Subgroups — H(3,𝔽₃)×C₃³⋊C₁₃ #23748629

Order 9477.

494 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃³⋊C₁₃	C₃	1	4	yes	maximal, complemented
2	C₃×C₃³⋊C₁₃	—	3	4	no	—
3	C₃×C₃³⋊C₁₃	C₃²	1	1	yes	characteristic
4	C₃³×H(3,𝔽₃)	C₁₃	1	1	yes	maximal, characteristic, complemented, Sylow
5	C₃³⋊C₁₃	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
6	C₁₃×H(3,𝔽₃)	—	27	1	no	maximal
7	C₃⁵	C₃×C₁₃	1	4	yes	complemented
8	C₃²×H(3,𝔽₃)	—	13	1	no	—
9	C₃²×H(3,𝔽₃)	—	13	8	no	—
10	C₃²×C₁₃	—	27	4	no	—
11	C₃⁴	—	3	4	no	—
12	C₃⁴	—	13	4	no	—
13	C₃⁴	—	13	8	no	—
14	C₃⁴	—	39	8	no	—
15	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
16	C₃×H(3,𝔽₃)	—	13	48	no	—
17	C₃×H(3,𝔽₃)	—	13	1	no	—
18	C₃×H(3,𝔽₃)	—	13	24	no	—
19	C₃×H(3,𝔽₃)	—	13	8	no	—
20	C₃×C₁₃	—	27	1	no	—
21	C₃×C₁₃	—	81	4	no	—
22	C₃³	—	13	2	no	—
23	C₃³	—	13	1	no	—
24	C₃³	—	13	24	no	—
25	C₃³	—	13	4	no	—
26	C₃³	—	13	8	no	—
27	C₃³	—	39	8	no	—
28	C₃³	—	39	4	no	—
29	C₃³	—	39	8	no	—
30	C₃³	—	39	16	no	—
31	C₃³	—	39	24	no	—
32	C₃³	—	39	48	no	—
33	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic, complemented
34	H(3,𝔽₃)	—	13	48	no	—
35	H(3,𝔽₃)	—	13	8	no	—
36	H(3,𝔽₃)	C₃³⋊C₁₃	1	1	yes	characteristic, direct product factor
37	C₁₃	—	27	1	no	Sylow
38	C₃²	—	13	1	no	—
39	C₃²	—	13	2	no	—
40	C₃²	—	13	6	no	—
41	C₃²	—	13	1	no	—
42	C₃²	—	13	8	no	—
43	C₃²	—	39	8	no	—
44	C₃²	—	39	4	no	—
45	C₃²	—	39	8	no	—
46	C₃²	—	39	16	no	—
47	C₃²	—	39	24	no	—
48	C₃²	—	39	48	no	—
49	C₃²	C₃×C₃³⋊C₁₃	1	4	yes	complemented
50	C₃	—	3	4	no	—
51	C₃	—	13	1	no	—
52	C₃	—	13	2	no	—
53	C₃	—	39	8	no	—
54	C₃	C₃²×C₃³⋊C₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃³⋊C₁₃	C₃	semidirect
4. C₃³×H(3,𝔽₃)	C₁₃	semidirect
5. C₃³⋊C₁₃	H(3,𝔽₃)	direct (N × H)
7. C₃⁵	C₃×C₁₃	semidirect
33. C₃³	C₁₃×H(3,𝔽₃)	semidirect
36. H(3,𝔽₃)	C₃³⋊C₁₃	direct (N × H)
49. C₃²	C₃×C₃³⋊C₁₃	semidirect

Subgroups — H(3,𝔽3)×C33⋊C13 #23748629

Conjugacy classes of subgroups

Complements

Subgroups — H(3,𝔽₃)×C₃³⋊C₁₃ #23748629