Subgroups — C₁₃×#10624709 #23744860

Order 9477.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₃×C₁₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#6875	C₃	1	9	yes	maximal, complemented
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₁₃×C₂₇⋊C₃	—	3	2	no	—
7	C₁₃×C₂₇⋊C₃	—	3	2	no	—
8	C₁₃×C₂₇⋊C₃	C₉	1	6	yes	complemented
9	C₁₃×C₂₇⋊C₃	C₃²	1	6	yes	—
10	C₁₃×C₂₇⋊C₃	C₃²	1	3	yes	—
11	C₃×C₁₃×C₂₇	—	3	2	no	—
12	C₃×C₁₃×C₂₇	C₉	1	3	yes	complemented
13	C₁₃×C₉⋊C₉	—	3	1	no	—
14	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
15	C₁₃×C₃²⋊C₉	—	3	1	no	—
16	C₉²×C₁₃	—	3	1	no	—
17	#10624709	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	3₋¹⁺²	1	1	yes	characteristic
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₁₃	3₋¹⁺²	1	1	yes	characteristic
23	C₃×C₉×C₁₃	3₋¹⁺²	1	1	yes	characteristic
24	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
25	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
26	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
27	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
28	C₁₃×C₂₇	—	3	6	no	—
29	C₁₃×C₂₇	C₃×C₉	1	9	yes	—
30	C₃×C₂₇⋊C₃	C₃×C₁₃	1	2	yes	—
31	C₃×C₂₇⋊C₃	C₃×C₁₃	1	1	yes	characteristic
32	#6887	C₃×C₁₃	1	1	yes	characteristic
33	#6875	C₃×C₁₃	1	9	yes	complemented
34	C₃²×C₁₃	—	9	1	no	—
35	C₃²×C₁₃	C₉⋊C₉	1	2	yes	—
36	C₃²×C₁₃	C₉⋊C₉	1	1	yes	characteristic
37	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₉×C₁₃	—	9	3	no	—
39	C₉×C₁₃	C₉⋊C₉	1	2	yes	—
40	C₉×C₁₃	C₉⋊C₉	1	2	yes	—
41	C₉×C₁₃	C₉⋊C₉	1	1	yes	characteristic
42	C₉×C₁₃	C₉⋊C₉	1	1	yes	characteristic
43	C₉×C₁₃	C₃²×C₉	1	1	yes	characteristic
44	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
45	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
46	C₂₇⋊C₃	—	3	2	no	—
47	C₂₇⋊C₃	—	3	2	no	—
48	C₂₇⋊C₃	C₉×C₁₃	1	6	yes	complemented
49	C₂₇⋊C₃	C₃²×C₁₃	1	6	yes	—
50	C₂₇⋊C₃	C₃²×C₁₃	1	3	yes	—
51	C₃×C₂₇	—	3	2	no	—
52	C₃×C₂₇	C₉×C₁₃	1	3	yes	complemented
53	C₉⋊C₉	—	3	1	no	—
54	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
55	C₃²⋊C₉	—	3	1	no	—
56	C₉²	—	3	1	no	—
57	C₃×C₁₃	—	3	1	no	—
58	C₃×C₁₃	—	3	2	no	—
59	C₃×C₁₃	—	3	1	no	—
60	C₃×C₁₃	C₃×C₉⋊C₉	1	1	yes	characteristic
61	C₃³	C₁₃×3₋¹⁺²	1	1	yes	characteristic
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
64	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
65	C₃×C₉	C₁₃×3₋¹⁺²	1	1	yes	characteristic
66	C₃×C₉	C₁₃×3₋¹⁺²	1	1	yes	characteristic
67	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
68	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
69	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
70	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
71	C₂₇	—	3	6	no	—
72	C₂₇	C₃×C₉×C₁₃	1	9	yes	—
73	C₁₃	#10624709	1	1	yes	characteristic, direct product factor, Sylow
74	C₃²	—	9	1	no	—
75	C₃²	C₁₃×C₉⋊C₉	1	1	yes	characteristic
76	C₃²	C₁₃×C₉⋊C₉	1	2	yes	—
77	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
78	C₉	—	9	3	no	—
79	C₉	C₁₃×C₉⋊C₉	1	1	yes	characteristic
80	C₉	C₁₃×C₉⋊C₉	1	2	yes	—
81	C₉	C₁₃×C₉⋊C₉	1	2	yes	—
82	C₉	C₁₃×C₉⋊C₉	1	1	yes	characteristic
83	C₉	C₃²×C₉×C₁₃	1	1	yes	characteristic
84	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	—	3	2	no	—
88	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₁₃	C₉⋊C₉
commutator	C₉	C₃²×C₉×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃×C₁₃	C₃×C₉⋊C₉
prime radical	C₃³×C₁₃	3₋¹⁺²
LCS	G ▷ C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#6875	C₃	semidirect
8. C₁₃×C₂₇⋊C₃	C₉	semidirect
12. C₃×C₁₃×C₂₇	C₉	semidirect
17. #10624709	C₁₃	direct (N × H)
33. #6875	C₃×C₁₃	semidirect
48. C₂₇⋊C₃	C₉×C₁₃	semidirect
52. C₃×C₂₇	C₉×C₁₃	semidirect
73. C₁₃	#10624709	direct (N × H)

Subgroups — C13×#10624709 #23744860

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624709 #23744860