Subgroups — C₁₃×#10624599 #23744750

Order 9477.

344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	2	yes	maximal, complemented
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₁₃×#6856	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×H(3,𝔽₃)	—	3	2	no	—
6	C₃×C₁₃×H(3,𝔽₃)	—	3	4	no	—
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	6	yes	—
8	C₃²×C₉×C₁₃	—	3	2	no	—
9	C₁₃×C₃²⋊C₉	—	3	2	no	—
10	C₁₃×C₃²⋊C₉	—	3	2	no	—
11	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
12	#10624599	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	6	no	—
14	C₃³×C₁₃	—	3	6	no	—
15	C₃³×C₁₃	—	9	2	no	—
16	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
18	C₃³×C₁₃	C₃³	1	1	yes	characteristic
19	C₁₃×H(3,𝔽₃)	—	9	6	no	—
20	C₁₃×H(3,𝔽₃)	—	9	6	no	—
21	C₁₃×H(3,𝔽₃)	—	9	12	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	9	6	no	—
24	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	2	yes	complemented
25	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	complemented
26	#6856	C₃×C₁₃	1	9	yes	complemented
27	C₃²×C₁₃	—	3	2	no	—
28	C₃²×C₁₃	—	3	4	no	—
29	C₃²×C₁₃	—	3	2	no	—
30	C₃²×C₁₃	—	3	2	no	—
31	C₃²×C₁₃	—	3	2	no	—
32	C₃²×C₁₃	—	3	2	no	—
33	C₃²×C₁₃	—	9	9	no	—
34	C₃²×C₁₃	—	9	12	no	—
35	C₃²×C₁₃	—	9	6	no	—
36	C₃²×C₁₃	—	9	6	no	—
37	C₃²×C₁₃	#732	1	6	yes	—
38	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₁₃	—	9	6	no	—
40	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
41	C₃×H(3,𝔽₃)	—	3	2	no	—
42	C₃×H(3,𝔽₃)	—	3	4	no	—
43	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	6	yes	—
44	C₃²×C₉	—	3	2	no	—
45	C₃²⋊C₉	—	3	2	no	—
46	C₃²⋊C₉	—	3	2	no	—
47	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
48	C₃×C₁₃	—	3	6	no	—
49	C₃×C₁₃	—	9	1	no	—
50	C₃×C₁₃	—	9	1	no	—
51	C₃×C₁₃	—	27	6	no	—
52	C₃×C₁₃	C₃×#732	1	2	yes	—
53	C₃×C₁₃	#6909	1	2	yes	—
54	C₃³	—	3	6	no	—
55	C₃³	—	3	6	no	—
56	C₃³	—	9	2	no	—
57	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
58	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
59	C₃³	C₃³×C₁₃	1	1	yes	characteristic
60	H(3,𝔽₃)	—	9	6	no	—
61	H(3,𝔽₃)	—	9	6	no	—
62	H(3,𝔽₃)	—	9	12	no	—
63	C₃×C₉	—	3	6	no	—
64	C₃×C₉	—	9	6	no	—
65	C₁₃	#10624599	1	1	yes	characteristic, direct product factor, Sylow
66	C₃²	—	3	2	no	—
67	C₃²	—	3	4	no	—
68	C₃²	—	3	2	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	9	9	no	—
73	C₃²	—	9	12	no	—
74	C₃²	—	9	6	no	—
75	C₃²	—	9	6	no	—
76	C₃²	C₁₃×#732	1	6	yes	—
77	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	C₉	—	9	6	no	—
79	C₃	—	3	6	no	—
80	C₃	—	9	1	no	—
81	C₃	—	9	1	no	—
82	C₃	—	27	6	no	—
83	C₃	C₃×C₁₃×#732	1	2	yes	—
84	C₃	C₁₃×#6909	1	2	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 ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃²⋊H(3,𝔽₃)	C₃	semidirect
2. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
3. C₁₃×#6856	C₃	semidirect
12. #10624599	C₁₃	direct (N × H)
24. C₃²⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
25. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
26. #6856	C₃×C₁₃	semidirect
65. C₁₃	#10624599	direct (N × H)

Subgroups — C13×#10624599 #23744750

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624599 #23744750