Subgroups — C₁₃×#10624456 #23744607

Order 9477.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₃²⋊C₂₇	C₃	1	3	yes	maximal, complemented
3	C₁₃×#737	—	3	9	no	—
4	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
5	C₃×C₁₃×3₋¹⁺²	C₉	1	2	yes	—
6	C₃×C₁₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	—	3	1	no	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₃×C₁₃×C₂₇	—	3	3	no	—
10	#10624456	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	—	3	1	no	—
12	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
13	C₁₃×3₋¹⁺²	—	3	18	no	—
14	C₁₃×3₋¹⁺²	—	3	6	no	—
15	C₁₃×H(3,𝔽₃)	—	3	3	no	—
16	C₃×C₉×C₁₃	—	3	2	no	—
17	C₃×C₉×C₁₃	—	3	9	no	—
18	C₃×C₉×C₁₃	—	3	3	no	—
19	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
21	C₁₃×C₂₇	—	9	3	no	—
22	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
23	C₃²⋊C₂₇	C₃×C₁₃	1	3	yes	complemented
24	C₃²×C₁₃	—	3	1	no	—
25	C₃²×C₁₃	—	3	3	no	—
26	C₃²×C₁₃	—	3	3	no	—
27	C₃²×C₁₃	—	9	3	no	—
28	C₃²×C₁₃	C₃²⋊C₉	1	1	yes	characteristic
29	C₉×C₁₃	—	3	6	no	—
30	C₉×C₁₃	—	3	2	no	—
31	C₉×C₁₃	AΣL(1,𝔽₂₇)	1	3	yes	—
32	#737	—	3	9	no	—
33	C₃×3₋¹⁺²	—	3	2	no	—
34	C₃×3₋¹⁺²	C₉×C₁₃	1	2	yes	—
35	C₃×H(3,𝔽₃)	C₉×C₁₃	1	1	yes	characteristic
36	C₃²×C₉	—	3	1	no	—
37	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
38	C₃×C₂₇	—	3	3	no	—
39	C₃×C₁₃	—	9	1	no	—
40	C₃×C₁₃	—	9	3	no	—
41	C₃×C₁₃	#6866	1	1	yes	characteristic
42	C₃×C₁₃	#6872	1	3	yes	—
43	C₃³	—	3	1	no	—
44	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
45	3₋¹⁺²	—	3	18	no	—
46	3₋¹⁺²	—	3	6	no	—
47	H(3,𝔽₃)	—	3	3	no	—
48	C₃×C₉	—	3	2	no	—
49	C₃×C₉	—	3	9	no	—
50	C₃×C₉	—	3	3	no	—
51	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
52	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
53	C₂₇	—	9	3	no	—
54	C₁₃	#10624456	1	1	yes	characteristic, direct product factor, Sylow
55	C₃²	—	3	1	no	—
56	C₃²	—	3	3	no	—
57	C₃²	—	3	3	no	—
58	C₃²	—	9	3	no	—
59	C₃²	C₁₃×C₃²⋊C₉	1	1	yes	characteristic
60	C₉	—	3	6	no	—
61	C₉	—	3	2	no	—
62	C₉	C₁₃×AΣL(1,𝔽₂₇)	1	3	yes	—
63	C₃	—	9	1	no	—
64	C₃	—	9	3	no	—
65	C₃	C₁₃×#6866	1	1	yes	characteristic
66	C₃	C₁₃×#6872	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₁₃	H(3,𝔽₃)
commutator	C₃³	C₃×C₉×C₁₃
Frattini, cosocle	C₃²×C₉	C₃²×C₁₃
socle	C₃²×C₁₃	C₃²⋊C₉
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₉
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₃²⋊C₂₇	C₃	semidirect
10. #10624456	C₁₃	direct (N × H)
23. C₃²⋊C₂₇	C₃×C₁₃	semidirect
54. C₁₃	#10624456	direct (N × H)

Subgroups — C13×#10624456 #23744607

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624456 #23744607