Subgroups — C₁₃×#9541 #15695880

Order 3328.

460 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
12	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₄×C₈×C₁₃	—	2	1	no	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₁₃×#340	C₄	1	1	yes	characteristic
21	C₁₃×#340	C₄	1	1	yes	characteristic
22	C₁₃×#336	—	2	1	no	—
23	C₁₃×#335	—	2	2	no	—
24	C₁₃×D₄⋊C₈	—	2	2	no	—
25	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	—	2	1	no	—
27	C₂²×C₈×C₁₃	—	2	1	no	—
28	C₂²×C₈×C₁₃	—	2	1	no	—
29	C₂²×C₈×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
34	C₄×D₄×C₁₃	—	2	1	no	—
35	C₄×D₄×C₁₃	—	2	1	no	—
36	C₄×D₄×C₁₃	—	2	1	no	—
37	C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
42	C₂×C₄²×C₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
44	C₁₃×C₄⋊C₈	—	2	1	no	—
45	C₁₃×C₄⋊C₈	—	2	1	no	—
46	C₁₃×C₄⋊C₈	—	2	1	no	—
47	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
48	C₁₃×#102	—	2	2	no	—
49	C₁₃×#102	C₈	1	4	yes	complemented
50	C₁₃×C₂²⋊C₈	—	4	2	no	—
51	C₁₃×C₂²⋊C₈	—	4	2	no	—
52	C₄×C₈×C₁₃	—	2	1	no	—
53	C₄×C₈×C₁₃	—	2	1	no	—
54	C₄×C₈×C₁₃	—	2	1	no	—
55	C₄×C₈×C₁₃	—	2	1	no	—
56	C₄×C₈×C₁₃	—	2	1	no	—
57	C₄×C₈×C₁₃	—	2	1	no	—
58	C₄×C₈×C₁₃	—	4	2	no	—
59	C₁₃×#95	—	2	1	no	—
60	#9541	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₃	—	2	1	no	—
62	C₂×D₄×C₁₃	—	2	1	no	—
63	C₂×D₄×C₁₃	—	2	1	no	—
64	C₂×D₄×C₁₃	—	2	1	no	—
65	C₂×D₄×C₁₃	—	2	1	no	—
66	C₂×D₄×C₁₃	—	2	1	no	—
67	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	1	no	—
71	C₂²×C₄×C₁₃	—	4	1	no	—
72	C₂²×C₄×C₁₃	—	4	1	no	—
73	C₂²×C₄×C₁₃	—	4	1	no	—
74	C₂²×C₄×C₁₃	—	4	1	no	—
75	C₂²×C₄×C₁₃	—	4	1	no	—
76	C₂²×C₄×C₁₃	—	4	1	no	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
80	C₂×C₈×C₁₃	—	2	1	no	—
81	C₂×C₈×C₁₃	—	2	1	no	—
82	C₂×C₈×C₁₃	—	2	1	no	—
83	C₂×C₈×C₁₃	—	2	1	no	—
84	C₂×C₈×C₁₃	—	2	2	no	—
85	C₂×C₈×C₁₃	—	2	1	no	—
86	C₂×C₈×C₁₃	—	2	2	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	1	no	—
92	C₂×C₈×C₁₃	—	4	1	no	—
93	C₂×C₈×C₁₃	—	4	1	no	—
94	C₂×C₈×C₁₃	—	4	1	no	—
95	C₂×C₈×C₁₃	—	4	1	no	—
96	C₂×C₈×C₁₃	—	4	1	no	—
97	C₂×C₈×C₁₃	—	4	1	no	—
98	C₂×C₈×C₁₃	—	4	1	no	—
99	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
100	C₂×C₈×C₁₃	D₈	1	2	yes	—
101	C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
106	C₁₃×C₄⋊C₄	M₁₆	1	2	yes	—
107	C₁₃×C₂²⋊C₄	—	4	1	no	—
108	C₁₃×C₂²⋊C₄	—	4	1	no	—
109	C₄²×C₁₃	—	4	1	no	—
110	C₄²×C₁₃	—	4	1	no	—
111	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₃	#41	1	1	yes	characteristic
113	C₄²×C₁₃	#41	1	1	yes	characteristic
114	C₄²×C₁₃	#41	1	1	yes	characteristic
115	#1954	C₂×C₁₃	1	1	yes	characteristic
116	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
118	C₂×#335	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
120	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#1273	C₂×C₁₃	1	1	yes	characteristic, complemented
122	C₂³×C₁₃	—	2	2	no	—
123	C₂³×C₁₃	—	4	1	no	—
124	C₂³×C₁₃	—	4	1	no	—
125	C₂³×C₁₃	—	4	1	no	—
126	C₂³×C₁₃	—	4	1	no	—
127	C₂³×C₁₃	—	4	1	no	—
128	C₂³×C₁₃	—	4	1	no	—
129	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
130	D₄×C₁₃	—	2	2	no	—
131	D₄×C₁₃	—	2	2	no	—
132	D₄×C₁₃	—	4	1	no	—
133	D₄×C₁₃	—	4	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	4	1	no	—
139	C₂×C₄×C₁₃	—	4	1	no	—
140	C₂×C₄×C₁₃	—	4	1	no	—
141	C₂×C₄×C₁₃	—	4	1	no	—
142	C₂×C₄×C₁₃	—	4	1	no	—
143	C₂×C₄×C₁₃	—	4	1	no	—
144	C₂×C₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	8	1	no	—
146	C₂×C₄×C₁₃	—	8	1	no	—
147	C₂×C₄×C₁₃	—	8	1	no	—
148	C₂×C₄×C₁₃	—	8	1	no	—
149	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
157	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
161	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
163	C₈×C₁₃	—	2	2	no	—
164	C₈×C₁₃	—	2	2	no	—
165	C₈×C₁₃	—	4	2	no	—
166	C₈×C₁₃	—	4	1	no	—
167	C₈×C₁₃	—	4	2	no	—
168	C₈×C₁₃	—	4	1	no	—
169	C₈×C₁₃	—	8	1	no	—
170	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×#102	C₄×C₁₃	1	1	yes	characteristic
174	C₂×#102	C₄×C₁₃	1	1	yes	characteristic
175	C₂×C₂²⋊C₈	—	2	1	no	—
176	C₂×C₂²⋊C₈	—	2	1	no	—
177	C₂×C₄×C₈	—	2	1	no	—
178	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
181	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
182	#340	C₄×C₁₃	1	1	yes	characteristic
183	#340	C₄×C₁₃	1	1	yes	characteristic
184	#336	—	2	1	no	—
185	#335	—	2	2	no	—
186	D₄⋊C₈	—	2	2	no	—
187	C₂²×C₁₃	—	4	2	no	—
188	C₂²×C₁₃	—	4	2	no	—
189	C₂²×C₁₃	—	4	2	no	—
190	C₂²×C₁₃	—	8	1	no	—
191	C₂²×C₁₃	—	8	1	no	—
192	C₂²×C₁₃	—	8	1	no	—
193	C₂²×C₁₃	—	8	1	no	—
194	C₂²×C₁₃	#388	1	1	yes	characteristic
195	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
196	C₂²×C₁₃	#435	1	1	yes	characteristic
197	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
198	C₂²×C₁₃	#440	1	1	yes	characteristic
199	C₂²×C₁₃	#443	1	1	yes	characteristic
200	C₂²×C₁₃	#444	1	1	yes	characteristic
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	—	4	2	no	—
204	C₄×C₁₃	—	4	2	no	—
205	C₄×C₁₃	—	8	1	no	—
206	C₄×C₁₃	#431	1	1	yes	characteristic
207	C₄×C₁₃	#433	1	1	yes	characteristic
208	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
209	C₄×C₁₃	#436	1	1	yes	characteristic
210	C₄×C₁₃	#459	1	1	yes	characteristic
211	C₄×C₁₃	#464	1	1	yes	characteristic
212	C₄×C₁₃	#480	1	1	yes	characteristic
213	C₄×C₁₃	#482	1	1	yes	characteristic
214	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
215	C₂³×C₄	—	2	1	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	2	1	no	—
218	C₂²×C₈	—	2	1	no	—
219	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
220	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
221	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
222	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
233	C₄⋊C₈	—	2	1	no	—
234	C₄⋊C₈	—	2	1	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
237	#102	—	2	2	no	—
238	#102	C₈×C₁₃	1	4	yes	complemented
239	C₂²⋊C₈	—	4	2	no	—
240	C₂²⋊C₈	—	4	2	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	2	1	no	—
244	C₄×C₈	—	2	1	no	—
245	C₄×C₈	—	2	1	no	—
246	C₄×C₈	—	2	1	no	—
247	C₄×C₈	—	4	2	no	—
248	#95	—	2	1	no	—
249	C₂×C₁₃	—	8	2	no	—
250	C₂×C₁₃	C₈×D₈	1	1	yes	characteristic
251	C₂×C₁₃	SD₁₆⋊C₈	1	1	yes	characteristic
252	C₂×C₁₃	#1581	1	1	yes	characteristic
253	C₂×C₁₃	#1588	1	1	yes	characteristic
254	C₂×C₁₃	#1923	1	1	yes	characteristic
255	C₂×C₁₃	#1925	1	1	yes	characteristic
256	C₂×C₁₃	#1929	1	1	yes	characteristic
257	C₂⁴	—	2	1	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
296	C₂×C₈	C₁₃×D₈	1	2	yes	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
302	C₄⋊C₄	C₁₃×M₁₆	1	2	yes	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₄²	C₁₃×#41	1	1	yes	characteristic
309	C₄²	C₁₃×#41	1	1	yes	characteristic
310	C₄²	C₁₃×#41	1	1	yes	characteristic
311	C₁₃	#9541	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
320	D₄	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
342	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
343	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
344	C₂×C₄	C₁₃×#126	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
347	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
348	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
349	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
350	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
351	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	1	no	—
359	C₈	—	8	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	C₁₃×#388	1	1	yes	characteristic
368	C₂²	C₈×D₄×C₁₃	1	1	yes	characteristic
369	C₂²	C₁₃×#435	1	1	yes	characteristic
370	C₂²	C₄×C₁₃×D₈	1	1	yes	characteristic
371	C₂²	C₁₃×#440	1	1	yes	characteristic
372	C₂²	C₁₃×#443	1	1	yes	characteristic
373	C₂²	C₁₃×#444	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	C₁₃×#431	1	1	yes	characteristic
380	C₄	C₁₃×#433	1	1	yes	characteristic
381	C₄	C₈×D₄×C₁₃	1	1	yes	characteristic
382	C₄	C₁₃×#436	1	1	yes	characteristic
383	C₄	C₁₃×#459	1	1	yes	characteristic
384	C₄	C₁₃×#464	1	1	yes	characteristic
385	C₄	C₁₃×#480	1	1	yes	characteristic
386	C₄	C₁₃×#482	1	1	yes	characteristic
387	C₂	—	8	2	no	—
388	C₂	C₈×C₁₃×D₈	1	1	yes	characteristic
389	C₂	C₁₃×SD₁₆⋊C₈	1	1	yes	characteristic
390	C₂	C₁₃×#1581	1	1	yes	characteristic
391	C₂	C₁₃×#1588	1	1	yes	characteristic
392	C₂	C₁₃×#1923	1	1	yes	characteristic
393	C₂	C₁₃×#1925	1	1	yes	characteristic
394	C₂	C₁₃×#1929	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
4. C₂×C₁₃×#335	C₂	semidirect
6. C₁₃×#1279	C₂	semidirect
7. C₁₃×#1273	C₂	semidirect
49. C₁₃×#102	C₈	semidirect
60. #9541	C₁₃	direct (N × H)
116. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
118. C₂×#335	C₂×C₁₃	semidirect
120. #1279	C₂×C₁₃	semidirect
121. #1273	C₂×C₁₃	semidirect
238. #102	C₈×C₁₃	semidirect
311. C₁₃	#9541	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×#1954	2
C₈×C₁₃×C₄⋊C₄	2
C₄×C₁₃×#102	2
C₂×C₁₃×#335	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
C₁₃×#1273	2
#9541	13

Subgroups — C13×#9541 #15695880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9541 #15695880