Subgroups — C₁₃×#10624710 #23744861

Order 9477.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²×C₁₃	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	C₉×C₁₃×C₂₇	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₁₃	C₉	1	2	yes	—
6	C₃²×C₉×C₁₃	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×C₂₇	C₃²	1	9	yes	—
9	C₉²×C₁₃	C₉	1	2	yes	—
10	C₉²×C₁₃	C₉	1	4	yes	—
11	C₉²×C₁₃	C₃²	1	2	yes	—
12	C₉²×C₁₃	C₃²	1	1	yes	characteristic
13	#10624710	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₃	—	3	6	no	—
16	C₃×C₉×C₁₃	—	3	3	no	—
17	C₃×C₉×C₁₃	C₂₇	1	9	yes	complemented
18	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₁₃	C₃×C₉	1	4	yes	—
20	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
23	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
24	C₁₃×C₂₇	—	3	9	no	—
25	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
26	C₉⋊C₂₇	C₃×C₁₃	1	6	yes	complemented
27	C₃²⋊C₂₇	C₃×C₁₃	1	3	yes	—
28	C₉×C₂₇	C₃×C₁₃	1	3	yes	complemented
29	C₃²×C₁₃	—	3	1	no	—
30	C₃²×C₁₃	—	3	2	no	—
31	C₃²×C₁₃	C₃×C₂₇	1	3	yes	—
32	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
33	C₉×C₁₃	—	3	2	no	—
34	C₉×C₁₃	—	3	4	no	—
35	C₉×C₁₃	C₃×C₂₇	1	6	yes	—
36	C₉×C₁₃	C₃×C₂₇	1	3	yes	—
37	C₉×C₁₃	C₂₇⋊C₃	1	6	yes	—
38	C₉×C₁₃	#737	1	3	yes	—
39	C₃²×C₉	C₉×C₁₃	1	2	yes	—
40	C₃²×C₉	C₉×C₁₃	1	1	yes	characteristic
41	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
42	C₃×C₂₇	C₃²×C₁₃	1	9	yes	—
43	C₉²	C₉×C₁₃	1	2	yes	—
44	C₉²	C₉×C₁₃	1	4	yes	—
45	C₉²	C₃²×C₁₃	1	2	yes	—
46	C₉²	C₃²×C₁₃	1	1	yes	characteristic
47	C₃×C₁₃	—	3	3	no	—
48	C₃×C₁₃	#6887	1	1	yes	characteristic
49	C₃×C₁₃	C₃²×C₂₇	1	1	yes	characteristic
50	C₃×C₁₃	C₃×C₂₇⋊C₃	1	2	yes	—
51	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
52	C₃×C₉	—	3	6	no	—
53	C₃×C₉	—	3	3	no	—
54	C₃×C₉	C₁₃×C₂₇	1	9	yes	complemented
55	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
56	C₃×C₉	C₃×C₉×C₁₃	1	4	yes	—
57	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
58	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
59	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
60	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
61	C₂₇	—	3	9	no	—
62	C₁₃	#10624710	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	—	3	1	no	—
64	C₃²	—	3	2	no	—
65	C₃²	C₃×C₁₃×C₂₇	1	3	yes	—
66	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
67	C₉	—	3	2	no	—
68	C₉	—	3	4	no	—
69	C₉	C₃×C₁₃×C₂₇	1	6	yes	—
70	C₉	C₃×C₁₃×C₂₇	1	3	yes	—
71	C₉	C₁₃×C₂₇⋊C₃	1	6	yes	—
72	C₉	C₁₃×#737	1	3	yes	—
73	C₃	—	3	3	no	—
74	C₃	C₁₃×#6887	1	1	yes	characteristic
75	C₃	C₃²×C₁₃×C₂₇	1	1	yes	characteristic
76	C₃	C₃×C₁₃×C₂₇⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₉²×C₁₃	C₃²
commutator	C₃	C₃²×C₁₃×C₂₇
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃²×C₁₃	C₃²×C₉
prime radical	C₃³×C₁₃	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉²×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. C₉×C₁₃×C₂₇	C₃	semidirect
13. #10624710	C₁₃	direct (N × H)
17. C₃×C₉×C₁₃	C₂₇	semidirect
26. C₉⋊C₂₇	C₃×C₁₃	semidirect
28. C₉×C₂₇	C₃×C₁₃	semidirect
54. C₃×C₉	C₁₃×C₂₇	semidirect
62. C₁₃	#10624710	direct (N × H)

Subgroups — C13×#10624710 #23744861

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624710 #23744861