Subgroups — C₁₃×#9883 #15696222

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#389	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	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
7	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
10	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₃×#97	—	2	1	no	—
13	C₁₃×#389	—	2	1	no	—
14	C₁₃×#389	—	2	1	no	—
15	C₁₃×#389	—	2	1	no	—
16	C₁₃×#389	—	2	1	no	—
17	C₂×C₁₃×#95	C₂²	1	2	yes	—
18	C₁₃×#336	—	2	1	no	—
19	C₁₃×#336	—	2	1	no	—
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₃	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
36	C₂×C₄²×C₁₃	—	4	2	no	—
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	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₁₃×C₄⋊C₈	—	4	2	no	—
42	C₁₃×C₂²⋊C₈	—	2	2	no	—
43	C₁₃×C₂²⋊C₈	—	2	4	no	—
44	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
45	C₁₃×#97	—	4	2	no	—
46	C₁₃×#95	—	2	2	no	—
47	C₁₃×#95	—	2	2	no	—
48	#9883	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	—	2	2	no	—
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	4	no	—
59	C₂²×C₄×C₁₃	—	4	1	no	—
60	C₂²×C₄×C₁₃	—	4	1	no	—
61	C₂²×C₄×C₁₃	—	4	1	no	—
62	C₂²×C₄×C₁₃	—	4	2	no	—
63	C₂²×C₄×C₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₃	—	4	2	no	—
65	C₂²×C₄×C₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
74	C₂²×C₄×C₁₃	#41	1	2	yes	—
75	C₂×C₈×C₁₃	—	2	4	no	—
76	C₂×C₈×C₁₃	—	4	2	no	—
77	C₂×C₈×C₁₃	—	4	2	no	—
78	C₂×C₈×C₁₃	—	4	2	no	—
79	C₂×C₈×C₁₃	—	4	2	no	—
80	C₂×C₈×C₁₃	—	4	2	no	—
81	C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₁₃×C₄⋊C₄	—	4	2	no	—
84	C₁₃×C₄⋊C₄	—	4	4	no	—
85	C₁₃×C₄⋊C₄	—	4	2	no	—
86	C₁₃×C₄⋊C₄	—	4	4	no	—
87	C₄²×C₁₃	—	2	2	no	—
88	C₄²×C₁₃	—	2	2	no	—
89	C₄²×C₁₃	—	4	1	no	—
90	C₄²×C₁₃	—	4	1	no	—
91	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
92	#1797	C₂×C₁₃	1	1	yes	characteristic
93	#1749	C₂×C₁₃	1	1	yes	characteristic
94	#1280	C₂×C₁₃	1	4	yes	—
95	C₂³×C₁₃	—	2	1	no	—
96	C₂³×C₁₃	—	2	1	no	—
97	C₂³×C₁₃	—	2	1	no	—
98	C₂³×C₁₃	—	2	1	no	—
99	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
101	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
102	C₂³×C₁₃	#131	1	2	yes	—
103	C₂×C₄×C₁₃	—	2	8	no	—
104	C₂×C₄×C₁₃	—	2	1	no	—
105	C₂×C₄×C₁₃	—	2	1	no	—
106	C₂×C₄×C₁₃	—	2	1	no	—
107	C₂×C₄×C₁₃	—	2	1	no	—
108	C₂×C₄×C₁₃	—	2	1	no	—
109	C₂×C₄×C₁₃	—	2	1	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	4	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	—	4	2	no	—
119	C₂×C₄×C₁₃	—	4	2	no	—
120	C₂×C₄×C₁₃	—	4	4	no	—
121	C₂×C₄×C₁₃	—	4	4	no	—
122	C₂×C₄×C₁₃	—	4	2	no	—
123	C₂×C₄×C₁₃	—	4	2	no	—
124	C₂×C₄×C₁₃	—	4	4	no	—
125	C₂×C₄×C₁₃	—	4	2	no	—
126	C₂×C₄×C₁₃	—	4	2	no	—
127	C₂×C₄×C₁₃	—	4	2	no	—
128	C₂×C₄×C₁₃	—	8	4	no	—
129	C₂×C₄×C₁₃	#99	1	2	yes	—
130	C₂×C₄×C₁₃	#100	1	2	yes	—
131	C₂×C₄×C₁₃	#101	1	2	yes	—
132	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
134	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
135	C₈×C₁₃	—	4	4	no	—
136	C₈×C₁₃	—	8	2	no	—
137	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
138	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
139	C₂²×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
140	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
141	C₂×C₄⋊C₈	—	2	1	no	—
142	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
143	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
144	C₂×#97	—	2	1	no	—
145	#389	—	2	1	no	—
146	#389	—	2	1	no	—
147	#389	—	2	1	no	—
148	#389	—	2	1	no	—
149	C₂×#95	C₂²×C₁₃	1	2	yes	—
150	#336	—	2	1	no	—
151	#336	—	2	1	no	—
152	C₂²×C₁₃	—	2	2	no	—
153	C₂²×C₁₃	—	2	2	no	—
154	C₂²×C₁₃	—	2	2	no	—
155	C₂²×C₁₃	—	2	2	no	—
156	C₂²×C₁₃	—	2	2	no	—
157	C₂²×C₁₃	—	2	2	no	—
158	C₂²×C₁₃	#391	1	1	yes	characteristic
159	C₂²×C₁₃	#407	1	1	yes	characteristic
160	C₂²×C₁₃	#408	1	1	yes	characteristic
161	C₂²×C₁₃	C₂×#99	1	1	yes	characteristic
162	C₂²×C₁₃	#410	1	1	yes	characteristic
163	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
164	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
165	C₂²×C₁₃	#446	1	4	yes	—
166	C₄×C₁₃	—	2	2	no	—
167	C₄×C₁₃	—	2	2	no	—
168	C₄×C₁₃	—	2	2	no	—
169	C₄×C₁₃	—	2	2	no	—
170	C₄×C₁₃	—	2	1	no	—
171	C₄×C₁₃	—	2	1	no	—
172	C₄×C₁₃	—	4	4	no	—
173	C₄×C₁₃	—	4	1	no	—
174	C₄×C₁₃	—	8	2	no	—
175	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
176	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
177	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
178	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
179	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
180	C₂²×C₈	—	2	2	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₄⋊C₄	—	2	4	no	—
185	C₂×C₄⋊C₄	—	2	2	no	—
186	C₂×C₄⋊C₄	—	2	1	no	—
187	C₂×C₄⋊C₄	—	2	1	no	—
188	C₂×C₄⋊C₄	—	2	2	no	—
189	C₂×C₄⋊C₄	—	4	2	no	—
190	C₂×C₄⋊C₄	—	4	4	no	—
191	C₂×C₄²	—	4	2	no	—
192	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
193	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
194	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
195	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
196	C₄⋊C₈	—	4	2	no	—
197	C₂²⋊C₈	—	2	2	no	—
198	C₂²⋊C₈	—	2	4	no	—
199	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	—
200	#97	—	4	2	no	—
201	#95	—	2	2	no	—
202	#95	—	2	2	no	—
203	C₂×C₁₃	—	2	4	no	—
204	C₂×C₁₃	#1463	1	1	yes	characteristic
205	C₂×C₁₃	#1466	1	1	yes	characteristic
206	C₂×C₁₃	#1470	1	1	yes	characteristic
207	C₂×C₁₃	#1471	1	1	yes	characteristic
208	C₂×C₁₃	#1985	1	1	yes	characteristic
209	C₂×C₁₃	#1996	1	1	yes	characteristic
210	C₂×C₁₃	#1997	1	1	yes	characteristic
211	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
212	C₂²×C₄	—	2	2	no	—
213	C₂²×C₄	—	2	2	no	—
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	4	1	no	—
222	C₂²×C₄	—	4	1	no	—
223	C₂²×C₄	—	4	1	no	—
224	C₂²×C₄	—	4	2	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
231	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₄	C₁₃×M₁₆	1	4	yes	—
233	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
235	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
236	C₂²×C₄	C₁₃×#41	1	2	yes	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	4	2	no	—
239	C₂×C₈	—	4	2	no	—
240	C₂×C₈	—	4	2	no	—
241	C₂×C₈	—	4	2	no	—
242	C₂×C₈	—	4	2	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	2	4	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	4	4	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	—	4	4	no	—
249	C₄²	—	2	2	no	—
250	C₄²	—	2	2	no	—
251	C₄²	—	4	1	no	—
252	C₄²	—	4	1	no	—
253	C₁₃	#9883	1	1	yes	characteristic, direct product factor, Sylow
254	C₂³	—	2	1	no	—
255	C₂³	—	2	1	no	—
256	C₂³	—	2	1	no	—
257	C₂³	—	2	1	no	—
258	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
259	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
260	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
261	C₂³	C₁₃×#131	1	2	yes	—
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	4	4	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	4	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	8	4	no	—
288	C₂×C₄	C₁₃×#99	1	2	yes	—
289	C₂×C₄	C₁₃×#100	1	2	yes	—
290	C₂×C₄	C₁₃×#101	1	2	yes	—
291	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
292	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
293	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
294	C₈	—	4	4	no	—
295	C₈	—	8	2	no	—
296	C₂²	—	2	2	no	—
297	C₂²	—	2	2	no	—
298	C₂²	—	2	2	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	C₁₃×#391	1	1	yes	characteristic
303	C₂²	C₁₃×#407	1	1	yes	characteristic
304	C₂²	C₁₃×#408	1	1	yes	characteristic
305	C₂²	C₂×C₁₃×#99	1	1	yes	characteristic
306	C₂²	C₁₃×#410	1	1	yes	characteristic
307	C₂²	C₂×C₁₃×#100	1	1	yes	characteristic
308	C₂²	C₂×C₁₃×#101	1	1	yes	characteristic
309	C₂²	C₁₃×#446	1	4	yes	—
310	C₄	—	2	2	no	—
311	C₄	—	2	2	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	2	no	—
315	C₄	—	2	2	no	—
316	C₄	—	4	1	no	—
317	C₄	—	4	4	no	—
318	C₄	—	8	2	no	—
319	C₂	—	2	4	no	—
320	C₂	C₁₃×#1463	1	1	yes	characteristic
321	C₂	C₁₃×#1466	1	1	yes	characteristic
322	C₂	C₁₃×#1470	1	1	yes	characteristic
323	C₂	C₁₃×#1471	1	1	yes	characteristic
324	C₂	C₁₃×#1985	1	1	yes	characteristic
325	C₂	C₁₃×#1996	1	1	yes	characteristic
326	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
48. #9883	C₁₃	direct (N × H)
253. C₁₃	#9883	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×#389	2
C₁₃×#1797	2
C₁₃×#1749	2
C₁₃×#1280	2
#9883	13

Subgroups — C13×#9883 #15696222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9883 #15696222