Subgroups — C₁₃×#10624894 #23745045

Order 9477.

1148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#737	C₃	1	3	yes	maximal, complemented
2	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6893	C₃	1	24	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	8	yes	maximal, complemented
5	C₃×C₁₃×C₃²⋊C₉	C₃	1	4	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	4	yes	—
7	C₁₃×#737	—	3	27	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	24	yes	complemented
9	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
10	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	8	yes	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₃	C₃²	1	12	yes	complemented
13	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
14	C₁₃×C₃²⋊C₉	C₃²	1	8	yes	—
15	C₁₃×C₃²⋊C₉	C₃²	1	24	yes	complemented
16	C₁₃×C₃²⋊C₉	C₃²	1	48	yes	complemented
17	#10624894	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	—	3	12	no	—
19	C₃³×C₁₃	—	3	12	no	—
20	C₃³×C₁₃	—	9	8	no	—
21	C₃³×C₁₃	C₃³	1	8	yes	—
22	C₃³×C₁₃	C₃³	1	4	yes	—
23	C₃³×C₁₃	C₃³	1	1	yes	characteristic
24	C₁₃×3₋¹⁺²	—	3	72	no	—
25	C₁₃×H(3,𝔽₃)	—	3	24	no	—
26	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
27	C₃×C₉×C₁₃	—	3	36	no	—
28	C₃×C₉×C₁₃	C₃³	1	3	yes	—
29	C₃×C₉×C₁₃	C₃³	1	24	yes	—
30	C₃×#737	C₃×C₁₃	1	3	yes	complemented
31	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
32	#6893	C₃×C₁₃	1	24	yes	complemented
33	#6891	C₃×C₁₃	1	8	yes	complemented
34	C₃×C₃²⋊C₉	C₃×C₁₃	1	4	yes	complemented
35	C₃²×C₁₃	—	3	1	no	—
36	C₃²×C₁₃	—	3	4	no	—
37	C₃²×C₁₃	—	3	2	no	—
38	C₃²×C₁₃	—	3	8	no	—
39	C₃²×C₁₃	—	3	8	no	—
40	C₃²×C₁₃	—	3	8	no	—
41	C₃²×C₁₃	—	3	16	no	—
42	C₃²×C₁₃	—	9	36	no	—
43	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
44	C₃²×C₁₃	#737	1	3	yes	complemented
45	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
46	C₉×C₁₃	—	3	3	no	—
47	C₉×C₁₃	—	3	24	no	—
48	C₃⁴	C₃²×C₁₃	1	4	yes	—
49	#737	—	3	27	no	—
50	C₃×3₋¹⁺²	C₃²×C₁₃	1	24	yes	complemented
51	C₃×H(3,𝔽₃)	—	3	9	no	—
52	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	8	yes	—
53	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
54	C₃²×C₉	C₃²×C₁₃	1	12	yes	complemented
55	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
56	C₃²⋊C₉	C₃²×C₁₃	1	8	yes	—
57	C₃²⋊C₉	C₃²×C₁₃	1	24	yes	complemented
58	C₃²⋊C₉	C₃²×C₁₃	1	48	yes	complemented
59	C₃×C₁₃	—	3	3	no	—
60	C₃×C₁₃	—	3	12	no	—
61	C₃×C₁₃	—	9	8	no	—
62	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
63	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
64	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
65	C₃³	—	3	12	no	—
66	C₃³	—	3	12	no	—
67	C₃³	—	9	8	no	—
68	C₃³	C₃³×C₁₃	1	8	yes	—
69	C₃³	C₃³×C₁₃	1	4	yes	—
70	C₃³	C₃³×C₁₃	1	1	yes	characteristic
71	3₋¹⁺²	—	3	72	no	—
72	H(3,𝔽₃)	—	3	24	no	—
73	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	9	yes	—
74	C₃×C₉	—	3	36	no	—
75	C₃×C₉	C₃³×C₁₃	1	3	yes	—
76	C₃×C₉	C₃³×C₁₃	1	24	yes	—
77	C₁₃	#10624894	1	1	yes	characteristic, direct product factor, Sylow
78	C₃²	—	3	1	no	—
79	C₃²	—	3	4	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	8	no	—
82	C₃²	—	3	8	no	—
83	C₃²	—	3	8	no	—
84	C₃²	—	3	16	no	—
85	C₃²	—	9	36	no	—
86	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
87	C₃²	C₁₃×#737	1	3	yes	complemented
88	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
89	C₉	—	3	3	no	—
90	C₉	—	3	24	no	—
91	C₃	—	3	3	no	—
92	C₃	—	3	12	no	—
93	C₃	—	9	8	no	—
94	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
95	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
96	C₃	C₁₃×3₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
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
1. C₃×C₁₃×#737	C₃	semidirect
3. C₁₃×#6893	C₃	semidirect
4. C₁₃×#6891	C₃	semidirect
5. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
8. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
12. C₃²×C₉×C₁₃	C₃²	semidirect
15. C₁₃×C₃²⋊C₉	C₃²	semidirect
16. C₁₃×C₃²⋊C₉	C₃²	semidirect
17. #10624894	C₁₃	direct (N × H)
30. C₃×#737	C₃×C₁₃	semidirect
32. #6893	C₃×C₁₃	semidirect
33. #6891	C₃×C₁₃	semidirect
34. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
44. C₃²×C₁₃	#737	semidirect
50. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
54. C₃²×C₉	C₃²×C₁₃	semidirect
57. C₃²⋊C₉	C₃²×C₁₃	semidirect
58. C₃²⋊C₉	C₃²×C₁₃	semidirect
77. C₁₃	#10624894	direct (N × H)
87. C₃²	C₁₃×#737	semidirect

Subgroups — C13×#10624894 #23745045

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624894 #23745045