Subgroups — C₁₃×#10624577 #23744728

Order 9477.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	4	yes	maximal
2	C₁₃×#6855	C₃	1	8	yes	maximal
3	C₁₃×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₉×C₁₃	C₃²	1	8	yes	—
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
7	C₁₃×C₉⋊C₉	—	3	12	no	—
8	#10624577	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃³×C₁₃	C₃³	1	1	yes	characteristic
10	C₃×C₉×C₁₃	—	3	4	no	—
11	C₃×C₉×C₁₃	—	3	8	no	—
12	C₃×C₉×C₁₃	—	3	8	no	—
13	C₃×C₉×C₁₃	—	3	4	no	—
14	C₃×C₉×C₁₃	—	3	24	no	—
15	C₃×C₉×C₁₃	3₋¹⁺²	1	12	yes	—
16	C₃×C₉⋊C₉	C₃×C₁₃	1	4	yes	—
17	#6855	C₃×C₁₃	1	8	yes	—
18	#6855	C₃×C₁₃	1	1	yes	characteristic
19	C₃²×C₁₃	C₃×3₋¹⁺²	1	4	yes	—
20	C₃²×C₁₃	#737	1	1	yes	characteristic
21	C₃²×C₁₃	#737	1	8	yes	—
22	C₉×C₁₃	—	3	12	no	—
23	C₉×C₁₃	—	9	8	no	—
24	C₉×C₁₃	—	9	1	no	—
25	C₃²×C₉	C₃²×C₁₃	1	8	yes	—
26	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
27	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
28	C₉⋊C₉	—	3	12	no	—
29	C₃×C₁₃	#6895	1	4	yes	—
30	C₃×C₁₃	#6899	1	8	yes	—
31	C₃×C₁₃	#6900	1	1	yes	characteristic
32	C₃³	C₃³×C₁₃	1	1	yes	characteristic
33	C₃×C₉	—	3	4	no	—
34	C₃×C₉	—	3	8	no	—
35	C₃×C₉	—	3	8	no	—
36	C₃×C₉	—	3	4	no	—
37	C₃×C₉	—	3	24	no	—
38	C₃×C₉	C₁₃×3₋¹⁺²	1	12	yes	—
39	C₁₃	#10624577	1	1	yes	characteristic, direct product factor, Sylow
40	C₃²	C₃×C₁₃×3₋¹⁺²	1	4	yes	—
41	C₃²	C₁₃×#737	1	1	yes	characteristic
42	C₃²	C₁₃×#737	1	8	yes	—
43	C₉	—	3	12	no	—
44	C₉	—	9	8	no	—
45	C₉	—	9	1	no	—
46	C₃	C₁₃×#6895	1	4	yes	—
47	C₃	C₁₃×#6899	1	8	yes	—
48	C₃	C₁₃×#6900	1	1	yes	characteristic

	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
8. #10624577	C₁₃	direct (N × H)
39. C₁₃	#10624577	direct (N × H)

Subgroups — C13×#10624577 #23744728

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624577 #23744728