Subgroups — C₁₃×#25927 #15712266

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2642	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2028	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1882	C₂	1	4	yes	maximal
9	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#137	C₂²	1	2	yes	—
11	C₁₃×#557	—	2	2	no	—
12	C₁₃×#554	—	2	2	no	—
13	C₁₃×#554	—	2	4	no	—
14	C₁₃×#544	—	2	2	no	—
15	C₁₃×#544	C₂²	1	2	yes	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#533	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	—	2	1	no	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₁₃×#520	C₂²	1	2	yes	—
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₁₃×#491	—	2	1	no	—
24	C₁₃×#491	—	2	1	no	—
25	C₁₃×#487	—	2	2	no	—
26	C₁₃×#462	—	2	2	no	—
27	C₁₃×#461	—	2	2	no	—
28	C₁₃×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#104	C₂²	1	2	yes	—
30	C₁₃×#419	C₂²	1	2	yes	—
31	C₁₃×#419	C₂²	1	4	yes	—
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#400	—	2	4	no	—
34	C₁₃×#391	C₂²	1	4	yes	—
35	C₁₃×#376	C₂²	1	1	yes	characteristic
36	C₁₃×#343	C₂²	1	4	yes	—
37	C₁₃×#339	C₂²	1	4	yes	—
38	C₁₃×#339	C₂²	1	2	yes	—
39	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₁₃×#137	—	2	8	no	—
42	C₂×C₁₃×Q₁₆	—	2	2	no	—
43	C₂×C₁₃×SD₁₆	—	2	2	no	—
44	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
45	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	2	4	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
53	C₁₃×#125	—	2	4	no	—
54	C₁₃×#125	—	2	4	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×#125	—	2	2	no	—
57	C₁₃×#125	—	2	1	no	—
58	C₁₃×#125	—	2	1	no	—
59	C₁₃×#125	—	2	2	no	—
60	C₁₃×#125	D₄	1	1	yes	characteristic
61	C₁₃×#125	D₄	1	1	yes	characteristic
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	4	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	D₄	1	2	yes	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	4	no	—
74	C₄×D₄×C₁₃	D₄	1	2	yes	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×#117	C₂³	1	1	yes	characteristic
78	C₁₃×#117	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#104	—	2	4	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	2	4	no	—
91	C₁₃×#103	—	2	4	no	—
92	C₁₃×#97	—	2	1	no	—
93	C₄×C₈×C₁₃	—	2	1	no	—
94	C₁₃×#95	—	2	8	no	—
95	C₁₃×#95	—	2	2	no	—
96	#25927	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	#41	1	4	yes	—
99	C₂×Q₈×C₁₃	—	2	4	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	4	no	—
104	C₂×Q₈×C₁₃	—	2	4	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₁₃×Q₁₆	—	4	4	no	—
117	C₁₃×SD₁₆	—	4	4	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	4	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₃	—	2	4	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	1	2	yes	—
153	#3504	C₂×C₁₃	1	1	yes	characteristic
154	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#3039	C₂×C₁₃	1	1	yes	characteristic
156	#2642	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2028	C₂×C₁₃	1	4	yes	complemented
158	#1998	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1995	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1882	C₂×C₁₃	1	4	yes	—
161	#1759	C₂×C₁₃	1	1	yes	characteristic
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	1	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	4	4	no	—
168	Q₈×C₁₃	—	8	2	no	—
169	Q₈×C₁₃	—	8	4	no	—
170	Q₈×C₁₃	#124	1	2	yes	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	2	1	no	—
173	D₄×C₁₃	#124	1	2	yes	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	—	8	4	no	—
188	C₂×C₄×C₁₃	#120	1	2	yes	—
189	C₂×C₄×C₁₃	#120	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
194	C₈×C₁₃	—	4	2	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₂×#137	C₂²×C₁₃	1	2	yes	—
197	#557	—	2	2	no	—
198	#554	—	2	2	no	—
199	#554	—	2	4	no	—
200	#544	—	2	2	no	—
201	#544	C₂²×C₁₃	1	2	yes	—
202	#533	—	2	1	no	—
203	#533	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#125	—	2	1	no	—
206	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
207	#520	C₂²×C₁₃	1	2	yes	—
208	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
209	#491	—	2	1	no	—
210	#491	—	2	1	no	—
211	#487	—	2	2	no	—
212	#462	—	2	2	no	—
213	#461	—	2	2	no	—
214	#423	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#104	C₂²×C₁₃	1	2	yes	—
216	#419	C₂²×C₁₃	1	4	yes	—
217	#419	C₂²×C₁₃	1	2	yes	—
218	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
219	#400	—	2	4	no	—
220	#391	C₂²×C₁₃	1	4	yes	—
221	#376	C₂²×C₁₃	1	1	yes	characteristic
222	#343	C₂²×C₁₃	1	4	yes	—
223	#339	C₂²×C₁₃	1	4	yes	—
224	#339	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
229	C₂²×C₁₃	#548	1	2	yes	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	4	4	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	8	2	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
240	C₄×C₁₃	#536	1	1	yes	characteristic
241	C₄×C₁₃	#548	1	2	yes	—
242	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
244	#137	—	2	8	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
248	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
256	#125	—	2	4	no	—
257	#125	—	2	4	no	—
258	#125	—	2	2	no	—
259	#125	—	2	2	no	—
260	#125	—	2	1	no	—
261	#125	—	2	1	no	—
262	#125	—	2	2	no	—
263	#125	D₄×C₁₃	1	1	yes	characteristic
264	#125	D₄×C₁₃	1	1	yes	characteristic
265	C₂²⋊Q₈	—	2	4	no	—
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	D₄×C₁₃	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	D₄×C₁₃	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	—	2	1	no	—
280	#117	C₂³×C₁₃	1	1	yes	characteristic
281	#117	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
290	C₄⋊C₈	—	2	2	no	—
291	#104	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	#97	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	#95	—	2	2	no	—
298	#95	—	2	8	no	—
299	C₂×C₁₃	—	2	2	no	—
300	C₂×C₁₃	—	4	2	no	—
301	C₂×C₁₃	#2436	1	1	yes	characteristic
302	C₂×C₁₃	#3022	1	2	yes	—
303	#41	—	2	2	no	—
304	#41	C₁₃×#41	1	4	yes	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
322	Q₁₆	—	4	4	no	—
323	SD₁₆	—	4	4	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
345	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₄²	—	2	4	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₁₃	1	2	yes	—
359	C₁₃	#25927	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	1	no	—
361	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
362	Q₈	—	2	1	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	4	no	—
366	Q₈	—	8	2	no	—
367	Q₈	—	8	4	no	—
368	Q₈	C₁₃×#124	1	2	yes	—
369	D₄	—	2	4	no	—
370	D₄	—	2	1	no	—
371	D₄	C₁₃×#124	1	2	yes	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	C₁₃×#120	1	2	yes	—
387	C₂×C₄	C₁₃×#120	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
390	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
391	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
398	C₂²	C₁₃×#548	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	2	no	—
407	C₄	—	8	2	no	—
408	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
409	C₄	C₁₃×#536	1	1	yes	characteristic
410	C₄	C₁₃×#548	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	4	2	no	—
413	C₂	C₁₃×#2436	1	1	yes	characteristic
414	C₂	C₁₃×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3139	C₂	semidirect
4. C₁₃×#2642	C₂	semidirect
5. C₁₃×#2028	C₂	semidirect
6. C₁₃×#1998	C₂	semidirect
7. C₁₃×#1995	C₂	semidirect
96. #25927	C₁₃	direct (N × H)
154. #3139	C₂×C₁₃	semidirect
156. #2642	C₂×C₁₃	semidirect
157. #2028	C₂×C₁₃	semidirect
158. #1998	C₂×C₁₃	semidirect
159. #1995	C₂×C₁₃	semidirect
359. C₁₃	#25927	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×#3504	2
C₁₃×#3139	2
C₁₃×#3039	2
C₁₃×#2642	2
C₁₃×#2028	2
C₁₃×#1998	2
C₁₃×#1995	2
C₁₃×#1882	2
C₁₃×#1759	2
#25927	13

Subgroups — C13×#25927 #15712266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25927 #15712266