Subgroups — C₁₃×#10624713 #23744864

Order 9477.

172 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×C₉⋊C₂₇	C₃	1	6	yes	maximal, complemented
3	C₁₃×C₃²⋊C₂₇	C₃	1	3	yes	maximal
4	C₁₃×#6864	C₃	1	2	yes	maximal, complemented
5	C₉×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×C₂₇	C₃²	1	3	yes	—
8	C₃×C₁₃×C₂₇	C₃²	1	6	yes	—
9	C₁₃×C₉⋊C₉	C₉	1	6	yes	—
10	C₁₃×C₃²⋊C₉	C₉	1	3	yes	—
11	C₉²×C₁₃	C₃²	1	1	yes	characteristic
12	C₉²×C₁₃	C₃²	1	2	yes	—
13	#10624713	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₃	—	3	3	no	—
16	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
17	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
18	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×C₂₇	—	3	3	no	—
21	C₁₃×C₂₇	—	3	6	no	—
22	#6887	C₃×C₁₃	1	1	yes	characteristic
23	C₉⋊C₂₇	C₃×C₁₃	1	6	yes	complemented
24	C₃²⋊C₂₇	C₃×C₁₃	1	3	yes	—
25	#6864	C₃×C₁₃	1	2	yes	complemented
26	C₉×C₂₇	C₃×C₁₃	1	1	yes	characteristic, complemented
27	C₃²×C₁₃	—	3	1	no	—
28	C₃²×C₁₃	—	3	3	no	—
29	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
30	C₉×C₁₃	—	3	2	no	—
31	C₉×C₁₃	—	3	3	no	—
32	C₉×C₁₃	—	3	6	no	—
33	C₉×C₁₃	#737	1	3	yes	—
34	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
35	C₃×C₂₇	C₃²×C₁₃	1	3	yes	—
36	C₃×C₂₇	C₃²×C₁₃	1	6	yes	—
37	C₉⋊C₉	C₉×C₁₃	1	6	yes	—
38	C₃²⋊C₉	C₉×C₁₃	1	3	yes	—
39	C₉²	C₃²×C₁₃	1	1	yes	characteristic
40	C₉²	C₃²×C₁₃	1	2	yes	—
41	C₃×C₁₃	—	9	1	no	—
42	C₃×C₁₃	#6887	1	1	yes	characteristic
43	C₃×C₁₃	#6903	1	3	yes	—
44	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
47	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
48	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
49	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
50	C₂₇	—	3	3	no	—
51	C₂₇	—	3	6	no	—
52	C₁₃	#10624713	1	1	yes	characteristic, direct product factor, Sylow
53	C₃²	—	3	1	no	—
54	C₃²	—	3	3	no	—
55	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
56	C₉	—	3	2	no	—
57	C₉	—	3	3	no	—
58	C₉	—	3	6	no	—
59	C₉	C₁₃×#737	1	3	yes	—
60	C₃	—	9	1	no	—
61	C₃	C₁₃×#6887	1	1	yes	characteristic
62	C₃	C₁₃×#6903	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₉⋊C₂₇	C₃	semidirect
4. C₁₃×#6864	C₃	semidirect
5. C₉×C₁₃×C₂₇	C₃	semidirect
13. #10624713	C₁₃	direct (N × H)
23. C₉⋊C₂₇	C₃×C₁₃	semidirect
25. #6864	C₃×C₁₃	semidirect
26. C₉×C₂₇	C₃×C₁₃	semidirect
52. C₁₃	#10624713	direct (N × H)

Subgroups — C13×#10624713 #23744864

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624713 #23744864