Subgroups — C₁₃×#10624931 #23745082

Order 9477.

978 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
3	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6910	C₃	1	24	yes	maximal, complemented
5	C₃×C₁₃×#731	C₃	1	12	yes	maximal, complemented
6	C₁₃×#737	—	3	9	no	—
7	C₁₃×#737	—	3	18	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	24	yes	complemented
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	8	yes	complemented
10	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	12	yes	—
12	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₁₃	C₃²	1	4	yes	complemented
14	C₁₃×#731	C₃²	1	9	yes	complemented
15	C₁₃×#731	C₃²	1	72	yes	complemented
16	#10624931	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	3	12	no	—
18	C₃³×C₁₃	C₃³	1	4	yes	—
19	C₁₃×3₋¹⁺²	—	3	48	no	—
20	C₁₃×3₋¹⁺²	—	3	24	no	—
21	C₁₃×3₋¹⁺²	C₃³	1	18	yes	—
22	C₁₃×H(3,𝔽₃)	—	3	24	no	—
23	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
24	C₁₃×H(3,𝔽₃)	C₃³	1	9	yes	—
25	C₃×C₉×C₁₃	—	3	12	no	—
26	C₃×C₉×C₁₃	—	3	24	no	—
27	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
28	C₃×C₉×C₁₃	C₃³	1	8	yes	—
29	3₋¹⁺⁴	C₃×C₁₃	1	2	yes	complemented
30	H(5,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
31	C₃×#737	C₃×C₁₃	1	1	yes	characteristic, complemented
32	#6910	C₃×C₁₃	1	24	yes	complemented
33	C₃×#731	C₃×C₁₃	1	12	yes	complemented
34	C₃²×C₁₃	—	3	9	no	—
35	C₃²×C₁₃	—	9	4	no	—
36	C₃²×C₁₃	—	27	12	no	—
37	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
38	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
39	C₉×C₁₃	—	3	1	no	—
40	C₉×C₁₃	—	3	18	no	—
41	C₉×C₁₃	—	3	8	no	—
42	#737	—	3	9	no	—
43	#737	—	3	18	no	—
44	C₃×3₋¹⁺²	C₃²×C₁₃	1	24	yes	complemented
45	C₃×3₋¹⁺²	C₃²×C₁₃	1	8	yes	complemented
46	C₃×H(3,𝔽₃)	—	3	9	no	—
47	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	12	yes	—
48	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
49	C₃²×C₉	C₃²×C₁₃	1	4	yes	complemented
50	#731	C₃²×C₁₃	1	9	yes	complemented
51	#731	C₃²×C₁₃	1	72	yes	complemented
52	C₃×C₁₃	—	3	1	no	—
53	C₃×C₁₃	—	3	12	no	—
54	C₃×C₁₃	—	9	9	no	—
55	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
56	C₃³	—	3	12	no	—
57	C₃³	C₃³×C₁₃	1	4	yes	—
58	3₋¹⁺²	—	3	48	no	—
59	3₋¹⁺²	—	3	24	no	—
60	3₋¹⁺²	C₃³×C₁₃	1	18	yes	—
61	H(3,𝔽₃)	—	3	24	no	—
62	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	9	yes	—
63	H(3,𝔽₃)	C₃³×C₁₃	1	9	yes	—
64	C₃×C₉	—	3	12	no	—
65	C₃×C₉	—	3	24	no	—
66	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
67	C₃×C₉	C₃³×C₁₃	1	8	yes	—
68	C₁₃	#10624931	1	1	yes	characteristic, direct product factor, Sylow
69	C₃²	—	3	9	no	—
70	C₃²	—	9	4	no	—
71	C₃²	—	27	12	no	—
72	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
73	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
74	C₉	—	3	1	no	—
75	C₉	—	3	18	no	—
76	C₉	—	3	8	no	—
77	C₃	—	3	1	no	—
78	C₃	—	3	12	no	—
79	C₃	—	9	9	no	—
80	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
prime radical	C₁₃×H(5,𝔽₃)	C₃
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
3. C₃×C₁₃×#737	C₃	semidirect
4. C₁₃×#6910	C₃	semidirect
5. C₃×C₁₃×#731	C₃	semidirect
8. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
9. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
13. C₃²×C₉×C₁₃	C₃²	semidirect
14. C₁₃×#731	C₃²	semidirect
15. C₁₃×#731	C₃²	semidirect
16. #10624931	C₁₃	direct (N × H)
29. 3₋¹⁺⁴	C₃×C₁₃	semidirect
31. C₃×#737	C₃×C₁₃	semidirect
32. #6910	C₃×C₁₃	semidirect
33. C₃×#731	C₃×C₁₃	semidirect
44. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
45. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
49. C₃²×C₉	C₃²×C₁₃	semidirect
50. #731	C₃²×C₁₃	semidirect
51. #731	C₃²×C₁₃	semidirect
68. C₁₃	#10624931	direct (N × H)

Subgroups — C13×#10624931 #23745082

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624931 #23745082