Subgroups — C₁₃×#10624761 #23744912

Order 9477.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#6910	C₃	1	8	yes	maximal, complemented
3	C₃×C₁₃×AΣL(1,𝔽₂₇)	C₃	1	4	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic, complemented
5	C₃×C₁₃×3₋¹⁺²	C₃²	1	8	yes	complemented
6	C₃×C₁₃×H(3,𝔽₃)	—	3	12	no	—
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	4	yes	—
8	C₁₃×#731	—	3	24	no	—
9	C₁₃×AΣL(1,𝔽₂₇)	—	3	12	no	—
10	#10624761	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	—	3	9	no	—
12	C₃³×C₁₃	—	3	4	no	—
13	C₃³×C₁₃	—	3	4	no	—
14	C₃³×C₁₃	—	9	3	no	—
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×3₋¹⁺²	—	3	8	no	—
17	C₁₃×3₋¹⁺²	—	3	16	no	—
18	C₁₃×H(3,𝔽₃)	—	3	18	no	—
19	C₁₃×H(3,𝔽₃)	—	3	8	no	—
20	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	12	yes	—
21	C₃×C₉×C₁₃	—	3	8	no	—
22	H(5,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic, complemented
23	#6910	C₃×C₁₃	1	8	yes	complemented
24	C₃×AΣL(1,𝔽₂₇)	C₃×C₁₃	1	4	yes	complemented
25	C₃²×C₁₃	—	3	12	no	—
26	C₃²×C₁₃	—	9	1	no	—
27	C₃²×C₁₃	—	9	12	no	—
28	C₃²×C₁₃	—	9	1	no	—
29	C₃²×C₁₃	—	27	4	no	—
30	C₃²×C₁₃	—	27	9	no	—
31	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	4	yes	—
32	C₉×C₁₃	—	9	8	no	—
33	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic, complemented
34	C₃×3₋¹⁺²	C₃²×C₁₃	1	8	yes	complemented
35	C₃×H(3,𝔽₃)	—	3	12	no	—
36	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	4	yes	—
37	#731	—	3	24	no	—
38	AΣL(1,𝔽₂₇)	—	3	12	no	—
39	C₃×C₁₃	—	3	4	no	—
40	C₃×C₁₃	—	9	12	no	—
41	C₃×C₁₃	—	9	3	no	—
42	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
43	C₃³	—	3	9	no	—
44	C₃³	—	3	4	no	—
45	C₃³	—	3	4	no	—
46	C₃³	—	9	3	no	—
47	C₃³	C₃³×C₁₃	1	1	yes	characteristic
48	3₋¹⁺²	—	3	8	no	—
49	3₋¹⁺²	—	3	16	no	—
50	H(3,𝔽₃)	—	3	18	no	—
51	H(3,𝔽₃)	—	3	8	no	—
52	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	12	yes	—
53	C₃×C₉	—	3	8	no	—
54	C₁₃	#10624761	1	1	yes	characteristic, direct product factor, Sylow
55	C₃²	—	3	12	no	—
56	C₃²	—	9	1	no	—
57	C₃²	—	9	12	no	—
58	C₃²	—	9	1	no	—
59	C₃²	—	27	4	no	—
60	C₃²	—	27	9	no	—
61	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	4	yes	—
62	C₉	—	9	8	no	—
63	C₃	—	3	4	no	—
64	C₃	—	9	12	no	—
65	C₃	—	9	3	no	—
66	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×H(5,𝔽₃)	C₃	semidirect
2. C₁₃×#6910	C₃	semidirect
3. C₃×C₁₃×AΣL(1,𝔽₂₇)	C₃	semidirect
4. C₃⁴×C₁₃	C₃²	semidirect
5. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
10. #10624761	C₁₃	direct (N × H)
22. H(5,𝔽₃)	C₃×C₁₃	semidirect
23. #6910	C₃×C₁₃	semidirect
24. C₃×AΣL(1,𝔽₂₇)	C₃×C₁₃	semidirect
33. C₃⁴	C₃²×C₁₃	semidirect
34. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
54. C₁₃	#10624761	direct (N × H)

Subgroups — C13×#10624761 #23744912

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624761 #23744912