₃×C₃²⋊H(3,𝔽₃)	C₃	semidirect
14. #10624735	C₁₃	direct (N × H)
22. C₃³×C₁₃	H(3,𝔽₃)	semidirect
29. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
30. C₃×AΣL(1,𝔽₂₇)	C₃×C₁₃	semidirect
31. #6891	C₃×C₁₃	semidirect
32. C₃²⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
69. C₃³	C₁₃×H(3,𝔽₃)	semidirect
76. C₁₃	#10624735	direct (N × H)

Subgroups — C13×#10624735 #23744886

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624735 #23744886