Subgroups — C₁₃×#10624681 #23744832

Order 9477.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#6864	C₃	1	6	yes	maximal, complemented
5	C₉×C₁₃×C₂₇	C₃	1	3	yes	maximal, complemented
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₁₃×C₂₇⋊C₃	C₉	1	18	yes	complemented
8	C₃×C₁₃×C₂₇	C₉	1	9	yes	complemented
9	C₃×C₁₃×C₂₇	C₃²	1	6	yes	—
10	C₃×C₁₃×C₂₇	C₃²	1	2	yes	—
11	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
12	C₁₃×C₉⋊C₉	C₉	1	6	yes	—
13	C₁₃×C₃²⋊C₉	C₉	1	3	yes	—
14	C₉²×C₁₃	C₃²	1	3	yes	—
15	#10624681	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
18	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
20	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
21	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×C₂₇	C₃×C₉	1	6	yes	—
23	C₁₃×C₂₇	C₃×C₉	1	3	yes	—
24	C₁₃×C₂₇	C₃×C₉	1	18	yes	—
25	C₃×C₂₇⋊C₃	C₃×C₁₃	1	2	yes	—
26	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic
27	#6887	C₃×C₁₃	1	1	yes	characteristic
28	#6864	C₃×C₁₃	1	6	yes	complemented
29	C₉×C₂₇	C₃×C₁₃	1	3	yes	complemented
30	C₃²×C₁₃	—	3	3	no	—
31	C₃²×C₁₃	C₉²	1	3	yes	—
32	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
33	C₉×C₁₃	—	3	9	no	—
34	C₉×C₁₃	C₉²	1	6	yes	—
35	C₉×C₁₃	C₃²×C₉	1	1	yes	characteristic
36	C₉×C₁₃	C₃²×C₉	1	2	yes	—
37	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
38	C₂₇⋊C₃	C₉×C₁₃	1	18	yes	complemented
39	C₃×C₂₇	C₉×C₁₃	1	9	yes	complemented
40	C₃×C₂₇	C₃²×C₁₃	1	6	yes	—
41	C₃×C₂₇	C₃²×C₁₃	1	2	yes	—
42	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
43	C₉⋊C₉	C₉×C₁₃	1	6	yes	—
44	C₃²⋊C₉	C₉×C₁₃	1	3	yes	—
45	C₉²	C₃²×C₁₃	1	3	yes	—
46	C₃×C₁₃	—	3	3	no	—
47	C₃×C₁₃	C₃×C₉²	1	1	yes	characteristic
48	C₃×C₁₃	#6903	1	3	yes	—
49	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
50	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
51	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
52	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
53	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
54	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
55	C₂₇	C₃×C₉×C₁₃	1	6	yes	—
56	C₂₇	C₃×C₉×C₁₃	1	3	yes	—
57	C₂₇	C₃×C₉×C₁₃	1	18	yes	—
58	C₁₃	#10624681	1	1	yes	characteristic, direct product factor, Sylow
59	C₃²	—	3	3	no	—
60	C₃²	C₉²×C₁₃	1	3	yes	—
61	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
62	C₉	—	3	9	no	—
63	C₉	C₉²×C₁₃	1	6	yes	—
64	C₉	C₃²×C₉×C₁₃	1	1	yes	characteristic
65	C₉	C₃²×C₉×C₁₃	1	2	yes	—
66	C₃	—	3	3	no	—
67	C₃	C₃×C₉²×C₁₃	1	1	yes	characteristic
68	C₃	C₁₃×#6903	1	3	yes	—

	subgroup	G/H
center	C₃×C₁₃×C₂₇	C₃²
commutator	C₃	C₃×C₉²×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃²×C₁₃	C₃²×C₉
prime radical	C₃³×C₁₃	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#6864	C₃	semidirect
5. C₉×C₁₃×C₂₇	C₃	semidirect
7. C₁₃×C₂₇⋊C₃	C₉	semidirect
8. C₃×C₁₃×C₂₇	C₉	semidirect
15. #10624681	C₁₃	direct (N × H)
28. #6864	C₃×C₁₃	semidirect
29. C₉×C₂₇	C₃×C₁₃	semidirect
38. C₂₇⋊C₃	C₉×C₁₃	semidirect
39. C₃×C₂₇	C₉×C₁₃	semidirect
58. C₁₃	#10624681	direct (N × H)

Subgroups — C13×#10624681 #23744832

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624681 #23744832