Subgroups — C₁₃×H(3,𝔽₃)² #23745044

Order 9477.

2102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	8	yes	maximal, complemented
2	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	32	yes	maximal, complemented
3	C₃⁴×C₁₃	C₃²	1	16	yes	complemented
4	C₃×C₁₃×H(3,𝔽₃)	—	3	72	no	—
5	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	2	yes	—
6	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	64	yes	complemented
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	48	yes	complemented
8	H(3,𝔽₃)²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃³×C₁₃	—	3	96	no	—
10	C₃³×C₁₃	—	9	32	no	—
11	C₃³×C₁₃	C₃³	1	32	yes	—
12	C₃³×C₁₃	C₃³	1	8	yes	—
13	C₁₃×H(3,𝔽₃)	—	3	192	no	—
14	C₁₃×H(3,𝔽₃)	—	9	48	no	—
15	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	18	yes	direct product factor
16	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	8	yes	complemented
17	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	32	yes	complemented
18	C₃²×C₁₃	—	3	8	no	—
19	C₃²×C₁₃	—	3	16	no	—
20	C₃²×C₁₃	—	3	64	no	—
21	C₃²×C₁₃	—	3	64	no	—
22	C₃²×C₁₃	—	9	144	no	—
23	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	24	yes	complemented
24	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
25	C₃⁴	C₃²×C₁₃	1	16	yes	complemented
26	C₃×H(3,𝔽₃)	—	3	72	no	—
27	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	2	yes	—
28	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	64	yes	complemented
29	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	48	yes	complemented
30	C₃×C₁₃	—	3	24	no	—
31	C₃×C₁₃	—	9	32	no	—
32	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	2	yes	—
33	C₃×C₁₃	H(5,𝔽₃)	1	2	yes	—
34	C₃³	—	3	96	no	—
35	C₃³	—	9	32	no	—
36	C₃³	C₃³×C₁₃	1	32	yes	—
37	C₃³	C₃³×C₁₃	1	8	yes	—
38	H(3,𝔽₃)	—	3	192	no	—
39	H(3,𝔽₃)	—	9	48	no	—
40	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	18	yes	direct product factor
41	C₁₃	H(3,𝔽₃)²	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²	—	3	8	no	—
43	C₃²	—	3	16	no	—
44	C₃²	—	3	64	no	—
45	C₃²	—	3	64	no	—
46	C₃²	—	9	144	no	—
47	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	24	yes	complemented
48	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
49	C₃	—	3	24	no	—
50	C₃	—	9	32	no	—
51	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	2	yes	—
52	C₃	C₁₃×H(5,𝔽₃)	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×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. C₁₃×C₃²⋊H(3,𝔽₃)	C₃	semidirect
3. C₃⁴×C₁₃	C₃²	semidirect
6. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
7. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
8. H(3,𝔽₃)²	C₁₃	direct (N × H)
15. C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	direct (N × H)
16. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
17. C₃²⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
23. C₃²×C₁₃	C₃×H(3,𝔽₃)	semidirect
25. C₃⁴	C₃²×C₁₃	semidirect
28. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
29. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
40. H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	direct (N × H)
41. C₁₃	H(3,𝔽₃)²	direct (N × H)
47. C₃²	C₃×C₁₃×H(3,𝔽₃)	semidirect

Subgroups — C13×H(3,𝔽3)2 #23745044

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×H(3,𝔽₃)² #23745044