Subgroups — C₁₃×#10624907 #23745058

Order 9477.

622 conjugacy classes of subgroups.

The subgroup lattice has 298 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	3	yes	maximal, complemented
2	C₁₃×#6899	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6898	C₃	1	3	yes	maximal, complemented
4	C₁₃×#6897	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6897	C₃	1	3	yes	maximal, complemented
6	C₁₃×#6896	C₃	1	3	yes	maximal, complemented
7	C₁₃×#6895	C₃	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#6895	C₃	1	3	yes	maximal, complemented
9	C₁₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#6894	C₃	1	3	yes	maximal, complemented
14	C₁₃×#6893	C₃	1	1	yes	maximal, characteristic
15	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
16	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
17	C₉×C₁₃×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
18	C₉×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
19	C₉×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
20	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
21	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
22	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
24	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
25	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
26	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
27	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
28	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
29	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
30	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
31	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
32	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
33	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
34	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
35	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
36	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
37	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
38	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
39	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
40	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
41	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
42	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
43	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
44	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
45	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
46	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
47	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
48	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
49	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
50	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
51	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
52	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
53	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
54	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
55	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
56	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
57	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
58	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
59	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
60	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
61	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
62	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
63	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
64	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
65	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
66	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
67	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
68	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
69	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
70	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
71	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
72	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
73	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
74	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
75	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
76	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
77	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
78	C₉²×C₁₃	C₃²	1	3	yes	—
79	C₉²×C₁₃	C₃²	1	3	yes	—
80	C₉²×C₁₃	C₃²	1	3	yes	—
81	#10624907	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₃³×C₁₃	C₃³	1	3	yes	—
83	C₃³×C₁₃	C₃³	1	1	yes	characteristic
84	C₁₃×3₋¹⁺²	—	3	3	no	—
85	C₁₃×3₋¹⁺²	—	3	3	no	—
86	C₁₃×3₋¹⁺²	—	3	9	no	—
87	C₁₃×3₋¹⁺²	—	9	3	no	—
88	C₁₃×H(3,𝔽₃)	—	3	3	no	—
89	C₃×C₉×C₁₃	—	3	3	no	—
90	C₃×C₉×C₁₃	—	3	3	no	—
91	C₃×C₉×C₁₃	—	9	1	no	—
92	C₃×C₉×C₁₃	—	9	3	no	—
93	C₃×C₉×C₁₃	—	9	1	no	—
94	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
95	C₃×C₉×C₁₃	C₃³	1	3	yes	—
96	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
97	C₃×C₉×C₁₃	C₃³	1	3	yes	—
98	C₃×C₉×C₁₃	C₃³	1	3	yes	—
99	C₃×C₉×C₁₃	C₃³	1	3	yes	—
100	C₃×C₉×C₁₃	C₃³	1	3	yes	—
101	C₃×C₉×C₁₃	C₃³	1	3	yes	—
102	C₃×C₉×C₁₃	C₃³	1	3	yes	—
103	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
104	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
105	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
106	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
107	C₃×C₉×C₁₃	C₃³	1	3	yes	—
108	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
109	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
110	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
111	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
112	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
113	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
114	#6899	C₃×C₁₃	1	3	yes	complemented
115	#6899	C₃×C₁₃	1	3	yes	complemented
116	#6898	C₃×C₁₃	1	3	yes	complemented
117	#6897	C₃×C₁₃	1	3	yes	complemented
118	#6897	C₃×C₁₃	1	3	yes	complemented
119	#6896	C₃×C₁₃	1	3	yes	complemented
120	#6895	C₃×C₁₃	1	1	yes	characteristic, complemented
121	#6895	C₃×C₁₃	1	3	yes	complemented
122	#6894	C₃×C₁₃	1	1	yes	characteristic, complemented
123	#6894	C₃×C₁₃	1	1	yes	characteristic, complemented
124	#6894	C₃×C₁₃	1	1	yes	characteristic, complemented
125	#6894	C₃×C₁₃	1	1	yes	characteristic, complemented
126	#6894	C₃×C₁₃	1	3	yes	complemented
127	#6893	C₃×C₁₃	1	1	yes	characteristic
128	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
129	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
130	C₉×3₋¹⁺²	C₃×C₁₃	1	3	yes	complemented
131	C₉×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic, complemented
132	C₉×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic, complemented
133	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
134	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
135	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
136	C₃²×C₁₃	—	3	1	no	—
137	C₃²×C₁₃	—	3	1	no	—
138	C₃²×C₁₃	—	3	1	no	—
139	C₃²×C₁₃	—	3	3	no	—
140	C₃²×C₁₃	—	3	3	no	—
141	C₃²×C₁₃	—	3	3	no	—
142	C₃²×C₁₃	—	3	3	no	—
143	C₃²×C₁₃	#737	1	3	yes	—
144	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
145	C₉×C₁₃	—	3	1	no	—
146	C₉×C₁₃	—	3	1	no	—
147	C₉×C₁₃	—	3	1	no	—
148	C₉×C₁₃	—	3	1	no	—
149	C₉×C₁₃	—	3	1	no	—
150	C₉×C₁₃	—	3	3	no	—
151	C₉×C₁₃	—	3	3	no	—
152	C₉×C₁₃	—	3	3	no	—
153	C₉×C₁₃	—	3	3	no	—
154	C₉×C₁₃	—	3	1	no	—
155	C₉×C₁₃	—	3	3	no	—
156	C₉×C₁₃	—	3	1	no	—
157	C₉×C₁₃	—	3	1	no	—
158	C₉×C₁₃	—	3	1	no	—
159	C₉×C₁₃	—	3	3	no	—
160	C₉×C₁₃	—	3	1	no	—
161	C₉×C₁₃	—	3	1	no	—
162	C₉×C₁₃	—	3	3	no	—
163	C₉×C₁₃	—	3	3	no	—
164	C₉×C₁₃	#737	1	3	yes	—
165	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
166	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
167	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
168	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
169	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
170	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
171	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
172	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
173	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
174	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
175	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
176	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
177	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
178	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
179	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
180	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
181	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
182	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
183	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
184	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
185	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
186	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
187	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
188	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
189	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
190	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
191	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
192	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
193	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
194	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
195	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
196	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
197	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
198	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
199	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
200	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
201	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
202	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
203	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
204	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
205	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
206	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
207	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
208	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
209	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
210	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
211	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
212	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
213	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
214	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
215	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
216	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
217	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
218	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
219	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
220	C₉²	C₃²×C₁₃	1	3	yes	—
221	C₉²	C₃²×C₁₃	1	3	yes	—
222	C₉²	C₃²×C₁₃	1	3	yes	—
223	C₃×C₁₃	—	3	3	no	—
224	C₃×C₁₃	—	9	3	no	—
225	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
226	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
227	C₃×C₁₃	3₋¹⁺⁴	1	1	yes	characteristic
228	C₃×C₁₃	3₋¹⁺⁴	1	1	yes	characteristic
229	C₃³	C₃³×C₁₃	1	3	yes	—
230	C₃³	C₃³×C₁₃	1	1	yes	characteristic
231	3₋¹⁺²	—	3	3	no	—
232	3₋¹⁺²	—	3	3	no	—
233	3₋¹⁺²	—	3	9	no	—
234	3₋¹⁺²	—	9	3	no	—
235	H(3,𝔽₃)	—	3	3	no	—
236	C₃×C₉	—	3	3	no	—
237	C₃×C₉	—	3	3	no	—
238	C₃×C₉	—	9	1	no	—
239	C₃×C₉	—	9	3	no	—
240	C₃×C₉	—	9	1	no	—
241	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
242	C₃×C₉	C₃³×C₁₃	1	3	yes	—
243	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
244	C₃×C₉	C₃³×C₁₃	1	3	yes	—
245	C₃×C₉	C₃³×C₁₃	1	3	yes	—
246	C₃×C₉	C₃³×C₁₃	1	3	yes	—
247	C₃×C₉	C₃³×C₁₃	1	3	yes	—
248	C₃×C₉	C₃³×C₁₃	1	3	yes	—
249	C₃×C₉	C₃³×C₁₃	1	3	yes	—
250	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
251	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
252	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
253	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
254	C₃×C₉	C₃³×C₁₃	1	3	yes	—
255	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
256	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
257	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
258	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
259	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
260	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
261	C₁₃	#10624907	1	1	yes	characteristic, direct product factor, Sylow
262	C₃²	—	3	1	no	—
263	C₃²	—	3	1	no	—
264	C₃²	—	3	1	no	—
265	C₃²	—	3	3	no	—
266	C₃²	—	3	3	no	—
267	C₃²	—	3	3	no	—
268	C₃²	—	3	3	no	—
269	C₃²	C₁₃×#737	1	3	yes	—
270	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
271	C₉	—	3	1	no	—
272	C₉	—	3	1	no	—
273	C₉	—	3	1	no	—
274	C₉	—	3	1	no	—
275	C₉	—	3	1	no	—
276	C₉	—	3	3	no	—
277	C₉	—	3	3	no	—
278	C₉	—	3	3	no	—
279	C₉	—	3	3	no	—
280	C₉	—	3	1	no	—
281	C₉	—	3	1	no	—
282	C₉	—	3	3	no	—
283	C₉	—	3	1	no	—
284	C₉	—	3	1	no	—
285	C₉	—	3	1	no	—
286	C₉	—	3	3	no	—
287	C₉	—	3	1	no	—
288	C₉	—	3	3	no	—
289	C₉	—	3	3	no	—
290	C₉	C₁₃×#737	1	3	yes	—
291	C₃	—	3	3	no	—
292	C₃	—	9	3	no	—
293	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
294	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
295	C₃	C₁₃×3₋¹⁺⁴	1	1	yes	characteristic
296	C₃	C₁₃×3₋¹⁺⁴	1	1	yes	characteristic

	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×#6899	C₃	semidirect
3. C₁₃×#6898	C₃	semidirect
4. C₁₃×#6897	C₃	semidirect
5. C₁₃×#6897	C₃	semidirect
6. C₁₃×#6896	C₃	semidirect
7. C₁₃×#6895	C₃	semidirect
8. C₁₃×#6895	C₃	semidirect
9. C₁₃×#6894	C₃	semidirect
10. C₁₃×#6894	C₃	semidirect
11. C₁₃×#6894	C₃	semidirect
12. C₁₃×#6894	C₃	semidirect
13. C₁₃×#6894	C₃	semidirect
17. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
18. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
19. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
21. C₁₃×#6887	C₃	semidirect
22. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
81. #10624907	C₁₃	direct (N × H)
114. #6899	C₃×C₁₃	semidirect
115. #6899	C₃×C₁₃	semidirect
116. #6898	C₃×C₁₃	semidirect
117. #6897	C₃×C₁₃	semidirect
118. #6897	C₃×C₁₃	semidirect
119. #6896	C₃×C₁₃	semidirect
120. #6895	C₃×C₁₃	semidirect
121. #6895	C₃×C₁₃	semidirect
122. #6894	C₃×C₁₃	semidirect
123. #6894	C₃×C₁₃	semidirect
124. #6894	C₃×C₁₃	semidirect
125. #6894	C₃×C₁₃	semidirect
126. #6894	C₃×C₁₃	semidirect
130. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
131. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
132. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
134. #6887	C₃×C₁₃	semidirect
135. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
261. C₁₃	#10624907	direct (N × H)

Subgroups — C13×#10624907 #23745058

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624907 #23745058