Subgroups — C₁₃×#10624900 #23745051

Order 9477.

730 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6895	C₃	1	8	yes	maximal, complemented
3	C₁₃×#6894	C₃	1	8	yes	maximal, complemented
4	C₁₃×#6894	C₃	1	16	yes	maximal, complemented
5	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
6	C₉×C₁₃×H(3,𝔽₃)	C₃	1	2	yes	maximal
7	C₃×C₁₃×C₉⋊C₉	C₃	1	4	yes	maximal, complemented
8	C₁₃×#737	—	3	9	no	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	8	yes	—
10	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
11	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
13	C₃²×C₉×C₁₃	C₃²	1	8	yes	—
14	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
15	C₁₃×C₉⋊C₉	C₃²	1	16	yes	—
16	C₁₃×C₉⋊C₉	C₃²	1	8	yes	—
17	C₁₃×C₉⋊C₉	C₃²	1	8	yes	—
18	C₁₃×C₉⋊C₉	C₃²	1	48	yes	—
19	C₁₃×C₃²⋊C₉	C₃²	1	8	yes	—
20	C₁₃×C₃²⋊C₉	C₃²	1	16	yes	—
21	#10624900	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃³×C₁₃	C₃³	1	4	yes	—
23	C₁₃×3₋¹⁺²	—	3	24	no	—
24	C₁₃×H(3,𝔽₃)	3₋¹⁺²	1	9	yes	—
25	C₃×C₉×C₁₃	—	3	12	no	—
26	C₃×C₉×C₁₃	—	3	12	no	—
27	C₃×C₉×C₁₃	—	9	8	no	—
28	C₃×C₉×C₁₃	C₃³	1	8	yes	—
29	C₃×C₉×C₁₃	C₃³	1	16	yes	—
30	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
31	C₃×C₉×C₁₃	C₃³	1	2	yes	—
32	C₃×C₉×C₁₃	C₃³	1	8	yes	—
33	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
34	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
35	#6895	C₃×C₁₃	1	8	yes	complemented
36	#6894	C₃×C₁₃	1	8	yes	complemented
37	#6894	C₃×C₁₃	1	16	yes	complemented
38	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
39	C₉×H(3,𝔽₃)	C₃×C₁₃	1	2	yes	—
40	C₃×C₉⋊C₉	C₃×C₁₃	1	4	yes	complemented
41	C₃²×C₁₃	—	3	4	no	—
42	C₃²×C₁₃	—	3	8	no	—
43	C₃²×C₁₃	C₃×3₋¹⁺²	1	12	yes	—
44	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
45	C₉×C₁₃	—	3	1	no	—
46	C₉×C₁₃	—	3	8	no	—
47	C₉×C₁₃	—	3	8	no	—
48	C₉×C₁₃	—	3	2	no	—
49	C₉×C₁₃	—	3	16	no	—
50	C₉×C₁₃	#737	1	3	yes	complemented
51	#737	—	3	9	no	—
52	C₃×3₋¹⁺²	C₃²×C₁₃	1	8	yes	—
53	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
54	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
55	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
56	C₃²×C₉	C₃²×C₁₃	1	8	yes	—
57	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
58	C₉⋊C₉	C₃²×C₁₃	1	16	yes	—
59	C₉⋊C₉	C₃²×C₁₃	1	8	yes	—
60	C₉⋊C₉	C₃²×C₁₃	1	8	yes	—
61	C₉⋊C₉	C₃²×C₁₃	1	48	yes	—
62	C₃²⋊C₉	C₃²×C₁₃	1	8	yes	—
63	C₃²⋊C₉	C₃²×C₁₃	1	16	yes	—
64	C₃×C₁₃	—	3	12	no	—
65	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
66	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
67	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
68	C₃³	C₃³×C₁₃	1	4	yes	—
69	3₋¹⁺²	—	3	24	no	—
70	H(3,𝔽₃)	C₁₃×3₋¹⁺²	1	9	yes	—
71	C₃×C₉	—	3	12	no	—
72	C₃×C₉	—	3	12	no	—
73	C₃×C₉	—	9	8	no	—
74	C₃×C₉	C₃³×C₁₃	1	8	yes	—
75	C₃×C₉	C₃³×C₁₃	1	16	yes	—
76	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
77	C₃×C₉	C₃³×C₁₃	1	2	yes	—
78	C₃×C₉	C₃³×C₁₃	1	8	yes	—
79	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
80	C₁₃	#10624900	1	1	yes	characteristic, direct product factor, Sylow
81	C₃²	—	3	4	no	—
82	C₃²	—	3	8	no	—
83	C₃²	C₃×C₁₃×3₋¹⁺²	1	12	yes	—
84	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
85	C₉	—	3	1	no	—
86	C₉	—	3	8	no	—
87	C₉	—	3	8	no	—
88	C₉	—	3	2	no	—
89	C₉	—	3	16	no	—
90	C₉	C₁₃×#737	1	3	yes	complemented
91	C₃	—	3	12	no	—
92	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
93	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
94	C₃	C₁₃×3₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6895	C₃	semidirect
3. C₁₃×#6894	C₃	semidirect
4. C₁₃×#6894	C₃	semidirect
7. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
21. #10624900	C₁₃	direct (N × H)
35. #6895	C₃×C₁₃	semidirect
36. #6894	C₃×C₁₃	semidirect
37. #6894	C₃×C₁₃	semidirect
40. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
50. C₉×C₁₃	#737	semidirect
80. C₁₃	#10624900	direct (N × H)
90. C₉	C₁₃×#737	semidirect

Subgroups — C13×#10624900 #23745051

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624900 #23745051