Subgroups — C₁₃×#10624694 #23744845

Order 9477.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6869	C₃	1	9	yes	maximal, complemented
4	C₁₃×#737	—	3	3	no	—
5	C₁₃×#737	—	3	6	no	—
6	C₃×C₁₃×3₋¹⁺²	C₉	1	2	yes	—
7	C₃×C₁₃×3₋¹⁺²	C₉	1	6	yes	—
8	C₃×C₁₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₁₃×C₂₇⋊C₃	—	3	6	no	—
12	C₁₃×C₂₇⋊C₃	C₃²	1	9	yes	—
13	C₃×C₁₃×C₂₇	—	3	3	no	—
14	#10624694	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	C₃×C₉	1	3	yes	—
16	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
17	C₁₃×3₋¹⁺²	—	3	6	no	—
18	C₁₃×3₋¹⁺²	—	3	18	no	—
19	C₁₃×H(3,𝔽₃)	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	3	no	—
21	C₃×C₉×C₁₃	—	3	6	no	—
22	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
23	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
25	C₃×C₉×C₁₃	3₋¹⁺²	1	6	yes	—
26	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
27	C₁₃×C₂₇	—	3	9	no	—
28	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
29	C₃×C₂₇⋊C₃	C₃×C₁₃	1	3	yes	complemented
30	#6869	C₃×C₁₃	1	9	yes	complemented
31	C₃²×C₁₃	—	3	3	no	—
32	C₃²×C₁₃	—	9	1	no	—
33	C₃²×C₁₃	—	9	3	no	—
34	C₃²×C₁₃	C₃²⋊C₉	1	3	yes	—
35	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
36	C₉×C₁₃	—	3	6	no	—
37	C₉×C₁₃	C₃²⋊C₉	1	6	yes	—
38	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
40	#737	—	3	3	no	—
41	#737	—	3	6	no	—
42	C₃×3₋¹⁺²	C₉×C₁₃	1	2	yes	—
43	C₃×3₋¹⁺²	C₉×C₁₃	1	6	yes	—
44	C₃×H(3,𝔽₃)	C₉×C₁₃	1	1	yes	characteristic
45	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
46	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
47	C₂₇⋊C₃	—	3	6	no	—
48	C₂₇⋊C₃	C₃²×C₁₃	1	9	yes	—
49	C₃×C₂₇	—	3	3	no	—
50	C₃×C₁₃	—	3	1	no	—
51	C₃×C₁₃	—	3	3	no	—
52	C₃×C₁₃	—	9	3	no	—
53	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
54	C₃³	C₃×C₉×C₁₃	1	3	yes	—
55	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
56	3₋¹⁺²	—	3	6	no	—
57	3₋¹⁺²	—	3	18	no	—
58	H(3,𝔽₃)	—	3	3	no	—
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	6	no	—
61	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
62	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
63	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
64	C₃×C₉	C₁₃×3₋¹⁺²	1	6	yes	—
65	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
66	C₂₇	—	3	9	no	—
67	C₁₃	#10624694	1	1	yes	characteristic, direct product factor, Sylow
68	C₃²	—	3	3	no	—
69	C₃²	—	9	1	no	—
70	C₃²	—	9	3	no	—
71	C₃²	C₁₃×C₃²⋊C₉	1	3	yes	—
72	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
73	C₉	—	3	6	no	—
74	C₉	C₁₃×C₃²⋊C₉	1	6	yes	—
75	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
76	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
77	C₃	—	3	1	no	—
78	C₃	—	3	3	no	—
79	C₃	—	9	3	no	—
80	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
3. C₁₃×#6869	C₃	semidirect
14. #10624694	C₁₃	direct (N × H)
29. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
30. #6869	C₃×C₁₃	semidirect
67. C₁₃	#10624694	direct (N × H)

Subgroups — C13×#10624694 #23744845

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624694 #23744845