Subgroups — D₁₃×#2178 #16016315

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#508	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#443	C₂	1	2	yes	maximal, complemented
3	#13116718	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116717	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116716	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116715	C₂	1	2	yes	maximal, complemented
7	#13116714	C₂	1	2	yes	maximal, complemented
8	D₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#359	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#135	C₂²	1	2	yes	—
13	D₁₃×#131	—	2	2	no	—
14	C₁₃×#508	C₂²	1	1	yes	characteristic
15	C₁₃×#443	C₂²	1	2	yes	complemented
16	#11718857	C₂²	1	2	yes	complemented
17	#11718855	C₂²	1	2	yes	—
18	#11718805	—	2	2	no	—
19	#11718580	C₄	1	1	yes	characteristic, complemented
20	D₁₃×Q₃₂	C₄	1	1	yes	characteristic, complemented
21	#11718577	C₄	1	2	yes	complemented
22	D₁₃×SD₃₂	C₄	1	2	yes	complemented
23	#11718573	C₄	1	1	yes	characteristic, complemented
24	D₁₃×D₁₆	C₄	1	1	yes	characteristic, complemented
25	#11718565	C₂²	1	1	yes	characteristic
26	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
28	#11718556	C₂²	1	2	yes	complemented
29	D₁₃×#108	C₂²	1	2	yes	—
30	#11718485	—	2	2	no	—
31	D₁₃×#104	—	2	2	no	—
32	#11718361	C₂²	1	2	yes	complemented
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#368	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#359	C₂²	1	2	yes	complemented
36	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
37	#11718159	C₂²	1	2	yes	complemented
38	#11718102	C₂²	1	2	yes	complemented
39	#11718098	C₂²	1	1	yes	characteristic, complemented
40	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
42	#11718089	C₂²	1	2	yes	complemented
43	#11718085	C₂²	1	2	yes	complemented
44	C₄×#6090	C₂²	1	1	yes	characteristic, complemented
45	#41×D₁₃	—	2	2	no	—
46	C₁₃×#135	C₂³	1	2	yes	—
47	C₁₃×#131	—	2	2	no	—
48	#88204	—	2	2	no	—
49	#88202	—	2	2	no	—
50	#88173	C₂×C₄	1	2	yes	—
51	Q₁₆×D₁₃	C₂×C₄	1	2	yes	—
52	#88170	—	2	2	no	—
53	SD₁₆×D₁₃	—	2	2	no	—
54	#88166	C₂×C₄	1	2	yes	—
55	D₈×D₁₃	C₂×C₄	1	2	yes	—
56	#88161	—	2	2	no	—
57	#88161	—	4	2	no	—
58	M₁₆×D₁₃	—	2	2	no	—
59	M₁₆×D₁₃	—	4	2	no	—
60	#88158	C₂³	1	2	yes	—
61	#88155	—	2	2	no	—
62	#88155	—	4	2	no	—
63	C₂×C₈×D₁₃	—	4	2	no	—
64	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
66	C₄²×D₁₃	D₄	1	1	yes	characteristic
67	C₁₃×Q₃₂	C₂×C₄	1	1	yes	characteristic, complemented
68	C₁₃×SD₃₂	C₂×C₄	1	2	yes	complemented
69	C₁₃×D₁₆	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
72	C₁₃×#108	C₂³	1	2	yes	—
73	C₁₃×#104	—	2	2	no	—
74	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	#88077	—	2	2	no	—
76	#88069	C₂×C₄	1	2	yes	complemented
77	#88068	C₂×C₄	1	2	yes	complemented
78	#88067	C₂×C₄	1	2	yes	complemented
79	#88066	C₂×C₄	1	2	yes	complemented
80	#88065	—	2	2	no	—
81	#88062	—	2	2	no	—
82	#88059	C₂³	1	2	yes	—
83	C₈×Dic₁₃	D₄	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₂×#6090	C₂³	1	1	yes	characteristic
86	C₂×#6090	C₂³	1	1	yes	characteristic
87	#88045	—	2	2	no	—
88	C₄×#1055	D₄	1	1	yes	characteristic
89	Dic₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
90	#88040	C₂×C₄	1	2	yes	complemented
91	D₂₀₈	C₂×C₄	1	1	yes	characteristic, complemented
92	C₁₆×D₁₃	—	2	1	no	—
93	C₁₆×D₁₃	—	2	1	no	—
94	C₁₆×D₁₃	C₂×C₄	1	1	yes	characteristic
95	C₁₆×D₁₃	C₂×C₄	1	1	yes	characteristic
96	C₁₆×D₁₃	C₂×C₄	1	1	yes	characteristic
97	C₁₆×D₁₃	C₂×C₄	1	1	yes	characteristic
98	C₂×#2178	—	13	1	no	maximal, Sylow
99	C₁₃×#41	—	2	2	no	—
100	#6131	—	2	2	no	—
101	Q₈×D₁₃	—	2	2	no	—
102	#6129	—	2	2	no	—
103	#6129	—	4	2	no	—
104	D₄×D₁₃	—	2	2	no	—
105	D₄×D₁₃	—	4	2	no	—
106	#6127	—	2	2	no	—
107	#6127	—	4	2	no	—
108	C₂×C₄×D₁₃	—	2	1	no	—
109	C₂×C₄×D₁₃	—	4	2	no	—
110	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
111	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
112	C₁₃×SD₁₆	—	2	2	no	—
113	C₁₃×D₈	C₂²×C₄	1	2	yes	—
114	C₁₃×M₁₆	—	2	2	no	—
115	C₁₃×M₁₆	—	4	2	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
120	#6107	—	2	2	no	—
121	#6106	—	2	2	no	—
122	#6105	—	2	2	no	—
123	#6104	—	2	2	no	—
124	C₄×Dic₁₃	—	2	1	no	—
125	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
126	#6099	—	2	2	no	—
127	#6099	—	4	2	no	—
128	C₂×#1055	—	4	2	no	—
129	C₂×#1055	C₂×D₄	1	1	yes	characteristic
130	C₂×#1055	C₂×D₄	1	1	yes	characteristic
131	Dic₅₂	C₂²×C₄	1	2	yes	—
132	D₁₀₄	C₂²×C₄	1	2	yes	—
133	#6095	—	2	2	no	—
134	#6094	—	4	2	no	—
135	#6094	—	4	2	no	—
136	#6094	—	4	2	no	—
137	C₈×D₁₃	—	4	2	no	—
138	C₈×D₁₃	—	4	2	no	—
139	C₈×D₁₃	—	4	2	no	—
140	C₈×D₁₃	D₈	1	1	yes	characteristic
141	C₈×D₁₃	D₈	1	1	yes	characteristic
142	C₈×D₁₃	D₈	1	1	yes	characteristic
143	C₈×D₁₃	D₈	1	1	yes	characteristic
144	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₈×D₁₃	#41	1	1	yes	characteristic
147	C₈×D₁₃	#41	1	1	yes	characteristic
148	C₁₃×C₁₆	—	2	1	no	—
149	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
151	#6090	—	2	1	no	—
152	#6090	C₂²×C₄	1	1	yes	characteristic
153	#6090	C₂²×C₄	1	1	yes	characteristic
154	C₂×#508	—	13	1	no	—
155	C₂×#443	—	13	2	no	—
156	#2178	—	13	1	no	—
157	#2178	—	13	2	no	—
158	#2178	—	13	1	no	—
159	#2178	—	13	2	no	—
160	#2178	—	13	1	no	—
161	#2178	D₁₃	1	1	yes	characteristic, direct product factor
162	C₂×#368	—	13	1	no	—
163	C₂×#359	—	13	2	no	—
164	C₂×C₄×C₁₆	—	13	1	no	—
165	C₂²×D₁₃	—	4	2	no	—
166	C₂²×D₁₃	#135	1	1	yes	characteristic
167	Q₈×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂²⋊D₁₃	—	4	2	no	—
174	C₂²⋊D₁₃	—	4	2	no	—
175	C₂²⋊D₁₃	—	4	2	no	—
176	C₂×Dic₁₃	—	2	1	no	—
177	C₂×Dic₁₃	—	4	2	no	—
178	C₂×Dic₁₃	#135	1	1	yes	characteristic
179	D₅₂	—	2	2	no	—
180	D₅₂	—	4	2	no	—
181	C₄×D₁₃	—	2	4	no	—
182	C₄×D₁₃	—	4	2	no	—
183	C₄×D₁₃	—	4	2	no	—
184	C₄×D₁₃	—	4	2	no	—
185	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
186	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
187	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
188	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
189	Dic₂₆	—	2	2	no	—
190	Dic₂₆	—	4	2	no	—
191	C₈×C₁₃	—	4	2	no	—
192	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
193	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
194	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
196	#1055	—	4	2	no	—
197	#1055	C₄×D₄	1	1	yes	characteristic
198	#1055	C₄×D₄	1	1	yes	characteristic
199	#1055	C₂×D₈	1	1	yes	characteristic
200	#1055	C₂×D₈	1	1	yes	characteristic
201	C₂×#135	—	13	2	no	—
202	C₂×#131	—	26	2	no	—
203	#508	—	13	2	no	—
204	#508	—	13	1	no	—
205	#508	—	13	2	no	—
206	#508	—	13	1	no	—
207	#508	—	13	1	no	—
208	#508	C₂×D₁₃	1	1	yes	characteristic
209	C₂×Q₃₂	—	13	1	no	—
210	C₂×SD₃₂	—	13	2	no	—
211	C₂×D₁₆	—	13	1	no	—
212	C₂²×C₁₆	—	13	1	no	—
213	C₂²×C₁₆	—	13	1	no	—
214	#443	—	13	2	no	—
215	#443	—	13	2	no	—
216	#443	—	13	2	no	—
217	#443	—	26	2	no	—
218	#443	—	26	2	no	—
219	#443	C₂×D₁₃	1	2	yes	complemented
220	C₂×#108	—	13	2	no	—
221	C₂×#104	—	26	2	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	#368	—	13	1	no	—
224	#368	—	13	2	no	—
225	#368	C₂×D₁₃	1	1	yes	characteristic, complemented
226	#359	—	13	2	no	—
227	#359	—	13	2	no	—
228	#359	—	13	2	no	—
229	#359	C₂×D₁₃	1	2	yes	complemented
230	C₄×C₁₆	—	13	1	no	—
231	C₄×C₁₆	—	13	1	no	—
232	C₄×C₁₆	—	13	1	no	—
233	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
236	C₂×D₁₃	—	2	2	no	—
237	C₂×D₁₃	—	4	2	no	—
238	C₂×D₁₃	—	8	4	no	—
239	C₂×D₁₃	C₄×D₈	1	1	yes	characteristic
240	C₂×D₁₃	C₄×D₈	1	1	yes	characteristic
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
245	Dic₁₃	—	2	2	no	—
246	Dic₁₃	—	4	2	no	—
247	Dic₁₃	C₄×D₈	1	1	yes	characteristic
248	Dic₁₃	C₄×D₈	1	1	yes	characteristic
249	C₂×#41	—	26	2	no	—
250	#135	—	13	2	no	—
251	#135	—	13	2	no	—
252	#135	—	13	2	no	—
253	#135	—	26	2	no	—
254	#135	—	26	2	no	—
255	#135	C₂²×D₁₃	1	2	yes	—
256	C₂×Q₁₆	—	13	2	no	—
257	C₂×SD₁₆	—	26	2	no	—
258	C₂×D₈	—	13	2	no	—
259	#131	—	2	2	no	—
260	#131	—	26	2	no	—
261	#131	—	26	2	no	—
262	#131	—	26	2	no	—
263	#131	—	52	2	no	—
264	#131	—	52	2	no	—
265	C₂×M₁₆	—	26	2	no	—
266	C₂×M₁₆	—	52	2	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	52	2	no	—
270	C₂×C₄²	—	13	1	no	—
271	Q₃₂	—	13	2	no	—
272	Q₃₂	—	13	1	no	—
273	Q₃₂	C₄×D₁₃	1	1	yes	characteristic, complemented
274	SD₃₂	—	13	2	no	—
275	SD₃₂	—	13	2	no	—
276	SD₃₂	—	13	2	no	—
277	SD₃₂	C₄×D₁₃	1	2	yes	complemented
278	D₁₆	—	13	2	no	—
279	D₁₆	—	13	1	no	—
280	D₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
281	C₂×C₁₆	—	13	1	no	—
282	C₂×C₁₆	—	13	1	no	—
283	C₂×C₁₆	—	13	1	no	—
284	C₂×C₁₆	—	13	1	no	—
285	C₂×C₁₆	—	13	1	no	—
286	C₂×C₁₆	—	13	1	no	—
287	C₂×C₁₆	—	26	1	no	—
288	C₂×C₁₆	—	26	1	no	—
289	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
291	#108	—	13	2	no	—
292	#108	—	26	2	no	—
293	#108	C₂²×D₁₃	1	2	yes	—
294	#104	—	2	2	no	—
295	#104	—	26	2	no	—
296	#104	—	26	2	no	—
297	#104	—	26	2	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
302	C₂×C₁₃	—	2	1	no	—
303	C₂×C₁₃	—	8	2	no	—
304	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
305	D₁₃	—	2	1	no	—
306	D₁₃	—	8	2	no	—
307	D₁₃	#2178	1	2	yes	direct product factor
308	#41	—	2	2	no	—
309	#41	—	26	2	no	—
310	#41	—	26	2	no	—
311	#41	—	26	2	no	—
312	#41	—	52	2	no	—
313	#41	—	52	2	no	—
314	C₂×Q₈	—	26	2	no	—
315	C₂×D₄	—	26	2	no	—
316	C₂×D₄	—	52	2	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	26	1	no	—
319	C₂²×C₄	—	52	2	no	—
320	Q₁₆	—	13	2	no	—
321	Q₁₆	—	26	2	no	—
322	Q₁₆	C₂×C₄×D₁₃	1	2	yes	—
323	SD₁₆	—	2	2	no	—
324	SD₁₆	—	26	2	no	—
325	SD₁₆	—	26	2	no	—
326	SD₁₆	—	26	2	no	—
327	D₈	—	13	2	no	—
328	D₈	—	26	2	no	—
329	D₈	C₂×C₄×D₁₃	1	2	yes	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	—	26	2	no	—
333	M₁₆	—	52	2	no	—
334	M₁₆	—	52	2	no	—
335	M₁₆	—	52	2	no	—
336	M₁₆	—	52	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	13	1	no	—
342	C₂×C₈	—	13	1	no	—
343	C₂×C₈	—	13	1	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	1	no	—
347	C₂×C₈	—	13	1	no	—
348	C₂×C₈	—	52	2	no	—
349	C₂×C₈	—	52	2	no	—
350	C₂×C₈	—	52	2	no	—
351	C₂×C₈	—	52	2	no	—
352	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
354	C₄²	—	13	1	no	—
355	C₄²	—	26	1	no	—
356	C₄²	D₄×D₁₃	1	1	yes	characteristic
357	C₁₆	—	2	1	no	—
358	C₁₆	—	13	1	no	—
359	C₁₆	—	13	1	no	—
360	C₁₆	—	26	1	no	—
361	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
362	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
363	C₁₃	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
364	C₂³	—	13	1	no	—
365	C₂³	—	52	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	26	2	no	—
368	Q₈	—	52	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	26	2	no	—
372	D₄	—	52	2	no	—
373	D₄	—	52	2	no	—
374	D₄	—	52	2	no	—
375	D₄	—	52	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	26	4	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	52	2	no	—
386	C₂×C₄	—	52	2	no	—
387	C₂×C₄	—	52	2	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	13	1	no	—
392	C₈	—	13	1	no	—
393	C₈	—	13	1	no	—
394	C₈	—	13	1	no	—
395	C₈	—	52	2	no	—
396	C₈	D₈×D₁₃	1	1	yes	characteristic
397	C₈	D₈×D₁₃	1	1	yes	characteristic
398	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
399	C₈	#41×D₁₃	1	1	yes	characteristic
400	C₂²	—	4	2	no	—
401	C₂²	—	13	1	no	—
402	C₂²	—	13	1	no	—
403	C₂²	—	26	2	no	—
404	C₂²	—	52	2	no	—
405	C₂²	—	104	4	no	—
406	C₂²	D₁₃×#135	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	13	1	no	—
410	C₄	—	13	1	no	—
411	C₄	—	26	2	no	—
412	C₄	—	52	2	no	—
413	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
414	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	—	13	2	no	—
418	C₂	—	26	1	no	—
419	C₂	—	104	2	no	—
420	C₂	C₄×D₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2178	C₂
socle	C₂×C₁₃	C₂×C₄×D₈
prime radical	D₁₃×#508	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2178	D₁₃
hypocenter	C₁₃	C₂×#2178
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. D₁₃×#443	C₂	semidirect
3. #13116718	C₂	semidirect
4. #13116717	C₂	semidirect
5. #13116716	C₂	semidirect
6. #13116715	C₂	semidirect
7. #13116714	C₂	semidirect
8. D₁₃×#368	C₂	semidirect
9. D₁₃×#359	C₂	semidirect
10. C₄×C₁₆×D₁₃	C₂	semidirect
11. C₁₃×#2178	C₂	semidirect
15. C₁₃×#443	C₂²	semidirect
16. #11718857	C₂²	semidirect
19. #11718580	C₄	semidirect
20. D₁₃×Q₃₂	C₄	semidirect
21. #11718577	C₄	semidirect
22. D₁₃×SD₃₂	C₄	semidirect
23. #11718573	C₄	semidirect
24. D₁₃×D₁₆	C₄	semidirect
28. #11718556	C₂²	semidirect
32. #11718361	C₂²	semidirect
34. C₁₃×#368	C₂²	semidirect
35. C₁₃×#359	C₂²	semidirect
36. C₄×C₁₃×C₁₆	C₂²	semidirect
37. #11718159	C₂²	semidirect
38. #11718102	C₂²	semidirect
39. #11718098	C₂²	semidirect
40. C₁₆×Dic₁₃	C₂²	semidirect
41. C₁₆×Dic₁₃	C₂²	semidirect
42. #11718089	C₂²	semidirect
43. #11718085	C₂²	semidirect
44. C₄×#6090	C₂²	semidirect
67. C₁₃×Q₃₂	C₂×C₄	semidirect
68. C₁₃×SD₃₂	C₂×C₄	semidirect
69. C₁₃×D₁₆	C₂×C₄	semidirect
76. #88069	C₂×C₄	semidirect
77. #88068	C₂×C₄	semidirect
78. #88067	C₂×C₄	semidirect
79. #88066	C₂×C₄	semidirect
89. Dic₁₀₄	C₂×C₄	semidirect
90. #88040	C₂×C₄	semidirect
91. D₂₀₈	C₂×C₄	semidirect
161. #2178	D₁₃	direct (N × H)
219. #443	C₂×D₁₃	semidirect
225. #368	C₂×D₁₃	semidirect
229. #359	C₂×D₁₃	semidirect
233. C₄×C₁₆	C₂×D₁₃	semidirect
273. Q₃₂	C₄×D₁₃	semidirect
277. SD₃₂	C₄×D₁₃	semidirect
280. D₁₆	C₄×D₁₃	semidirect
307. D₁₃	#2178	direct (N × H)
363. C₁₃	C₂×#2178	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#508	2
D₁₃×#443	2
#13116718	2
#13116717	2
#13116716	2
#13116715	2
#13116714	2
D₁₃×#368	2
D₁₃×#359	2
C₄×C₁₆×D₁₃	2
C₁₃×#2178	2
C₂×#2178	13

Subgroups — D13×#2178 #16016315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2178 #16016315