Subgroups — C₃×C₁₃×#6903 #23745068

Order 9477.

848 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×#6903	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₁₃×C₂₇⋊C₃	C₃	1	8	yes	maximal, complemented
4	C₃²×C₁₃×C₂₇	C₃	1	4	yes	maximal, complemented
5	C₁₃×#737	C₉	1	18	yes	—
6	C₁₃×#737	C₃²	1	9	yes	—
7	C₃×C₁₃×3₋¹⁺²	C₉	1	8	yes	—
8	C₃×C₁₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
9	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
10	C₁₃×C₂₇⋊C₃	C₃²	1	72	yes	complemented
11	C₃×C₁₃×C₂₇	C₃²	1	8	yes	—
12	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
13	C₃×C₁₃×C₂₇	C₃²	1	36	yes	complemented
14	C₃×#6903	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	C₃×C₉	1	4	yes	—
16	C₁₃×3₋¹⁺²	C₃×C₉	1	72	yes	—
17	C₁₃×H(3,𝔽₃)	C₃×C₉	1	9	yes	—
18	C₃×C₉×C₁₃	C₃×C₉	1	8	yes	—
19	C₃×C₉×C₁₃	C₃×C₉	1	24	yes	—
20	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
21	C₃×C₉×C₁₃	C₃³	1	12	yes	—
22	C₁₃×C₂₇	C₃³	1	24	yes	—
23	C₁₃×C₂₇	C₃³	1	3	yes	—
24	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
25	#6903	C₃×C₁₃	1	27	yes	direct product factor
26	C₃×C₂₇⋊C₃	C₃×C₁₃	1	8	yes	complemented
27	C₃²×C₂₇	C₃×C₁₃	1	4	yes	complemented
28	C₃²×C₁₃	—	3	12	no	—
29	C₃²×C₁₃	C₃²×C₉	1	12	yes	—
30	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₁₃	C₃²×C₉	1	2	yes	—
32	C₉×C₁₃	C₃²×C₉	1	24	yes	—
33	C₉×C₁₃	C₃⁴	1	1	yes	characteristic
34	#737	C₉×C₁₃	1	18	yes	—
35	#737	C₃²×C₁₃	1	9	yes	—
36	C₃×3₋¹⁺²	C₉×C₁₃	1	8	yes	—
37	C₃×H(3,𝔽₃)	C₉×C₁₃	1	1	yes	characteristic
38	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
39	C₂₇⋊C₃	C₃²×C₁₃	1	72	yes	complemented
40	C₃×C₂₇	C₃²×C₁₃	1	8	yes	—
41	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
42	C₃×C₂₇	C₃²×C₁₃	1	36	yes	complemented
43	C₃×C₁₃	—	3	12	no	—
44	C₃×C₁₃	#6903	1	3	yes	direct product factor
45	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
46	C₃³	C₃×C₉×C₁₃	1	4	yes	—
47	3₋¹⁺²	C₃×C₉×C₁₃	1	72	yes	—
48	H(3,𝔽₃)	C₃×C₉×C₁₃	1	9	yes	—
49	C₃×C₉	C₃×C₉×C₁₃	1	8	yes	—
50	C₃×C₉	C₃×C₉×C₁₃	1	24	yes	—
51	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
52	C₃×C₉	C₃³×C₁₃	1	12	yes	—
53	C₂₇	C₃³×C₁₃	1	3	yes	—
54	C₂₇	C₃³×C₁₃	1	24	yes	—
55	C₁₃	C₃×#6903	1	1	yes	characteristic, direct product factor, Sylow
56	C₃²	—	3	12	no	—
57	C₃²	C₃²×C₉×C₁₃	1	12	yes	—
58	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
59	C₉	C₃²×C₉×C₁₃	1	2	yes	—
60	C₉	C₃²×C₉×C₁₃	1	24	yes	—
61	C₉	C₃⁴×C₁₃	1	1	yes	characteristic
62	C₃	—	3	12	no	—
63	C₃	C₁₃×#6903	1	3	yes	direct product factor
64	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₁₃×C₂₇	C₃²
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₉	C₃⁴×C₁₃
socle	C₃²×C₁₃	C₃²×C₉
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6903	C₃	direct (N × H)
3. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
4. C₃²×C₁₃×C₂₇	C₃	semidirect
10. C₁₃×C₂₇⋊C₃	C₃²	semidirect
13. C₃×C₁₃×C₂₇	C₃²	semidirect
14. C₃×#6903	C₁₃	direct (N × H)
25. #6903	C₃×C₁₃	direct (N × H)
26. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
27. C₃²×C₂₇	C₃×C₁₃	semidirect
39. C₂₇⋊C₃	C₃²×C₁₃	semidirect
42. C₃×C₂₇	C₃²×C₁₃	semidirect
44. C₃×C₁₃	#6903	direct (N × H)
55. C₁₃	C₃×#6903	direct (N × H)
63. C₃	C₁₃×#6903	direct (N × H)

Subgroups — C3×C13×#6903 #23745068

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6903 #23745068