Subgroups — D₁₃×#2230 #16017645

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×#443	C₂	1	1	yes	maximal, characteristic
3	#13117008	C₂	1	1	yes	maximal, characteristic, complemented
4	#13117007	C₂	1	1	yes	maximal, characteristic, complemented
5	#13117006	C₂	1	2	yes	maximal, complemented
6	#13117005	C₂	1	2	yes	maximal, complemented
7	#13117004	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₃×#365	C₂	1	2	yes	maximal, complemented
9	D₁₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#360	C₂	1	2	yes	maximal
11	C₁₃×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#135	C₂²	1	1	yes	characteristic
13	D₁₃×#131	—	2	1	no	—
14	D₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#443	C₂²	1	1	yes	characteristic
17	#11718857	C₂²	1	1	yes	characteristic
18	#11718805	—	2	1	no	—
19	#11718740	—	2	1	no	—
20	D₁₃×M₃₂	C₂²	1	2	yes	—
21	#11718556	C₂²	1	1	yes	characteristic
22	D₁₃×#108	C₂²	1	1	yes	characteristic
23	D₁₃×#106	—	2	1	no	—
24	D₁₃×#106	C₂²	1	2	yes	—
25	#11718516	—	2	1	no	—
26	#11718516	C₂²	1	2	yes	complemented
27	#11718485	—	2	1	no	—
28	D₁₃×#104	—	2	1	no	—
29	#11718361	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
31	#11718341	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#365	C₂²	1	2	yes	complemented
33	C₁₃×#364	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#360	C₂²	1	2	yes	—
35	#11718158	C₂²	1	2	yes	—
36	#11718110	C₂²	1	2	yes	—
37	#11718105	C₂²	1	2	yes	complemented
38	#11718103	C₂²	1	2	yes	complemented
39	#11718086	C₂²	1	2	yes	complemented
40	#11718080	C₂²	1	2	yes	—
41	#11718079	C₂²	1	2	yes	complemented
42	#11718055	C₂²	1	1	yes	characteristic, complemented
43	#41×D₁₃	—	2	1	no	—
44	C₂×Q₈×D₁₃	—	4	1	no	—
45	C₁₃×#135	C₂³	1	1	yes	characteristic
46	C₁₃×#131	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	#88204	—	2	1	no	—
49	#88202	—	2	1	no	—
50	#88198	—	4	1	no	—
51	#88173	Q₈	1	1	yes	characteristic, complemented
52	Q₁₆×D₁₃	Q₈	1	1	yes	characteristic, complemented
53	#88170	—	2	1	no	—
54	SD₁₆×D₁₃	—	2	1	no	—
55	#88166	Q₈	1	1	yes	characteristic, complemented
56	D₈×D₁₃	Q₈	1	1	yes	characteristic, complemented
57	#88161	—	2	1	no	—
58	#88161	—	4	1	no	—
59	M₁₆×D₁₃	—	2	1	no	—
60	M₁₆×D₁₃	—	4	1	no	—
61	#88158	C₂³	1	1	yes	characteristic
62	#88155	—	2	1	no	—
63	#88155	—	4	1	no	—
64	C₂×C₈×D₁₃	—	4	1	no	—
65	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₄×D₁₃	—	2	2	no	—
68	C₄⋊C₄×D₁₃	—	4	1	no	—
69	#88142	—	2	2	no	—
70	#88142	—	4	1	no	—
71	C₄²×D₁₃	D₄	1	1	yes	characteristic
72	#88123	—	2	1	no	—
73	C₁₃×M₃₂	C₂³	1	2	yes	—
74	C₁₃×#108	C₂³	1	1	yes	characteristic
75	C₁₃×#106	—	2	1	no	—
76	C₁₃×#106	C₂³	1	2	yes	—
77	C₁₃×#104	—	2	1	no	—
78	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	#88077	—	2	1	no	—
80	#88065	—	2	1	no	—
81	#88062	—	2	1	no	—
82	#88059	C₂³	1	1	yes	characteristic
83	#88057	—	2	1	no	—
84	#88057	C₂³	1	2	yes	—
85	C₈×Dic₁₃	D₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
87	#88052	C₂³	1	2	yes	—
88	#88048	—	2	2	no	—
89	#88048	—	2	2	no	—
90	#88045	—	2	1	no	—
91	C₄×#1055	D₄	1	1	yes	characteristic
92	#88038	—	2	2	no	—
93	C₁₆×D₁₃	—	2	2	no	—
94	C₂×#2230	—	13	1	no	maximal, Sylow
95	C₁₃×#41	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	4	1	no	—
97	#6131	—	2	1	no	—
98	Q₈×D₁₃	—	2	1	no	—
99	Q₈×D₁₃	—	8	4	no	—
100	#6129	—	2	1	no	—
101	#6129	—	4	1	no	—
102	D₄×D₁₃	—	2	1	no	—
103	D₄×D₁₃	—	4	1	no	—
104	#6127	—	2	1	no	—
105	#6127	—	4	1	no	—
106	C₂×C₄×D₁₃	—	2	1	no	—
107	C₂×C₄×D₁₃	—	4	1	no	—
108	C₂×C₄×D₁₃	—	4	2	no	—
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×Dic₂₆	—	4	2	no	—
111	C₂×Dic₂₆	—	4	1	no	—
112	C₁₃×Q₁₆	C₂×Q₈	1	1	yes	characteristic, complemented
113	C₁₃×SD₁₆	—	2	1	no	—
114	C₁₃×D₈	C₂×Q₈	1	1	yes	characteristic, complemented
115	C₁₃×M₁₆	—	2	1	no	—
116	C₁₃×M₁₆	—	4	1	no	—
117	C₂×C₈×C₁₃	—	4	1	no	—
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
123	#6107	—	2	1	no	—
124	#6106	—	2	1	no	—
125	#6105	—	2	1	no	—
126	#6104	—	2	1	no	—
127	C₄⋊Dic₁₃	—	2	2	no	—
128	C₄⋊Dic₁₃	—	4	1	no	—
129	#6101	—	4	2	no	—
130	#6101	—	4	2	no	—
131	C₄×Dic₁₃	—	2	1	no	—
132	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
133	#6099	—	2	1	no	—
134	#6099	—	4	1	no	—
135	C₂×#1055	—	4	1	no	—
136	C₂×#1055	C₂×D₄	1	1	yes	characteristic
137	C₂×#1055	C₂×D₄	1	1	yes	characteristic
138	Dic₅₂	C₂×Q₈	1	1	yes	characteristic, complemented
139	D₁₀₄	C₂×Q₈	1	1	yes	characteristic, complemented
140	#6095	—	2	1	no	—
141	#6094	—	4	1	no	—
142	#6094	—	4	1	no	—
143	#6094	—	4	1	no	—
144	C₈×D₁₃	—	4	1	no	—
145	C₈×D₁₃	—	4	1	no	—
146	C₈×D₁₃	—	4	1	no	—
147	C₈×D₁₃	SD₁₆	1	1	yes	characteristic
148	C₈×D₁₃	SD₁₆	1	1	yes	characteristic
149	C₈×D₁₃	SD₁₆	1	1	yes	characteristic
150	C₈×D₁₃	SD₁₆	1	1	yes	characteristic
151	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
152	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
153	C₈×D₁₃	#41	1	1	yes	characteristic
154	C₈×D₁₃	#41	1	1	yes	characteristic
155	C₁₃×C₁₆	—	2	2	no	—
156	#6090	—	2	2	no	—
157	C₂×#498	—	13	1	no	—
158	C₂×#443	—	13	1	no	—
159	#2230	—	13	1	no	—
160	#2230	—	13	1	no	—
161	#2230	—	13	2	no	—
162	#2230	—	13	1	no	—
163	#2230	—	13	2	no	—
164	#2230	D₁₃	1	1	yes	characteristic, direct product factor
165	C₂×#365	—	13	2	no	—
166	C₂×#364	—	13	1	no	—
167	C₂×#360	—	13	2	no	—
168	C₂²×D₁₃	—	4	1	no	—
169	C₂²×D₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	1	no	—
171	Q₈×C₁₃	—	8	2	no	—
172	D₄×C₁₃	—	2	1	no	—
173	D₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂²⋊D₁₃	—	4	1	no	—
179	C₂²⋊D₁₃	—	4	1	no	—
180	C₂²⋊D₁₃	—	4	1	no	—
181	C₂×Dic₁₃	—	2	1	no	—
182	C₂×Dic₁₃	—	4	1	no	—
183	C₂×Dic₁₃	—	4	2	no	—
184	C₂×Dic₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
185	D₅₂	—	2	1	no	—
186	D₅₂	—	4	1	no	—
187	C₄×D₁₃	—	2	4	no	—
188	C₄×D₁₃	—	4	1	no	—
189	C₄×D₁₃	—	4	1	no	—
190	C₄×D₁₃	—	4	1	no	—
191	C₄×D₁₃	—	8	4	no	—
192	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
193	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
194	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
195	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
196	Dic₂₆	—	2	1	no	—
197	Dic₂₆	—	4	1	no	—
198	Dic₂₆	—	8	4	no	—
199	Dic₂₆	—	8	2	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₈×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
202	C₈×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
203	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
204	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
205	#1055	—	4	1	no	—
206	#1055	C₂²⋊Q₈	1	1	yes	characteristic
207	#1055	C₂²⋊Q₈	1	1	yes	characteristic
208	#1055	C₂×SD₁₆	1	1	yes	characteristic
209	#1055	C₂×SD₁₆	1	1	yes	characteristic
210	C₂×#135	—	13	1	no	—
211	C₂×#131	—	26	1	no	—
212	C₂×C₄⋊Q₈	—	26	1	no	—
213	C₂×M₃₂	—	13	2	no	—
214	#498	—	13	2	no	—
215	#498	—	13	1	no	—
216	#498	—	26	1	no	—
217	#498	—	26	1	no	—
218	#498	C₂×D₁₃	1	1	yes	characteristic, complemented
219	#443	—	13	1	no	—
220	#443	—	13	1	no	—
221	#443	—	13	1	no	—
222	#443	—	26	1	no	—
223	#443	—	26	1	no	—
224	#443	C₂×D₁₃	1	1	yes	characteristic
225	C₂×#108	—	13	1	no	—
226	C₂×#106	—	13	2	no	—
227	C₂×#106	—	26	1	no	—
228	C₂×#104	—	26	1	no	—
229	C₂×C₄×C₈	—	13	1	no	—
230	#365	—	13	2	no	—
231	#365	—	13	2	no	—
232	#365	—	13	2	no	—
233	#365	C₂×D₁₃	1	2	yes	complemented
234	#364	—	13	2	no	—
235	#364	—	13	1	no	—
236	#364	C₂×D₁₃	1	1	yes	characteristic, complemented
237	#360	—	13	2	no	—
238	#360	—	13	2	no	—
239	#360	—	13	2	no	—
240	#360	C₂×D₁₃	1	2	yes	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂×D₁₃	—	2	2	no	—
244	C₂×D₁₃	—	4	1	no	—
245	C₂×D₁₃	—	8	2	no	—
246	C₂×D₁₃	#476	1	1	yes	characteristic
247	C₂×D₁₃	#476	1	1	yes	characteristic
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
253	Dic₁₃	—	2	2	no	—
254	Dic₁₃	—	4	1	no	—
255	Dic₁₃	—	8	2	no	—
256	Dic₁₃	#476	1	1	yes	characteristic
257	Dic₁₃	#476	1	1	yes	characteristic
258	C₂×#41	—	26	1	no	—
259	C₂²×Q₈	—	52	1	no	—
260	#135	—	13	1	no	—
261	#135	—	13	1	no	—
262	#135	—	13	1	no	—
263	#135	—	26	1	no	—
264	#135	—	26	1	no	—
265	#135	C₂²×D₁₃	1	1	yes	characteristic
266	C₂×Q₁₆	—	13	1	no	—
267	C₂×SD₁₆	—	26	1	no	—
268	C₂×D₈	—	13	1	no	—
269	#131	—	2	1	no	—
270	#131	—	26	1	no	—
271	#131	—	26	1	no	—
272	#131	—	26	1	no	—
273	#131	—	52	1	no	—
274	#131	—	52	1	no	—
275	C₂×M₁₆	—	26	1	no	—
276	C₂×M₁₆	—	52	1	no	—
277	C₂²×C₈	—	13	1	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	52	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	26	2	no	—
282	C₄⋊Q₈	—	26	1	no	—
283	C₄⋊Q₈	—	52	1	no	—
284	C₄⋊Q₈	—	52	1	no	—
285	C₂×C₄⋊C₄	—	26	2	no	—
286	C₂×C₄⋊C₄	—	52	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	M₃₂	—	13	2	no	—
289	M₃₂	—	26	2	no	—
290	M₃₂	C₂²×D₁₃	1	2	yes	—
291	C₂×C₁₆	—	26	2	no	—
292	#108	—	13	1	no	—
293	#108	—	26	1	no	—
294	#108	C₂²×D₁₃	1	1	yes	characteristic
295	#106	—	2	1	no	—
296	#106	—	13	2	no	—
297	#106	—	26	2	no	—
298	#106	—	26	2	no	—
299	#106	—	26	1	no	—
300	#106	C₂²×D₁₃	1	2	yes	—
301	#104	—	2	1	no	—
302	#104	—	26	1	no	—
303	#104	—	26	1	no	—
304	#104	—	26	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₂×C₁₃	—	2	1	no	—
310	C₂×C₁₃	—	8	1	no	—
311	C₂×C₁₃	C₂×#476	1	1	yes	characteristic
312	D₁₃	—	2	1	no	—
313	D₁₃	—	8	1	no	—
314	D₁₃	#2230	1	2	yes	direct product factor
315	#41	—	2	1	no	—
316	#41	—	26	1	no	—
317	#41	—	26	1	no	—
318	#41	—	26	1	no	—
319	#41	—	52	1	no	—
320	#41	—	52	1	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	26	1	no	—
323	C₂×Q₈	—	52	1	no	—
324	C₂×Q₈	—	52	2	no	—
325	C₂×Q₈	—	104	4	no	—
326	C₂×D₄	—	26	1	no	—
327	C₂×D₄	—	52	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	26	1	no	—
330	C₂²×C₄	—	52	1	no	—
331	C₂²×C₄	—	52	2	no	—
332	Q₁₆	—	13	1	no	—
333	Q₁₆	—	26	1	no	—
334	Q₁₆	Q₈×D₁₃	1	1	yes	characteristic, complemented
335	SD₁₆	—	2	1	no	—
336	SD₁₆	—	26	1	no	—
337	SD₁₆	—	26	1	no	—
338	SD₁₆	—	26	1	no	—
339	D₈	—	13	1	no	—
340	D₈	—	26	1	no	—
341	D₈	Q₈×D₁₃	1	1	yes	characteristic, complemented
342	M₁₆	—	2	1	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	26	1	no	—
345	M₁₆	—	52	1	no	—
346	M₁₆	—	52	1	no	—
347	M₁₆	—	52	1	no	—
348	M₁₆	—	52	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	13	1	no	—
351	C₂×C₈	—	13	1	no	—
352	C₂×C₈	—	13	1	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	13	1	no	—
355	C₂×C₈	—	13	1	no	—
356	C₂×C₈	—	13	1	no	—
357	C₂×C₈	—	13	1	no	—
358	C₂×C₈	—	13	1	no	—
359	C₂×C₈	—	13	1	no	—
360	C₂×C₈	—	52	1	no	—
361	C₂×C₈	—	52	1	no	—
362	C₂×C₈	—	52	1	no	—
363	C₂×C₈	—	52	1	no	—
364	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	26	2	no	—
369	C₄⋊C₄	—	52	1	no	—
370	C₄⋊C₄	—	52	2	no	—
371	C₄⋊C₄	—	52	2	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	26	1	no	—
374	C₄²	D₄×D₁₃	1	1	yes	characteristic
375	C₁₆	—	2	2	no	—
376	C₁₆	—	26	2	no	—
377	C₁₃	C₂×#2230	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	13	1	no	—
379	C₂³	—	52	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	8	2	no	—
382	Q₈	—	26	1	no	—
383	Q₈	—	52	1	no	—
384	Q₈	—	104	2	no	—
385	Q₈	—	104	4	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	26	1	no	—
389	D₄	—	52	1	no	—
390	D₄	—	52	1	no	—
391	D₄	—	52	1	no	—
392	D₄	—	52	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	26	4	no	—
402	C₂×C₄	—	26	1	no	—
403	C₂×C₄	—	52	1	no	—
404	C₂×C₄	—	52	1	no	—
405	C₂×C₄	—	52	1	no	—
406	C₂×C₄	—	52	1	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	104	4	no	—
409	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	13	1	no	—
412	C₈	—	13	1	no	—
413	C₈	—	13	1	no	—
414	C₈	—	13	1	no	—
415	C₈	—	52	1	no	—
416	C₈	SD₁₆×D₁₃	1	1	yes	characteristic
417	C₈	SD₁₆×D₁₃	1	1	yes	characteristic
418	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
419	C₈	#41×D₁₃	1	1	yes	characteristic
420	C₂²	—	4	1	no	—
421	C₂²	—	13	1	no	—
422	C₂²	—	13	1	no	—
423	C₂²	—	26	2	no	—
424	C₂²	—	52	1	no	—
425	C₂²	—	104	2	no	—
426	C₂²	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	13	1	no	—
431	C₄	—	13	1	no	—
432	C₄	—	26	2	no	—
433	C₄	—	52	1	no	—
434	C₄	—	104	2	no	—
435	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
436	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	13	2	no	—
440	C₂	—	26	1	no	—
441	C₂	—	104	1	no	—
442	C₂	D₁₃×#476	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃×#476
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2230	C₂
socle	C₂×C₁₃	C₂×#476
prime radical	D₁₃×#135	C₂²
hypercenter	#2230	D₁₃
hypocenter	C₁₃	C₂×#2230
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. D₁₃×#498	C₂	semidirect
3. #13117008	C₂	semidirect
4. #13117007	C₂	semidirect
5. #13117006	C₂	semidirect
6. #13117005	C₂	semidirect
7. #13117004	C₂	semidirect
8. D₁₃×#365	C₂	semidirect
9. D₁₃×#364	C₂	semidirect
11. C₁₃×#2230	C₂	semidirect
15. C₁₃×#498	C₂²	semidirect
26. #11718516	C₂²	semidirect
31. #11718341	C₂²	semidirect
32. C₁₃×#365	C₂²	semidirect
33. C₁₃×#364	C₂²	semidirect
37. #11718105	C₂²	semidirect
38. #11718103	C₂²	semidirect
39. #11718086	C₂²	semidirect
41. #11718079	C₂²	semidirect
42. #11718055	C₂²	semidirect
51. #88173	Q₈	semidirect
52. Q₁₆×D₁₃	Q₈	semidirect
55. #88166	Q₈	semidirect
56. D₈×D₁₃	Q₈	semidirect
112. C₁₃×Q₁₆	C₂×Q₈	semidirect
114. C₁₃×D₈	C₂×Q₈	semidirect
138. Dic₅₂	C₂×Q₈	semidirect
139. D₁₀₄	C₂×Q₈	semidirect
164. #2230	D₁₃	direct (N × H)
218. #498	C₂×D₁₃	semidirect
233. #365	C₂×D₁₃	semidirect
236. #364	C₂×D₁₃	semidirect
314. D₁₃	#2230	direct (N × H)
334. Q₁₆	Q₈×D₁₃	semidirect
341. D₈	Q₈×D₁₃	semidirect
377. C₁₃	C₂×#2230	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#498	2
D₁₃×#443	2
#13117008	2
#13117007	2
#13117006	2
#13117005	2
#13117004	2
D₁₃×#365	2
D₁₃×#364	2
D₁₃×#360	2
C₁₃×#2230	2
C₂×#2230	13

Subgroups — D13×#2230 #16017645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2230 #16017645