Subgroups — C₁₃×#10049 #15696388

Order 3328.

714 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	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂²×C₁₃×SD₁₆	—	2	2	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#492	—	2	2	no	—
14	C₁₃×#492	—	2	2	no	—
15	C₁₃×#460	—	2	2	no	—
16	C₁₃×#460	—	2	2	no	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	—	2	1	no	—
20	C₂×C₁₃×#102	—	2	2	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#395	—	2	2	no	—
23	C₁₃×#391	—	2	1	no	—
24	C₁₃×#389	—	2	2	no	—
25	C₁₃×#384	—	2	1	no	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#333	—	2	2	no	—
28	C₁₃×Q₈⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂×C₁₃×SD₁₆	—	2	4	no	—
35	C₂×C₁₃×SD₁₆	—	2	8	no	—
36	C₂×C₁₃×SD₁₆	—	4	8	no	—
37	C₂×C₁₃×SD₁₆	—	4	2	no	—
38	C₂×C₁₃×SD₁₆	—	4	2	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×#127	—	2	1	no	—
47	C₁₃×#127	—	2	1	no	—
48	C₁₃×#127	—	2	1	no	—
49	C₁₃×#127	D₄	1	2	yes	—
50	C₄×Q₈×C₁₃	—	2	1	no	—
51	C₄×Q₈×C₁₃	—	2	1	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×#102	—	4	4	no	—
69	C₄×C₈×C₁₃	—	2	1	no	—
70	C₄×C₈×C₁₃	D₄	1	2	yes	—
71	C₁₃×#95	—	2	4	no	—
72	C₁₃×#95	—	2	1	no	—
73	#10049	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁴×C₁₃	—	4	1	no	—
75	C₂×Q₈×C₁₃	—	2	1	no	—
76	C₂×Q₈×C₁₃	—	2	1	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	2	1	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	—	2	1	no	—
81	C₂×Q₈×C₁₃	—	2	1	no	—
82	C₂×Q₈×C₁₃	—	4	4	no	—
83	C₂×Q₈×C₁₃	SD₁₆	1	2	yes	complemented
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	—	4	4	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₁₃×SD₁₆	—	4	16	no	—
105	C₁₃×SD₁₆	—	4	8	no	—
106	C₂×C₈×C₁₃	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	4	1	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	—	4	1	no	—
112	C₂×C₈×C₁₃	—	4	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	8	4	no	—
123	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
124	C₄²×C₁₃	—	4	1	no	—
125	C₄²×C₁₃	—	4	1	no	—
126	C₄²×C₁₃	—	4	1	no	—
127	C₄²×C₁₃	—	4	1	no	—
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	#41	1	1	yes	characteristic
132	C₂×#492	C₂×C₁₃	1	1	yes	characteristic
133	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
134	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#1982	C₂×C₁₃	1	1	yes	characteristic
136	C₂×#333	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	8	1	no	—
141	C₂³×C₁₃	—	8	2	no	—
142	C₂³×C₁₃	—	8	1	no	—
143	C₂³×C₁₃	—	8	2	no	—
144	C₂³×C₁₃	#120	1	1	yes	characteristic
145	Q₈×C₁₃	—	2	2	no	—
146	Q₈×C₁₃	—	2	2	no	—
147	Q₈×C₁₃	—	4	4	no	—
148	Q₈×C₁₃	—	4	1	no	—
149	Q₈×C₁₃	—	4	1	no	—
150	Q₈×C₁₃	—	8	2	no	—
151	D₄×C₁₃	—	4	4	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	4	no	—
155	D₄×C₁₃	—	8	2	no	—
156	D₄×C₁₃	—	8	1	no	—
157	D₄×C₁₃	—	8	1	no	—
158	D₄×C₁₃	—	8	1	no	—
159	D₄×C₁₃	—	8	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#137	1	2	yes	—
183	C₈×C₁₃	—	2	4	no	—
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	—	8	1	no	—
186	C₂²×SD₁₆	—	2	2	no	—
187	C₂²×SD₁₆	—	2	1	no	—
188	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
191	#492	—	2	2	no	—
192	#492	—	2	2	no	—
193	#460	—	2	2	no	—
194	#460	—	2	2	no	—
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#102	—	2	1	no	—
198	C₂×#102	—	2	2	no	—
199	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	#395	—	2	2	no	—
201	#391	—	2	1	no	—
202	#389	—	2	2	no	—
203	#384	—	2	1	no	—
204	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
205	#333	—	2	2	no	—
206	Q₈⋊C₈	—	2	2	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	16	2	no	—
211	C₂²×C₁₃	—	16	2	no	—
212	C₂²×C₁₃	#392	1	1	yes	characteristic
213	C₂²×C₁₃	#448	1	2	yes	—
214	C₂²×C₁₃	#448	1	1	yes	characteristic
215	C₂²×C₁₃	#449	1	1	yes	characteristic
216	C₂²×C₁₃	#453	1	2	yes	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	—	8	1	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	#450	1	1	yes	characteristic
224	C₄×C₁₃	#452	1	1	yes	characteristic
225	C₄×C₁₃	#461	1	2	yes	—
226	C₄×C₁₃	#465	1	1	yes	characteristic
227	C₄×C₁₃	#468	1	1	yes	characteristic
228	C₄×C₁₃	#492	1	1	yes	characteristic
229	C₄×C₁₃	#497	1	1	yes	characteristic
230	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
231	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	2	8	no	—
237	C₂×SD₁₆	—	4	8	no	—
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	—	2	1	no	—
249	#127	—	2	1	no	—
250	#127	D₄×C₁₃	1	2	yes	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
268	#102	—	2	4	no	—
269	#102	—	4	4	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	D₄×C₁₃	1	2	yes	—
272	#95	—	2	4	no	—
273	#95	—	2	1	no	—
274	C₂×C₁₃	—	16	2	no	—
275	C₂×C₁₃	#1622	1	2	yes	—
276	C₂×C₁₃	#1623	1	2	yes	—
277	C₂×C₁₃	#2000	1	1	yes	characteristic
278	C₂×C₁₃	#2002	1	1	yes	characteristic
279	C₂×C₁₃	#2013	1	1	yes	characteristic
280	C₂⁴	—	4	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	C₁₃×SD₁₆	1	2	yes	complemented
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
310	SD₁₆	—	4	16	no	—
311	SD₁₆	—	4	8	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	8	4	no	—
329	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
330	C₄²	—	4	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₄²	C₁₃×#41	1	1	yes	characteristic
338	C₁₃	#10049	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	4	2	no	—
340	C₂³	—	8	1	no	—
341	C₂³	—	8	2	no	—
342	C₂³	—	8	1	no	—
343	C₂³	—	8	2	no	—
344	C₂³	C₁₃×#120	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	8	2	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	4	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	1	no	—
359	D₄	—	8	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
372	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
373	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
374	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
375	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
376	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
379	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
380	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
381	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
382	C₂×C₄	C₁₃×#137	1	2	yes	—
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	8	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	C₁₃×#392	1	1	yes	characteristic
392	C₂²	C₁₃×#448	1	1	yes	characteristic
393	C₂²	C₁₃×#448	1	2	yes	—
394	C₂²	C₁₃×#449	1	1	yes	characteristic
395	C₂²	C₁₃×#453	1	2	yes	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	4	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	2	no	—
402	C₄	C₁₃×#450	1	1	yes	characteristic
403	C₄	C₁₃×#452	1	1	yes	characteristic
404	C₄	C₁₃×#461	1	2	yes	—
405	C₄	C₁₃×#465	1	1	yes	characteristic
406	C₄	C₁₃×#468	1	1	yes	characteristic
407	C₄	C₁₃×#492	1	1	yes	characteristic
408	C₄	C₁₃×#497	1	1	yes	characteristic
409	C₂	—	16	2	no	—
410	C₂	C₁₃×#1622	1	2	yes	—
411	C₂	C₁₃×#1623	1	2	yes	—
412	C₂	C₁₃×#2000	1	1	yes	characteristic
413	C₂	C₁₃×#2002	1	1	yes	characteristic
414	C₂	C₁₃×#2013	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2567	C₂	semidirect
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
73. #10049	C₁₃	direct (N × H)
83. C₂×Q₈×C₁₃	SD₁₆	semidirect
123. C₁₃×C₄⋊C₄	SD₁₆	semidirect
134. #2567	C₂×C₁₃	semidirect
136. C₂×#333	C₂×C₁₃	semidirect
137. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
138. #1279	C₂×C₁₃	semidirect
289. C₂×Q₈	C₁₃×SD₁₆	semidirect
329. C₄⋊C₄	C₁₃×SD₁₆	semidirect
338. C₁₃	#10049	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×#492	2
C₂×C₁₃×#460	2
C₁₃×#2567	2
C₁₃×#1982	2
C₂×C₁₃×#333	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1279	2
#10049	13

Subgroups — C13×#10049 #15696388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10049 #15696388