Subgroups — C₁₃×#9882 #15696221

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1280	C₂	1	4	yes	maximal
5	C₂³×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
9	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₃×#97	—	2	1	no	—
12	C₁₃×#391	—	2	1	no	—
13	C₁₃×#391	—	2	1	no	—
14	C₁₃×#391	—	2	1	no	—
15	C₁₃×#391	—	2	1	no	—
16	C₂×C₁₃×#95	C₄	1	2	yes	—
17	C₂×C₁₃×#95	C₂²	1	2	yes	—
18	C₁₃×#336	—	2	1	no	—
19	C₁₃×#336	—	2	1	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂²×Q₈×C₁₃	—	2	1	no	—
22	C₂²×Q₈×C₁₃	—	2	4	no	—
23	C₂²×Q₈×C₁₃	—	4	2	no	—
24	C₂²×Q₈×C₁₃	—	4	2	no	—
25	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
35	C₂×C₄²×C₁₃	—	4	2	no	—
36	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₁₃×C₄⋊C₈	—	4	2	no	—
41	C₁₃×C₂²⋊C₈	—	2	2	no	—
42	C₁₃×C₂²⋊C₈	—	2	4	no	—
43	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
44	C₁₃×#97	—	4	2	no	—
45	C₁₃×#95	—	2	2	no	—
46	C₁₃×#95	—	2	2	no	—
47	C₁₃×#95	—	2	2	no	—
48	C₁₃×#95	—	2	2	no	—
49	#9882	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×Q₈×C₁₃	—	2	4	no	—
52	C₂×Q₈×C₁₃	—	2	4	no	—
53	C₂×Q₈×C₁₃	—	4	16	no	—
54	C₂×Q₈×C₁₃	—	4	2	no	—
55	C₂×Q₈×C₁₃	—	4	2	no	—
56	C₂×Q₈×C₁₃	—	4	2	no	—
57	C₂×Q₈×C₁₃	—	4	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₃	—	2	2	no	—
65	C₂²×C₄×C₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₃	—	4	1	no	—
68	C₂²×C₄×C₁₃	—	4	1	no	—
69	C₂²×C₄×C₁₃	—	4	1	no	—
70	C₂²×C₄×C₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₃	—	4	2	no	—
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	—	4	2	no	—
74	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
79	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃	#41	1	2	yes	—
83	C₂×C₈×C₁₃	—	2	4	no	—
84	C₂×C₈×C₁₃	—	4	2	no	—
85	C₂×C₈×C₁₃	—	4	2	no	—
86	C₂×C₈×C₁₃	—	4	2	no	—
87	C₂×C₈×C₁₃	—	4	2	no	—
88	C₂×C₈×C₁₃	—	4	2	no	—
89	C₁₃×C₄⋊C₄	—	4	2	no	—
90	C₁₃×C₄⋊C₄	—	4	2	no	—
91	C₄²×C₁₃	—	2	2	no	—
92	C₄²×C₁₃	—	2	2	no	—
93	C₄²×C₁₃	—	4	1	no	—
94	C₄²×C₁₃	—	4	1	no	—
95	C₂×#391	C₂×C₁₃	1	1	yes	characteristic
96	#1797	C₂×C₁₃	1	1	yes	characteristic
97	#1749	C₂×C₁₃	1	1	yes	characteristic
98	#1280	C₂×C₁₃	1	4	yes	—
99	C₂³×C₁₃	—	2	1	no	—
100	C₂³×C₁₃	—	2	1	no	—
101	C₂³×C₁₃	—	2	1	no	—
102	C₂³×C₁₃	—	2	1	no	—
103	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
105	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
106	C₂³×C₁₃	#131	1	2	yes	—
107	Q₈×C₁₃	—	4	8	no	—
108	Q₈×C₁₃	—	4	8	no	—
109	C₂×C₄×C₁₃	—	2	8	no	—
110	C₂×C₄×C₁₃	—	2	1	no	—
111	C₂×C₄×C₁₃	—	2	1	no	—
112	C₂×C₄×C₁₃	—	2	1	no	—
113	C₂×C₄×C₁₃	—	2	1	no	—
114	C₂×C₄×C₁₃	—	2	1	no	—
115	C₂×C₄×C₁₃	—	2	1	no	—
116	C₂×C₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	1	no	—
119	C₂×C₄×C₁₃	—	2	1	no	—
120	C₂×C₄×C₁₃	—	2	4	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	1	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	4	2	no	—
125	C₂×C₄×C₁₃	—	4	2	no	—
126	C₂×C₄×C₁₃	—	4	4	no	—
127	C₂×C₄×C₁₃	—	4	4	no	—
128	C₂×C₄×C₁₃	—	4	2	no	—
129	C₂×C₄×C₁₃	—	4	2	no	—
130	C₂×C₄×C₁₃	—	4	4	no	—
131	C₂×C₄×C₁₃	—	4	2	no	—
132	C₂×C₄×C₁₃	—	4	2	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	—	8	4	no	—
135	C₂×C₄×C₁₃	#99	1	2	yes	—
136	C₂×C₄×C₁₃	#100	1	2	yes	—
137	C₂×C₄×C₁₃	#101	1	2	yes	—
138	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
141	C₈×C₁₃	—	4	4	no	—
142	C₈×C₁₃	—	8	2	no	—
143	C₂³×Q₈	C₄×C₁₃	1	1	yes	characteristic
144	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
145	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
146	C₂×C₄⋊C₈	—	2	1	no	—
147	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
149	C₂×#97	—	2	1	no	—
150	#391	—	2	1	no	—
151	#391	—	2	1	no	—
152	#391	—	2	1	no	—
153	#391	—	2	1	no	—
154	C₂×#95	C₄×C₁₃	1	2	yes	—
155	C₂×#95	C₂²×C₁₃	1	2	yes	—
156	#336	—	2	1	no	—
157	#336	—	2	1	no	—
158	C₂²×C₁₃	—	2	2	no	—
159	C₂²×C₁₃	—	2	2	no	—
160	C₂²×C₁₃	—	2	2	no	—
161	C₂²×C₁₃	—	2	2	no	—
162	C₂²×C₁₃	—	2	2	no	—
163	C₂²×C₁₃	—	2	2	no	—
164	C₂²×C₁₃	#391	1	1	yes	characteristic
165	C₂²×C₁₃	#407	1	1	yes	characteristic
166	C₂²×C₁₃	#408	1	1	yes	characteristic
167	C₂²×C₁₃	C₂×#99	1	1	yes	characteristic
168	C₂²×C₁₃	#410	1	1	yes	characteristic
169	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
170	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
171	C₂²×C₁₃	#446	1	4	yes	—
172	C₄×C₁₃	—	2	2	no	—
173	C₄×C₁₃	—	2	2	no	—
174	C₄×C₁₃	—	2	2	no	—
175	C₄×C₁₃	—	2	2	no	—
176	C₄×C₁₃	—	2	1	no	—
177	C₄×C₁₃	—	2	1	no	—
178	C₄×C₁₃	—	4	4	no	—
179	C₄×C₁₃	—	4	1	no	—
180	C₄×C₁₃	—	8	2	no	—
181	C₂²×Q₈	—	2	1	no	—
182	C₂²×Q₈	—	2	1	no	—
183	C₂²×Q₈	—	2	4	no	—
184	C₂²×Q₈	—	4	2	no	—
185	C₂²×Q₈	—	4	2	no	—
186	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
187	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
188	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
189	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
190	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
191	C₂²×C₈	—	2	2	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	1	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	—	4	2	no	—
196	C₂×C₄²	—	4	2	no	—
197	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
198	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
199	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
200	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
201	C₄⋊C₈	—	4	2	no	—
202	C₂²⋊C₈	—	2	2	no	—
203	C₂²⋊C₈	—	2	4	no	—
204	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	complemented
205	#97	—	4	2	no	—
206	#95	—	2	2	no	—
207	#95	—	2	2	no	—
208	#95	—	2	2	no	—
209	#95	—	2	2	no	—
210	C₂×C₁₃	—	2	4	no	—
211	C₂×C₁₃	#1462	1	1	yes	characteristic
212	C₂×C₁₃	#1467	1	1	yes	characteristic
213	C₂×C₁₃	#1469	1	1	yes	characteristic
214	C₂×C₁₃	#1472	1	1	yes	characteristic
215	C₂×C₁₃	#1985	1	1	yes	characteristic
216	C₂×C₁₃	#1996	1	1	yes	characteristic
217	C₂×C₁₃	#1997	1	1	yes	characteristic
218	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
219	C₂×Q₈	—	2	4	no	—
220	C₂×Q₈	—	2	4	no	—
221	C₂×Q₈	—	4	16	no	—
222	C₂×Q₈	—	4	2	no	—
223	C₂×Q₈	—	4	2	no	—
224	C₂×Q₈	—	4	2	no	—
225	C₂×Q₈	—	4	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	4	1	no	—
236	C₂²×C₄	—	4	1	no	—
237	C₂²×C₄	—	4	1	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₄	C₁₃×M₁₆	1	4	yes	—
247	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
249	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
250	C₂²×C₄	C₁₃×#41	1	2	yes	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	4	2	no	—
253	C₂×C₈	—	4	2	no	—
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	4	2	no	—
256	C₂×C₈	—	4	2	no	—
257	C₄⋊C₄	—	4	2	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	4	1	no	—
262	C₄²	—	4	1	no	—
263	C₁₃	#9882	1	1	yes	characteristic, direct product factor, Sylow
264	C₂³	—	2	1	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	1	no	—
268	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
270	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
271	C₂³	C₁₃×#131	1	2	yes	—
272	Q₈	—	4	8	no	—
273	Q₈	—	4	8	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	8	4	no	—
300	C₂×C₄	C₁₃×#99	1	2	yes	—
301	C₂×C₄	C₁₃×#100	1	2	yes	—
302	C₂×C₄	C₁₃×#101	1	2	yes	—
303	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
304	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
305	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
306	C₈	—	4	4	no	—
307	C₈	—	8	2	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	2	no	—
314	C₂²	C₁₃×#391	1	1	yes	characteristic
315	C₂²	C₁₃×#407	1	1	yes	characteristic
316	C₂²	C₁₃×#408	1	1	yes	characteristic
317	C₂²	C₂×C₁₃×#99	1	1	yes	characteristic
318	C₂²	C₁₃×#410	1	1	yes	characteristic
319	C₂²	C₂×C₁₃×#100	1	1	yes	characteristic
320	C₂²	C₂×C₁₃×#101	1	1	yes	characteristic
321	C₂²	C₁₃×#446	1	4	yes	—
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	4	no	—
330	C₄	—	8	2	no	—
331	C₂	—	2	4	no	—
332	C₂	C₁₃×#1462	1	1	yes	characteristic
333	C₂	C₁₃×#1467	1	1	yes	characteristic
334	C₂	C₁₃×#1469	1	1	yes	characteristic
335	C₂	C₁₃×#1472	1	1	yes	characteristic
336	C₂	C₁₃×#1985	1	1	yes	characteristic
337	C₂	C₁₃×#1996	1	1	yes	characteristic
338	C₂	C₁₃×#1997	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
43. C₁₃×C₂²⋊C₈	Q₈	semidirect
49. #9882	C₁₃	direct (N × H)
204. C₂²⋊C₈	Q₈×C₁₃	semidirect
263. C₁₃	#9882	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#391	2
C₁₃×#1797	2
C₁₃×#1749	2
C₁₃×#1280	2
#9882	13

Subgroups — C13×#9882 #15696221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9882 #15696221