Subgroups — C₁₃×#10624846 #23744997

Order 9477.

210 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	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6881	C₃	1	9	yes	maximal, complemented
5	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
6	C₃×C₁₃×H(3,𝔽₃)	—	3	2	no	—
7	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
8	C₁₃×#733	—	3	1	no	—
9	C₁₃×#733	—	3	1	no	—
10	C₁₃×#733	C₃²	1	3	yes	complemented
11	C₁₃×#732	—	3	2	no	—
12	C₁₃×#732	—	3	2	no	—
13	C₁₃×#732	C₃²	1	6	yes	complemented
14	C₁₃×C₉⋊C₉	—	3	1	no	—
15	C₁₃×C₉⋊C₉	C₃²	1	3	yes	complemented
16	C₁₃×C₃²⋊C₉	—	3	1	no	—
17	C₉²×C₁₃	—	3	1	no	—
18	#10624846	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃³×C₁₃	—	9	2	no	—
20	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₁₃×3₋¹⁺²	—	3	3	no	—
22	C₁₃×3₋¹⁺²	—	9	2	no	—
23	C₁₃×H(3,𝔽₃)	—	3	6	no	—
24	C₁₃×H(3,𝔽₃)	—	9	2	no	—
25	C₁₃×H(3,𝔽₃)	—	9	2	no	—
26	C₃×C₉×C₁₃	—	3	1	no	—
27	C₃×C₉×C₁₃	—	3	2	no	—
28	C₃×C₉×C₁₃	—	3	3	no	—
29	C₃×C₉×C₁₃	—	9	1	no	—
30	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
32	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
33	C₃×#733	C₃×C₁₃	1	1	yes	characteristic, complemented
34	C₃×#732	C₃×C₁₃	1	2	yes	complemented
35	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
36	#6881	C₃×C₁₃	1	9	yes	complemented
37	C₃²×C₁₃	—	9	1	no	—
38	C₃²×C₁₃	—	9	6	no	—
39	C₃²×C₁₃	—	27	6	no	—
40	C₃²×C₁₃	#732	1	1	yes	characteristic
41	C₃²×C₁₃	#732	1	2	yes	—
42	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₉×C₁₃	—	3	1	no	—
44	C₉×C₁₃	—	3	1	no	—
45	C₉×C₁₃	—	3	1	no	—
46	C₉×C₁₃	—	9	3	no	—
47	C₉×C₁₃	—	9	3	no	—
48	C₃×3₋¹⁺²	—	3	1	no	—
49	C₃×H(3,𝔽₃)	—	3	2	no	—
50	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
51	#733	—	3	1	no	—
52	#733	—	3	1	no	—
53	#733	C₃²×C₁₃	1	3	yes	complemented
54	#732	—	3	2	no	—
55	#732	—	3	2	no	—
56	#732	C₃²×C₁₃	1	6	yes	complemented
57	C₉⋊C₉	—	3	1	no	—
58	C₉⋊C₉	C₃²×C₁₃	1	3	yes	complemented
59	C₃²⋊C₉	—	3	1	no	—
60	C₉²	—	3	1	no	—
61	C₃×C₁₃	—	3	1	no	—
62	C₃×C₁₃	—	3	2	no	—
63	C₃×C₁₃	—	3	1	no	—
64	C₃×C₁₃	—	27	6	no	—
65	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
66	C₃³	—	9	2	no	—
67	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
68	3₋¹⁺²	—	3	3	no	—
69	3₋¹⁺²	—	9	2	no	—
70	H(3,𝔽₃)	—	3	6	no	—
71	H(3,𝔽₃)	—	9	2	no	—
72	H(3,𝔽₃)	—	9	2	no	—
73	C₃×C₉	—	3	1	no	—
74	C₃×C₉	—	3	2	no	—
75	C₃×C₉	—	3	3	no	—
76	C₃×C₉	—	9	1	no	—
77	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
79	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
80	C₁₃	#10624846	1	1	yes	characteristic, direct product factor, Sylow
81	C₃²	—	9	1	no	—
82	C₃²	—	9	6	no	—
83	C₃²	—	27	6	no	—
84	C₃²	C₁₃×#732	1	1	yes	characteristic
85	C₃²	C₁₃×#732	1	2	yes	—
86	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	3	1	no	—
90	C₉	—	9	3	no	—
91	C₉	—	9	3	no	—
92	C₃	—	3	1	no	—
93	C₃	—	3	2	no	—
94	C₃	—	3	1	no	—
95	C₃	—	27	6	no	—
96	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	C₃×#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×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. C₁₃×#6887	C₃	semidirect
4. C₁₃×#6881	C₃	semidirect
10. C₁₃×#733	C₃²	semidirect
13. C₁₃×#732	C₃²	semidirect
15. C₁₃×C₉⋊C₉	C₃²	semidirect
18. #10624846	C₁₃	direct (N × H)
33. C₃×#733	C₃×C₁₃	semidirect
34. C₃×#732	C₃×C₁₃	semidirect
35. #6887	C₃×C₁₃	semidirect
36. #6881	C₃×C₁₃	semidirect
53. #733	C₃²×C₁₃	semidirect
56. #732	C₃²×C₁₃	semidirect
58. C₉⋊C₉	C₃²×C₁₃	semidirect
80. C₁₃	#10624846	direct (N × H)

Subgroups — C13×#10624846 #23744997

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624846 #23744997