Subgroups — C₁₃×#10624930 #23745081

Order 9477.

1118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×3₋¹⁺⁴	C₃	1	2	yes	maximal, complemented
2	C₁₃×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6909	C₃	1	24	yes	maximal, complemented
5	C₃×C₁₃×AΣL(1,𝔽₂₇)	C₃	1	12	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	4	yes	complemented
7	C₁₃×#737	—	3	18	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)	—	3	9	no	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
12	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	8	yes	complemented
13	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	12	yes	complemented
14	C₁₃×AΣL(1,𝔽₂₇)	C₃²	1	9	yes	complemented
15	C₁₃×AΣL(1,𝔽₂₇)	C₃²	1	72	yes	complemented
16	#10624930	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	3	12	no	—
18	C₃³×C₁₃	—	3	12	no	—
19	C₃³×C₁₃	—	9	12	no	—
20	C₃³×C₁₃	C₃³	1	1	yes	characteristic
21	C₃³×C₁₃	C₃³	1	8	yes	—
22	C₃³×C₁₃	C₃³	1	4	yes	—
23	C₁₃×3₋¹⁺²	—	3	48	no	—
24	C₁₃×3₋¹⁺²	C₃³	1	18	yes	—
25	C₁₃×H(3,𝔽₃)	—	3	24	no	—
26	C₁₃×H(3,𝔽₃)	—	3	24	no	—
27	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
28	C₁₃×H(3,𝔽₃)	C₃³	1	9	yes	—
29	C₃×C₉×C₁₃	—	3	24	no	—
30	3₋¹⁺⁴	C₃×C₁₃	1	2	yes	complemented
31	H(5,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic, complemented
32	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic, complemented
33	#6909	C₃×C₁₃	1	24	yes	complemented
34	C₃×AΣL(1,𝔽₂₇)	C₃×C₁₃	1	12	yes	complemented
35	C₃²×C₁₃	—	3	3	no	—
36	C₃²×C₁₃	—	3	1	no	—
37	C₃²×C₁₃	—	3	8	no	—
38	C₃²×C₁₃	—	3	9	no	—
39	C₃²×C₁₃	—	9	4	no	—
40	C₃²×C₁₃	—	9	36	no	—
41	C₃²×C₁₃	—	9	8	no	—
42	C₃²×C₁₃	—	27	12	no	—
43	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
44	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
45	C₉×C₁₃	—	3	18	no	—
46	C₃⁴	C₃²×C₁₃	1	4	yes	complemented
47	#737	—	3	18	no	—
48	C₃×3₋¹⁺²	C₃²×C₁₃	1	24	yes	complemented
49	C₃×H(3,𝔽₃)	—	3	9	no	—
50	C₃×H(3,𝔽₃)	—	3	9	no	—
51	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
52	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	8	yes	complemented
53	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	12	yes	complemented
54	AΣL(1,𝔽₂₇)	C₃²×C₁₃	1	9	yes	complemented
55	AΣL(1,𝔽₂₇)	C₃²×C₁₃	1	72	yes	complemented
56	C₃×C₁₃	—	3	3	no	—
57	C₃×C₁₃	—	3	1	no	—
58	C₃×C₁₃	—	3	12	no	—
59	C₃×C₁₃	—	9	8	no	—
60	C₃×C₁₃	—	9	9	no	—
61	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
62	C₃³	—	3	12	no	—
63	C₃³	—	3	12	no	—
64	C₃³	—	9	12	no	—
65	C₃³	C₃³×C₁₃	1	1	yes	characteristic
66	C₃³	C₃³×C₁₃	1	8	yes	—
67	C₃³	C₃³×C₁₃	1	4	yes	—
68	3₋¹⁺²	—	3	48	no	—
69	3₋¹⁺²	C₃³×C₁₃	1	18	yes	—
70	H(3,𝔽₃)	—	3	24	no	—
71	H(3,𝔽₃)	—	3	24	no	—
72	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	9	yes	—
73	H(3,𝔽₃)	C₃³×C₁₃	1	9	yes	—
74	C₃×C₉	—	3	24	no	—
75	C₁₃	#10624930	1	1	yes	characteristic, direct product factor, Sylow
76	C₃²	—	3	3	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	3	8	no	—
79	C₃²	—	3	9	no	—
80	C₃²	—	9	4	no	—
81	C₃²	—	9	36	no	—
82	C₃²	—	9	8	no	—
83	C₃²	—	27	12	no	—
84	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
85	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
86	C₉	—	3	18	no	—
87	C₃	—	3	1	no	—
88	C₃	—	3	3	no	—
89	C₃	—	3	12	no	—
90	C₃	—	9	8	no	—
91	C₃	—	9	9	no	—
92	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×3₋¹⁺⁴	C₃	semidirect
2. C₁₃×H(5,𝔽₃)	C₃	semidirect
3. C₃²×C₁₃×H(3,𝔽₃)	C₃	semidirect
4. C₁₃×#6909	C₃	semidirect
5. C₃×C₁₃×AΣL(1,𝔽₂₇)	C₃	semidirect
6. C₃⁴×C₁₃	C₃²	semidirect
8. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
12. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
13. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
14. C₁₃×AΣL(1,𝔽₂₇)	C₃²	semidirect
15. C₁₃×AΣL(1,𝔽₂₇)	C₃²	semidirect
16. #10624930	C₁₃	direct (N × H)
30. 3₋¹⁺⁴	C₃×C₁₃	semidirect
31. H(5,𝔽₃)	C₃×C₁₃	semidirect
32. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
33. #6909	C₃×C₁₃	semidirect
34. C₃×AΣL(1,𝔽₂₇)	C₃×C₁₃	semidirect
46. C₃⁴	C₃²×C₁₃	semidirect
48. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
52. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
53. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
54. AΣL(1,𝔽₂₇)	C₃²×C₁₃	semidirect
55. AΣL(1,𝔽₂₇)	C₃²×C₁₃	semidirect
75. C₁₃	#10624930	direct (N × H)

Subgroups — C13×#10624930 #23745081

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624930 #23745081