Subgroups — C₁₃×#8932 #15695271

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1540	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1278	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#131	—	2	1	no	—
9	C₁₃×#532	C₂²	1	1	yes	characteristic
10	C₁₃×#436	—	2	1	no	—
11	C₁₃×#435	—	2	2	no	—
12	C₈×D₄×C₁₃	—	2	1	no	—
13	C₁₃×#431	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#108	—	2	1	no	—
15	C₁₃×#423	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₃×#408	—	2	1	no	—
19	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#341	—	2	1	no	—
22	C₁₃×#334	—	2	1	no	—
23	C₁₃×#334	—	2	1	no	—
24	C₁₃×#332	C₄	1	1	yes	characteristic
25	C₁₃×#332	C₄	1	1	yes	characteristic
26	C₁₃×#331	C₄	1	1	yes	characteristic
27	C₁₃×#331	C₄	1	1	yes	characteristic
28	C₁₃×D₄⋊C₈	—	2	2	no	—
29	C₂×C₁₃×#41	—	2	1	no	—
30	C₁₃×#131	—	4	2	no	—
31	C₁₃×#131	—	4	2	no	—
32	C₂×C₁₃×M₁₆	—	2	2	no	—
33	C₂×C₁₃×M₁₆	—	2	1	no	—
34	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
35	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	—	2	2	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
41	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
42	C₁₃×#124	—	2	1	no	—
43	C₁₃×#121	—	2	1	no	—
44	C₁₃×#121	Q₈	1	2	yes	—
45	C₄×D₄×C₁₃	—	2	1	no	—
46	C₄×D₄×C₁₃	D₄	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#108	—	4	2	no	—
49	C₁₃×C₄⋊C₈	—	2	1	no	—
50	C₁₃×C₄⋊C₈	—	2	1	no	—
51	C₁₃×C₄⋊C₈	—	2	1	no	—
52	C₁₃×C₄⋊C₈	—	2	1	no	—
53	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
58	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
59	C₁₃×C₂²⋊C₈	—	2	2	no	—
60	C₁₃×C₂²⋊C₈	—	2	2	no	—
61	C₁₃×C₂²⋊C₈	—	2	1	no	—
62	C₁₃×#97	—	2	1	no	—
63	C₄×C₈×C₁₃	—	2	1	no	—
64	C₄×C₈×C₁₃	—	2	1	no	—
65	C₄×C₈×C₁₃	—	2	1	no	—
66	C₄×C₈×C₁₃	—	2	1	no	—
67	#8932	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₁₃×#41	—	4	1	no	—
69	C₁₃×#41	—	4	1	no	—
70	C₁₃×#41	—	4	1	no	—
71	C₁₃×#41	—	4	1	no	—
72	C₂×Q₈×C₁₃	—	2	1	no	—
73	C₂×D₄×C₁₃	—	2	2	no	—
74	C₂×D₄×C₁₃	—	2	1	no	—
75	C₂×D₄×C₁₃	—	2	1	no	—
76	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
81	C₁₃×M₁₆	—	2	1	no	—
82	C₁₃×M₁₆	—	2	1	no	—
83	C₁₃×M₁₆	—	2	1	no	—
84	C₁₃×M₁₆	—	4	4	no	—
85	C₁₃×M₁₆	—	4	1	no	—
86	C₁₃×M₁₆	—	4	1	no	—
87	C₁₃×M₁₆	SD₁₆	1	2	yes	—
88	C₂×C₈×C₁₃	—	2	1	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	1	no	—
91	C₂×C₈×C₁₃	—	2	1	no	—
92	C₂×C₈×C₁₃	—	2	1	no	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₂×C₈×C₁₃	—	2	1	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	1	no	—
97	C₂×C₈×C₁₃	—	4	4	no	—
98	C₂×C₈×C₁₃	—	4	1	no	—
99	C₂×C₈×C₁₃	—	4	1	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	—	4	1	no	—
102	C₂×C₈×C₁₃	—	4	1	no	—
103	C₂×C₈×C₁₃	—	4	1	no	—
104	C₂×C₈×C₁₃	—	4	1	no	—
105	C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
107	C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₁₃×C₂²⋊C₄	—	2	2	no	—
109	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₃	#41	1	1	yes	characteristic
113	#2935	C₂×C₁₃	1	1	yes	characteristic
114	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
115	#1570	C₂×C₁₃	1	1	yes	characteristic, complemented
116	#1540	C₂×C₁₃	1	1	yes	characteristic
117	#1492	C₂×C₁₃	1	1	yes	characteristic
118	#1278	C₂×C₁₃	1	1	yes	characteristic, complemented
119	#1277	C₂×C₁₃	1	1	yes	characteristic, complemented
120	C₂³×C₁₃	—	2	2	no	—
121	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
122	Q₈×C₁₃	—	4	1	no	—
123	Q₈×C₁₃	—	4	1	no	—
124	D₄×C₁₃	—	4	2	no	—
125	D₄×C₁₃	—	4	2	no	—
126	D₄×C₁₃	—	4	2	no	—
127	D₄×C₁₃	—	4	1	no	—
128	D₄×C₁₃	—	4	1	no	—
129	D₄×C₁₃	—	4	1	no	—
130	D₄×C₁₃	—	4	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	4	1	no	—
135	C₂×C₄×C₁₃	—	4	2	no	—
136	C₂×C₄×C₁₃	—	4	2	no	—
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
145	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₈×C₁₃	—	2	2	no	—
148	C₈×C₁₃	—	4	2	no	—
149	C₈×C₁₃	—	4	1	no	—
150	C₈×C₁₃	—	4	1	no	—
151	C₈×C₁₃	—	4	1	no	—
152	C₈×C₁₃	—	4	1	no	—
153	C₈×C₁₃	—	4	1	no	—
154	C₈×C₁₃	—	4	1	no	—
155	C₈×C₁₃	—	4	1	no	—
156	C₈×C₁₃	—	8	1	no	—
157	C₂×#131	—	2	1	no	—
158	#532	C₂²×C₁₃	1	1	yes	characteristic
159	#436	—	2	1	no	—
160	#435	—	2	2	no	—
161	C₈×D₄	—	2	1	no	—
162	#431	C₂²×C₁₃	1	1	yes	characteristic
163	C₂×#108	—	2	1	no	—
164	#423	C₂²×C₁₃	1	1	yes	characteristic
165	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
167	#408	—	2	1	no	—
168	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
170	#341	—	2	1	no	—
171	#334	—	2	1	no	—
172	#334	—	2	1	no	—
173	#332	C₄×C₁₃	1	1	yes	characteristic
174	#332	C₄×C₁₃	1	1	yes	characteristic
175	#331	C₄×C₁₃	1	1	yes	characteristic
176	#331	C₄×C₁₃	1	1	yes	characteristic
177	D₄⋊C₈	—	2	2	no	—
178	C₂²×C₁₃	—	2	1	no	—
179	C₂²×C₁₃	—	2	1	no	—
180	C₂²×C₁₃	—	4	2	no	—
181	C₂²×C₁₃	—	4	2	no	—
182	C₂²×C₁₃	—	4	2	no	—
183	C₂²×C₁₃	#385	1	1	yes	characteristic
184	C₂²×C₁₃	#476	1	1	yes	characteristic
185	C₂²×C₁₃	#478	1	1	yes	characteristic
186	C₄×C₁₃	—	2	1	no	—
187	C₄×C₁₃	—	2	1	no	—
188	C₄×C₁₃	—	2	1	no	—
189	C₄×C₁₃	—	4	2	no	—
190	C₄×C₁₃	C₄×SD₁₆	1	1	yes	characteristic
191	C₄×C₁₃	#442	1	1	yes	characteristic
192	C₄×C₁₃	#443	1	1	yes	characteristic
193	C₄×C₁₃	#444	1	1	yes	characteristic
194	C₄×C₁₃	#449	1	1	yes	characteristic
195	C₄×C₁₃	#450	1	1	yes	characteristic
196	C₂×#41	—	2	1	no	—
197	#131	—	4	2	no	—
198	#131	—	4	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	1	no	—
201	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
202	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	1	no	—
205	C₂²×C₈	—	2	1	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
208	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
209	#124	—	2	1	no	—
210	#121	—	2	1	no	—
211	#121	Q₈×C₁₃	1	2	yes	—
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	D₄×C₁₃	1	2	yes	—
214	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
215	#108	—	4	2	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	—	2	1	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
221	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
222	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
224	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
225	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
226	C₂²⋊C₈	—	2	2	no	—
227	C₂²⋊C₈	—	2	2	no	—
228	C₂²⋊C₈	—	2	1	no	—
229	#97	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	2	1	no	—
234	C₂×C₁₃	—	2	1	no	—
235	C₂×C₁₃	—	2	1	no	—
236	C₂×C₁₃	—	8	2	no	—
237	C₂×C₁₃	#1858	1	1	yes	characteristic
238	C₂×C₁₃	#1864	1	1	yes	characteristic
239	C₂×C₁₃	#1866	1	1	yes	characteristic
240	#41	—	4	1	no	—
241	#41	—	4	1	no	—
242	#41	—	4	1	no	—
243	#41	—	4	1	no	—
244	C₂×Q₈	—	2	1	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	1	no	—
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
251	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
253	M₁₆	—	2	1	no	—
254	M₁₆	—	2	1	no	—
255	M₁₆	—	2	1	no	—
256	M₁₆	—	4	4	no	—
257	M₁₆	—	4	1	no	—
258	M₁₆	—	4	1	no	—
259	M₁₆	C₁₃×SD₁₆	1	2	yes	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	4	4	no	—
270	C₂×C₈	—	4	1	no	—
271	C₂×C₈	—	4	1	no	—
272	C₂×C₈	—	4	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	4	1	no	—
276	C₂×C₈	—	4	1	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
282	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
284	C₄²	C₁₃×#41	1	1	yes	characteristic
285	C₁₃	#8932	1	1	yes	characteristic, direct product factor, Sylow
286	C₂³	—	2	2	no	—
287	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
288	Q₈	—	4	1	no	—
289	Q₈	—	4	1	no	—
290	D₄	—	4	2	no	—
291	D₄	—	4	2	no	—
292	D₄	—	4	2	no	—
293	D₄	—	4	1	no	—
294	D₄	—	4	1	no	—
295	D₄	—	4	1	no	—
296	D₄	—	4	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
307	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
308	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
309	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
310	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
311	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₈	—	2	2	no	—
314	C₈	—	4	2	no	—
315	C₈	—	4	1	no	—
316	C₈	—	4	1	no	—
317	C₈	—	4	1	no	—
318	C₈	—	4	1	no	—
319	C₈	—	4	1	no	—
320	C₈	—	4	1	no	—
321	C₈	—	4	1	no	—
322	C₈	—	8	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	2	no	—
328	C₂²	C₁₃×#385	1	1	yes	characteristic
329	C₂²	C₁₃×#476	1	1	yes	characteristic
330	C₂²	C₁₃×#478	1	1	yes	characteristic
331	C₄	—	2	1	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	4	2	no	—
335	C₄	C₄×C₁₃×SD₁₆	1	1	yes	characteristic
336	C₄	C₁₃×#442	1	1	yes	characteristic
337	C₄	C₁₃×#443	1	1	yes	characteristic
338	C₄	C₁₃×#444	1	1	yes	characteristic
339	C₄	C₁₃×#449	1	1	yes	characteristic
340	C₄	C₁₃×#450	1	1	yes	characteristic
341	C₂	—	2	1	no	—
342	C₂	—	2	1	no	—
343	C₂	—	8	2	no	—
344	C₂	C₁₃×#1858	1	1	yes	characteristic
345	C₂	C₁₃×#1864	1	1	yes	characteristic
346	C₂	C₁₃×#1866	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#385
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1950	C₂	semidirect
3. C₁₃×#1570	C₂	semidirect
6. C₁₃×#1278	C₂	semidirect
7. C₁₃×#1277	C₂	semidirect
67. #8932	C₁₃	direct (N × H)
114. #1950	C₂×C₁₃	semidirect
115. #1570	C₂×C₁₃	semidirect
118. #1278	C₂×C₁₃	semidirect
119. #1277	C₂×C₁₃	semidirect
285. C₁₃	#8932	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2935	2
C₁₃×#1950	2
C₁₃×#1570	2
C₁₃×#1540	2
C₁₃×#1492	2
C₁₃×#1278	2
C₁₃×#1277	2
#8932	13

Subgroups — C13×#8932 #15695271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8932 #15695271