Subgroups — D₁₃×#463 #13124256

Order 1664.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718826	C₂	1	1	yes	maximal, characteristic, complemented
7	#11718814	C₂	1	1	yes	maximal, characteristic, complemented
8	#11718718	C₂	1	1	yes	maximal, characteristic, complemented
9	#11718677	C₂	1	1	yes	maximal, characteristic, complemented
10	#11718505	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#11718480	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	#11718448	C₂	1	1	yes	maximal, characteristic, complemented
15	D₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₃	—	2	1	no	—
20	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
23	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	#88201	C₂²	1	1	yes	characteristic, complemented
25	C₂×#6106	C₂²	1	1	yes	characteristic, complemented
26	#88190	C₂²	1	1	yes	characteristic, complemented
27	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6105	C₂²	1	1	yes	characteristic, complemented
29	C₂×#6104	C₂²	1	1	yes	characteristic
30	C₂×#6104	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊D₁₃	—	2	1	no	—
32	SD₁₆×D₁₃	—	2	4	no	—
33	D₈×D₁₃	—	2	4	no	—
34	C₂×D₁₀₄	C₂²	1	1	yes	characteristic
35	C₂×#6095	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
38	#88147	C₂²	1	1	yes	characteristic, complemented
39	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
40	#88139	—	2	1	no	—
41	#88139	—	2	1	no	—
42	#88135	—	2	1	no	—
43	C₂²⋊C₄×D₁₃	—	2	1	no	—
44	C₂²⋊C₄×D₁₃	—	2	1	no	—
45	C₂²⋊C₄×D₁₃	—	2	1	no	—
46	#88129	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
48	C₄²×D₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
52	#88075	C₂²	1	1	yes	characteristic, complemented
53	#88072	C₂²	1	1	yes	characteristic, complemented
54	#88061	C₂²	1	1	yes	characteristic, complemented
55	#88056	C₂²	1	1	yes	characteristic, complemented
56	#88054	C₂²	1	1	yes	characteristic, complemented
57	#88054	C₂²	1	1	yes	characteristic, complemented
58	#88050	C₂²	1	1	yes	characteristic, complemented
59	#88049	C₂²	1	1	yes	characteristic, complemented
60	C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃	—	2	1	no	—
62	C₂³×D₁₃	—	2	1	no	—
63	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	—	2	1	no	—
67	C₂×C₂²⋊D₁₃	—	2	1	no	—
68	C₂×C₂²⋊D₁₃	—	2	1	no	—
69	C₂²×Dic₁₃	—	2	1	no	—
70	Q₈×D₁₃	—	2	2	no	—
71	Q₈×D₁₃	—	2	2	no	—
72	D₄×D₁₃	—	2	2	no	—
73	D₄×D₁₃	—	2	2	no	—
74	D₄×D₁₃	—	2	2	no	—
75	D₄×D₁₃	D₄	1	4	yes	—
76	C₂×D₅₂	C₂³	1	1	yes	characteristic
77	C₂×D₅₂	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₃	—	2	1	no	—
79	C₂×C₄×D₁₃	—	2	1	no	—
80	C₂×C₄×D₁₃	—	2	1	no	—
81	C₂×C₄×D₁₃	—	2	1	no	—
82	C₂×C₄×D₁₃	—	4	4	no	—
83	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₆	—	2	1	no	—
87	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
88	C₁₃×SD₁₆	—	2	2	no	—
89	C₁₃×D₈	—	2	2	no	—
90	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²⋊Dic₁₃	—	2	1	no	—
98	C₂²⋊Dic₁₃	—	2	1	no	—
99	C₂²⋊Dic₁₃	—	2	1	no	—
100	#6106	—	2	2	no	—
101	#6105	—	2	2	no	—
102	#6104	—	2	2	no	—
103	#6104	—	2	2	no	—
104	#6103	—	2	1	no	—
105	#6103	—	2	1	no	—
106	#6103	—	2	1	no	—
107	#6103	—	2	1	no	—
108	#6103	—	2	1	no	—
109	#6103	—	2	1	no	—
110	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
111	#6101	—	2	1	no	—
112	C₄×Dic₁₃	D₄	1	1	yes	characteristic
113	C₄×Dic₁₃	D₄	1	1	yes	characteristic
114	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
115	C₂×#1055	C₂³	1	1	yes	characteristic
116	C₂×#1055	C₂³	1	1	yes	characteristic
117	D₁₀₄	—	2	2	no	—
118	#6095	—	2	2	no	—
119	C₈×D₁₃	—	2	2	no	—
120	C₈×D₁₃	—	2	2	no	—
121	C₂×#463	—	13	1	no	maximal, Sylow
122	C₂³×C₁₃	—	2	1	no	—
123	C₂³×C₁₃	—	2	1	no	—
124	C₂²×D₁₃	—	2	1	no	—
125	C₂²×D₁₃	—	2	4	no	—
126	C₂²×D₁₃	—	2	1	no	—
127	C₂²×D₁₃	—	4	2	no	—
128	C₂²×D₁₃	—	4	2	no	—
129	C₂²×D₁₃	—	4	2	no	—
130	C₂²×D₁₃	—	4	2	no	—
131	C₂²×D₁₃	—	4	2	no	—
132	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
133	Q₈×C₁₃	—	2	1	no	—
134	Q₈×C₁₃	—	2	1	no	—
135	D₄×C₁₃	—	2	1	no	—
136	D₄×C₁₃	—	2	1	no	—
137	D₄×C₁₃	—	2	1	no	—
138	D₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂²⋊D₁₃	—	2	4	no	—
146	C₂²⋊D₁₃	—	4	2	no	—
147	C₂×Dic₁₃	—	2	1	no	—
148	C₂×Dic₁₃	—	2	1	no	—
149	C₂×Dic₁₃	—	4	2	no	—
150	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
153	D₅₂	—	2	1	no	—
154	D₅₂	—	2	1	no	—
155	D₅₂	—	2	1	no	—
156	D₅₂	C₂×D₄	1	2	yes	—
157	C₄×D₁₃	—	2	2	no	—
158	C₄×D₁₃	—	2	2	no	—
159	C₄×D₁₃	—	4	2	no	—
160	C₄×D₁₃	—	4	2	no	—
161	C₄×D₁₃	—	4	2	no	—
162	C₄×D₁₃	—	4	2	no	—
163	C₄×D₁₃	C₂×D₄	1	2	yes	—
164	C₄×D₁₃	#41	1	2	yes	—
165	Dic₂₆	—	2	1	no	—
166	Dic₂₆	—	2	1	no	—
167	Dic₂₆	—	4	2	no	—
168	C₈×C₁₃	—	2	1	no	—
169	C₈×C₁₃	—	2	1	no	—
170	#1055	—	2	1	no	—
171	#1055	—	2	1	no	—
172	C₂²×SD₁₆	—	13	1	no	—
173	C₂²×D₈	—	13	1	no	—
174	C₂×#124	—	13	1	no	—
175	C₂×C₄×D₄	—	13	1	no	—
176	#463	—	13	1	no	—
177	#463	—	13	1	no	—
178	#463	—	13	1	no	—
179	#463	—	13	1	no	—
180	#463	—	13	1	no	—
181	#463	—	13	1	no	—
182	#463	—	13	1	no	—
183	#463	D₁₃	1	1	yes	characteristic, direct product factor
184	C₂×C₄⋊C₈	—	13	1	no	—
185	C₂×#103	—	13	1	no	—
186	C₂×#102	—	13	1	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	4	1	no	—
189	C₂²×C₁₃	—	4	1	no	—
190	C₂²×C₁₃	—	4	1	no	—
191	C₂²×C₁₃	—	4	1	no	—
192	C₂²×C₁₃	—	4	1	no	—
193	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×D₁₃	—	2	2	no	—
195	C₂×D₁₃	—	4	1	no	—
196	C₂×D₁₃	—	4	1	no	—
197	C₂×D₁₃	—	4	8	no	—
198	C₂×D₁₃	—	4	1	no	—
199	C₂×D₁₃	—	4	1	no	—
200	C₂×D₁₃	—	4	1	no	—
201	C₂×D₁₃	—	8	4	no	—
202	C₂×D₁₃	#121	1	2	yes	—
203	C₂×D₁₃	#135	1	2	yes	—
204	C₂×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
205	C₄×C₁₃	—	2	1	no	—
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	4	1	no	—
208	C₄×C₁₃	—	4	1	no	—
209	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	Dic₁₃	—	2	1	no	—
212	Dic₁₃	—	2	1	no	—
213	Dic₁₃	—	4	1	no	—
214	Dic₁₃	—	4	1	no	—
215	Dic₁₃	#121	1	2	yes	—
216	C₂²×Q₈	—	13	1	no	—
217	C₂²×D₄	—	13	1	no	—
218	C₂²×D₄	—	13	1	no	—
219	C₂³×C₄	—	26	1	no	—
220	C₂×SD₁₆	—	13	1	no	—
221	C₂×SD₁₆	—	13	1	no	—
222	C₂×SD₁₆	—	13	1	no	—
223	C₂×SD₁₆	—	26	4	no	—
224	C₂×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
225	C₂×D₈	—	13	1	no	—
226	C₂×D₈	—	13	1	no	—
227	C₂×D₈	—	13	1	no	—
228	C₂×D₈	—	26	4	no	—
229	C₂×D₈	C₂×D₁₃	1	1	yes	characteristic
230	C₂²×C₈	—	13	1	no	—
231	C₂²×C₈	—	13	1	no	—
232	#124	—	13	1	no	—
233	#124	—	13	1	no	—
234	#124	—	13	1	no	—
235	#124	—	26	1	no	—
236	#124	—	26	1	no	—
237	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
238	C₄×D₄	—	13	1	no	—
239	C₄×D₄	—	13	1	no	—
240	C₄×D₄	—	13	1	no	—
241	C₄×D₄	—	26	1	no	—
242	C₄×D₄	—	26	1	no	—
243	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
244	C₂×C₄⋊C₄	—	13	1	no	—
245	C₂×C₂²⋊C₄	—	26	1	no	—
246	C₂×C₂²⋊C₄	—	26	1	no	—
247	C₂×C₂²⋊C₄	—	26	1	no	—
248	C₂×C₄²	—	13	1	no	—
249	C₄⋊C₈	—	13	1	no	—
250	C₄⋊C₈	—	13	1	no	—
251	C₄⋊C₈	—	13	1	no	—
252	C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
253	#103	—	13	1	no	—
254	#103	—	13	1	no	—
255	#103	—	13	1	no	—
256	#103	C₂×D₁₃	1	1	yes	characteristic, complemented
257	#102	—	13	1	no	—
258	#102	—	13	1	no	—
259	#102	—	13	1	no	—
260	#102	C₂×D₁₃	1	1	yes	characteristic, complemented
261	C₂×C₁₃	—	4	2	no	—
262	C₂×C₁₃	—	8	1	no	—
263	C₂×C₁₃	C₂×#121	1	1	yes	characteristic
264	C₂×C₁₃	C₂×#135	1	1	yes	characteristic
265	C₂×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	D₁₃	—	4	2	no	—
267	D₁₃	—	8	1	no	—
268	D₁₃	#463	1	4	yes	direct product factor
269	C₂⁴	—	26	1	no	—
270	C₂⁴	—	26	1	no	—
271	C₂×Q₈	—	13	1	no	—
272	C₂×Q₈	—	26	1	no	—
273	C₂×Q₈	—	26	2	no	—
274	C₂×Q₈	—	26	2	no	—
275	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
276	C₂×D₄	—	13	4	no	—
277	C₂×D₄	—	13	1	no	—
278	C₂×D₄	—	13	1	no	—
279	C₂×D₄	—	26	2	no	—
280	C₂×D₄	—	26	2	no	—
281	C₂×D₄	—	26	2	no	—
282	C₂×D₄	—	26	1	no	—
283	C₂×D₄	—	26	1	no	—
284	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
285	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	26	1	no	—
291	C₂²×C₄	—	26	1	no	—
292	C₂²×C₄	—	26	1	no	—
293	C₂²×C₄	—	26	1	no	—
294	C₂²×C₄	—	26	1	no	—
295	C₂²×C₄	—	52	4	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	26	2	no	—
298	SD₁₆	—	26	2	no	—
299	SD₁₆	—	26	2	no	—
300	D₈	—	2	2	no	—
301	D₈	—	26	2	no	—
302	D₈	—	26	2	no	—
303	D₈	—	26	2	no	—
304	C₂×C₈	—	13	1	no	—
305	C₂×C₈	—	13	1	no	—
306	C₂×C₈	—	26	2	no	—
307	C₂×C₈	—	26	2	no	—
308	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₄⋊C₄	—	13	1	no	—
311	C₄⋊C₄	—	26	1	no	—
312	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	26	1	no	—
317	C₂²⋊C₄	—	26	1	no	—
318	C₂²⋊C₄	—	26	1	no	—
319	C₂²⋊C₄	—	26	1	no	—
320	C₂²⋊C₄	—	26	1	no	—
321	C₂²⋊C₄	—	26	1	no	—
322	C₂²⋊C₄	—	26	1	no	—
323	C₂²⋊C₄	—	26	1	no	—
324	C₂²⋊C₄	—	26	1	no	—
325	C₄²	—	13	1	no	—
326	C₄²	—	13	1	no	—
327	C₄²	—	13	1	no	—
328	C₄²	C₂²×D₁₃	1	1	yes	characteristic
329	C₁₃	C₂×#463	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	13	1	no	—
333	C₂³	—	26	4	no	—
334	C₂³	—	26	1	no	—
335	C₂³	—	26	1	no	—
336	C₂³	—	52	2	no	—
337	C₂³	—	52	2	no	—
338	C₂³	—	52	2	no	—
339	C₂³	—	52	2	no	—
340	C₂³	—	52	2	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	26	1	no	—
344	Q₈	—	26	1	no	—
345	Q₈	—	52	2	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	13	2	no	—
350	D₄	—	26	4	no	—
351	D₄	—	26	1	no	—
352	D₄	—	26	1	no	—
353	D₄	—	26	1	no	—
354	D₄	—	52	2	no	—
355	D₄	D₄×D₁₃	1	2	yes	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	13	2	no	—
361	C₂×C₄	—	13	2	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	1	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	52	2	no	—
369	C₂×C₄	—	52	2	no	—
370	C₂×C₄	—	52	2	no	—
371	C₂×C₄	—	52	2	no	—
372	C₂×C₄	—	52	2	no	—
373	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
374	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	26	1	no	—
379	C₈	—	26	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	13	2	no	—
387	C₂²	—	13	2	no	—
388	C₂²	—	13	2	no	—
389	C₂²	—	26	2	no	—
390	C₂²	—	52	8	no	—
391	C₂²	—	52	1	no	—
392	C₂²	—	52	1	no	—
393	C₂²	—	52	1	no	—
394	C₂²	—	52	1	no	—
395	C₂²	—	52	1	no	—
396	C₂²	—	104	4	no	—
397	C₂²	C₂×D₄×D₁₃	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	13	2	no	—
403	C₄	—	26	1	no	—
404	C₄	—	26	1	no	—
405	C₄	—	52	1	no	—
406	C₄	—	52	1	no	—
407	C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
408	C₄	#41×D₁₃	1	1	yes	characteristic
409	C₂	—	4	2	no	—
410	C₂	—	8	1	no	—
411	C₂	—	13	4	no	—
412	C₂	—	52	2	no	—
413	C₂	—	104	1	no	—
414	C₂	D₁₃×#121	1	1	yes	characteristic
415	C₂	D₁₃×#135	1	1	yes	characteristic
416	C₂	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₁₃×#463	C₂
socle	C₂²×C₁₃	C₂²×D₄
prime radical	C₂×D₈×D₁₃	C₂
hypercenter	#463	D₁₃
hypocenter	C₁₃	C₂×#463
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₁₃	C₂	semidirect
3. D₁₃×#124	C₂	semidirect
4. C₄×D₄×D₁₃	C₂	semidirect
5. C₁₃×#463	C₂	semidirect
6. #11718826	C₂	semidirect
7. #11718814	C₂	semidirect
8. #11718718	C₂	semidirect
9. #11718677	C₂	semidirect
10. #11718505	C₂	semidirect
11. D₁₃×C₄⋊C₈	C₂	semidirect
12. #11718480	C₂	semidirect
13. D₁₃×#103	C₂	semidirect
14. #11718448	C₂	semidirect
15. D₁₃×#102	C₂	semidirect
20. C₂×C₁₃×SD₁₆	C₂²	semidirect
22. C₁₃×#124	C₂²	semidirect
23. C₄×D₄×C₁₃	C₂²	semidirect
24. #88201	C₂²	semidirect
25. C₂×#6106	C₂²	semidirect
26. #88190	C₂²	semidirect
27. D₄×Dic₁₃	C₂²	semidirect
28. C₂×#6105	C₂²	semidirect
35. C₂×#6095	C₂²	semidirect
38. #88147	C₂²	semidirect
46. #88129	C₂²	semidirect
47. C₄×D₅₂	C₂²	semidirect
49. C₁₃×C₄⋊C₈	C₂²	semidirect
50. C₁₃×#103	C₂²	semidirect
51. C₁₃×#102	C₂²	semidirect
52. #88075	C₂²	semidirect
53. #88072	C₂²	semidirect
54. #88061	C₂²	semidirect
55. #88056	C₂²	semidirect
56. #88054	C₂²	semidirect
57. #88054	C₂²	semidirect
58. #88050	C₂²	semidirect
59. #88049	C₂²	semidirect
60. C₄⋊#1055	C₂²	semidirect
183. #463	D₁₃	direct (N × H)
224. C₂×SD₁₆	C₂×D₁₃	semidirect
237. #124	C₂×D₁₃	semidirect
243. C₄×D₄	C₂×D₁₃	semidirect
252. C₄⋊C₈	C₂×D₁₃	semidirect
256. #103	C₂×D₁₃	semidirect
260. #102	C₂×D₁₃	semidirect
268. D₁₃	#463	direct (N × H)
329. C₁₃	C₂×#463	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₃	2
C₂×D₈×D₁₃	2
D₁₃×#124	2
C₄×D₄×D₁₃	2
C₁₃×#463	2
#11718826	2
#11718814	2
#11718718	2
#11718677	2
#11718505	2
D₁₃×C₄⋊C₈	2
#11718480	2
D₁₃×#103	2
#11718448	2
D₁₃×#102	2
C₂×#463	13

Subgroups — D13×#463 #13124256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#463 #13124256