Subgroups — C₁₃×#20563 #15706902

Order 3328.

954 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#435	C₂	1	2	yes	maximal
2	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1753	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1752	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1750	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1729	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	2	yes	—
14	C₁₃×#435	C₄	1	16	yes	complemented
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#390	C₄	1	2	yes	—
24	C₁₃×#389	C₄	1	2	yes	—
25	C₁₃×#388	C₄	1	4	yes	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₄³×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#336	C₂²	1	1	yes	characteristic
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂×C₁₃×M₁₆	—	4	2	no	—
38	C₂×C₁₃×M₁₆	—	4	2	no	—
39	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
40	C₂²×C₈×C₁₃	—	4	2	no	—
41	C₂²×C₈×C₁₃	—	4	2	no	—
42	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
48	C₁₃×#117	—	4	2	no	—
49	C₁₃×#117	—	4	2	no	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
63	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
64	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
65	C₁₃×#97	—	4	1	no	—
66	C₁₃×#97	—	4	1	no	—
67	C₁₃×#97	—	4	2	no	—
68	C₁₃×#97	C₂×C₄	1	8	yes	—
69	C₄×C₈×C₁₃	—	4	2	no	—
70	C₁₃×#95	C₂×C₄	1	4	yes	—
71	C₁₃×#95	C₂×C₄	1	2	yes	—
72	#20563	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
74	C₂×D₄×C₁₃	—	4	2	no	—
75	C₂×D₄×C₁₃	C₄²	1	4	yes	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₁₃×M₁₆	—	4	8	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	4	8	no	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
103	C₁₃×C₄⋊C₄	—	4	2	no	—
104	C₁₃×C₄⋊C₄	—	4	4	no	—
105	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
106	C₁₃×C₂²⋊C₄	—	4	4	no	—
107	C₁₃×C₂²⋊C₄	—	4	4	no	—
108	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	—	2	1	no	—
114	C₄²×C₁₃	—	4	2	no	—
115	C₄²×C₁₃	—	4	2	no	—
116	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
117	C₂×#435	C₂×C₁₃	1	2	yes	—
118	#2293	C₂×C₁₃	1	1	yes	characteristic
119	#1771	C₂×C₁₃	1	2	yes	complemented
120	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#1753	C₂×C₁₃	1	2	yes	complemented
122	#1752	C₂×C₁₃	1	2	yes	complemented
123	#1750	C₂×C₁₃	1	2	yes	complemented
124	#1745	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#1729	C₂×C₁₃	1	2	yes	complemented
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	2	4	no	—
129	C₂³×C₁₃	—	2	4	no	—
130	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
131	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
132	D₄×C₁₃	—	4	4	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
153	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
156	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
157	C₈×C₁₃	—	2	4	no	—
158	C₈×C₁₃	—	2	4	no	—
159	C₈×C₁₃	—	2	4	no	—
160	C₈×C₁₃	—	2	4	no	—
161	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
162	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
163	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
164	C₂×#117	C₂²×C₁₃	1	2	yes	—
165	#435	C₄×C₁₃	1	16	yes	complemented
166	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
167	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
168	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
169	C₂×#97	C₂²×C₁₃	1	2	yes	—
170	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×#97	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
174	#390	C₄×C₁₃	1	2	yes	—
175	#389	C₄×C₁₃	1	2	yes	—
176	#388	C₄×C₁₃	1	4	yes	—
177	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
178	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
179	C₄³	C₂²×C₁₃	1	1	yes	characteristic
180	#336	C₂²×C₁₃	1	1	yes	characteristic
181	#336	C₂²×C₁₃	1	2	yes	—
182	#336	C₂²×C₁₃	1	2	yes	—
183	#336	C₂²×C₁₃	1	2	yes	—
184	#336	C₂²×C₁₃	1	1	yes	characteristic
185	#336	C₂²×C₁₃	1	2	yes	—
186	C₂²×C₁₃	—	2	4	no	—
187	C₂²×C₁₃	—	2	4	no	—
188	C₂²×C₁₃	—	2	4	no	—
189	C₂²×C₁₃	—	4	4	no	—
190	C₂²×C₁₃	—	4	4	no	—
191	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
192	C₂²×C₁₃	#518	1	1	yes	characteristic
193	C₂²×C₁₃	#520	1	1	yes	characteristic
194	C₂²×C₁₃	#568	1	2	yes	—
195	C₂²×C₁₃	#568	1	2	yes	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	—	2	4	no	—
199	C₄×C₁₃	—	4	2	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	—	4	2	no	—
202	C₄×C₁₃	#518	1	2	yes	—
203	C₄×C₁₃	#520	1	2	yes	—
204	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
205	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
206	C₂×M₁₆	—	4	2	no	—
207	C₂×M₁₆	—	4	2	no	—
208	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
209	C₂²×C₈	—	4	2	no	—
210	C₂²×C₈	—	4	2	no	—
211	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	—
212	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
213	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
214	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
215	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
216	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
217	#117	—	4	2	no	—
218	#117	—	4	2	no	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
224	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
229	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
231	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
232	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
233	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
234	#97	—	4	1	no	—
235	#97	—	4	1	no	—
236	#97	—	4	2	no	—
237	#97	C₂×C₄×C₁₃	1	8	yes	—
238	C₄×C₈	—	4	2	no	—
239	#95	C₂×C₄×C₁₃	1	4	yes	—
240	#95	C₂×C₄×C₁₃	1	2	yes	—
241	C₂×C₁₃	—	4	4	no	—
242	C₂×C₁₃	#2275	1	1	yes	characteristic
243	C₂×C₁₃	#2873	1	1	yes	characteristic
244	C₂×C₁₃	#2875	1	1	yes	characteristic
245	C₂×C₁₃	#2980	1	2	yes	—
246	C₂×C₁₃	#2995	1	2	yes	—
247	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
248	C₂×D₄	—	4	2	no	—
249	C₂×D₄	C₄²×C₁₃	1	4	yes	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
262	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
263	M₁₆	—	4	8	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	4	8	no	—
273	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
274	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
275	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
276	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₂²⋊C₄	C₄²×C₁₃	1	8	yes	—
283	C₄²	—	2	2	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	4	2	no	—
289	C₄²	—	4	2	no	—
290	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
291	C₁₃	#20563	1	1	yes	characteristic, direct product factor, Sylow
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	C₂×C₄²×C₁₃	1	4	yes	—
297	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
298	D₄	—	4	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
317	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
318	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
319	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
320	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
322	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
323	C₈	—	2	4	no	—
324	C₈	—	2	4	no	—
325	C₈	—	2	4	no	—
326	C₈	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	4	no	—
332	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
333	C₂²	C₁₃×#518	1	1	yes	characteristic
334	C₂²	C₁₃×#520	1	1	yes	characteristic
335	C₂²	C₁₃×#568	1	2	yes	—
336	C₂²	C₁₃×#568	1	2	yes	—
337	C₄	—	2	4	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	4	2	no	—
341	C₄	—	4	4	no	—
342	C₄	—	4	2	no	—
343	C₄	C₁₃×#518	1	2	yes	—
344	C₄	C₁₃×#520	1	2	yes	—
345	C₂	—	4	4	no	—
346	C₂	C₁₃×#2275	1	1	yes	characteristic
347	C₂	C₁₃×#2873	1	1	yes	characteristic
348	C₂	C₁₃×#2875	1	1	yes	characteristic
349	C₂	C₁₃×#2980	1	2	yes	—
350	C₂	C₁₃×#2995	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1771	C₂	semidirect
4. C₁₃×#1767	C₂	semidirect
5. C₁₃×#1753	C₂	semidirect
6. C₁₃×#1752	C₂	semidirect
7. C₁₃×#1750	C₂	semidirect
8. C₁₃×#1745	C₂	semidirect
9. C₁₃×#1729	C₂	semidirect
14. C₁₃×#435	C₄	semidirect
72. #20563	C₁₃	direct (N × H)
119. #1771	C₂×C₁₃	semidirect
120. #1767	C₂×C₁₃	semidirect
121. #1753	C₂×C₁₃	semidirect
122. #1752	C₂×C₁₃	semidirect
123. #1750	C₂×C₁₃	semidirect
124. #1745	C₂×C₁₃	semidirect
125. #1729	C₂×C₁₃	semidirect
165. #435	C₄×C₁₃	semidirect
291. C₁₃	#20563	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×C₁₃×#435	2
C₁₃×#2293	2
C₁₃×#1771	2
C₁₃×#1767	2
C₁₃×#1753	2
C₁₃×#1752	2
C₁₃×#1750	2
C₁₃×#1745	2
C₁₃×#1729	2
#20563	13

Subgroups — C13×#20563 #15706902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20563 #15706902