Subgroups — C₁₃×#10624841 #23744992

Order 9477.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6908	C₃	1	3	yes	maximal, complemented
2	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6880	C₃	1	2	yes	maximal, complemented
4	C₁₃×#6879	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#6878	C₃	1	6	yes	maximal, complemented
6	C₁₃×#737	—	3	3	no	—
7	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
8	C₁₃×#733	C₃²	1	6	yes	—
9	C₁₃×#732	C₃²	1	3	yes	—
10	C₁₃×#731	—	3	3	no	—
11	C₁₃×AΣL(1,𝔽₂₇)	—	3	3	no	—
12	C₁₃×C₉⋊C₉	—	3	1	no	—
13	C₁₃×C₉⋊C₉	—	3	1	no	—
14	C₁₃×C₃²⋊C₉	—	3	1	no	—
15	C₉²×C₁₃	C₃²	1	2	yes	—
16	C₉²×C₁₃	C₃²	1	1	yes	characteristic
17	#10624841	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₁₃×3₋¹⁺²	—	3	6	no	—
20	C₁₃×3₋¹⁺²	—	9	6	no	—
21	C₁₃×H(3,𝔽₃)	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	3	no	—
23	C₃×C₉×C₁₃	—	3	2	no	—
24	C₃×C₉×C₁₃	—	3	1	no	—
25	C₃×C₉×C₁₃	—	9	3	no	—
26	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
29	#6908	C₃×C₁₃	1	3	yes	complemented
30	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
31	#6880	C₃×C₁₃	1	2	yes	complemented
32	#6879	C₃×C₁₃	1	1	yes	characteristic, complemented
33	#6878	C₃×C₁₃	1	6	yes	complemented
34	C₃²×C₁₃	—	3	1	no	—
35	C₃²×C₁₃	—	9	1	no	—
36	C₃²×C₁₃	—	9	3	no	—
37	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₉×C₁₃	—	3	1	no	—
39	C₉×C₁₃	—	3	1	no	—
40	C₉×C₁₃	—	9	2	no	—
41	C₉×C₁₃	—	9	1	no	—
42	C₉×C₁₃	—	9	6	no	—
43	C₉×C₁₃	#732	1	3	yes	—
44	#737	—	3	3	no	—
45	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
46	#733	C₃²×C₁₃	1	6	yes	—
47	#732	C₃²×C₁₃	1	3	yes	—
48	#731	—	3	3	no	—
49	AΣL(1,𝔽₂₇)	—	3	3	no	—
50	C₉⋊C₉	—	3	1	no	—
51	C₉⋊C₉	—	3	1	no	—
52	C₃²⋊C₉	—	3	1	no	—
53	C₉²	C₃²×C₁₃	1	2	yes	—
54	C₉²	C₃²×C₁₃	1	1	yes	characteristic
55	C₃×C₁₃	—	3	1	no	—
56	C₃×C₁₃	—	9	1	no	—
57	C₃×C₁₃	—	27	3	no	—
58	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
59	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
60	3₋¹⁺²	—	3	6	no	—
61	3₋¹⁺²	—	9	6	no	—
62	H(3,𝔽₃)	—	3	3	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	3	2	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	9	3	no	—
67	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
68	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
69	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
70	C₁₃	#10624841	1	1	yes	characteristic, direct product factor, Sylow
71	C₃²	—	3	1	no	—
72	C₃²	—	9	1	no	—
73	C₃²	—	9	3	no	—
74	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
75	C₉	—	3	1	no	—
76	C₉	—	3	1	no	—
77	C₉	—	9	2	no	—
78	C₉	—	9	1	no	—
79	C₉	—	9	6	no	—
80	C₉	C₁₃×#732	1	3	yes	—
81	C₃	—	3	1	no	—
82	C₃	—	9	1	no	—
83	C₃	—	27	3	no	—
84	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	C₃×#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃×C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#6908	C₃	semidirect
2. C₁₃×#6887	C₃	semidirect
3. C₁₃×#6880	C₃	semidirect
4. C₁₃×#6879	C₃	semidirect
5. C₁₃×#6878	C₃	semidirect
17. #10624841	C₁₃	direct (N × H)
29. #6908	C₃×C₁₃	semidirect
30. #6887	C₃×C₁₃	semidirect
31. #6880	C₃×C₁₃	semidirect
32. #6879	C₃×C₁₃	semidirect
33. #6878	C₃×C₁₃	semidirect
70. C₁₃	#10624841	direct (N × H)

Subgroups — C13×#10624841 #23744992

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624841 #23744992