Subgroups — C₁₃×#9672 #15696011

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1461	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1460	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₄×C₁₃×SD₁₆	—	2	1	no	—
12	C₄×C₁₃×SD₁₆	—	2	1	no	—
13	C₄×C₁₃×SD₁₆	—	2	1	no	—
14	C₄×C₁₃×SD₁₆	—	2	1	no	—
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₁₃×#431	C₂²	1	1	yes	characteristic
17	C₁₃×#431	C₂²	1	1	yes	characteristic
18	C₁₃×#431	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₄	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₄	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#335	—	2	1	no	—
24	C₁₃×#334	—	2	1	no	—
25	C₁₃×Q₈⋊C₈	—	2	2	no	—
26	C₁₃×D₄⋊C₈	—	2	2	no	—
27	C₁₃×#324	—	2	2	no	—
28	C₁₃×#323	—	2	2	no	—
29	C₁₃×#322	—	2	1	no	—
30	C₁₃×#322	—	2	1	no	—
31	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	—	2	1	no	—
34	C₂×C₁₃×SD₁₆	—	2	2	no	—
35	C₂×C₁₃×SD₁₆	—	2	2	no	—
36	C₂×C₁₃×SD₁₆	—	2	1	no	—
37	C₂×C₁₃×SD₁₆	—	2	1	no	—
38	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₄×Q₈×C₁₃	—	2	1	no	—
41	C₄×Q₈×C₁₃	—	2	1	no	—
42	C₄×Q₈×C₁₃	—	2	1	no	—
43	C₄×Q₈×C₁₃	—	2	1	no	—
44	C₄×D₄×C₁₃	—	2	1	no	—
45	C₄×D₄×C₁₃	—	2	1	no	—
46	C₄×D₄×C₁₃	—	2	1	no	—
47	C₄×D₄×C₁₃	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₂×C₄²×C₁₃	—	2	1	no	—
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#106	—	2	1	no	—
55	C₁₃×#106	—	2	1	no	—
56	C₁₃×C₄⋊C₈	—	2	1	no	—
57	C₁₃×C₄⋊C₈	—	2	1	no	—
58	C₁₃×C₄⋊C₈	—	2	1	no	—
59	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
60	C₁₃×#103	—	2	1	no	—
61	C₁₃×#103	—	2	1	no	—
62	C₁₃×#102	—	2	1	no	—
63	C₁₃×#102	—	2	1	no	—
64	C₁₃×C₂²⋊C₈	—	2	1	no	—
65	C₁₃×C₂²⋊C₈	—	2	1	no	—
66	C₁₃×C₂²⋊C₈	—	2	1	no	—
67	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
68	C₄×C₈×C₁₃	—	2	1	no	—
69	C₄×C₈×C₁₃	—	2	1	no	—
70	C₄×C₈×C₁₃	—	2	1	no	—
71	C₄×C₈×C₁₃	—	2	1	no	—
72	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
73	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
74	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
76	#9672	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	1	no	—
78	C₂×Q₈×C₁₃	—	2	1	no	—
79	C₂×Q₈×C₁₃	—	2	1	no	—
80	C₂×Q₈×C₁₃	—	2	1	no	—
81	C₂×Q₈×C₁₃	—	2	1	no	—
82	C₂×Q₈×C₁₃	—	2	1	no	—
83	C₂×Q₈×C₁₃	M₁₆	1	2	yes	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	M₁₆	1	2	yes	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
94	C₂²×C₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	—	8	2	no	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
99	C₁₃×SD₁₆	—	2	4	no	—
100	C₁₃×SD₁₆	—	2	4	no	—
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	4	1	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₂²⋊C₄	—	4	1	no	—
120	C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₄²×C₁₃	—	4	1	no	—
122	C₄²×C₁₃	—	4	1	no	—
123	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	#41	1	1	yes	characteristic
127	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
128	#1564	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#1479	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#1478	C₂×C₁₃	1	1	yes	characteristic
131	#1461	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#1460	C₂×C₁₃	1	1	yes	characteristic
133	#1452	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂³×C₁₃	—	2	2	no	—
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	—	4	1	no	—
137	C₂³×C₁₃	—	8	1	no	—
138	C₂³×C₁₃	—	8	1	no	—
139	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
140	Q₈×C₁₃	—	2	2	no	—
141	Q₈×C₁₃	—	2	2	no	—
142	Q₈×C₁₃	—	4	1	no	—
143	Q₈×C₁₃	—	4	1	no	—
144	D₄×C₁₃	—	2	2	no	—
145	D₄×C₁₃	—	2	2	no	—
146	D₄×C₁₃	—	4	1	no	—
147	D₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	8	2	no	—
156	C₂×C₄×C₁₃	—	8	2	no	—
157	C₂×C₄×C₁₃	—	8	1	no	—
158	C₂×C₄×C₁₃	—	8	1	no	—
159	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
164	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
169	C₈×C₁₃	—	2	1	no	—
170	C₈×C₁₃	—	2	1	no	—
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	—	2	1	no	—
173	C₈×C₁₃	—	4	2	no	—
174	C₈×C₁₃	—	4	2	no	—
175	C₈×C₁₃	—	8	1	no	—
176	C₈×C₁₃	—	8	1	no	—
177	C₂²×SD₁₆	C₄×C₁₃	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
180	C₄×SD₁₆	—	2	1	no	—
181	C₄×SD₁₆	—	2	1	no	—
182	C₄×SD₁₆	—	2	1	no	—
183	C₄×SD₁₆	—	2	1	no	—
184	#431	C₂²×C₁₃	1	1	yes	characteristic
185	#431	C₂²×C₁₃	1	1	yes	characteristic
186	#431	C₂²×C₁₃	1	1	yes	characteristic
187	#431	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#106	C₄×C₁₃	1	1	yes	characteristic
189	C₂×#103	C₄×C₁₃	1	1	yes	characteristic
190	C₂×#102	C₄×C₁₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
192	#335	—	2	1	no	—
193	#334	—	2	1	no	—
194	Q₈⋊C₈	—	2	2	no	—
195	D₄⋊C₈	—	2	2	no	—
196	#324	—	2	2	no	—
197	#323	—	2	2	no	—
198	#322	—	2	1	no	—
199	#322	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	4	2	no	—
203	C₂²×C₁₃	—	8	2	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	—	8	1	no	—
206	C₂²×C₁₃	—	8	1	no	—
207	C₂²×C₁₃	#390	1	1	yes	characteristic
208	C₂²×C₁₃	#435	1	1	yes	characteristic
209	C₂²×C₁₃	#435	1	1	yes	characteristic
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	4	2	no	—
214	C₄×C₁₃	—	8	1	no	—
215	C₄×C₁₃	—	8	1	no	—
216	C₄×C₁₃	#407	1	1	yes	characteristic
217	C₄×C₁₃	#408	1	1	yes	characteristic
218	C₄×C₁₃	#435	1	1	yes	characteristic
219	C₄×C₁₃	#435	1	1	yes	characteristic
220	C₄×C₁₃	#471	1	2	yes	—
221	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
222	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	—	2	1	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×SD₁₆	—	2	1	no	—
227	C₂×SD₁₆	—	2	1	no	—
228	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
229	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	#106	—	2	1	no	—
245	#106	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
250	#103	—	2	1	no	—
251	#103	—	2	1	no	—
252	#102	—	2	1	no	—
253	#102	—	2	1	no	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	—	2	1	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
263	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
264	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
265	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
266	C₂×C₁₃	—	2	1	no	—
267	C₂×C₁₃	—	2	1	no	—
268	C₂×C₁₃	—	8	2	no	—
269	C₂×C₁₃	#1955	1	1	yes	characteristic
270	C₂×C₁₃	#1976	1	1	yes	characteristic
271	C₂×C₁₃	#1977	1	1	yes	characteristic
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	C₁₃×M₁₆	1	2	yes	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	C₁₃×M₁₆	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
294	SD₁₆	—	2	4	no	—
295	SD₁₆	—	2	4	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₄²	C₁₃×#41	1	1	yes	characteristic
322	C₁₃	#9672	1	1	yes	characteristic, direct product factor, Sylow
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	8	1	no	—
327	C₂³	—	8	1	no	—
328	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	4	1	no	—
332	Q₈	—	4	1	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	—	8	1	no	—
348	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
351	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
352	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
353	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
354	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
355	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
356	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
357	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₈	—	8	1	no	—
365	C₈	—	8	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	1	no	—
373	C₂²	C₁₃×#390	1	1	yes	characteristic
374	C₂²	C₁₃×#435	1	1	yes	characteristic
375	C₂²	C₁₃×#435	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	1	no	—
382	C₄	C₁₃×#407	1	1	yes	characteristic
383	C₄	C₁₃×#408	1	1	yes	characteristic
384	C₄	C₁₃×#435	1	1	yes	characteristic
385	C₄	C₁₃×#435	1	1	yes	characteristic
386	C₄	C₁₃×#471	1	2	yes	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	8	2	no	—
390	C₂	C₁₃×#1955	1	1	yes	characteristic
391	C₂	C₁₃×#1976	1	1	yes	characteristic
392	C₂	C₁₃×#1977	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#390
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1564	C₂	semidirect
3. C₁₃×#1479	C₂	semidirect
5. C₁₃×#1461	C₂	semidirect
7. C₁₃×#1452	C₂	semidirect
76. #9672	C₁₃	direct (N × H)
128. #1564	C₂×C₁₃	semidirect
129. #1479	C₂×C₁₃	semidirect
131. #1461	C₂×C₁₃	semidirect
133. #1452	C₂×C₁₃	semidirect
322. C₁₃	#9672	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×C₄×C₁₃×SD₁₆	2
C₁₃×#1564	2
C₁₃×#1479	2
C₁₃×#1478	2
C₁₃×#1461	2
C₁₃×#1460	2
C₁₃×#1452	2
#9672	13

Subgroups — C13×#9672 #15696011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9672 #15696011