Subgroups — C₁₃×#10624638 #23744789

Order 9477.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
2	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6861	C₃	1	3	yes	maximal, complemented
4	C₁₃×#6859	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6856	C₃	1	3	yes	maximal, complemented
6	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×C₉⋊C₉	—	3	2	no	—
10	C₁₃×C₃²⋊C₉	—	3	6	no	—
11	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
12	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
13	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₉²×C₁₃	—	3	1	no	—
15	#10624638	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	3	3	no	—
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₁₃×3₋¹⁺²	—	9	9	no	—
19	C₁₃×H(3,𝔽₃)	—	9	3	no	—
20	C₃×C₉×C₁₃	—	3	3	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	3	no	—
23	C₃×C₉×C₁₃	—	3	3	no	—
24	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
25	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
26	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	3	yes	complemented
27	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
28	#6861	C₃×C₁₃	1	3	yes	complemented
29	#6859	C₃×C₁₃	1	3	yes	complemented
30	#6856	C₃×C₁₃	1	3	yes	complemented
31	C₃²×C₁₃	—	3	3	no	—
32	C₃²×C₁₃	—	3	1	no	—
33	C₃²×C₁₃	—	9	3	no	—
34	C₃²×C₁₃	—	9	6	no	—
35	C₃²×C₁₃	—	9	3	no	—
36	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₉×C₁₃	—	3	2	no	—
38	C₉×C₁₃	—	9	3	no	—
39	C₉×C₁₃	—	9	3	no	—
40	C₉×C₁₃	—	9	3	no	—
41	C₉×C₁₃	#732	1	3	yes	—
42	C₃×3₋¹⁺²	—	3	3	no	—
43	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
44	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
45	C₉⋊C₉	—	3	2	no	—
46	C₃²⋊C₉	—	3	6	no	—
47	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
48	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
49	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
50	C₉²	—	3	1	no	—
51	C₃×C₁₃	—	9	1	no	—
52	C₃×C₁₃	—	27	3	no	—
53	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
54	C₃×C₁₃	#6913	1	3	yes	—
55	C₃³	—	3	3	no	—
56	C₃³	C₃³×C₁₃	1	1	yes	characteristic
57	3₋¹⁺²	—	9	9	no	—
58	H(3,𝔽₃)	—	9	3	no	—
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
64	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
65	C₁₃	#10624638	1	1	yes	characteristic, direct product factor, Sylow
66	C₃²	—	3	1	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	9	3	no	—
69	C₃²	—	9	3	no	—
70	C₃²	—	9	6	no	—
71	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
72	C₉	—	3	2	no	—
73	C₉	—	9	3	no	—
74	C₉	—	9	3	no	—
75	C₉	—	9	3	no	—
76	C₉	C₁₃×#732	1	3	yes	—
77	C₃	—	9	1	no	—
78	C₃	—	27	3	no	—
79	C₃	C₃×C₁₃×#732	1	1	yes	characteristic
80	C₃	C₁₃×#6913	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
2. C₁₃×#6887	C₃	semidirect
3. C₁₃×#6861	C₃	semidirect
4. C₁₃×#6859	C₃	semidirect
5. C₁₃×#6856	C₃	semidirect
15. #10624638	C₁₃	direct (N × H)
26. C₉⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
27. #6887	C₃×C₁₃	semidirect
28. #6861	C₃×C₁₃	semidirect
29. #6859	C₃×C₁₃	semidirect
30. #6856	C₃×C₁₃	semidirect
65. C₁₃	#10624638	direct (N × H)

Subgroups — C13×#10624638 #23744789

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624638 #23744789