Subgroups — C₁₃×#10624904 #23745055

Order 9477.

622 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6899	C₃	1	6	yes	maximal, complemented
2	C₁₃×#6898	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6897	C₃	1	6	yes	maximal, complemented
4	C₁₃×#6896	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6895	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#6894	C₃	1	2	yes	maximal, complemented
7	C₁₃×#6894	C₃	1	2	yes	maximal, complemented
8	C₁₃×#6894	C₃	1	6	yes	maximal, complemented
9	C₁₃×#6893	C₃	1	1	yes	maximal, characteristic
10	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
11	C₉×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
12	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
13	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#6887	C₃	1	3	yes	maximal, complemented
15	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
17	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
18	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
19	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
20	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
21	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
22	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
23	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
24	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
25	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
26	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
27	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
28	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
29	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
30	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
31	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
32	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
33	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
34	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
35	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
36	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
37	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
38	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
39	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
40	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
41	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
42	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
43	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
44	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
45	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
46	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
47	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
48	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
49	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
50	C₉²×C₁₃	C₃²	1	3	yes	—
51	C₉²×C₁₃	C₃²	1	6	yes	—
52	#10624904	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₃³×C₁₃	C₃³	1	3	yes	—
54	C₃³×C₁₃	C₃³	1	1	yes	characteristic
55	C₁₃×3₋¹⁺²	—	3	6	no	—
56	C₁₃×3₋¹⁺²	—	9	6	no	—
57	C₁₃×H(3,𝔽₃)	—	3	3	no	—
58	C₃×C₉×C₁₃	—	3	3	no	—
59	C₃×C₉×C₁₃	—	3	3	no	—
60	C₃×C₉×C₁₃	—	3	9	no	—
61	C₃×C₉×C₁₃	—	9	2	no	—
62	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
63	C₃×C₉×C₁₃	C₃³	1	3	yes	—
64	C₃×C₉×C₁₃	C₃³	1	2	yes	—
65	C₃×C₉×C₁₃	C₃³	1	6	yes	—
66	C₃×C₉×C₁₃	C₃³	1	6	yes	—
67	C₃×C₉×C₁₃	C₃³	1	6	yes	—
68	C₃×C₉×C₁₃	C₃³	1	3	yes	—
69	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
70	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
71	C₃×C₉×C₁₃	C₃³	1	2	yes	—
72	C₃×C₉×C₁₃	C₃³	1	2	yes	—
73	C₃×C₉×C₁₃	C₃³	1	2	yes	—
74	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
75	#6899	C₃×C₁₃	1	6	yes	complemented
76	#6898	C₃×C₁₃	1	3	yes	complemented
77	#6897	C₃×C₁₃	1	6	yes	complemented
78	#6896	C₃×C₁₃	1	3	yes	complemented
79	#6895	C₃×C₁₃	1	1	yes	characteristic, complemented
80	#6894	C₃×C₁₃	1	2	yes	complemented
81	#6894	C₃×C₁₃	1	2	yes	complemented
82	#6894	C₃×C₁₃	1	6	yes	complemented
83	#6893	C₃×C₁₃	1	1	yes	characteristic
84	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	2	yes	—
85	C₉×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
86	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
87	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
88	#6887	C₃×C₁₃	1	3	yes	complemented
89	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
90	C₃²×C₁₃	—	3	1	no	—
91	C₃²×C₁₃	—	3	2	no	—
92	C₃²×C₁₃	—	3	3	no	—
93	C₃²×C₁₃	—	3	3	no	—
94	C₃²×C₁₃	—	3	6	no	—
95	C₃²×C₁₃	#737	1	3	yes	—
96	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
97	C₉×C₁₃	—	3	1	no	—
98	C₉×C₁₃	—	3	2	no	—
99	C₉×C₁₃	—	3	3	no	—
100	C₉×C₁₃	—	3	1	no	—
101	C₉×C₁₃	—	3	1	no	—
102	C₉×C₁₃	—	3	3	no	—
103	C₉×C₁₃	—	3	6	no	—
104	C₉×C₁₃	—	3	2	no	—
105	C₉×C₁₃	—	3	2	no	—
106	C₉×C₁₃	—	3	2	no	—
107	C₉×C₁₃	—	3	6	no	—
108	C₉×C₁₃	—	3	6	no	—
109	C₉×C₁₃	#737	1	3	yes	—
110	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
111	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
112	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
113	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
114	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
115	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
116	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
117	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
118	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
119	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
120	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
121	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
122	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
123	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
124	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
125	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
126	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
127	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
128	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
129	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
130	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
131	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
132	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
133	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
134	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
135	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
136	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
137	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
138	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
139	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
140	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
141	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
142	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
143	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
144	C₉²	C₃²×C₁₃	1	3	yes	—
145	C₉²	C₃²×C₁₃	1	6	yes	—
146	C₃×C₁₃	—	3	3	no	—
147	C₃×C₁₃	—	9	3	no	—
148	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
149	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
150	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
151	C₃³	C₃³×C₁₃	1	3	yes	—
152	C₃³	C₃³×C₁₃	1	1	yes	characteristic
153	3₋¹⁺²	—	3	6	no	—
154	3₋¹⁺²	—	9	6	no	—
155	H(3,𝔽₃)	—	3	3	no	—
156	C₃×C₉	—	3	3	no	—
157	C₃×C₉	—	3	3	no	—
158	C₃×C₉	—	3	9	no	—
159	C₃×C₉	—	9	2	no	—
160	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
161	C₃×C₉	C₃³×C₁₃	1	3	yes	—
162	C₃×C₉	C₃³×C₁₃	1	2	yes	—
163	C₃×C₉	C₃³×C₁₃	1	6	yes	—
164	C₃×C₉	C₃³×C₁₃	1	6	yes	—
165	C₃×C₉	C₃³×C₁₃	1	6	yes	—
166	C₃×C₉	C₃³×C₁₃	1	3	yes	—
167	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
168	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
169	C₃×C₉	C₃³×C₁₃	1	2	yes	—
170	C₃×C₉	C₃³×C₁₃	1	2	yes	—
171	C₃×C₉	C₃³×C₁₃	1	2	yes	—
172	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
173	C₁₃	#10624904	1	1	yes	characteristic, direct product factor, Sylow
174	C₃²	—	3	1	no	—
175	C₃²	—	3	2	no	—
176	C₃²	—	3	3	no	—
177	C₃²	—	3	3	no	—
178	C₃²	—	3	6	no	—
179	C₃²	C₁₃×#737	1	3	yes	—
180	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
181	C₉	—	3	1	no	—
182	C₉	—	3	2	no	—
183	C₉	—	3	3	no	—
184	C₉	—	3	1	no	—
185	C₉	—	3	1	no	—
186	C₉	—	3	3	no	—
187	C₉	—	3	6	no	—
188	C₉	—	3	2	no	—
189	C₉	—	3	2	no	—
190	C₉	—	3	2	no	—
191	C₉	—	3	6	no	—
192	C₉	—	3	6	no	—
193	C₉	C₁₃×#737	1	3	yes	—
194	C₃	—	3	3	no	—
195	C₃	—	9	3	no	—
196	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
197	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
198	C₃	C₁₃×3₋¹⁺⁴	1	2	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
1. C₁₃×#6899	C₃	semidirect
2. C₁₃×#6898	C₃	semidirect
3. C₁₃×#6897	C₃	semidirect
4. C₁₃×#6896	C₃	semidirect
5. C₁₃×#6895	C₃	semidirect
6. C₁₃×#6894	C₃	semidirect
7. C₁₃×#6894	C₃	semidirect
8. C₁₃×#6894	C₃	semidirect
11. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
13. C₁₃×#6887	C₃	semidirect
14. C₁₃×#6887	C₃	semidirect
15. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
52. #10624904	C₁₃	direct (N × H)
75. #6899	C₃×C₁₃	semidirect
76. #6898	C₃×C₁₃	semidirect
77. #6897	C₃×C₁₃	semidirect
78. #6896	C₃×C₁₃	semidirect
79. #6895	C₃×C₁₃	semidirect
80. #6894	C₃×C₁₃	semidirect
81. #6894	C₃×C₁₃	semidirect
82. #6894	C₃×C₁₃	semidirect
85. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
87. #6887	C₃×C₁₃	semidirect
88. #6887	C₃×C₁₃	semidirect
89. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
173. C₁₃	#10624904	direct (N × H)

Subgroups — C13×#10624904 #23745055

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624904 #23745055