Subgroups — C₃×C₉×C₁₃×H(3,𝔽₃) #23745010

Order 9477.

1688 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₉×C₁₃	C₃	1	4	yes	maximal, complemented
3	C₉×C₁₃×H(3,𝔽₃)	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	8	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	4	yes	—
6	C₃×C₁₃×H(3,𝔽₃)	C₉	1	27	yes	direct product factor
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
8	C₃²×C₉×C₁₃	—	3	36	no	—
9	C₃²×C₉×C₁₃	C₃²	1	8	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₃²×C₉×C₁₃	C₃²	1	36	yes	complemented
12	C₁₃×C₃²⋊C₉	C₃²	1	72	yes	complemented
13	C₃×C₉×H(3,𝔽₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	3	12	no	—
15	C₃³×C₁₃	—	3	24	no	—
16	C₃³×C₁₃	C₃×C₉	1	36	yes	complemented
17	C₃³×C₁₃	C₃³	1	12	yes	—
18	C₃³×C₁₃	C₃³	1	1	yes	characteristic
19	C₁₃×H(3,𝔽₃)	C₃×C₉	1	81	yes	direct product factor
20	C₃×C₉×C₁₃	—	3	24	no	—
21	C₃×C₉×C₁₃	—	3	108	no	—
22	C₃×C₉×C₁₃	H(3,𝔽₃)	1	9	yes	direct product factor
23	C₃×C₉×C₁₃	C₃³	1	24	yes	—
24	C₃×C₉×C₁₃	C₃³	1	3	yes	—
25	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
26	C₃³×C₉	C₃×C₁₃	1	4	yes	complemented
27	C₉×H(3,𝔽₃)	C₃×C₁₃	1	27	yes	direct product factor
28	C₃×C₃²⋊C₉	C₃×C₁₃	1	8	yes	complemented
29	C₃²×C₁₃	—	3	12	no	—
30	C₃²×C₁₃	—	3	24	no	—
31	C₃²×C₁₃	—	3	108	no	—
32	C₃²×C₁₃	C₃²×C₉	1	3	yes	—
33	C₃²×C₁₃	C₃²×C₉	1	36	yes	complemented
34	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
35	C₃²×C₁₃	#737	1	6	yes	—
36	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
37	C₉×C₁₃	—	3	24	no	—
38	C₉×C₁₃	C₃×H(3,𝔽₃)	1	9	yes	direct product factor
39	C₃⁴	C₃²×C₁₃	1	4	yes	—
40	C₃×H(3,𝔽₃)	C₉×C₁₃	1	27	yes	direct product factor
41	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	9	yes	—
42	C₃²×C₉	—	3	36	no	—
43	C₃²×C₉	C₃²×C₁₃	1	8	yes	—
44	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
45	C₃²×C₉	C₃²×C₁₃	1	36	yes	complemented
46	C₃²⋊C₉	C₃²×C₁₃	1	72	yes	complemented
47	C₃×C₁₃	—	3	36	no	—
48	C₃×C₁₃	C₉×H(3,𝔽₃)	1	9	yes	direct product factor
49	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
50	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
51	C₃×C₁₃	C₃×#737	1	2	yes	—
52	C₃³	—	3	12	no	—
53	C₃³	—	3	24	no	—
54	C₃³	C₃×C₉×C₁₃	1	36	yes	complemented
55	C₃³	C₃³×C₁₃	1	12	yes	—
56	C₃³	C₃³×C₁₃	1	1	yes	characteristic
57	H(3,𝔽₃)	C₃×C₉×C₁₃	1	81	yes	direct product factor
58	C₃×C₉	—	3	24	no	—
59	C₃×C₉	—	3	108	no	—
60	C₃×C₉	C₁₃×H(3,𝔽₃)	1	9	yes	direct product factor
61	C₃×C₉	C₃³×C₁₃	1	24	yes	—
62	C₃×C₉	C₃³×C₁₃	1	3	yes	—
63	C₁₃	C₃×C₉×H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
64	C₃²	—	3	108	no	—
65	C₃²	—	3	12	no	—
66	C₃²	—	3	24	no	—
67	C₃²	C₃²×C₉×C₁₃	1	3	yes	—
68	C₃²	C₃²×C₉×C₁₃	1	36	yes	complemented
69	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
70	C₃²	C₁₃×#737	1	6	yes	—
71	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
72	C₉	—	3	24	no	—
73	C₉	C₃×C₁₃×H(3,𝔽₃)	1	9	yes	direct product factor
74	C₃	—	3	36	no	—
75	C₃	C₉×C₁₃×H(3,𝔽₃)	1	9	yes	direct product factor
76	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic
77	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	C₃	C₃×C₁₃×#737	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃³×C₉×C₁₃	C₃	semidirect
3. C₉×C₁₃×H(3,𝔽₃)	C₃	direct (N × H)
4. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
6. C₃×C₁₃×H(3,𝔽₃)	C₉	direct (N × H)
11. C₃²×C₉×C₁₃	C₃²	semidirect
12. C₁₃×C₃²⋊C₉	C₃²	semidirect
13. C₃×C₉×H(3,𝔽₃)	C₁₃	direct (N × H)
16. C₃³×C₁₃	C₃×C₉	semidirect
19. C₁₃×H(3,𝔽₃)	C₃×C₉	direct (N × H)
22. C₃×C₉×C₁₃	H(3,𝔽₃)	direct (N × H)
26. C₃³×C₉	C₃×C₁₃	semidirect
27. C₉×H(3,𝔽₃)	C₃×C₁₃	direct (N × H)
28. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
33. C₃²×C₁₃	C₃²×C₉	semidirect
38. C₉×C₁₃	C₃×H(3,𝔽₃)	direct (N × H)
40. C₃×H(3,𝔽₃)	C₉×C₁₃	direct (N × H)
45. C₃²×C₉	C₃²×C₁₃	semidirect
46. C₃²⋊C₉	C₃²×C₁₃	semidirect
48. C₃×C₁₃	C₉×H(3,𝔽₃)	direct (N × H)
54. C₃³	C₃×C₉×C₁₃	semidirect
57. H(3,𝔽₃)	C₃×C₉×C₁₃	direct (N × H)
60. C₃×C₉	C₁₃×H(3,𝔽₃)	direct (N × H)
63. C₁₃	C₃×C₉×H(3,𝔽₃)	direct (N × H)
68. C₃²	C₃²×C₉×C₁₃	semidirect
73. C₉	C₃×C₁₃×H(3,𝔽₃)	direct (N × H)
75. C₃	C₉×C₁₃×H(3,𝔽₃)	direct (N × H)

Subgroups — C3×C9×C13×H(3,𝔽3) #23745010

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₉×C₁₃×H(3,𝔽₃) #23745010