Subgroups — C₁₃×#10624457 #23744608

Order 9477.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₃²⋊C₂₇	C₃	1	3	yes	maximal
3	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
4	C₃×C₁₃×C₂₇	—	3	3	no	—
5	C₁₃×C₉⋊C₉	—	3	2	no	—
6	C₁₃×C₃²⋊C₉	C₉	1	3	yes	—
7	C₉²×C₁₃	—	3	1	no	—
8	#10624457	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
10	C₃×C₉×C₁₃	—	3	3	no	—
11	C₃×C₉×C₁₃	—	3	3	no	—
12	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
14	C₁₃×C₂₇	—	9	3	no	—
15	#6887	C₃×C₁₃	1	1	yes	characteristic
16	C₃²⋊C₂₇	C₃×C₁₃	1	3	yes	—
17	C₃²×C₁₃	—	3	1	no	—
18	C₃²×C₁₃	—	3	3	no	—
19	C₃²×C₁₃	C₃²⋊C₉	1	1	yes	characteristic
20	C₉×C₁₃	—	3	2	no	—
21	C₉×C₁₃	—	9	3	no	—
22	C₉×C₁₃	#731	1	3	yes	—
23	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
24	C₃×C₂₇	—	3	3	no	—
25	C₉⋊C₉	—	3	2	no	—
26	C₃²⋊C₉	C₉×C₁₃	1	3	yes	—
27	C₉²	—	3	1	no	—
28	C₃×C₁₃	—	9	1	no	—
29	C₃×C₁₃	#6867	1	1	yes	characteristic
30	C₃×C₁₃	#6872	1	3	yes	—
31	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
32	C₃×C₉	—	3	3	no	—
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
36	C₂₇	—	9	3	no	—
37	C₁₃	#10624457	1	1	yes	characteristic, direct product factor, Sylow
38	C₃²	—	3	1	no	—
39	C₃²	—	3	3	no	—
40	C₃²	C₁₃×C₃²⋊C₉	1	1	yes	characteristic
41	C₉	—	3	2	no	—
42	C₉	—	9	3	no	—
43	C₉	C₁₃×#731	1	3	yes	—
44	C₃	—	9	1	no	—
45	C₃	C₁₃×#6867	1	1	yes	characteristic
46	C₃	C₁₃×#6872	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
8. #10624457	C₁₃	direct (N × H)
37. C₁₃	#10624457	direct (N × H)

Subgroups — C13×#10624457 #23744608

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624457 #23744608