Subgroups — C₁₃×#12787 #15699126

Order 3328.

450 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#350	C₂	1	2	yes	maximal
5	C₁₃×#1379	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#131	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×#41	C₄	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₁₃×#405	—	2	1	no	—
12	C₁₃×#405	—	2	1	no	—
13	C₁₃×#405	C₄	1	1	yes	characteristic
14	C₁₃×#405	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×M₁₆	—	2	1	no	—
16	C₄×C₁₃×M₁₆	C₄	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	—	2	1	no	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×C₄⋊C₁₆	—	2	1	no	—
20	C₁₃×C₄⋊C₁₆	—	2	1	no	—
21	C₁₃×C₄⋊C₁₆	—	2	1	no	—
22	C₁₃×C₄⋊C₁₆	—	2	1	no	—
23	C₁₃×#350	—	2	4	no	—
24	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
25	C₁₃×#131	—	2	2	no	—
26	C₁₃×#131	—	2	2	no	—
27	C₁₃×#131	—	2	1	no	—
28	C₁₃×#131	—	2	1	no	—
29	C₁₃×#131	D₄	1	2	yes	—
30	C₁₃×#131	Q₈	1	2	yes	—
31	C₂×C₁₃×M₁₆	—	2	1	no	—
32	C₂×C₁₃×M₁₆	—	2	1	no	—
33	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₄×Q₈×C₁₃	C₈	1	1	yes	characteristic
40	C₄×Q₈×C₁₃	C₈	1	1	yes	characteristic
41	C₄×D₄×C₁₃	—	2	1	no	—
42	C₄×D₄×C₁₃	—	2	1	no	—
43	C₄×D₄×C₁₃	C₈	1	1	yes	characteristic
44	C₄×D₄×C₁₃	C₈	1	1	yes	characteristic
45	C₁₃×#117	—	2	1	no	—
46	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	—	2	1	no	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₁₃×M₃₂	—	2	2	no	—
50	C₁₃×M₃₂	—	2	2	no	—
51	C₂×C₁₃×C₁₆	—	2	2	no	—
52	C₂×C₁₃×C₁₆	—	2	2	no	—
53	C₂×C₁₃×C₁₆	—	2	2	no	—
54	C₂×C₁₃×C₁₆	—	2	2	no	—
55	C₁₃×#97	—	2	1	no	—
56	C₁₃×#97	—	2	1	no	—
57	C₁₃×#97	—	2	1	no	—
58	C₄×C₈×C₁₃	—	2	1	no	—
59	C₄×C₈×C₁₃	—	2	1	no	—
60	C₄×C₈×C₁₃	—	2	1	no	—
61	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
62	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
63	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
64	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
65	#12787	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₁₃×#41	—	2	1	no	—
67	C₁₃×#41	—	2	1	no	—
68	C₁₃×#41	C₄⋊C₄	1	2	yes	—
69	C₁₃×#41	M₁₆	1	2	yes	—
70	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
71	C₂×D₄×C₁₃	—	2	1	no	—
72	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	—	2	1	no	—
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₁₃×M₁₆	—	2	4	no	—
80	C₁₃×M₁₆	—	2	1	no	—
81	C₁₃×M₁₆	—	2	1	no	—
82	C₁₃×M₁₆	—	2	2	no	—
83	C₁₃×M₁₆	—	2	2	no	—
84	C₁₃×M₁₆	C₄⋊C₄	1	2	yes	—
85	C₁₃×M₁₆	M₁₆	1	2	yes	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	—	2	1	no	—
88	C₂×C₈×C₁₃	—	2	1	no	—
89	C₂×C₈×C₁₃	—	2	1	no	—
90	C₂×C₈×C₁₃	—	2	1	no	—
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
99	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
100	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
101	C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
104	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
105	C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₄²×C₁₃	—	2	1	no	—
109	C₄²×C₁₃	—	2	1	no	—
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
115	C₁₃×C₁₆	—	4	2	no	—
116	C₁₃×C₁₆	—	4	2	no	—
117	C₄×#131	C₂×C₁₃	1	1	yes	characteristic
118	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
120	C₂×#350	C₂×C₁₃	1	2	yes	—
121	#1379	C₂×C₁₃	1	2	yes	complemented
122	C₂³×C₁₃	—	2	1	no	—
123	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
124	Q₈×C₁₃	—	2	1	no	—
125	Q₈×C₁₃	C₄⋊C₈	1	2	yes	—
126	D₄×C₁₃	—	2	2	no	—
127	D₄×C₁₃	—	2	2	no	—
128	D₄×C₁₃	—	2	1	no	—
129	D₄×C₁₃	C₄⋊C₈	1	2	yes	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	4	1	no	—
137	C₂×C₄×C₁₃	—	4	2	no	—
138	C₂×C₄×C₁₃	—	4	2	no	—
139	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
149	C₈×C₁₃	—	2	2	no	—
150	C₈×C₁₃	—	2	1	no	—
151	C₈×C₁₃	—	2	2	no	—
152	C₈×C₁₃	—	2	1	no	—
153	C₈×C₁₃	#121	1	1	yes	characteristic
154	C₈×C₁₃	#121	1	1	yes	characteristic
155	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
156	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×#131	C₄×C₁₃	1	1	yes	characteristic
158	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
159	C₄×#41	C₄×C₁₃	1	1	yes	characteristic
160	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
161	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
162	#405	—	2	1	no	—
163	#405	—	2	1	no	—
164	#405	C₄×C₁₃	1	1	yes	characteristic
165	#405	C₂²×C₁₃	1	1	yes	characteristic
166	C₄×M₁₆	—	2	1	no	—
167	C₄×M₁₆	C₄×C₁₃	1	1	yes	characteristic
168	C₂×C₄×C₈	—	2	1	no	—
169	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
170	C₄⋊C₁₆	—	2	1	no	—
171	C₄⋊C₁₆	—	2	1	no	—
172	C₄⋊C₁₆	—	2	1	no	—
173	C₄⋊C₁₆	—	2	1	no	—
174	#350	—	2	4	no	—
175	C₂²×C₁₃	—	2	1	no	—
176	C₂²×C₁₃	—	2	1	no	—
177	C₂²×C₁₃	—	2	2	no	—
178	C₂²×C₁₃	—	4	1	no	—
179	C₂²×C₁₃	—	4	1	no	—
180	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
181	C₂²×C₁₃	#423	1	1	yes	characteristic
182	C₂²×C₁₃	#432	1	1	yes	characteristic
183	C₄×C₁₃	—	2	2	no	—
184	C₄×C₁₃	—	2	1	no	—
185	C₄×C₁₃	—	2	1	no	—
186	C₄×C₁₃	—	2	1	no	—
187	C₄×C₁₃	—	4	1	no	—
188	C₄×C₁₃	—	4	1	no	—
189	C₄×C₁₃	#350	1	2	yes	complemented
190	C₄×C₁₃	#380	1	1	yes	characteristic
191	C₄×C₁₃	#407	1	1	yes	characteristic
192	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
193	C₄×C₁₃	#431	1	1	yes	characteristic
194	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
195	#131	—	2	2	no	—
196	#131	—	2	2	no	—
197	#131	—	2	1	no	—
198	#131	—	2	1	no	—
199	#131	D₄×C₁₃	1	2	yes	—
200	#131	Q₈×C₁₃	1	2	yes	—
201	C₂×M₁₆	—	2	1	no	—
202	C₂×M₁₆	—	2	1	no	—
203	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
204	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
205	C₂²×C₈	—	2	1	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
209	C₄×Q₈	C₈×C₁₃	1	1	yes	characteristic
210	C₄×Q₈	C₈×C₁₃	1	1	yes	characteristic
211	C₄×D₄	—	2	1	no	—
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	C₈×C₁₃	1	1	yes	characteristic
214	C₄×D₄	C₈×C₁₃	1	1	yes	characteristic
215	#117	—	2	1	no	—
216	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
217	C₂×C₄²	—	2	1	no	—
218	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
219	M₃₂	—	2	2	no	—
220	M₃₂	—	2	2	no	—
221	C₂×C₁₆	—	2	2	no	—
222	C₂×C₁₆	—	2	2	no	—
223	C₂×C₁₆	—	2	2	no	—
224	C₂×C₁₆	—	2	2	no	—
225	#97	—	2	1	no	—
226	#97	—	2	1	no	—
227	#97	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
232	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
233	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
234	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
235	C₂×C₁₃	—	2	1	no	—
236	C₂×C₁₃	—	2	1	no	—
237	C₂×C₁₃	—	4	2	no	—
238	C₂×C₁₃	#1797	1	1	yes	characteristic
239	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
240	C₂×C₁₃	#2117	1	1	yes	characteristic
241	#41	—	2	1	no	—
242	#41	—	2	1	no	—
243	#41	C₁₃×C₄⋊C₄	1	2	yes	—
244	#41	C₁₃×M₁₆	1	2	yes	—
245	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
246	C₂×D₄	—	2	1	no	—
247	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
252	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
254	M₁₆	—	2	4	no	—
255	M₁₆	—	2	1	no	—
256	M₁₆	—	2	1	no	—
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	2	no	—
259	M₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
260	M₁₆	C₁₃×M₁₆	1	2	yes	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
271	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
273	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
274	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
275	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
279	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	1	no	—
282	C₂²⋊C₄	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	1	no	—
286	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
288	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
289	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
290	C₁₆	—	4	2	no	—
291	C₁₆	—	4	2	no	—
292	C₁₃	#12787	1	1	yes	characteristic, direct product factor, Sylow
293	C₂³	—	2	1	no	—
294	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
295	Q₈	—	2	1	no	—
296	Q₈	C₁₃×C₄⋊C₈	1	2	yes	—
297	D₄	—	2	2	no	—
298	D₄	—	2	2	no	—
299	D₄	—	2	1	no	—
300	D₄	C₁₃×C₄⋊C₈	1	2	yes	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
311	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
312	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
313	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
314	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
318	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
319	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
320	C₈	—	2	2	no	—
321	C₈	—	2	1	no	—
322	C₈	—	2	2	no	—
323	C₈	—	2	1	no	—
324	C₈	C₁₃×#121	1	1	yes	characteristic
325	C₈	C₁₃×#121	1	1	yes	characteristic
326	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
327	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	4	1	no	—
332	C₂²	—	4	1	no	—
333	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
334	C₂²	C₁₃×#423	1	1	yes	characteristic
335	C₂²	C₁₃×#432	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	1	no	—
342	C₄	C₁₃×#350	1	2	yes	complemented
343	C₄	C₁₃×#380	1	1	yes	characteristic
344	C₄	C₁₃×#407	1	1	yes	characteristic
345	C₄	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
346	C₄	C₁₃×#431	1	1	yes	characteristic
347	C₂	—	2	1	no	—
348	C₂	—	2	1	no	—
349	C₂	—	4	2	no	—
350	C₂	C₁₃×#1797	1	1	yes	characteristic
351	C₂	C₂×C₁₃×#350	1	1	yes	characteristic
352	C₂	C₁₃×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2150	C₂	semidirect
3. C₂×C₁₃×C₄⋊C₁₆	C₂	semidirect
5. C₁₃×#1379	C₂	semidirect
65. #12787	C₁₃	direct (N × H)
118. #2150	C₂×C₁₃	semidirect
119. C₂×C₄⋊C₁₆	C₂×C₁₃	semidirect
121. #1379	C₂×C₁₃	semidirect
189. C₄×C₁₃	#350	semidirect
292. C₁₃	#12787	direct (N × H)
342. C₄	C₁₃×#350	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#131	2
C₁₃×#2150	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×C₁₃×#350	2
C₁₃×#1379	2
#12787	13

Subgroups — C13×#12787 #15699126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12787 #15699126