Subgroups — C₁₃×#32529 #15718868

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2513	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2092	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2054	C₂	1	2	yes	maximal
5	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#106	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#397	—	2	2	no	—
22	C₁₃×#397	—	2	2	no	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#390	C₂²	1	2	yes	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#388	—	2	2	no	—
28	C₁₃×#388	—	2	2	no	—
29	C₁₃×#382	C₂²	1	2	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
36	C₂×C₁₃×D₈	—	2	2	no	—
37	C₂×C₁₃×D₈	—	4	1	no	—
38	C₂×C₁₃×D₈	—	4	1	no	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
44	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
48	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₄²×C₁₃	—	2	2	no	—
55	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#107	—	2	2	no	—
58	C₁₃×#107	—	4	1	no	—
59	C₁₃×#107	—	4	1	no	—
60	C₁₃×#106	—	4	2	no	—
61	C₁₃×C₄⋊C₈	—	2	4	no	—
62	C₁₃×C₄⋊C₈	—	4	1	no	—
63	C₁₃×#102	—	2	4	no	—
64	C₁₃×#102	—	4	2	no	—
65	C₁₃×#102	—	4	2	no	—
66	C₄×C₈×C₁₃	—	4	1	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	D₄	1	2	yes	—
72	#32529	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	2	no	—
74	C₂×D₄×C₁₃	—	2	2	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₁₃×D₈	—	4	4	no	—
89	C₂×C₈×C₁₃	—	2	1	no	—
90	C₂×C₈×C₁₃	—	2	1	no	—
91	C₂×C₈×C₁₃	—	2	1	no	—
92	C₂×C₈×C₁₃	—	2	1	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	#41	1	2	yes	—
97	C₂×C₈×C₁₃	#41	1	2	yes	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	8	2	no	—
107	C₁₃×C₂²⋊C₄	—	4	4	no	—
108	C₁₃×C₂²⋊C₄	—	4	4	no	—
109	C₁₃×C₂²⋊C₄	—	8	2	no	—
110	C₁₃×C₂²⋊C₄	—	8	2	no	—
111	C₁₃×C₂²⋊C₄	—	8	2	no	—
112	C₁₃×C₂²⋊C₄	—	8	2	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	1	no	—
115	C₄²×C₁₃	—	2	1	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	8	2	no	—
118	#2513	C₂×C₁₃	1	2	yes	complemented
119	#2092	C₂×C₁₃	1	2	yes	complemented
120	#2065	C₂×C₁₃	1	2	yes	complemented
121	#2054	C₂×C₁₃	1	2	yes	—
122	#1970	C₂×C₁₃	1	1	yes	characteristic
123	#1949	C₂×C₁₃	1	2	yes	complemented
124	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
126	#1925	C₂×C₁₃	1	2	yes	complemented
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	—	4	2	no	—
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
135	D₄×C₁₃	—	4	2	no	—
136	D₄×C₁₃	—	4	2	no	—
137	D₄×C₁₃	—	4	2	no	—
138	D₄×C₁₃	—	4	2	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	2	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	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	#135	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
166	C₈×C₁₃	—	2	2	no	—
167	C₈×C₁₃	—	2	2	no	—
168	C₈×C₁₃	—	4	2	no	—
169	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
170	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×#106	C₂²×C₁₃	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×#102	C₂²×C₁₃	1	2	yes	—
177	C₂×#102	C₂²×C₁₃	1	2	yes	—
178	C₂×#102	C₂²×C₁₃	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
180	#397	—	2	2	no	—
181	#397	—	2	2	no	—
182	#390	C₂²×C₁₃	1	2	yes	—
183	#390	C₂²×C₁₃	1	2	yes	—
184	#390	C₂²×C₁₃	1	2	yes	—
185	#389	C₂²×C₁₃	1	2	yes	—
186	#388	—	2	2	no	—
187	#388	—	2	2	no	—
188	#382	C₂²×C₁₃	1	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
190	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
191	#340	C₂²×C₁₃	1	2	yes	—
192	#340	C₂²×C₁₃	1	2	yes	—
193	#336	C₂²×C₁₃	1	2	yes	—
194	C₂²×C₁₃	—	8	2	no	—
195	C₂²×C₁₃	—	8	2	no	—
196	C₂²×C₁₃	—	8	2	no	—
197	C₂²×C₁₃	—	8	2	no	—
198	C₂²×C₁₃	—	8	2	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	—	8	2	no	—
201	C₂²×C₁₃	#537	1	1	yes	characteristic
202	C₂²×C₁₃	#547	1	1	yes	characteristic
203	C₂²×C₁₃	#550	1	1	yes	characteristic
204	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
205	C₂²×C₁₃	#575	1	1	yes	characteristic
206	C₂²×C₁₃	#576	1	1	yes	characteristic
207	C₂²×C₁₃	#576	1	1	yes	characteristic
208	C₄×C₁₃	—	2	2	no	—
209	C₄×C₁₃	—	4	2	no	—
210	C₄×C₁₃	—	4	2	no	—
211	C₄×C₁₃	—	4	1	no	—
212	C₄×C₁₃	—	8	2	no	—
213	C₄×C₁₃	—	8	2	no	—
214	C₄×C₁₃	—	8	2	no	—
215	C₄×C₁₃	#538	1	1	yes	characteristic
216	C₄×C₁₃	#539	1	1	yes	characteristic
217	C₄×C₁₃	#556	1	1	yes	characteristic
218	C₄×C₁₃	#563	1	1	yes	characteristic
219	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
220	C₂×D₈	—	2	2	no	—
221	C₂×D₈	—	4	1	no	—
222	C₂×D₈	—	4	1	no	—
223	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
240	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
241	#107	—	2	2	no	—
242	#107	—	4	1	no	—
243	#107	—	4	1	no	—
244	#106	—	4	2	no	—
245	C₄⋊C₈	—	2	4	no	—
246	C₄⋊C₈	—	4	1	no	—
247	#102	—	2	4	no	—
248	#102	—	4	2	no	—
249	#102	—	4	2	no	—
250	C₄×C₈	—	4	1	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	D₄×C₁₃	1	2	yes	—
256	C₂×C₁₃	—	16	2	no	—
257	C₂×C₁₃	#2727	1	1	yes	characteristic
258	C₂×C₁₃	#3250	1	1	yes	characteristic
259	C₂×C₁₃	#3259	1	1	yes	characteristic
260	C₂×C₁₃	#3341	1	1	yes	characteristic
261	C₂×C₁₃	#3355	1	1	yes	characteristic
262	C₂×C₁₃	#3396	1	1	yes	characteristic
263	C₂×C₁₃	#3403	1	1	yes	characteristic
264	C₂⁴	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
279	D₈	—	4	4	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₁₃×#41	1	2	yes	—
288	C₂×C₈	C₁₃×#41	1	2	yes	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	8	2	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	8	2	no	—
301	C₂²⋊C₄	—	8	2	no	—
302	C₂²⋊C₄	—	8	2	no	—
303	C₂²⋊C₄	—	8	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	8	2	no	—
309	C₁₃	#32529	1	1	yes	characteristic, direct product factor, Sylow
310	C₂³	—	4	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
318	D₄	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₁₃×#135	1	2	yes	—
343	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
344	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
345	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
348	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	C₁₃×#537	1	1	yes	characteristic
360	C₂²	C₁₃×#547	1	1	yes	characteristic
361	C₂²	C₁₃×#550	1	1	yes	characteristic
362	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
363	C₂²	C₁₃×#575	1	1	yes	characteristic
364	C₂²	C₁₃×#576	1	1	yes	characteristic
365	C₂²	C₁₃×#576	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	—	8	2	no	—
373	C₄	C₁₃×#538	1	1	yes	characteristic
374	C₄	C₁₃×#539	1	1	yes	characteristic
375	C₄	C₁₃×#556	1	1	yes	characteristic
376	C₄	C₁₃×#563	1	1	yes	characteristic
377	C₂	—	16	2	no	—
378	C₂	C₁₃×#2727	1	1	yes	characteristic
379	C₂	C₁₃×#3250	1	1	yes	characteristic
380	C₂	C₁₃×#3259	1	1	yes	characteristic
381	C₂	C₁₃×#3341	1	1	yes	characteristic
382	C₂	C₁₃×#3355	1	1	yes	characteristic
383	C₂	C₁₃×#3396	1	1	yes	characteristic
384	C₂	C₁₃×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2513	C₂	semidirect
2. C₁₃×#2092	C₂	semidirect
3. C₁₃×#2065	C₂	semidirect
6. C₁₃×#1949	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1939	C₂	semidirect
9. C₁₃×#1925	C₂	semidirect
72. #32529	C₁₃	direct (N × H)
118. #2513	C₂×C₁₃	semidirect
119. #2092	C₂×C₁₃	semidirect
120. #2065	C₂×C₁₃	semidirect
123. #1949	C₂×C₁₃	semidirect
124. #1942	C₂×C₁₃	semidirect
125. #1939	C₂×C₁₃	semidirect
126. #1925	C₂×C₁₃	semidirect
309. C₁₃	#32529	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×#2513	2
C₁₃×#2092	2
C₁₃×#2065	2
C₁₃×#2054	2
C₁₃×#1970	2
C₁₃×#1949	2
C₁₃×#1942	2
C₁₃×#1939	2
C₁₃×#1925	2
#32529	13

Subgroups — C13×#32529 #15718868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32529 #15718868