Subgroups — C₁₃×#10624683 #23744834

Order 9477.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₁₃×C₃²⋊C₂₇	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	3	no	—
6	C₃²×C₉×C₁₃	—	3	6	no	—
7	C₃²×C₉×C₁₃	C₉	1	2	yes	—
8	C₃²×C₉×C₁₃	C₉	1	6	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₁₃×C₂₇⋊C₃	—	3	9	no	—
12	C₃×C₁₃×C₂₇	C₃²	1	9	yes	complemented
13	#10624683	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	3	3	no	—
15	C₃³×C₁₃	—	3	9	no	—
16	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
17	C₃³×C₁₃	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₁₃	—	3	6	no	—
19	C₃×C₉×C₁₃	—	3	18	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	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
29	C₃×C₂₇⋊C₃	C₃×C₁₃	1	3	yes	complemented
30	C₃²⋊C₂₇	C₃×C₁₃	1	9	yes	complemented
31	C₃²×C₁₃	—	3	27	no	—
32	C₃²×C₁₃	—	3	3	no	—
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	3	6	no	—
35	C₃²×C₁₃	C₃²⋊C₉	1	3	yes	—
36	C₃²×C₁₃	C₂₇⋊C₃	1	9	yes	complemented
37	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
38	C₉×C₁₃	—	3	6	no	—
39	C₉×C₁₃	C₃²⋊C₉	1	6	yes	—
40	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
42	C₃⁴	C₉×C₁₃	1	1	yes	characteristic
43	C₃²×C₉	—	3	3	no	—
44	C₃²×C₉	—	3	6	no	—
45	C₃²×C₉	C₉×C₁₃	1	2	yes	—
46	C₃²×C₉	C₉×C₁₃	1	6	yes	—
47	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
48	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
49	C₂₇⋊C₃	—	3	9	no	—
50	C₃×C₂₇	C₃²×C₁₃	1	9	yes	complemented
51	C₃×C₁₃	—	3	3	no	—
52	C₃×C₁₃	—	3	9	no	—
53	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
54	C₃×C₁₃	C₃×C₂₇⋊C₃	1	3	yes	—
55	C₃³	—	3	3	no	—
56	C₃³	—	3	9	no	—
57	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
58	C₃³	C₃×C₉×C₁₃	1	3	yes	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	3	18	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	6	no	—
63	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
64	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
65	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
66	C₃×C₉	C₁₃×3₋¹⁺²	1	6	yes	—
67	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
68	C₂₇	—	3	9	no	—
69	C₁₃	#10624683	1	1	yes	characteristic, direct product factor, Sylow
70	C₃²	—	3	27	no	—
71	C₃²	—	3	3	no	—
72	C₃²	—	3	3	no	—
73	C₃²	—	3	6	no	—
74	C₃²	C₁₃×C₃²⋊C₉	1	3	yes	—
75	C₃²	C₁₃×C₂₇⋊C₃	1	9	yes	complemented
76	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
77	C₉	—	3	6	no	—
78	C₉	C₁₃×C₃²⋊C₉	1	6	yes	—
79	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
80	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
81	C₃	—	3	3	no	—
82	C₃	—	3	9	no	—
83	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic
84	C₃	C₃×C₁₃×C₂₇⋊C₃	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	C₃⁴×C₁₃	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. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
3. C₁₃×C₃²⋊C₂₇	C₃	semidirect
12. C₃×C₁₃×C₂₇	C₃²	semidirect
13. #10624683	C₁₃	direct (N × H)
29. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
30. C₃²⋊C₂₇	C₃×C₁₃	semidirect
36. C₃²×C₁₃	C₂₇⋊C₃	semidirect
50. C₃×C₂₇	C₃²×C₁₃	semidirect
69. C₁₃	#10624683	direct (N × H)
75. C₃²	C₁₃×C₂₇⋊C₃	semidirect

Subgroups — C13×#10624683 #23744834

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624683 #23744834