Subgroups — C₁₃×#10624516 #23744667

Order 9477.

100 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×#6869	C₃	1	3	yes	maximal
3	C₃²×C₉×C₁₃	—	3	1	no	—
4	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
5	C₁₃×C₂₇⋊C₃	—	3	3	no	—
6	C₁₃×C₉⋊C₉	—	3	1	no	—
7	C₁₃×C₉⋊C₉	—	3	1	no	—
8	C₁₃×C₉⋊C₉	C₉	1	3	yes	—
9	#10624516	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃³×C₁₃	3₋¹⁺²	1	1	yes	characteristic
11	C₃×C₉×C₁₃	—	3	3	no	—
12	C₃×C₉×C₁₃	—	3	3	no	—
13	C₃×C₉×C₁₃	—	9	3	no	—
14	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃×C₉×C₁₃	3₋¹⁺²	1	1	yes	characteristic
17	C₁₃×C₂₇	—	9	3	no	—
18	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
19	#6869	C₃×C₁₃	1	3	yes	—
20	C₃²×C₁₃	—	3	3	no	—
21	C₃²×C₁₃	—	3	1	no	—
22	C₃²×C₁₃	C₃²⋊C₉	1	1	yes	characteristic
23	C₉×C₁₃	—	3	1	no	—
24	C₉×C₁₃	—	3	1	no	—
25	C₉×C₁₃	—	9	3	no	—
26	C₉×C₁₃	#731	1	3	yes	—
27	C₃²×C₉	—	3	1	no	—
28	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
29	C₂₇⋊C₃	—	3	3	no	—
30	C₉⋊C₉	—	3	1	no	—
31	C₉⋊C₉	—	3	1	no	—
32	C₉⋊C₉	C₉×C₁₃	1	3	yes	—
33	C₃×C₁₃	—	3	1	no	—
34	C₃×C₁₃	—	3	3	no	—
35	C₃×C₁₃	#6867	1	1	yes	characteristic
36	C₃³	C₁₃×3₋¹⁺²	1	1	yes	characteristic
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	—	3	3	no	—
39	C₃×C₉	—	9	3	no	—
40	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
41	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃×C₉	C₁₃×3₋¹⁺²	1	1	yes	characteristic
43	C₂₇	—	9	3	no	—
44	C₁₃	#10624516	1	1	yes	characteristic, direct product factor, Sylow
45	C₃²	—	3	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	C₁₃×C₃²⋊C₉	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	C₁₃×#731	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	3	3	no	—
54	C₃	C₁₃×#6867	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	#6867
commutator	C₃×C₉	C₃×C₉×C₁₃
Frattini, cosocle	C₃²×C₉	C₃²×C₁₃
prime radical	C₃³×C₁₃	3₋¹⁺²
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃×C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
9. #10624516	C₁₃	direct (N × H)
44. C₁₃	#10624516	direct (N × H)

Subgroups — C13×#10624516 #23744667

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624516 #23744667