Subgroups — C₁₃×#10624488 #23744639

Order 9477.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#732	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6868	C₃	1	2	yes	maximal, complemented
3	C₁₃×#6855	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×H(3,𝔽₃)	—	3	1	no	—
5	C₃²×C₉×C₁₃	—	3	1	no	—
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₁₃×#732	—	3	3	no	—
8	C₁₃×C₃²⋊C₉	—	3	2	no	—
9	#10624488	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃³×C₁₃	—	9	1	no	—
11	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
12	C₁₃×H(3,𝔽₃)	—	3	3	no	—
13	C₁₃×H(3,𝔽₃)	—	9	2	no	—
14	C₃×C₉×C₁₃	—	3	3	no	—
15	C₃×C₉×C₁₃	—	3	1	no	—
16	C₃×C₉×C₁₃	—	3	2	no	—
17	C₃×C₉×C₁₃	—	3	1	no	—
18	C₃×C₉×C₁₃	—	9	2	no	—
19	C₃×C₉×C₁₃	—	9	1	no	—
20	C₃×C₉×C₁₃	—	9	2	no	—
21	C₃×#732	C₃×C₁₃	1	1	yes	characteristic
22	#6868	C₃×C₁₃	1	2	yes	complemented
23	#6855	C₃×C₁₃	1	1	yes	characteristic, complemented
24	C₃²×C₁₃	—	3	1	no	—
25	C₃²×C₁₃	—	3	2	no	—
26	C₃²×C₁₃	—	9	3	no	—
27	C₃²×C₁₃	—	27	1	no	—
28	C₃²×C₁₃	—	27	2	no	—
29	C₃²×C₁₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
30	C₃²×C₁₃	#731	1	2	yes	—
31	C₃²×C₁₃	#732	1	1	yes	characteristic
32	C₉×C₁₃	—	9	3	no	—
33	C₉×C₁₃	—	9	1	no	—
34	C₉×C₁₃	—	27	2	no	—
35	C₃×H(3,𝔽₃)	—	3	1	no	—
36	C₃²×C₉	—	3	1	no	—
37	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
38	#732	—	3	3	no	—
39	C₃²⋊C₉	—	3	2	no	—
40	C₃×C₁₃	—	3	1	no	—
41	C₃×C₁₃	—	3	2	no	—
42	C₃×C₁₃	—	27	3	no	—
43	C₃×C₁₃	#6859	1	1	yes	characteristic
44	C₃×C₁₃	#6878	1	1	yes	characteristic
45	C₃×C₁₃	#6881	1	2	yes	—
46	C₃³	—	9	1	no	—
47	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
48	H(3,𝔽₃)	—	3	3	no	—
49	H(3,𝔽₃)	—	9	2	no	—
50	C₃×C₉	—	3	3	no	—
51	C₃×C₉	—	3	1	no	—
52	C₃×C₉	—	3	2	no	—
53	C₃×C₉	—	3	1	no	—
54	C₃×C₉	—	9	2	no	—
55	C₃×C₉	—	9	1	no	—
56	C₃×C₉	—	9	2	no	—
57	C₁₃	#10624488	1	1	yes	characteristic, direct product factor, Sylow
58	C₃²	—	3	1	no	—
59	C₃²	—	3	2	no	—
60	C₃²	—	9	3	no	—
61	C₃²	—	27	1	no	—
62	C₃²	—	27	2	no	—
63	C₃²	C₁₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
64	C₃²	C₁₃×#731	1	2	yes	—
65	C₃²	C₁₃×#732	1	1	yes	characteristic
66	C₉	—	9	3	no	—
67	C₉	—	9	1	no	—
68	C₉	—	27	2	no	—
69	C₃	—	3	1	no	—
70	C₃	—	3	2	no	—
71	C₃	—	27	3	no	—
72	C₃	C₁₃×#6859	1	1	yes	characteristic
73	C₃	C₁₃×#6878	1	1	yes	characteristic
74	C₃	C₁₃×#6881	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	#732
commutator, Frattini, cosocle	C₃²×C₉	C₃²×C₁₃
prime radical	C₃×C₁₃×#732	C₃
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ 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
2. C₁₃×#6868	C₃	semidirect
3. C₁₃×#6855	C₃	semidirect
9. #10624488	C₁₃	direct (N × H)
22. #6868	C₃×C₁₃	semidirect
23. #6855	C₃×C₁₃	semidirect
57. C₁₃	#10624488	direct (N × H)

Subgroups — C13×#10624488 #23744639

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624488 #23744639