Subgroups — C₁₃×#26265 #15712604

Order 3328.

802 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×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2446	C₂	1	2	yes	maximal
4	C₁₃×#2056	C₂	1	2	yes	maximal
5	C₁₃×#2043	C₂	1	2	yes	maximal
6	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1878	C₂	1	2	yes	maximal
11	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#494	—	2	4	no	—
18	C₁₃×#441	—	2	4	no	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#400	—	2	2	no	—
30	C₁₃×#398	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#391	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#387	—	2	2	no	—
36	C₁₃×#387	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂×C₁₃×Q₁₆	—	2	4	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	—	2	2	no	—
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	4	no	—
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	4	2	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	4	2	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	4	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×#106	—	2	2	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×#103	—	2	4	no	—
75	C₁₃×#103	—	4	2	no	—
76	C₁₃×#103	—	4	2	no	—
77	C₁₃×#103	—	4	2	no	—
78	C₁₃×#97	—	2	2	no	—
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	D₄	1	2	yes	—
89	#26265	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₁₃×Q₁₆	—	2	8	no	—
112	C₁₃×Q₁₆	—	4	8	no	—
113	C₁₃×Q₁₆	—	4	4	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₃	#41	1	2	yes	—
124	C₂×C₈×C₁₃	#41	1	2	yes	—
125	C₂×C₈×C₁₃	#41	1	2	yes	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	4	4	no	—
142	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
143	C₂×#441	C₂×C₁₃	1	1	yes	characteristic
144	#2446	C₂×C₁₃	1	2	yes	—
145	#2056	C₂×C₁₃	1	2	yes	—
146	#2043	C₂×C₁₃	1	2	yes	—
147	#1971	C₂×C₁₃	1	1	yes	characteristic
148	#1971	C₂×C₁₃	1	1	yes	characteristic
149	#1971	C₂×C₁₃	1	1	yes	characteristic
150	#1941	C₂×C₁₃	1	1	yes	characteristic
151	#1878	C₂×C₁₃	1	2	yes	—
152	#1771	C₂×C₁₃	1	1	yes	characteristic
153	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₁₃	—	2	4	no	—
155	Q₈×C₁₃	—	2	4	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	2	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	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	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	#137	1	4	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	4	1	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	#123	1	4	yes	—
194	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
195	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
196	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
199	#494	—	2	4	no	—
200	#441	—	2	4	no	—
201	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#103	C₂²×C₁₃	1	2	yes	—
205	C₂×#103	C₂²×C₁₃	1	2	yes	—
206	C₂×#103	C₂²×C₁₃	1	2	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	#400	—	2	2	no	—
212	#398	—	2	2	no	—
213	#391	C₂²×C₁₃	1	2	yes	—
214	#391	C₂²×C₁₃	1	2	yes	—
215	#391	C₂²×C₁₃	1	2	yes	—
216	#389	C₂²×C₁₃	1	2	yes	—
217	#387	—	2	2	no	—
218	#387	—	2	2	no	—
219	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	#340	C₂²×C₁₃	1	2	yes	—
221	#336	C₂²×C₁₃	1	1	yes	characteristic
222	#336	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×C₁₃	#532	1	1	yes	characteristic
224	C₂²×C₁₃	D₄²	1	1	yes	characteristic
225	C₂²×C₁₃	#550	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#137	1	2	yes	—
227	C₂²×C₁₃	#578	1	2	yes	—
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	4	1	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
237	C₄×C₁₃	#540	1	1	yes	characteristic
238	C₄×C₁₃	#546	1	1	yes	characteristic
239	C₄×C₁₃	#559	1	1	yes	characteristic
240	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
241	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
242	C₂×Q₁₆	—	2	4	no	—
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	—	2	2	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×Q₁₆	—	2	4	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	4	2	no	—
250	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₄⋊Q₈	—	2	4	no	—
256	C₄⋊Q₈	—	4	2	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	4	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	#106	—	2	2	no	—
271	#106	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	#103	—	2	4	no	—
274	#103	—	4	2	no	—
275	#103	—	4	2	no	—
276	#103	—	4	2	no	—
277	#97	—	2	2	no	—
278	#97	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	D₄×C₁₃	1	2	yes	—
288	C₂×C₁₃	#2445	1	1	yes	characteristic
289	C₂×C₁₃	#3177	1	1	yes	characteristic
290	C₂×C₁₃	#3185	1	1	yes	characteristic
291	C₂×C₁₃	#3270	1	2	yes	—
292	C₂×C₁₃	#3398	1	2	yes	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
314	Q₁₆	—	2	8	no	—
315	Q₁₆	—	4	8	no	—
316	Q₁₆	—	4	4	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
326	C₂×C₈	C₁₃×#41	1	2	yes	—
327	C₂×C₈	C₁₃×#41	1	2	yes	—
328	C₂×C₈	C₁₃×#41	1	2	yes	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	4	no	—
345	C₁₃	#26265	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	C₁₃×#137	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
380	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
381	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	C₁₃×#123	1	4	yes	—
387	C₂²	C₁₃×#532	1	1	yes	characteristic
388	C₂²	D₄²×C₁₃	1	1	yes	characteristic
389	C₂²	C₁₃×#550	1	1	yes	characteristic
390	C₂²	C₂×C₁₃×#137	1	2	yes	—
391	C₂²	C₁₃×#578	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
401	C₄	C₁₃×#540	1	1	yes	characteristic
402	C₄	C₁₃×#546	1	1	yes	characteristic
403	C₄	C₁₃×#559	1	1	yes	characteristic
404	C₂	C₁₃×#2445	1	1	yes	characteristic
405	C₂	C₁₃×#3177	1	1	yes	characteristic
406	C₂	C₁₃×#3185	1	1	yes	characteristic
407	C₂	C₁₃×#3270	1	2	yes	—
408	C₂	C₁₃×#3398	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
89. #26265	C₁₃	direct (N × H)
345. C₁₃	#26265	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×#494	2
C₂×C₁₃×#441	2
C₁₃×#2446	2
C₁₃×#2056	2
C₁₃×#2043	2
C₁₃×#1971	2
C₁₃×#1941	2
C₁₃×#1878	2
C₁₃×#1771	2
#26265	13

Subgroups — C13×#26265 #15712604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26265 #15712604