Subgroups — C₄×D₁₃×D₁₆ #16016176

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×D₈×D₁₃	C₂	1	2	yes	maximal, complemented
3	C₄×D₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116682	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#88066	C₂	1	2	yes	maximal, complemented
7	#13116680	C₂	1	2	yes	maximal, complemented
8	D₁₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#357	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₁₃	C₂²	1	2	yes	—
13	C₄×D₄×D₁₃	—	2	2	no	—
14	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
16	D₈×Dic₁₃	C₂²	1	2	yes	complemented
17	C₂×#88066	C₂²	1	2	yes	—
18	C₄×#6104	—	2	2	no	—
19	D₁₃×D₁₆	C₄	1	8	yes	direct product factor
20	C₂×D₂₀₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
23	D₁₃×#107	C₂²	1	2	yes	—
24	#11718533	C₂²	1	2	yes	complemented
25	D₁₃×#102	—	2	2	no	—
26	#11718417	—	2	2	no	—
27	C₄×D₁₀₄	C₂²	1	2	yes	complemented
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#357	C₂²	1	2	yes	complemented
31	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
32	#11718154	C₂²	1	2	yes	complemented
33	#11718101	C₂²	1	2	yes	complemented
34	#11718096	C₂²	1	1	yes	characteristic, complemented
35	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
37	#11718083	C₂²	1	2	yes	complemented
38	#11718081	C₂²	1	2	yes	complemented
39	C₄×#6090	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₁₃	—	2	2	no	—
41	C₂²×C₄×D₁₃	—	4	2	no	—
42	C₂×C₁₃×D₈	C₂³	1	2	yes	—
43	C₄×D₄×C₁₃	—	2	2	no	—
44	D₄×Dic₁₃	—	2	2	no	—
45	C₂×#6104	—	2	2	no	—
46	C₄×C₂²⋊D₁₃	—	4	2	no	—
47	D₈×D₁₃	—	2	4	no	—
48	D₈×D₁₃	C₂×C₄	1	8	yes	complemented
49	C₂×D₁₀₄	C₂³	1	2	yes	—
50	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
52	#88147	—	2	2	no	—
53	C₄⋊C₄×D₁₃	—	2	2	no	—
54	#88135	—	4	2	no	—
55	C₂²⋊C₄×D₁₃	—	4	2	no	—
56	C₄×D₅₂	—	2	2	no	—
57	C₄²×D₁₃	D₄	1	1	yes	characteristic
58	C₁₃×D₁₆	C₂×C₄	1	4	yes	complemented
59	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
61	C₁₃×#107	C₂³	1	2	yes	—
62	C₁₃×#102	—	2	2	no	—
63	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	#88072	—	2	2	no	—
65	#88066	C₂×C₄	1	8	yes	complemented
66	#88061	—	2	2	no	—
67	#88058	C₂³	1	2	yes	—
68	C₈×Dic₁₃	D₄	1	1	yes	characteristic
69	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
70	C₂×#6090	C₂³	1	1	yes	characteristic
71	C₂×#6090	C₂³	1	1	yes	characteristic
72	#88049	—	2	2	no	—
73	#88047	—	2	2	no	—
74	C₄×#1055	D₄	1	1	yes	characteristic
75	D₂₀₈	C₂×C₄	1	4	yes	complemented
76	C₁₆×D₁₃	—	2	2	no	—
77	C₁₆×D₁₃	C₂×C₄	1	4	yes	complemented
78	C₂×C₄×D₁₆	—	13	1	no	maximal, Sylow
79	C₂³×D₁₃	—	4	2	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	4	2	no	—
82	C₂×C₂²⋊D₁₃	—	4	2	no	—
83	C₂²×Dic₁₃	—	4	2	no	—
84	D₄×D₁₃	—	2	8	no	—
85	D₄×D₁₃	—	4	4	no	—
86	C₂×D₅₂	—	2	2	no	—
87	C₂×C₄×D₁₃	—	4	2	no	—
88	C₂×C₄×D₁₃	—	4	2	no	—
89	C₂×C₄×D₁₃	—	4	2	no	—
90	C₂×C₄×D₁₃	—	8	8	no	—
91	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
92	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
94	C₁₃×D₈	—	2	2	no	—
95	C₁₃×D₈	C₂²×C₄	1	4	yes	complemented
96	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₂²⋊C₄	—	4	2	no	—
100	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²⋊Dic₁₃	—	4	2	no	—
102	#6104	—	2	8	no	—
103	#6103	—	4	2	no	—
104	#6103	—	4	2	no	—
105	C₄⋊Dic₁₃	—	2	2	no	—
106	#6101	—	4	2	no	—
107	C₄×Dic₁₃	D₈	1	1	yes	characteristic
108	C₄×Dic₁₃	D₈	1	1	yes	characteristic
109	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×#1055	C₂×D₄	1	1	yes	characteristic
111	C₂×#1055	C₂×D₄	1	1	yes	characteristic
112	D₁₀₄	—	2	2	no	—
113	D₁₀₄	C₂²×C₄	1	4	yes	complemented
114	C₈×D₁₃	—	2	2	no	—
115	C₈×D₁₃	C₂²×C₄	1	2	yes	—
116	C₈×D₁₃	#41	1	2	yes	—
117	C₁₃×C₁₆	—	2	1	no	—
118	C₁₃×C₁₆	C₂²×C₄	1	2	yes	complemented
119	#6090	—	2	1	no	—
120	#6090	C₂²×C₄	1	2	yes	complemented
121	C₂²×D₁₆	—	13	1	no	—
122	C₂×C₄×D₈	—	13	2	no	—
123	C₄×D₁₆	—	13	1	no	—
124	C₄×D₁₆	—	13	2	no	—
125	C₄×D₁₆	—	13	1	no	—
126	C₄×D₁₆	—	13	2	no	—
127	C₄×D₁₆	—	13	1	no	—
128	C₄×D₁₆	D₁₃	1	1	yes	characteristic, direct product factor
129	C₂×#366	—	13	1	no	—
130	C₂×#357	—	13	2	no	—
131	C₂×C₄×C₁₆	—	13	1	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂²×D₁₃	—	4	2	no	—
134	C₂²×D₁₃	—	4	8	no	—
135	C₂²×D₁₃	—	8	4	no	—
136	C₂²×D₁₃	—	8	4	no	—
137	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
138	D₄×C₁₃	—	2	4	no	—
139	D₄×C₁₃	—	4	2	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	8	4	no	—
142	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
145	C₂²⋊D₁₃	—	4	8	no	—
146	C₂×Dic₁₃	—	4	2	no	—
147	C₂×Dic₁₃	—	8	4	no	—
148	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
149	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
150	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
151	D₅₂	—	2	4	no	—
152	D₅₂	—	4	2	no	—
153	C₄×D₁₃	—	2	2	no	—
154	C₄×D₁₃	—	8	4	no	—
155	C₄×D₁₃	—	8	4	no	—
156	C₄×D₁₃	—	8	4	no	—
157	C₄×D₁₃	D₁₆	1	4	yes	direct product factor
158	C₄×D₁₃	C₄×D₄	1	2	yes	—
159	C₄×D₁₃	#135	1	2	yes	—
160	C₈×C₁₃	—	2	1	no	—
161	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
163	#1055	—	2	1	no	—
164	#1055	C₄×D₄	1	2	yes	—
165	C₂²×D₈	—	13	2	no	—
166	C₂×C₄×D₄	—	26	2	no	—
167	C₂×D₁₆	—	13	2	no	—
168	C₂×D₁₆	—	13	8	no	—
169	C₂×D₁₆	—	13	1	no	—
170	C₂×D₁₆	C₂×D₁₃	1	1	yes	characteristic
171	C₂²×C₁₆	—	13	1	no	—
172	C₂²×C₁₆	—	13	1	no	—
173	C₄×D₈	—	13	2	no	—
174	C₄×D₈	—	13	2	no	—
175	C₄×D₈	—	13	2	no	—
176	C₄×D₈	—	26	2	no	—
177	C₄×D₈	—	26	2	no	—
178	C₄×D₈	C₂×D₁₃	1	2	yes	complemented
179	C₂×#107	—	13	2	no	—
180	C₂×#102	—	26	2	no	—
181	C₂×C₄×C₈	—	13	1	no	—
182	#366	—	13	1	no	—
183	#366	—	13	2	no	—
184	#366	C₂×D₁₃	1	1	yes	characteristic, complemented
185	#357	—	13	2	no	—
186	#357	—	13	2	no	—
187	#357	—	13	2	no	—
188	#357	C₂×D₁₃	1	2	yes	complemented
189	C₄×C₁₆	—	13	1	no	—
190	C₄×C₁₆	—	13	1	no	—
191	C₄×C₁₆	—	13	1	no	—
192	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
193	C₂²×C₁₃	—	4	4	no	—
194	C₂²×C₁₃	—	8	2	no	—
195	C₂²×C₁₃	—	8	2	no	—
196	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
197	C₂×D₁₃	—	4	4	no	—
198	C₂×D₁₃	—	8	2	no	—
199	C₂×D₁₃	—	8	2	no	—
200	C₂×D₁₃	—	8	16	no	—
201	C₂×D₁₃	C₄×D₈	1	2	yes	—
202	C₂×D₁₃	C₂×D₁₆	1	2	yes	—
203	C₂×D₁₃	#508	1	2	yes	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	8	2	no	—
206	C₄×C₁₃	C₂×D₁₆	1	2	yes	complemented
207	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
209	Dic₁₃	—	2	1	no	—
210	Dic₁₃	—	8	2	no	—
211	Dic₁₃	C₄×D₈	1	2	yes	—
212	Dic₁₃	C₂×D₁₆	1	2	yes	complemented
213	C₂²×D₄	—	26	2	no	—
214	C₂³×C₄	—	52	2	no	—
215	C₂×D₈	—	13	8	no	—
216	C₂×D₈	—	13	2	no	—
217	C₂×D₈	—	26	4	no	—
218	C₂×D₈	—	26	2	no	—
219	C₂×D₈	C₂²×D₁₃	1	2	yes	—
220	C₂²×C₈	—	13	1	no	—
221	C₂²×C₈	—	13	1	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	26	2	no	—
224	C₄×D₄	—	26	2	no	—
225	C₄×D₄	—	26	2	no	—
226	C₄×D₄	—	52	2	no	—
227	C₄×D₄	—	52	2	no	—
228	C₂×C₄⋊C₄	—	26	2	no	—
229	C₂×C₂²⋊C₄	—	52	2	no	—
230	C₂×C₄²	—	13	1	no	—
231	D₁₆	—	13	8	no	—
232	D₁₆	—	13	4	no	—
233	D₁₆	C₄×D₁₃	1	4	yes	direct product factor
234	C₂×C₁₆	—	13	1	no	—
235	C₂×C₁₆	—	13	4	no	—
236	C₂×C₁₆	—	13	1	no	—
237	C₂×C₁₆	—	26	2	no	—
238	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
239	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
240	#107	—	13	2	no	—
241	#107	—	26	2	no	—
242	#107	C₂²×D₁₃	1	2	yes	—
243	#102	—	2	2	no	—
244	#102	—	26	2	no	—
245	#102	—	26	2	no	—
246	#102	—	26	2	no	—
247	C₄×C₈	—	13	1	no	—
248	C₄×C₈	—	13	1	no	—
249	C₄×C₈	—	13	1	no	—
250	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
251	C₂×C₁₃	—	8	4	no	—
252	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
253	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
255	D₁₃	—	8	4	no	—
256	D₁₃	C₄×D₁₆	1	4	yes	direct product factor
257	C₂⁴	—	52	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	26	8	no	—
260	C₂×D₄	—	26	2	no	—
261	C₂×D₄	—	52	4	no	—
262	C₂×D₄	—	52	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	13	1	no	—
265	C₂²×C₄	—	13	1	no	—
266	C₂²×C₄	—	13	1	no	—
267	C₂²×C₄	—	52	2	no	—
268	C₂²×C₄	—	52	2	no	—
269	C₂²×C₄	—	52	2	no	—
270	C₂²×C₄	—	52	2	no	—
271	C₂²×C₄	—	104	8	no	—
272	D₈	—	2	2	no	—
273	D₈	—	13	4	no	—
274	D₈	—	26	8	no	—
275	D₈	—	26	2	no	—
276	D₈	C₂×C₄×D₁₃	1	4	yes	complemented
277	C₂×C₈	—	13	1	no	—
278	C₂×C₈	—	13	2	no	—
279	C₂×C₈	—	13	2	no	—
280	C₂×C₈	—	13	1	no	—
281	C₂×C₈	—	26	2	no	—
282	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
283	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	26	2	no	—
286	C₄⋊C₄	—	52	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₂²⋊C₄	—	52	2	no	—
289	C₂²⋊C₄	—	52	2	no	—
290	C₂²⋊C₄	—	52	2	no	—
291	C₄²	—	13	1	no	—
292	C₄²	—	13	1	no	—
293	C₄²	—	13	1	no	—
294	C₄²	D₄×D₁₃	1	1	yes	characteristic
295	C₁₆	—	2	1	no	—
296	C₁₆	—	13	2	no	—
297	C₁₆	—	26	1	no	—
298	C₁₆	C₂×C₄×D₁₃	1	2	yes	complemented
299	C₁₃	C₂×C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
300	C₂³	—	4	2	no	—
301	C₂³	—	13	1	no	—
302	C₂³	—	52	8	no	—
303	C₂³	—	52	2	no	—
304	C₂³	—	104	4	no	—
305	C₂³	—	104	4	no	—
306	D₄	—	2	4	no	—
307	D₄	—	4	2	no	—
308	D₄	—	26	4	no	—
309	D₄	—	52	8	no	—
310	D₄	—	52	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	—	13	1	no	—
314	C₂×C₄	—	13	1	no	—
315	C₂×C₄	—	13	2	no	—
316	C₂×C₄	—	13	2	no	—
317	C₂×C₄	—	13	4	no	—
318	C₂×C₄	—	13	1	no	—
319	C₂×C₄	—	26	2	no	—
320	C₂×C₄	—	52	2	no	—
321	C₂×C₄	—	104	4	no	—
322	C₂×C₄	—	104	4	no	—
323	C₂×C₄	—	104	4	no	—
324	C₂×C₄	—	104	4	no	—
325	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
326	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
328	C₈	—	2	1	no	—
329	C₈	—	13	2	no	—
330	C₈	—	26	1	no	—
331	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
332	C₈	#41×D₁₃	1	1	yes	characteristic
333	C₂²	—	4	4	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	13	2	no	—
337	C₂²	—	13	2	no	—
338	C₂²	—	13	2	no	—
339	C₂²	—	52	4	no	—
340	C₂²	—	104	16	no	—
341	C₂²	—	104	2	no	—
342	C₂²	—	104	2	no	—
343	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	8	2	no	—
346	C₄	—	13	2	no	—
347	C₄	—	13	2	no	—
348	C₄	—	26	1	no	—
349	C₄	—	104	2	no	—
350	C₄	D₁₃×D₁₆	1	2	yes	direct product factor
351	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
352	C₄	D₁₃×#135	1	1	yes	characteristic
353	C₂	—	8	4	no	—
354	C₂	—	13	4	no	—
355	C₂	—	104	4	no	—
356	C₂	C₄×D₈×D₁₃	1	1	yes	characteristic
357	C₂	C₂×D₁₃×D₁₆	1	1	yes	characteristic
358	C₂	D₁₃×#508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₄×C₁₃×D₁₆	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×D₁₃×D₁₆	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₄×D₁₆	D₁₃
hypocenter	C₁₃	C₂×C₄×D₁₆
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×D₈×D₁₃	C₂	semidirect
3. C₄×D₂₀₈	C₂	semidirect
4. D₁₆×Dic₁₃	C₂	semidirect
5. #13116682	C₂	semidirect
6. C₄×#88066	C₂	semidirect
7. #13116680	C₂	semidirect
8. D₁₃×#366	C₂	semidirect
9. D₁₃×#357	C₂	semidirect
10. C₄×C₁₆×D₁₃	C₂	semidirect
11. C₄×C₁₃×D₁₆	C₂	semidirect
15. C₄×C₁₃×D₈	C₂²	semidirect
16. D₈×Dic₁₃	C₂²	semidirect
19. D₁₃×D₁₆	C₄	direct (N × H)
24. #11718533	C₂²	semidirect
27. C₄×D₁₀₄	C₂²	semidirect
29. C₁₃×#366	C₂²	semidirect
30. C₁₃×#357	C₂²	semidirect
31. C₄×C₁₃×C₁₆	C₂²	semidirect
32. #11718154	C₂²	semidirect
33. #11718101	C₂²	semidirect
34. #11718096	C₂²	semidirect
35. C₁₆×Dic₁₃	C₂²	semidirect
36. C₁₆×Dic₁₃	C₂²	semidirect
37. #11718083	C₂²	semidirect
38. #11718081	C₂²	semidirect
39. C₄×#6090	C₂²	semidirect
48. D₈×D₁₃	C₂×C₄	semidirect
58. C₁₃×D₁₆	C₂×C₄	semidirect
65. #88066	C₂×C₄	semidirect
75. D₂₀₈	C₂×C₄	semidirect
77. C₁₆×D₁₃	C₂×C₄	semidirect
95. C₁₃×D₈	C₂²×C₄	semidirect
113. D₁₀₄	C₂²×C₄	semidirect
118. C₁₃×C₁₆	C₂²×C₄	semidirect
120. #6090	C₂²×C₄	semidirect
128. C₄×D₁₆	D₁₃	direct (N × H)
157. C₄×D₁₃	D₁₆	direct (N × H)
178. C₄×D₈	C₂×D₁₃	semidirect
184. #366	C₂×D₁₃	semidirect
188. #357	C₂×D₁₃	semidirect
192. C₄×C₁₆	C₂×D₁₃	semidirect
206. C₄×C₁₃	C₂×D₁₆	semidirect
212. Dic₁₃	C₂×D₁₆	semidirect
233. D₁₆	C₄×D₁₃	direct (N × H)
256. D₁₃	C₄×D₁₆	direct (N × H)
276. D₈	C₂×C₄×D₁₃	semidirect
298. C₁₆	C₂×C₄×D₁₃	semidirect
299. C₁₃	C₂×C₄×D₁₆	semidirect
350. C₄	D₁₃×D₁₆	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×D₁₃×D₁₆	2
C₄×D₈×D₁₃	2
C₄×D₂₀₈	2
D₁₆×Dic₁₃	2
#13116682	2
C₄×#88066	2
#13116680	2
D₁₃×#366	2
D₁₃×#357	2
C₄×C₁₆×D₁₃	2
C₄×C₁₃×D₁₆	2
C₂×C₄×D₁₆	13

Subgroups — C4×D13×D16 #16016176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₃×D₁₆ #16016176