Subgroups — D₁₃⋊#2164 #16807051

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131204	C₂	1	2	yes	maximal, complemented
2	#13131203	C₂	1	2	yes	maximal, complemented
3	#13131202	C₂	1	2	yes	maximal, complemented
4	#13131201	C₂	1	2	yes	maximal, complemented
5	D₁₃⋊(C₄⋊C₁₆)	C₂	1	2	yes	maximal, complemented
6	D₁₃⋊(C₂²⋊C₁₆)	C₂	1	2	yes	maximal
7	#13131037	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
10	C₂×M₁₆×D₁₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	D₁₃×#117	C₄	1	1	yes	characteristic
13	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
14	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
15	C₁₃×#405	C₄	1	1	yes	characteristic
16	#11718783	C₂²	1	1	yes	characteristic
17	#11718762	C₄	1	1	yes	characteristic
18	#11718658	C₂²	1	1	yes	characteristic
19	#11718369	C₂²	1	1	yes	characteristic
20	#11718369	C₂²	1	1	yes	characteristic
21	D₁₃×#97	C₄	1	1	yes	characteristic
22	D₁₃×#97	C₄	1	1	yes	characteristic
23	#11718350	C₄	1	1	yes	characteristic
24	#11718350	C₄	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	C₂²⋊#6092	C₂²	1	4	yes	—
28	#11718260	C₂²	1	4	yes	complemented
29	#11718259	C₂²	1	4	yes	—
30	#11718258	C₂²	1	2	yes	complemented
31	#11718257	C₂²	1	2	yes	complemented
32	#11718231	C₂²	1	2	yes	complemented
33	C₄⋊#6092	C₂²	1	4	yes	complemented
34	C₄×#6092	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
39	#88180	C₂×C₄	1	1	yes	characteristic
40	C₂×#6099	C₂×C₄	1	1	yes	characteristic
41	C₂²×#1055	C₂³	1	1	yes	characteristic
42	M₁₆×D₁₃	—	2	4	no	—
43	C₂×#6094	C₂×C₄	1	1	yes	characteristic
44	C₂×#6094	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₃	—	2	4	no	—
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
52	#88146	C₈	1	2	yes	—
53	C₄⋊C₄×D₁₃	C₈	1	2	yes	—
54	C₂²⋊C₄×D₁₃	C₈	1	2	yes	—
55	#88131	C₈	1	2	yes	—
56	#88126	C₂×C₄	1	1	yes	characteristic
57	#88126	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#6092	C₂³	1	4	yes	—
61	C₂×#6092	C₂³	1	4	yes	—
62	D₁₃⋊C₁₆	—	2	4	no	—
63	D₁₃⋊C₁₆	—	2	4	no	—
64	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
66	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	#88055	C₂×C₄	1	1	yes	characteristic
69	#88055	C₂×C₄	1	1	yes	characteristic
70	#88055	C₂×C₄	1	1	yes	characteristic
71	#88055	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
75	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
76	#88043	C₂×C₄	1	1	yes	characteristic
77	#88043	C₂×C₄	1	1	yes	characteristic
78	C₄×#1055	C₂³	1	1	yes	characteristic
79	C₄×#1055	C₂³	1	1	yes	characteristic
80	C₂×#2164	—	13	1	no	maximal, Sylow
81	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
84	C₂×C₄×D₁₃	—	2	2	no	—
85	C₂×C₄×D₁₃	—	2	2	no	—
86	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
87	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
88	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₁₃×M₁₆	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
99	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
100	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
103	#6103	C₂×C₈	1	2	yes	—
104	#6103	C₂×C₈	1	2	yes	—
105	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
106	#6101	C₂×C₈	1	2	yes	—
107	#6101	C₂×C₈	1	2	yes	—
108	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
109	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
110	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
112	#6099	—	2	2	no	—
113	C₂×#1055	—	2	2	no	—
114	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
115	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
116	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
117	C₂×#1055	C₂⁴	1	1	yes	characteristic
118	#6094	—	2	2	no	—
119	#6094	—	2	2	no	—
120	C₈×D₁₃	—	2	2	no	—
121	C₈×D₁₃	—	2	2	no	—
122	C₈×D₁₃	—	2	2	no	—
123	C₈×D₁₃	—	2	2	no	—
124	C₈×D₁₃	M₁₆	1	4	yes	—
125	C₈×D₁₃	#41	1	4	yes	—
126	#6092	—	2	4	no	—
127	#6092	—	2	4	no	—
128	C₂×#405	—	13	1	no	—
129	#2164	—	13	2	no	—
130	#2164	—	13	2	no	—
131	#2164	—	13	2	no	—
132	#2164	—	13	2	no	—
133	C₂×C₄⋊C₁₆	—	13	2	no	—
134	C₂×C₂²⋊C₁₆	—	13	2	no	—
135	C₂×#346	—	13	1	no	—
136	C₂×C₄×C₁₆	—	13	1	no	—
137	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
138	C₂²×D₁₃	—	2	2	no	—
139	C₂²×D₁₃	—	2	4	no	—
140	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
141	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
145	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
146	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×Dic₁₃	—	2	2	no	—
149	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
150	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
151	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
153	C₄×D₁₃	—	2	2	no	—
154	C₄×D₁₃	—	2	4	no	—
155	C₄×D₁₃	—	2	4	no	—
156	C₄×D₁₃	—	2	1	no	—
157	C₄×D₁₃	—	2	1	no	—
158	C₄×D₁₃	—	2	2	no	—
159	C₄×D₁₃	#117	1	2	yes	—
160	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
161	C₈×C₁₃	—	2	1	no	—
162	C₈×C₁₃	—	2	1	no	—
163	C₈×C₁₃	#117	1	2	yes	—
164	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
165	#1055	—	2	1	no	—
166	#1055	—	2	1	no	—
167	#1055	C₂×M₁₆	1	2	yes	—
168	#1055	C₂×#41	1	2	yes	—
169	C₂²×M₁₆	—	13	1	no	—
170	C₂³×C₈	—	13	1	no	—
171	C₂×#117	—	13	1	no	—
172	C₂²×C₁₆	—	13	2	no	—
173	C₂²×C₁₆	—	13	2	no	—
174	#405	—	13	1	no	—
175	#405	—	13	1	no	—
176	#405	—	13	1	no	—
177	#405	—	13	1	no	—
178	#405	—	13	1	no	—
179	#405	—	13	1	no	—
180	#405	—	13	1	no	—
181	#405	#261	1	1	yes	characteristic
182	C₂×#97	—	13	1	no	—
183	C₂×#97	—	13	1	no	—
184	C₂×C₄×C₈	—	13	1	no	—
185	C₂×C₄×C₈	—	13	1	no	—
186	C₄⋊C₁₆	—	13	4	no	—
187	C₄⋊C₁₆	—	13	4	no	—
188	C₂²⋊C₁₆	—	13	4	no	—
189	C₂²⋊C₁₆	—	13	4	no	—
190	#346	—	13	2	no	—
191	#346	—	13	2	no	—
192	C₄×C₁₆	—	13	2	no	—
193	C₄×C₁₆	—	13	2	no	—
194	C₂²×C₁₃	—	2	2	no	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
197	C₂×D₁₃	—	2	2	no	—
198	C₂×D₁₃	—	2	1	no	—
199	C₂×D₁₃	—	4	4	no	—
200	C₂×D₁₃	#431	1	2	yes	—
201	C₂×D₁₃	#504	1	4	yes	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
206	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
207	Dic₁₃	—	2	2	no	—
208	Dic₁₃	—	2	2	no	—
209	Dic₁₃	—	2	1	no	—
210	Dic₁₃	#431	1	2	yes	—
211	C₂³×C₄	—	13	1	no	—
212	C₂×M₁₆	—	13	1	no	—
213	C₂×M₁₆	—	13	1	no	—
214	C₂×M₁₆	—	13	1	no	—
215	C₂×M₁₆	—	26	4	no	—
216	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
217	C₂²×C₈	—	13	1	no	—
218	C₂²×C₈	—	13	1	no	—
219	C₂²×C₈	—	13	1	no	—
220	C₂²×C₈	—	13	1	no	—
221	C₂²×C₈	—	13	1	no	—
222	C₂²×C₈	—	13	1	no	—
223	C₂²×C₈	—	13	1	no	—
224	C₂²×C₈	—	26	4	no	—
225	C₂²×C₈	C₂×#261	1	1	yes	characteristic
226	#117	—	13	1	no	—
227	#117	—	13	2	no	—
228	#117	—	13	2	no	—
229	#117	—	13	1	no	—
230	#117	—	13	1	no	—
231	#117	C₂×#261	1	1	yes	characteristic
232	C₂×C₄⋊C₄	—	13	2	no	—
233	C₂×C₂²⋊C₄	—	13	2	no	—
234	C₂×C₄²	—	13	1	no	—
235	C₂×C₄²	—	13	1	no	—
236	C₂×C₁₆	—	13	4	no	—
237	C₂×C₁₆	—	13	4	no	—
238	C₂×C₁₆	—	26	4	no	—
239	C₂×C₁₆	—	26	4	no	—
240	#97	—	13	1	no	—
241	#97	—	13	1	no	—
242	#97	—	13	1	no	—
243	#97	—	13	1	no	—
244	#97	—	13	1	no	—
245	#97	—	13	1	no	—
246	#97	C₂×#261	1	1	yes	characteristic
247	#97	C₂×#261	1	1	yes	characteristic
248	C₄×C₈	—	13	1	no	—
249	C₄×C₈	—	13	1	no	—
250	C₄×C₈	—	13	1	no	—
251	C₄×C₈	—	13	1	no	—
252	C₄×C₈	—	13	1	no	—
253	C₄×C₈	—	13	1	no	—
254	C₄×C₈	C₂×#261	1	1	yes	characteristic
255	C₄×C₈	C₂×#261	1	1	yes	characteristic
256	C₂×C₁₃	—	4	1	no	—
257	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
258	C₂×C₁₃	C₂×#504	1	2	yes	—
259	D₁₃	—	4	1	no	—
260	D₁₃	#2164	1	4	yes	complemented
261	C₂⁴	—	13	1	no	—
262	C₂²×C₄	—	13	1	no	—
263	C₂²×C₄	—	13	1	no	—
264	C₂²×C₄	—	13	2	no	—
265	C₂²×C₄	—	13	2	no	—
266	C₂²×C₄	—	13	1	no	—
267	C₂²×C₄	—	13	1	no	—
268	C₂²×C₄	—	13	1	no	—
269	C₂²×C₄	—	26	2	no	—
270	C₂²×C₄	—	26	2	no	—
271	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
272	M₁₆	—	2	2	no	—
273	M₁₆	—	26	2	no	—
274	M₁₆	—	26	2	no	—
275	M₁₆	—	26	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	13	1	no	—
278	C₂×C₈	—	13	1	no	—
279	C₂×C₈	—	13	4	no	—
280	C₂×C₈	—	13	4	no	—
281	C₂×C₈	—	13	1	no	—
282	C₂×C₈	—	13	1	no	—
283	C₂×C₈	—	26	2	no	—
284	C₂×C₈	—	26	2	no	—
285	C₂×C₈	—	26	2	no	—
286	C₂×C₈	—	26	2	no	—
287	C₂×C₈	—	26	2	no	—
288	C₂×C₈	C₂²×#261	1	1	yes	characteristic
289	C₂×C₈	C₂²×#261	1	1	yes	characteristic
290	C₂×C₈	C₂²×#261	1	1	yes	characteristic
291	C₂×C₈	C₂²×#261	1	1	yes	characteristic
292	C₄⋊C₄	—	13	2	no	—
293	C₄⋊C₄	—	13	2	no	—
294	C₄⋊C₄	—	13	2	no	—
295	C₄⋊C₄	D₁₃⋊C₈	1	2	yes	—
296	C₂²⋊C₄	—	13	2	no	—
297	C₂²⋊C₄	—	13	2	no	—
298	C₂²⋊C₄	—	13	2	no	—
299	C₂²⋊C₄	D₁₃⋊C₈	1	2	yes	—
300	C₄²	—	13	2	no	—
301	C₄²	—	13	2	no	—
302	C₄²	—	13	1	no	—
303	C₄²	—	13	1	no	—
304	C₄²	C₂²×#261	1	1	yes	characteristic
305	C₄²	C₂²×#261	1	1	yes	characteristic
306	C₁₆	—	26	4	no	—
307	C₁₆	—	26	4	no	—
308	C₁₃	C₂×#2164	1	1	yes	characteristic, complemented, Sylow
309	C₂³	—	13	1	no	—
310	C₂³	—	13	1	no	—
311	C₂³	—	26	2	no	—
312	C₂³	—	26	4	no	—
313	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	13	1	no	—
317	C₂×C₄	—	13	2	no	—
318	C₂×C₄	—	13	2	no	—
319	C₂×C₄	—	13	2	no	—
320	C₂×C₄	—	13	2	no	—
321	C₂×C₄	—	13	1	no	—
322	C₂×C₄	—	26	2	no	—
323	C₂×C₄	—	26	4	no	—
324	C₂×C₄	—	26	4	no	—
325	C₂×C₄	—	26	2	no	—
326	C₂×C₄	—	26	2	no	—
327	C₂×C₄	—	26	1	no	—
328	C₂×C₄	—	26	1	no	—
329	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
330	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
331	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
332	C₂×C₄	C₂³×#261	1	1	yes	characteristic
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	13	2	no	—
336	C₈	—	13	2	no	—
337	C₈	—	26	1	no	—
338	C₈	—	26	1	no	—
339	C₈	D₁₃⋊M₁₆	1	2	yes	—
340	C₈	#88237	1	2	yes	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	13	4	no	—
344	C₂²	—	13	2	no	—
345	C₂²	—	26	2	no	—
346	C₂²	—	26	1	no	—
347	C₂²	—	52	4	no	—
348	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	1	no	—
352	C₄	—	13	2	no	—
353	C₄	—	26	2	no	—
354	C₄	—	26	2	no	—
355	C₄	—	26	1	no	—
356	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
357	C₄	C₂×#88237	1	1	yes	characteristic
358	C₂	—	4	1	no	—
359	C₂	—	13	4	no	—
360	C₂	—	52	1	no	—
361	C₂	D₁₃⋊#431	1	1	yes	characteristic
362	C₂	D₁₃⋊#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	C₂×#2164
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
1. #13131204	C₂	semidirect
2. #13131203	C₂	semidirect
3. #13131202	C₂	semidirect
4. #13131201	C₂	semidirect
5. D₁₃⋊(C₄⋊C₁₆)	C₂	semidirect
7. #13131037	C₂	semidirect
8. C₄×D₁₃⋊C₁₆	C₂	semidirect
28. #11718260	C₂²	semidirect
30. #11718258	C₂²	semidirect
31. #11718257	C₂²	semidirect
32. #11718231	C₂²	semidirect
33. C₄⋊#6092	C₂²	semidirect
34. C₄×#6092	C₂²	semidirect
260. D₁₃	#2164	semidirect
308. C₁₃	C₂×#2164	semidirect

Maximal subgroups

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

subgroup	index
#13131204	2
#13131203	2
#13131202	2
#13131201	2
D₁₃⋊(C₄⋊C₁₆)	2
D₁₃⋊(C₂²⋊C₁₆)	2
#13131037	2
C₄×D₁₃⋊C₁₆	2
D₁₃×#405	2
C₂×#2164	13

Subgroups — D13⋊#2164 #16807051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#2164 #16807051