Subgroups — C₁₃×#10624711 #23744862

Order 9477.

206 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	C₁₃×#6864	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₁₃	C₉	1	1	yes	characteristic
6	C₃²×C₉×C₁₃	C₉	1	2	yes	—
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	1	yes	characteristic
11	C₉²×C₁₃	C₉	1	2	yes	—
12	C₉²×C₁₃	C₉	1	1	yes	characteristic
13	C₉²×C₁₃	C₃²	1	1	yes	characteristic
14	C₉²×C₁₃	C₃²	1	2	yes	—
15	#10624711	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₁₃	—	3	3	no	—
18	C₃×C₉×C₁₃	—	3	6	no	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
25	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
26	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
27	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
28	C₁₃×C₂₇	—	3	9	no	—
29	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
30	C₉⋊C₂₇	C₃×C₁₃	1	6	yes	complemented
31	C₃²⋊C₂₇	C₃×C₁₃	1	3	yes	—
32	#6864	C₃×C₁₃	1	3	yes	complemented
33	C₃²×C₁₃	—	3	1	no	—
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	C₂₇⋊C₃	1	3	yes	—
36	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
37	C₉×C₁₃	—	3	1	no	—
38	C₉×C₁₃	—	3	1	no	—
39	C₉×C₁₃	—	3	1	no	—
40	C₉×C₁₃	—	3	2	no	—
41	C₉×C₁₃	—	3	2	no	—
42	C₉×C₁₃	—	3	2	no	—
43	C₉×C₁₃	C₂₇⋊C₃	1	6	yes	—
44	C₉×C₁₃	#737	1	3	yes	—
45	C₃²×C₉	C₉×C₁₃	1	1	yes	characteristic
46	C₃²×C₉	C₉×C₁₃	1	2	yes	—
47	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
48	C₃×C₂₇	C₃²×C₁₃	1	9	yes	—
49	C₉²	C₉×C₁₃	1	2	yes	—
50	C₉²	C₉×C₁₃	1	1	yes	characteristic
51	C₉²	C₉×C₁₃	1	2	yes	—
52	C₉²	C₉×C₁₃	1	1	yes	characteristic
53	C₉²	C₃²×C₁₃	1	1	yes	characteristic
54	C₉²	C₃²×C₁₃	1	2	yes	—
55	C₃×C₁₃	—	3	3	no	—
56	C₃×C₁₃	#6887	1	1	yes	characteristic
57	C₃×C₁₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic
58	C₃×C₁₃	C₃×C₂₇⋊C₃	1	2	yes	—
59	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	6	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
64	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
65	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
66	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
67	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
68	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
69	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
70	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
71	C₂₇	—	3	9	no	—
72	C₁₃	#10624711	1	1	yes	characteristic, direct product factor, Sylow
73	C₃²	—	3	1	no	—
74	C₃²	—	3	2	no	—
75	C₃²	C₁₃×C₂₇⋊C₃	1	3	yes	—
76	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
77	C₉	—	3	1	no	—
78	C₉	—	3	1	no	—
79	C₉	—	3	1	no	—
80	C₉	—	3	2	no	—
81	C₉	—	3	2	no	—
82	C₉	—	3	2	no	—
83	C₉	C₁₃×C₂₇⋊C₃	1	6	yes	—
84	C₉	C₁₃×#737	1	3	yes	—
85	C₃	—	3	3	no	—
86	C₃	C₁₃×#6887	1	1	yes	characteristic
87	C₃	C₃×C₁₃×C₂₇⋊C₃	1	1	yes	characteristic
88	C₃	C₃×C₁₃×C₂₇⋊C₃	1	2	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
15. #10624711	C₁₃	direct (N × H)
30. C₉⋊C₂₇	C₃×C₁₃	semidirect
32. #6864	C₃×C₁₃	semidirect
72. C₁₃	#10624711	direct (N × H)

Subgroups — C13×#10624711 #23744862

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624711 #23744862