Subgroups — C₁₃×#10624887 #23745038

Order 9477.

698 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6900	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6899	C₃	1	6	yes	maximal, complemented
4	C₁₃×#6896	C₃	1	9	yes	maximal, complemented
5	C₁₃×#6894	C₃	1	6	yes	maximal, complemented
6	C₁₃×#6894	C₃	1	9	yes	maximal, complemented
7	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	3	yes	maximal
8	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#737	—	3	9	no	—
12	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
13	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
14	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
15	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
16	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
17	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
18	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
19	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
20	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
21	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
22	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
23	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
24	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
25	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
26	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
27	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
28	C₁₃×C₉⋊C₉	C₃²	1	36	yes	—
29	C₁₃×C₉⋊C₉	C₃²	1	18	yes	—
30	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
31	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
32	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
33	C₉²×C₁₃	C₃²	1	3	yes	—
34	C₉²×C₁₃	C₃²	1	3	yes	—
35	#10624887	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₃³×C₁₃	C₃³	1	3	yes	—
37	C₃³×C₁₃	C₃³	1	1	yes	characteristic
38	C₁₃×3₋¹⁺²	—	3	6	no	—
39	C₁₃×3₋¹⁺²	—	3	9	no	—
40	C₁₃×3₋¹⁺²	—	3	9	no	—
41	C₁₃×3₋¹⁺²	—	9	9	no	—
42	C₁₃×H(3,𝔽₃)	—	3	3	no	—
43	C₃×C₉×C₁₃	—	3	9	no	—
44	C₃×C₉×C₁₃	—	9	3	no	—
45	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
46	C₃×C₉×C₁₃	C₃³	1	9	yes	—
47	C₃×C₉×C₁₃	C₃³	1	9	yes	—
48	C₃×C₉×C₁₃	C₃³	1	6	yes	—
49	C₃×C₉×C₁₃	C₃³	1	6	yes	—
50	C₃×C₉×C₁₃	C₃³	1	3	yes	—
51	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
52	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
53	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
54	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
55	#6900	C₃×C₁₃	1	3	yes	complemented
56	#6899	C₃×C₁₃	1	6	yes	complemented
57	#6896	C₃×C₁₃	1	9	yes	complemented
58	#6894	C₃×C₁₃	1	6	yes	complemented
59	#6894	C₃×C₁₃	1	9	yes	complemented
60	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	3	yes	—
61	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
62	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
63	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
64	C₃²×C₁₃	—	3	3	no	—
65	C₃²×C₁₃	—	3	3	no	—
66	C₃²×C₁₃	—	3	9	no	—
67	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
68	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
69	C₉×C₁₃	—	3	6	no	—
70	C₉×C₁₃	—	3	6	no	—
71	C₉×C₁₃	—	3	3	no	—
72	C₉×C₁₃	—	3	9	no	—
73	C₉×C₁₃	—	3	9	no	—
74	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
75	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
76	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
77	#737	—	3	9	no	—
78	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
79	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
80	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
81	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
82	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
83	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
84	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
85	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
86	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
87	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
88	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
89	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
90	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
91	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
92	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
93	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
94	C₉⋊C₉	C₃²×C₁₃	1	36	yes	—
95	C₉⋊C₉	C₃²×C₁₃	1	18	yes	—
96	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
97	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
98	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
99	C₉²	C₃²×C₁₃	1	3	yes	—
100	C₉²	C₃²×C₁₃	1	3	yes	—
101	C₃×C₁₃	—	3	3	no	—
102	C₃×C₁₃	—	9	3	no	—
103	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
104	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	—
105	C₃³	C₃³×C₁₃	1	3	yes	—
106	C₃³	C₃³×C₁₃	1	1	yes	characteristic
107	3₋¹⁺²	—	3	6	no	—
108	3₋¹⁺²	—	3	9	no	—
109	3₋¹⁺²	—	3	9	no	—
110	3₋¹⁺²	—	9	9	no	—
111	H(3,𝔽₃)	—	3	3	no	—
112	C₃×C₉	—	3	9	no	—
113	C₃×C₉	—	9	3	no	—
114	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
115	C₃×C₉	C₃³×C₁₃	1	9	yes	—
116	C₃×C₉	C₃³×C₁₃	1	9	yes	—
117	C₃×C₉	C₃³×C₁₃	1	6	yes	—
118	C₃×C₉	C₃³×C₁₃	1	6	yes	—
119	C₃×C₉	C₃³×C₁₃	1	3	yes	—
120	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
121	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
122	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
123	C₁₃	#10624887	1	1	yes	characteristic, direct product factor, Sylow
124	C₃²	—	3	3	no	—
125	C₃²	—	3	3	no	—
126	C₃²	—	3	9	no	—
127	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
128	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
129	C₉	—	3	6	no	—
130	C₉	—	3	3	no	—
131	C₉	—	3	6	no	—
132	C₉	—	3	9	no	—
133	C₉	—	3	9	no	—
134	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
135	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
136	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
137	C₃	—	3	3	no	—
138	C₃	—	9	3	no	—
139	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
140	C₃	C₁₃×3₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
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
2. C₁₃×#6900	C₃	semidirect
3. C₁₃×#6899	C₃	semidirect
4. C₁₃×#6896	C₃	semidirect
5. C₁₃×#6894	C₃	semidirect
6. C₁₃×#6894	C₃	semidirect
8. C₁₃×#6887	C₃	semidirect
9. C₁₃×#6887	C₃	semidirect
10. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
35. #10624887	C₁₃	direct (N × H)
45. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
55. #6900	C₃×C₁₃	semidirect
56. #6899	C₃×C₁₃	semidirect
57. #6896	C₃×C₁₃	semidirect
58. #6894	C₃×C₁₃	semidirect
59. #6894	C₃×C₁₃	semidirect
61. #6887	C₃×C₁₃	semidirect
62. #6887	C₃×C₁₃	semidirect
63. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
114. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
123. C₁₃	#10624887	direct (N × H)

Subgroups — C13×#10624887 #23745038

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624887 #23745038