Subgroups — D₁₃×#1570 #15831972

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#13113608	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113607	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113606	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113605	C₂	1	4	yes	maximal, complemented
8	D₁₃×#334	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₁₃	—	2	1	no	—
11	C₂²×C₈×D₁₃	—	2	1	no	—
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#431	C₂²	1	1	yes	characteristic
14	C₁₃×#423	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	#11718779	—	2	1	no	—
17	C₂×#88054	—	2	1	no	—
18	#11718586	C₂²	1	1	yes	characteristic
19	#11718585	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	#11718498	—	2	1	no	—
22	#11718498	C₂²	1	2	yes	—
23	#11718494	C₄	1	2	yes	—
24	D₁₃×C₄⋊C₈	—	2	1	no	—
25	D₁₃×C₄⋊C₈	—	2	1	no	—
26	D₁₃×C₄⋊C₈	—	2	1	no	—
27	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
28	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
32	#11718379	C₄	1	2	yes	—
33	#11718346	C₂²	1	2	yes	—
34	C₄×C₈×D₁₃	C₂²	1	2	yes	—
35	C₁₃×#334	C₂²	1	4	yes	complemented
36	#11718072	C₂²	1	4	yes	complemented
37	#11718072	C₂²	1	4	yes	complemented
38	#11718049	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
42	C₂×C₁₃×M₁₆	—	2	1	no	—
43	C₂²×C₈×C₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
48	C₂×#6099	—	2	1	no	—
49	C₂²×#1055	—	2	1	no	—
50	M₁₆×D₁₃	—	4	4	no	—
51	C₂×#6094	—	2	2	no	—
52	C₂×C₈×D₁₃	—	2	2	no	—
53	C₂×C₈×D₁₃	—	2	2	no	—
54	C₂×C₈×D₁₃	—	2	2	no	—
55	C₂×C₈×D₁₃	—	4	4	no	—
56	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	C₄²×D₁₃	D₄	1	1	yes	characteristic
61	C₄²×D₁₃	Q₈	1	1	yes	characteristic
62	C₄²×D₁₃	Q₈	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
68	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
69	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
70	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₃	C₂³	1	2	yes	—
72	C₂²⋊#1055	C₂×C₄	1	2	yes	—
73	#88060	C₂×C₄	1	4	yes	—
74	#88054	—	2	2	no	—
75	#88054	—	2	2	no	—
76	#88054	—	2	2	no	—
77	#88054	—	2	2	no	—
78	#88054	C₂×C₄	1	4	yes	—
79	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
80	C₄⋊#1055	—	2	1	no	—
81	C₄⋊#1055	—	2	1	no	—
82	C₄⋊#1055	C₂×C₄	1	2	yes	—
83	C₄⋊#1055	C₂³	1	2	yes	—
84	C₄⋊#1055	C₂³	1	2	yes	—
85	C₄×#1055	C₂³	1	2	yes	—
86	C₂×#1570	—	13	1	no	maximal, Sylow
87	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	—	4	2	no	—
96	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	SD₁₆	1	4	yes	—
103	C₂×C₄×D₁₃	SD₁₆	1	4	yes	—
104	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₁₃×M₁₆	—	4	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	4	2	no	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
131	#6099	—	4	2	no	—
132	C₂×#1055	—	2	2	no	—
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	—	4	2	no	—
135	C₂×#1055	C₂²×C₄	1	4	yes	—
136	#6094	—	4	4	no	—
137	C₈×D₁₃	—	2	8	no	—
138	C₈×D₁₃	—	4	4	no	—
139	C₈×D₁₃	—	4	4	no	—
140	C₈×D₁₃	—	4	4	no	—
141	C₂×#431	—	13	1	no	—
142	C₂×#423	—	13	1	no	—
143	C₂²×C₄⋊C₈	—	13	1	no	—
144	#1570	—	13	1	no	—
145	#1570	—	13	1	no	—
146	#1570	—	13	1	no	—
147	#1570	—	13	4	no	—
148	#1570	D₁₃	1	1	yes	characteristic, direct product factor
149	C₂×#334	—	13	4	no	—
150	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×D₁₃	—	2	2	no	—
152	C₂²×D₁₃	—	2	2	no	—
153	C₂²×D₁₃	#106	1	4	yes	—
154	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
166	C₂×Dic₁₃	—	2	2	no	—
167	C₂×Dic₁₃	—	4	1	no	—
168	C₂×Dic₁₃	#106	1	4	yes	—
169	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	4	1	no	—
181	C₄×D₁₃	—	4	1	no	—
182	C₄×D₁₃	#106	1	4	yes	—
183	C₄×D₁₃	#106	1	4	yes	—
184	C₄×D₁₃	#131	1	4	yes	—
185	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
186	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
187	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
188	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
189	C₈×C₁₃	—	2	4	no	—
190	C₈×C₁₃	—	4	2	no	—
191	C₈×C₁₃	—	4	2	no	—
192	#1055	—	2	4	no	—
193	#1055	—	4	2	no	—
194	#1055	—	4	2	no	—
195	C₂²×M₁₆	—	26	1	no	—
196	C₂³×C₈	—	26	1	no	—
197	C₂²×C₄²	—	13	1	no	—
198	#431	—	13	1	no	—
199	#431	—	13	2	no	—
200	#431	—	13	2	no	—
201	#431	—	13	2	no	—
202	#431	C₂×D₁₃	1	1	yes	characteristic
203	#423	—	13	1	no	—
204	#423	—	13	2	no	—
205	#423	—	26	1	no	—
206	#423	—	26	1	no	—
207	#423	C₂×D₁₃	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	13	2	no	—
209	C₂×C₄⋊C₈	—	13	1	no	—
210	C₂×C₄⋊C₈	—	13	2	no	—
211	C₂×C₄⋊C₈	—	13	2	no	—
212	C₂×C₄⋊C₈	—	13	2	no	—
213	C₂×C₄⋊C₈	—	26	1	no	—
214	C₂×C₄⋊C₈	—	26	1	no	—
215	C₂×C₄⋊C₈	—	26	1	no	—
216	C₂×C₄⋊C₈	—	26	1	no	—
217	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	—	13	2	no	—
219	C₂×C₄×C₈	—	13	2	no	—
220	#334	—	13	4	no	—
221	#334	—	13	4	no	—
222	#334	—	13	4	no	—
223	#334	C₂×D₁₃	1	4	yes	complemented
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	C₂×#106	1	2	yes	—
227	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₂×D₁₃	—	2	1	no	—
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	8	no	—
231	C₂×D₁₃	#424	1	2	yes	—
232	C₂×D₁₃	C₂×#106	1	2	yes	—
233	C₂×D₁₃	C₂×#106	1	2	yes	—
234	C₂×D₁₃	#430	1	2	yes	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	C₂×#106	1	2	yes	—
239	C₄×C₁₃	C₂×#131	1	2	yes	—
240	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
241	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	—	2	1	no	—
245	Dic₁₃	#424	1	2	yes	—
246	Dic₁₃	C₂×#106	1	2	yes	—
247	Dic₁₃	C₂×#106	1	2	yes	—
248	C₂³×C₄	—	13	1	no	—
249	C₂³×C₄	—	13	1	no	—
250	C₂³×C₄	—	13	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	26	2	no	—
253	C₂×M₁₆	—	26	1	no	—
254	C₂×M₁₆	—	52	4	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	13	4	no	—
257	C₂²×C₈	—	26	2	no	—
258	C₂²×C₈	—	26	2	no	—
259	C₂²×C₈	—	26	2	no	—
260	C₂²×C₈	—	26	1	no	—
261	C₂²×C₈	—	52	4	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	13	4	no	—
277	C₄⋊C₈	—	13	2	no	—
278	C₄⋊C₈	—	13	2	no	—
279	C₄⋊C₈	—	13	2	no	—
280	C₄⋊C₈	—	26	2	no	—
281	C₄⋊C₈	—	26	2	no	—
282	C₄⋊C₈	—	26	2	no	—
283	C₄⋊C₈	—	26	2	no	—
284	C₄⋊C₈	—	26	1	no	—
285	C₄⋊C₈	—	26	1	no	—
286	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
287	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
288	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
289	C₂²⋊C₈	—	13	2	no	—
290	C₂²⋊C₈	—	13	4	no	—
291	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
292	C₄×C₈	—	13	4	no	—
293	C₄×C₈	—	13	2	no	—
294	C₄×C₈	C₂²×D₁₃	1	2	yes	—
295	C₂×C₁₃	—	2	2	no	—
296	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
297	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
298	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
299	D₁₃	—	2	2	no	—
300	D₁₃	#1570	1	4	yes	direct product factor
301	C₂⁴	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	4	no	—
306	C₂²×C₄	—	13	4	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	26	4	no	—
320	C₂²×C₄	—	52	2	no	—
321	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
323	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
324	M₁₆	—	4	2	no	—
325	M₁₆	—	52	4	no	—
326	M₁₆	—	52	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	13	4	no	—
331	C₂×C₈	—	26	8	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	—	26	2	no	—
334	C₂×C₈	—	52	4	no	—
335	C₂×C₈	—	52	4	no	—
336	C₂×C₈	—	52	4	no	—
337	C₂×C₈	—	52	2	no	—
338	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
339	C₄²	—	13	1	no	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	1	no	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
352	C₄²	D₄×D₁₃	1	1	yes	characteristic
353	C₄²	Q₈×D₁₃	1	1	yes	characteristic
354	C₄²	C₂³×D₁₃	1	1	yes	characteristic
355	C₁₃	C₂×#1570	1	1	yes	characteristic, complemented, Sylow
356	C₂³	—	13	1	no	—
357	C₂³	—	13	1	no	—
358	C₂³	—	13	4	no	—
359	C₂³	—	26	2	no	—
360	C₂³	—	26	2	no	—
361	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	13	4	no	—
368	C₂×C₄	—	13	4	no	—
369	C₂×C₄	—	13	2	no	—
370	C₂×C₄	—	13	2	no	—
371	C₂×C₄	—	13	2	no	—
372	C₂×C₄	—	13	2	no	—
373	C₂×C₄	—	13	4	no	—
374	C₂×C₄	—	13	4	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	2	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	52	1	no	—
385	C₂×C₄	—	52	1	no	—
386	C₂×C₄	—	52	1	no	—
387	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
388	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
389	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
390	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
391	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
392	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
395	C₈	—	2	4	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	26	4	no	—
399	C₈	—	52	2	no	—
400	C₈	—	52	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	13	2	no	—
404	C₂²	—	13	2	no	—
405	C₂²	—	13	2	no	—
406	C₂²	—	13	2	no	—
407	C₂²	—	26	8	no	—
408	C₂²	—	26	1	no	—
409	C₂²	—	26	1	no	—
410	C₂²	D₁₃×#106	1	2	yes	—
411	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	13	2	no	—
416	C₄	—	13	2	no	—
417	C₄	—	13	2	no	—
418	C₄	—	26	1	no	—
419	C₄	—	26	1	no	—
420	C₄	—	26	1	no	—
421	C₄	D₁₃×#106	1	2	yes	—
422	C₄	D₁₃×#131	1	2	yes	—
423	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
424	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	13	4	no	—
427	C₂	—	26	2	no	—
428	C₂	D₁₃×#424	1	1	yes	characteristic
429	C₂	C₂×D₁₃×#106	1	1	yes	characteristic
430	C₂	D₁₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1570	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1570	D₁₃
hypocenter	C₁₃	C₂×#1570
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

Complements

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

N	H ≅ G/N	type
4. #13113608	C₂	semidirect
5. #13113607	C₂	semidirect
6. #13113606	C₂	semidirect
7. #13113605	C₂	semidirect
8. D₁₃×#334	C₂	semidirect
9. C₁₃×#1570	C₂	semidirect
35. C₁₃×#334	C₂²	semidirect
36. #11718072	C₂²	semidirect
37. #11718072	C₂²	semidirect
38. #11718049	C₂²	semidirect
148. #1570	D₁₃	direct (N × H)
223. #334	C₂×D₁₃	semidirect
300. D₁₃	#1570	direct (N × H)
355. C₁₃	C₂×#1570	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₃×#431	2
D₁₃×#423	2
C₂×D₁₃×C₄⋊C₈	2
#13113608	2
#13113607	2
#13113606	2
#13113605	2
D₁₃×#334	2
C₁₃×#1570	2
C₂×#1570	13

Subgroups — D13×#1570 #15831972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1570 #15831972