Subgroups — C₁₃×#21290 #15707629

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#102	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#442	C₄	1	8	yes	complemented
15	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#388	—	2	2	no	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#381	—	2	2	no	—
34	C₁₃×#380	—	2	2	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₁₃×#376	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂×C₁₃×D₈	—	2	2	no	—
43	C₂×C₁₃×D₈	—	2	2	no	—
44	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₄×D₄×C₁₃	—	2	4	no	—
50	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	—	2	2	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#107	—	2	2	no	—
66	C₁₃×#106	—	2	2	no	—
67	C₁₃×#106	C₂×C₄	1	4	yes	—
68	C₁₃×#102	—	2	4	no	—
69	C₁₃×#102	—	2	4	no	—
70	C₁₃×#102	C₂×C₄	1	8	yes	—
71	C₁₃×#97	—	2	2	no	—
72	C₁₃×#97	—	2	2	no	—
73	C₁₃×#97	C₂×C₄	1	4	yes	—
74	C₄×C₈×C₁₃	—	2	2	no	—
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	D₄	1	2	yes	—
81	C₁₃×#95	D₄	1	2	yes	—
82	#21290	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	8	2	no	—
95	C₂²×C₄×C₁₃	—	8	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×D₈	—	2	8	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	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₃	#41	1	2	yes	—
111	C₂×C₈×C₁₃	#41	1	2	yes	—
112	C₂×C₈×C₁₃	#41	1	2	yes	—
113	C₂×C₈×C₁₃	#41	1	2	yes	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	8	2	no	—
120	C₁₃×C₄⋊C₄	—	8	2	no	—
121	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
122	C₁₃×C₂²⋊C₄	—	2	8	no	—
123	C₁₃×C₂²⋊C₄	—	8	2	no	—
124	C₁₃×C₂²⋊C₄	—	8	2	no	—
125	C₁₃×C₂²⋊C₄	—	8	2	no	—
126	C₁₃×C₂²⋊C₄	—	8	2	no	—
127	C₄²×C₁₃	—	2	1	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	2	1	no	—
131	C₄²×C₁₃	—	8	2	no	—
132	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₁₃	#41	1	2	yes	—
134	C₂×#442	C₂×C₁₃	1	1	yes	characteristic
135	#2319	C₂×C₁₃	1	2	yes	complemented
136	#1972	C₂×C₁₃	1	1	yes	characteristic
137	#1970	C₂×C₁₃	1	1	yes	characteristic
138	#1944	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1936	C₂×C₁₃	1	2	yes	complemented
141	#1934	C₂×C₁₃	1	2	yes	complemented
142	#1776	C₂×C₁₃	1	1	yes	characteristic, complemented
143	C₄×#102	C₂×C₁₃	1	2	yes	complemented
144	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂³×C₁₃	—	2	4	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	D₄×C₁₃	—	2	4	no	—
154	D₄×C₁₃	—	2	4	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	8	8	no	—
176	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
177	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	#117	1	4	yes	—
187	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
189	#442	C₄×C₁₃	1	8	yes	complemented
190	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#102	C₂²×C₁₃	1	2	yes	—
194	C₂×#102	C₂²×C₁₃	1	2	yes	—
195	C₂×#102	C₂²×C₁₃	1	2	yes	—
196	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
202	#390	C₂²×C₁₃	1	2	yes	—
203	#390	C₂²×C₁₃	1	2	yes	—
204	#389	C₂²×C₁₃	1	2	yes	—
205	#389	C₂²×C₁₃	1	2	yes	—
206	#388	—	2	2	no	—
207	#388	—	2	2	no	—
208	#381	—	2	2	no	—
209	#380	—	2	2	no	—
210	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
211	#376	C₂²×C₁₃	1	1	yes	characteristic
212	#340	C₂²×C₁₃	1	2	yes	—
213	#340	C₂²×C₁₃	1	2	yes	—
214	#340	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	—	4	4	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₁₃	#532	1	1	yes	characteristic
224	C₂²×C₁₃	#532	1	1	yes	characteristic
225	C₂²×C₁₃	#576	1	2	yes	—
226	C₂²×C₁₃	#577	1	2	yes	—
227	C₄×C₁₃	—	2	4	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	8	2	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
235	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
236	C₄×C₁₃	#529	1	1	yes	characteristic
237	C₄×C₁₃	#529	1	1	yes	characteristic
238	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
239	C₂³×C₄	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	—
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	#107	—	2	2	no	—
264	#106	—	2	2	no	—
265	#106	C₂×C₄×C₁₃	1	4	yes	—
266	#102	—	2	4	no	—
267	#102	—	2	4	no	—
268	#102	C₂×C₄×C₁₃	1	8	yes	—
269	#97	—	2	2	no	—
270	#97	—	2	2	no	—
271	#97	C₂×C₄×C₁₃	1	4	yes	—
272	C₄×C₈	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	D₄×C₁₃	1	2	yes	—
279	#95	D₄×C₁₃	1	2	yes	—
280	C₂×C₁₃	—	8	4	no	—
281	C₂×C₁₃	#2293	1	1	yes	characteristic
282	C₂×C₁₃	#2946	1	2	yes	—
283	C₂×C₁₃	#3173	1	1	yes	characteristic
284	C₂×C₁₃	#3176	1	1	yes	characteristic
285	C₂×C₁₃	#3179	1	2	yes	—
286	C₂⁴	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	—	8	2	no	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
304	D₈	—	2	8	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
312	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₁₃×#41	1	2	yes	—
314	C₂×C₈	C₁₃×#41	1	2	yes	—
315	C₂×C₈	C₁₃×#41	1	2	yes	—
316	C₂×C₈	C₁₃×#41	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	—	8	2	no	—
324	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₂²⋊C₄	—	8	2	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
336	C₄²	C₁₃×#41	1	2	yes	—
337	C₁₃	#21290	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	—	2	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
346	D₄	—	2	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
370	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	C₁₃×#117	1	4	yes	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
388	C₂²	C₁₃×#532	1	1	yes	characteristic
389	C₂²	C₁₃×#532	1	1	yes	characteristic
390	C₂²	C₁₃×#576	1	2	yes	—
391	C₂²	C₁₃×#577	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
400	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
401	C₄	C₁₃×#529	1	1	yes	characteristic
402	C₄	C₁₃×#529	1	1	yes	characteristic
403	C₂	—	8	4	no	—
404	C₂	C₁₃×#2293	1	1	yes	characteristic
405	C₂	C₁₃×#2946	1	2	yes	—
406	C₂	C₁₃×#3173	1	1	yes	characteristic
407	C₂	C₁₃×#3176	1	1	yes	characteristic
408	C₂	C₁₃×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2319	C₂	semidirect
5. C₁₃×#1944	C₂	semidirect
6. C₁₃×#1941	C₂	semidirect
7. C₁₃×#1936	C₂	semidirect
8. C₁₃×#1934	C₂	semidirect
9. C₁₃×#1776	C₂	semidirect
10. C₄×C₁₃×#102	C₂	semidirect
11. C₁₃×#1726	C₂	semidirect
14. C₁₃×#442	C₄	semidirect
82. #21290	C₁₃	direct (N × H)
135. #2319	C₂×C₁₃	semidirect
138. #1944	C₂×C₁₃	semidirect
139. #1941	C₂×C₁₃	semidirect
140. #1936	C₂×C₁₃	semidirect
141. #1934	C₂×C₁₃	semidirect
142. #1776	C₂×C₁₃	semidirect
143. C₄×#102	C₂×C₁₃	semidirect
144. #1726	C₂×C₁₃	semidirect
189. #442	C₄×C₁₃	semidirect
337. C₁₃	#21290	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×#442	2
C₁₃×#2319	2
C₁₃×#1972	2
C₁₃×#1970	2
C₁₃×#1944	2
C₁₃×#1941	2
C₁₃×#1936	2
C₁₃×#1934	2
C₁₃×#1776	2
C₄×C₁₃×#102	2
C₁₃×#1726	2
#21290	13

Subgroups — C13×#21290 #15707629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21290 #15707629