Subgroups — C₁₃×#10624576 #23744727

Order 9477.

254 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6855	C₃	1	9	yes	maximal
3	C₁₃×#6855	C₃	1	2	yes	maximal
4	C₁₃×#6855	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
6	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
7	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×C₉⋊C₉	—	3	3	no	—
10	#10624576	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	C₃³	1	1	yes	characteristic
12	C₃×C₉×C₁₃	—	3	2	no	—
13	C₃×C₉×C₁₃	—	3	1	no	—
14	C₃×C₉×C₁₃	—	3	3	no	—
15	C₃×C₉×C₁₃	—	3	6	no	—
16	C₃×C₉×C₁₃	—	3	18	no	—
17	C₃×C₉×C₁₃	—	3	3	no	—
18	C₃×C₉×C₁₃	—	3	9	no	—
19	C₃×C₉×C₁₃	—	3	9	no	—
20	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
21	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
22	#6855	C₃×C₁₃	1	9	yes	—
23	#6855	C₃×C₁₃	1	2	yes	—
24	#6855	C₃×C₁₃	1	1	yes	characteristic
25	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
26	C₃²×C₁₃	#737	1	2	yes	—
27	C₃²×C₁₃	#737	1	1	yes	characteristic
28	C₃²×C₁₃	#737	1	9	yes	—
29	C₉×C₁₃	—	3	3	no	—
30	C₉×C₁₃	—	9	6	no	—
31	C₉×C₁₃	—	9	3	no	—
32	C₉×C₁₃	—	9	3	no	—
33	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
34	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
35	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
36	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
37	C₉⋊C₉	—	3	3	no	—
38	C₃×C₁₃	#6895	1	1	yes	characteristic
39	C₃×C₁₃	#6897	1	6	yes	—
40	C₃×C₁₃	#6898	1	3	yes	—
41	C₃×C₁₃	#6899	1	3	yes	—
42	C₃³	C₃³×C₁₃	1	1	yes	characteristic
43	C₃×C₉	—	3	2	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	—	3	6	no	—
47	C₃×C₉	—	3	18	no	—
48	C₃×C₉	—	3	3	no	—
49	C₃×C₉	—	3	9	no	—
50	C₃×C₉	—	3	9	no	—
51	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
52	C₁₃	#10624576	1	1	yes	characteristic, direct product factor, Sylow
53	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
54	C₃²	C₁₃×#737	1	2	yes	—
55	C₃²	C₁₃×#737	1	1	yes	characteristic
56	C₃²	C₁₃×#737	1	9	yes	—
57	C₉	—	3	3	no	—
58	C₉	—	9	6	no	—
59	C₉	—	9	3	no	—
60	C₉	—	9	3	no	—
61	C₃	C₁₃×#6895	1	1	yes	characteristic
62	C₃	C₁₃×#6897	1	6	yes	—
63	C₃	C₁₃×#6898	1	3	yes	—
64	C₃	C₁₃×#6899	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₃³×C₁₃	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
10. #10624576	C₁₃	direct (N × H)
52. C₁₃	#10624576	direct (N × H)

Subgroups — C13×#10624576 #23744727

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624576 #23744727