Subgroups — C₃×C₁₃×#6881 #23744993

Order 9477.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#733	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×#732	C₃	1	2	yes	maximal, complemented
3	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6881	C₃	1	9	yes	maximal, direct product factor
5	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
6	C₃×C₁₃×H(3,𝔽₃)	—	3	2	no	—
7	C₃²×C₉×C₁₃	—	3	1	no	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×#733	—	3	2	no	—
10	C₁₃×#733	C₃²	1	3	yes	complemented
11	C₁₃×#732	—	3	4	no	—
12	C₁₃×#732	C₃²	1	6	yes	complemented
13	C₁₃×C₉⋊C₉	—	3	2	no	—
14	C₁₃×C₉⋊C₉	C₃²	1	3	yes	complemented
15	C₃×#6881	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	9	2	no	—
17	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₁₃×3₋¹⁺²	—	3	3	no	—
19	C₁₃×3₋¹⁺²	—	9	2	no	—
20	C₁₃×H(3,𝔽₃)	—	3	6	no	—
21	C₁₃×H(3,𝔽₃)	—	9	4	no	—
22	C₃×C₉×C₁₃	—	3	2	no	—
23	C₃×C₉×C₁₃	—	3	1	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	—	9	3	no	—
26	C₃×C₉×C₁₃	—	9	1	no	—
27	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
28	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
29	C₃×#733	C₃×C₁₃	1	1	yes	characteristic, complemented
30	C₃×#732	C₃×C₁₃	1	2	yes	complemented
31	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
32	#6881	C₃×C₁₃	1	9	yes	direct product factor
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	9	6	no	—
35	C₃²×C₁₃	—	27	6	no	—
36	C₃²×C₁₃	#732	1	2	yes	—
37	C₃²×C₁₃	#732	1	1	yes	characteristic
38	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₁₃	—	3	2	no	—
40	C₉×C₁₃	—	3	1	no	—
41	C₉×C₁₃	—	9	3	no	—
42	C₉×C₁₃	—	9	3	no	—
43	C₃×3₋¹⁺²	—	3	1	no	—
44	C₃×H(3,𝔽₃)	—	3	2	no	—
45	C₃²×C₉	—	3	1	no	—
46	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
47	#733	—	3	2	no	—
48	#733	C₃²×C₁₃	1	3	yes	complemented
49	#732	—	3	4	no	—
50	#732	C₃²×C₁₃	1	6	yes	complemented
51	C₉⋊C₉	—	3	2	no	—
52	C₉⋊C₉	C₃²×C₁₃	1	3	yes	complemented
53	C₃×C₁₃	—	3	1	no	—
54	C₃×C₁₃	—	3	2	no	—
55	C₃×C₁₃	—	27	6	no	—
56	C₃×C₁₃	#6881	1	3	yes	direct product factor
57	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
58	C₃³	—	9	2	no	—
59	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
60	3₋¹⁺²	—	3	3	no	—
61	3₋¹⁺²	—	9	2	no	—
62	H(3,𝔽₃)	—	3	6	no	—
63	H(3,𝔽₃)	—	9	4	no	—
64	C₃×C₉	—	3	2	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	9	3	no	—
68	C₃×C₉	—	9	1	no	—
69	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
70	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
71	C₁₃	C₃×#6881	1	1	yes	characteristic, direct product factor, Sylow
72	C₃²	—	3	3	no	—
73	C₃²	—	9	6	no	—
74	C₃²	—	27	6	no	—
75	C₃²	C₁₃×#732	1	2	yes	—
76	C₃²	C₁₃×#732	1	1	yes	characteristic
77	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	C₉	—	3	2	no	—
79	C₉	—	3	1	no	—
80	C₉	—	9	3	no	—
81	C₉	—	9	3	no	—
82	C₃	—	3	1	no	—
83	C₃	—	3	2	no	—
84	C₃	—	27	6	no	—
85	C₃	C₁₃×#6881	1	3	yes	direct product factor
86	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₁₃	#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃³×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×#733	C₃	semidirect
2. C₃×C₁₃×#732	C₃	semidirect
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
4. C₁₃×#6881	C₃	direct (N × H)
10. C₁₃×#733	C₃²	semidirect
12. C₁₃×#732	C₃²	semidirect
14. C₁₃×C₉⋊C₉	C₃²	semidirect
15. C₃×#6881	C₁₃	direct (N × H)
29. C₃×#733	C₃×C₁₃	semidirect
30. C₃×#732	C₃×C₁₃	semidirect
31. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
32. #6881	C₃×C₁₃	direct (N × H)
48. #733	C₃²×C₁₃	semidirect
50. #732	C₃²×C₁₃	semidirect
52. C₉⋊C₉	C₃²×C₁₃	semidirect
56. C₃×C₁₃	#6881	direct (N × H)
71. C₁₃	C₃×#6881	direct (N × H)
85. C₃	C₁₃×#6881	direct (N × H)

Subgroups — C3×C13×#6881 #23744993

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6881 #23744993