Subgroups — C₁₃×#3401 #13112459

Order 1664.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#496	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×#127	C₂²	1	1	yes	characteristic
27	C₁₃×#126	—	2	1	no	—
28	C₁₃×#126	—	2	1	no	—
29	C₁₃×#124	—	2	1	no	—
30	C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₁₃×#124	C₂²	1	1	yes	characteristic
34	C₁₃×#123	—	2	1	no	—
35	C₁₃×#123	—	2	1	no	—
36	C₁₃×C₂²⋊Q₈	—	2	1	no	—
37	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₄×D₄×C₁₃	—	2	1	no	—
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#117	—	2	1	no	—
46	C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₁₃×#102	C₂²	1	1	yes	characteristic
55	C₁₃×#102	C₂²	1	1	yes	characteristic
56	C₁₃×#97	C₂²	1	1	yes	characteristic
57	C₁₃×#97	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₃	—	2	1	no	—
64	C₂×D₄×C₁₃	—	2	1	no	—
65	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	1	no	—
71	C₁₃×Q₁₆	—	2	2	no	—
72	C₁₃×Q₁₆	—	4	1	no	—
73	C₁₃×SD₁₆	—	2	2	no	—
74	C₁₃×SD₁₆	—	4	1	no	—
75	C₁₃×SD₁₆	—	4	1	no	—
76	C₁₃×SD₁₆	—	4	1	no	—
77	C₁₃×SD₁₆	—	4	1	no	—
78	C₁₃×D₈	—	2	2	no	—
79	C₁₃×D₈	—	4	1	no	—
80	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₄²×C₁₃	—	2	1	no	—
106	C₄²×C₁₃	—	2	1	no	—
107	C₄²×C₁₃	—	2	1	no	—
108	C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	#3401	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₃	—	2	1	no	—
113	C₂³×C₁₃	—	2	1	no	—
114	C₂³×C₁₃	—	2	1	no	—
115	Q₈×C₁₃	—	2	1	no	—
116	Q₈×C₁₃	—	2	1	no	—
117	Q₈×C₁₃	—	2	1	no	—
118	Q₈×C₁₃	—	2	1	no	—
119	Q₈×C₁₃	—	2	1	no	—
120	Q₈×C₁₃	—	2	1	no	—
121	Q₈×C₁₃	—	4	1	no	—
122	D₄×C₁₃	—	2	1	no	—
123	D₄×C₁₃	—	2	1	no	—
124	D₄×C₁₃	—	2	1	no	—
125	D₄×C₁₃	—	2	1	no	—
126	D₄×C₁₃	—	2	1	no	—
127	D₄×C₁₃	—	2	1	no	—
128	D₄×C₁₃	—	4	2	no	—
129	D₄×C₁₃	—	8	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	4	2	no	—
136	C₂×C₄×C₁₃	—	8	1	no	—
137	C₂×C₄×C₁₃	—	8	1	no	—
138	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₈×C₁₃	—	2	1	no	—
146	C₈×C₁₃	—	2	1	no	—
147	C₈×C₁₃	—	2	1	no	—
148	C₈×C₁₃	#41	1	2	yes	—
149	#559	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#497	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#496	C₂×C₁₃	1	1	yes	characteristic
153	#495	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#464	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#464	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#463	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#463	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#461	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#460	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#446	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#442	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#441	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂²×C₁₃	—	4	1	no	—
165	C₂²×C₁₃	—	4	1	no	—
166	C₂²×C₁₃	—	4	1	no	—
167	C₂²×C₁₃	—	4	1	no	—
168	C₂²×C₁₃	—	4	1	no	—
169	C₂²×C₁₃	—	4	1	no	—
170	C₂²×C₁₃	—	4	1	no	—
171	C₂²×C₁₃	—	4	1	no	—
172	C₂²×C₁₃	—	4	1	no	—
173	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₄×C₁₃	—	2	1	no	—
175	C₄×C₁₃	—	2	1	no	—
176	C₄×C₁₃	—	2	1	no	—
177	C₄×C₁₃	—	2	1	no	—
178	C₄×C₁₃	—	2	1	no	—
179	C₄×C₁₃	—	2	1	no	—
180	C₄×C₁₃	—	4	1	no	—
181	C₄×C₁₃	—	4	1	no	—
182	C₄×C₁₃	—	4	1	no	—
183	C₄×C₁₃	—	4	1	no	—
184	C₄×C₁₃	—	4	1	no	—
185	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
197	#127	C₂²×C₁₃	1	1	yes	characteristic
198	#126	—	2	1	no	—
199	#126	—	2	1	no	—
200	#124	—	2	1	no	—
201	#124	C₂²×C₁₃	1	1	yes	characteristic
202	#124	C₂²×C₁₃	1	1	yes	characteristic
203	#124	C₂²×C₁₃	1	1	yes	characteristic
204	#124	C₂²×C₁₃	1	1	yes	characteristic
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
216	#117	—	2	1	no	—
217	#106	C₂²×C₁₃	1	1	yes	characteristic
218	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
221	#103	C₂²×C₁₃	1	1	yes	characteristic
222	#103	C₂²×C₁₃	1	1	yes	characteristic
223	#103	C₂²×C₁₃	1	1	yes	characteristic
224	#102	C₂²×C₁₃	1	1	yes	characteristic
225	#102	C₂²×C₁₃	1	1	yes	characteristic
226	#102	C₂²×C₁₃	1	1	yes	characteristic
227	#97	C₂²×C₁₃	1	1	yes	characteristic
228	#97	C₂²×C₁₃	1	1	yes	characteristic
229	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₁₃	—	8	1	no	—
231	C₂×C₁₃	—	8	1	no	—
232	C₂×C₁₃	—	8	1	no	—
233	C₂×C₁₃	#550	1	1	yes	characteristic
234	C₂×C₁₃	#575	1	1	yes	characteristic
235	C₂×C₁₃	#577	1	1	yes	characteristic
236	C₂×Q₈	D₄×C₁₃	1	1	yes	characteristic
237	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
240	C₂×D₄	—	2	1	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
243	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	Q₁₆	—	2	2	no	—
249	Q₁₆	—	4	1	no	—
250	SD₁₆	—	2	2	no	—
251	SD₁₆	—	4	1	no	—
252	SD₁₆	—	4	1	no	—
253	SD₁₆	—	4	1	no	—
254	SD₁₆	—	4	1	no	—
255	D₈	—	2	2	no	—
256	D₈	—	4	1	no	—
257	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	2	1	no	—
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
267	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
268	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
269	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²⋊C₄	—	2	1	no	—
272	C₂²⋊C₄	—	2	1	no	—
273	C₂²⋊C₄	—	2	1	no	—
274	C₂²⋊C₄	—	2	1	no	—
275	C₂²⋊C₄	—	2	1	no	—
276	C₂²⋊C₄	—	2	1	no	—
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	1	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₁₃	#3401	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	2	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	Q₈	—	2	1	no	—
293	Q₈	—	2	1	no	—
294	Q₈	—	2	1	no	—
295	Q₈	—	2	1	no	—
296	Q₈	—	2	1	no	—
297	Q₈	—	2	1	no	—
298	Q₈	—	4	1	no	—
299	D₄	—	2	1	no	—
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	2	1	no	—
303	D₄	—	2	1	no	—
304	D₄	—	2	1	no	—
305	D₄	—	4	2	no	—
306	D₄	—	8	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	8	1	no	—
314	C₂×C₄	—	8	1	no	—
315	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
322	C₈	—	2	1	no	—
323	C₈	—	2	1	no	—
324	C₈	—	2	1	no	—
325	C₈	C₁₃×#41	1	2	yes	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	1	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	1	no	—
346	C₄	—	4	1	no	—
347	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
348	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂	—	8	1	no	—
350	C₂	—	8	1	no	—
351	C₂	—	8	1	no	—
352	C₂	C₁₃×#550	1	1	yes	characteristic
353	C₂	C₁₃×#575	1	1	yes	characteristic
354	C₂	C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#559	C₂	semidirect
2. C₁₃×#556	C₂	semidirect
3. C₁₃×#497	C₂	semidirect
5. C₁₃×#495	C₂	semidirect
6. C₁₃×#464	C₂	semidirect
7. C₁₃×#464	C₂	semidirect
8. C₁₃×#463	C₂	semidirect
9. C₁₃×#463	C₂	semidirect
10. C₁₃×#461	C₂	semidirect
11. C₁₃×#460	C₂	semidirect
12. C₁₃×#446	C₂	semidirect
13. C₁₃×#442	C₂	semidirect
14. C₁₃×#441	C₂	semidirect
15. C₄×C₁₃×SD₁₆	C₂	semidirect
111. #3401	C₁₃	direct (N × H)
149. #559	C₂×C₁₃	semidirect
150. #556	C₂×C₁₃	semidirect
151. #497	C₂×C₁₃	semidirect
153. #495	C₂×C₁₃	semidirect
154. #464	C₂×C₁₃	semidirect
155. #464	C₂×C₁₃	semidirect
156. #463	C₂×C₁₃	semidirect
157. #463	C₂×C₁₃	semidirect
158. #461	C₂×C₁₃	semidirect
159. #460	C₂×C₁₃	semidirect
160. #446	C₂×C₁₃	semidirect
161. #442	C₂×C₁₃	semidirect
162. #441	C₂×C₁₃	semidirect
163. C₄×SD₁₆	C₂×C₁₃	semidirect
288. C₁₃	#3401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#559	2
C₁₃×#556	2
C₁₃×#497	2
C₁₃×#496	2
C₁₃×#495	2
C₁₃×#464	2
C₁₃×#463	2
C₁₃×#461	2
C₁₃×#460	2
C₁₃×#446	2
C₁₃×#442	2
C₁₃×#441	2
C₄×C₁₃×SD₁₆	2
#3401	13

Subgroups — C13×#3401 #13112459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3401 #13112459