Subgroups — D₁₃⋊#1564 #16794906

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 454 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	2	yes	maximal
2	#13130386	C₂	1	2	yes	maximal, complemented
3	#13130385	C₂	1	2	yes	maximal, complemented
4	#13130384	C₂	1	2	yes	maximal, complemented
5	#13130383	C₂	1	2	yes	maximal, complemented
6	D₁₃⋊#335	C₂	1	2	yes	maximal, complemented
7	D₁₃⋊#334	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#11719125	—	2	2	no	—
13	D₁₃⋊(C₂²⋊C₈)	—	2	2	no	—
14	#11719119	C₂²	1	4	yes	—
15	#11719051	C₂²	1	4	yes	—
16	D₁₃⋊(C₄⋊C₈)	C₂²	1	4	yes	—
17	#11719049	—	2	2	no	—
18	C₄×D₁₃⋊C₈	—	2	2	no	—
19	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
20	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₄	1	1	yes	characteristic
23	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
31	#11718256	C₂²	1	4	yes	complemented
32	#11718255	C₂²	1	4	yes	complemented
33	#11718254	C₂²	1	4	yes	complemented
34	#11718253	C₂²	1	4	yes	complemented
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
38	C₂×D₁₃⋊C₈	—	2	4	no	—
39	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
45	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
46	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	—	2	4	no	—
48	C₂×C₈×D₁₃	C₈	1	8	yes	complemented
49	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂²⋊#1057	—	2	4	no	—
66	#88112	—	2	4	no	—
67	#88111	—	2	4	no	—
68	C₄⋊#1057	C₂³	1	8	yes	—
69	C₄×#1057	—	2	4	no	—
70	C₄×#1057	—	2	4	no	—
71	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
83	C₄×#1055	C₂×C₄	1	1	yes	characteristic
84	C₄×#1055	C₂×C₄	1	1	yes	characteristic
85	C₄×#1055	C₂×C₄	1	1	yes	characteristic
86	C₄×#1055	C₂×C₄	1	1	yes	characteristic
87	C₂×#1564	—	13	1	no	maximal, Sylow
88	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₄×D₁₃	—	2	4	no	—
96	C₂×C₄×D₁₃	—	2	4	no	—
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	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
104	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×#1057	—	2	8	no	—
112	D₁₃⋊C₈	—	4	8	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	complemented
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂²×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	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×#1055	—	2	2	no	—
136	C₂×#1055	C₂×C₈	1	4	yes	complemented
137	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
138	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
139	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₈×D₁₃	—	2	2	no	—
142	C₈×D₁₃	—	2	2	no	—
143	C₈×D₁₃	—	2	2	no	—
144	C₈×D₁₃	—	2	2	no	—
145	C₈×D₁₃	C₂×C₈	1	4	yes	—
146	C₈×D₁₃	C₂×C₈	1	4	yes	—
147	C₈×D₁₃	C₂×C₈	1	4	yes	complemented
148	C₈×D₁₃	C₂×C₈	1	4	yes	complemented
149	C₂×#431	—	13	2	no	—
150	C₂²×C₄×C₈	—	13	1	no	—
151	#1564	—	13	2	no	—
152	#1564	—	13	2	no	—
153	#1564	—	13	2	no	—
154	#1564	—	13	2	no	—
155	C₂×#335	—	13	2	no	—
156	C₂×#334	—	13	2	no	—
157	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×D₁₃	—	2	2	no	—
159	C₂²×D₁₃	—	2	2	no	—
160	C₂²×D₁₃	C₄⋊C₈	1	4	yes	—
161	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
176	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
189	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
190	C₄×D₁₃	#108	1	4	yes	—
191	C₄×D₁₃	C₂²×C₈	1	2	yes	—
192	C₄×D₁₃	C₂²×C₈	1	2	yes	—
193	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
194	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
195	C₄×D₁₃	#135	1	4	yes	—
196	#1057	—	4	8	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	C₂²×C₈	1	2	yes	—
200	C₈×C₁₃	C₂²×C₈	1	2	yes	—
201	#1055	—	2	1	no	—
202	#1055	—	2	1	no	—
203	#1055	C₂²×C₈	1	2	yes	—
204	#1055	C₂²×C₈	1	2	yes	—
205	C₂³×C₈	—	13	1	no	—
206	C₂³×C₈	—	13	1	no	—
207	C₂²×C₄²	—	13	1	no	—
208	#431	—	13	4	no	—
209	#431	—	13	4	no	—
210	#431	—	26	2	no	—
211	#431	—	26	2	no	—
212	C₂×C₄⋊C₈	—	13	4	no	—
213	C₂×C₂²⋊C₈	—	26	2	no	—
214	C₂×C₄×C₈	—	13	1	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	C₂×C₄×C₈	—	13	1	no	—
217	C₂×C₄×C₈	—	13	1	no	—
218	C₂×C₄×C₈	—	13	1	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	C₂×C₄×C₈	—	26	2	no	—
226	C₂×C₄×C₈	#261	1	1	yes	characteristic
227	#335	—	13	4	no	—
228	#335	—	13	4	no	—
229	#334	—	13	4	no	—
230	#334	—	13	4	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
234	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₂×D₁₃	—	2	1	no	—
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	8	no	—
238	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
239	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
240	C₂×D₁₃	#427	1	2	yes	—
241	C₂×D₁₃	C₂×#108	1	2	yes	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
245	C₄×C₁₃	#427	1	2	yes	—
246	C₄×C₁₃	C₂×#108	1	2	yes	—
247	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
248	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
249	Dic₁₃	—	2	1	no	—
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
252	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
253	Dic₁₃	C₂×#108	1	2	yes	—
254	Dic₁₃	C₂×#135	1	2	yes	—
255	C₂³×C₄	—	13	1	no	—
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	8	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	1	no	—
265	C₂²×C₈	—	13	1	no	—
266	C₂²×C₈	—	13	1	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	26	4	no	—
270	C₂²×C₈	—	26	4	no	—
271	C₂²×C₈	C₂×#261	1	1	yes	characteristic
272	C₂²×C₈	C₂×#261	1	1	yes	characteristic
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	C₂×#261	1	1	yes	characteristic
285	C₄⋊C₈	—	13	8	no	—
286	C₄⋊C₈	—	26	4	no	—
287	C₂²⋊C₈	—	26	4	no	—
288	C₂²⋊C₈	—	26	4	no	—
289	C₄×C₈	—	13	1	no	—
290	C₄×C₈	—	13	1	no	—
291	C₄×C₈	—	13	1	no	—
292	C₄×C₈	—	13	1	no	—
293	C₄×C₈	—	13	1	no	—
294	C₄×C₈	—	13	1	no	—
295	C₄×C₈	—	13	1	no	—
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	26	4	no	—
302	C₄×C₈	—	26	4	no	—
303	C₄×C₈	C₂×#261	1	1	yes	characteristic
304	C₄×C₈	C₂×#261	1	1	yes	characteristic
305	C₄×C₈	C₂×#261	1	1	yes	characteristic
306	C₄×C₈	C₂×#261	1	1	yes	characteristic
307	C₂×C₁₃	—	2	2	no	—
308	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
310	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
311	D₁₃	—	2	2	no	—
312	D₁₃	#1564	1	4	yes	complemented
313	C₂⁴	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	4	no	—
316	C₂²×C₄	—	13	4	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	26	4	no	—
332	C₂²×C₄	—	26	4	no	—
333	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
334	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
335	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	13	4	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	4	no	—
341	C₂×C₈	—	13	4	no	—
342	C₂×C₈	—	13	4	no	—
343	C₂×C₈	—	13	4	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	—	26	8	no	—
352	C₂×C₈	—	52	8	no	—
353	C₂×C₈	D₁₃⋊C₈	1	4	yes	complemented
354	C₂×C₈	C₂²×#261	1	1	yes	characteristic
355	C₂×C₈	C₂²×#261	1	1	yes	characteristic
356	C₂×C₈	C₂²×#261	1	1	yes	characteristic
357	C₂×C₈	C₂²×#261	1	1	yes	characteristic
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	C₄⋊#261	1	1	yes	characteristic
371	C₄²	C₄⋊#261	1	1	yes	characteristic
372	C₄²	C₂²×#261	1	1	yes	characteristic
373	C₄²	C₂²×#261	1	1	yes	characteristic
374	C₁₃	C₂×#1564	1	1	yes	characteristic, complemented, Sylow
375	C₂³	—	13	1	no	—
376	C₂³	—	13	4	no	—
377	C₂³	—	13	1	no	—
378	C₂³	—	26	2	no	—
379	C₂³	—	26	2	no	—
380	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	13	4	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	4	no	—
389	C₂×C₄	—	13	4	no	—
390	C₂×C₄	—	13	4	no	—
391	C₂×C₄	—	13	4	no	—
392	C₂×C₄	—	13	2	no	—
393	C₂×C₄	—	13	2	no	—
394	C₂×C₄	—	13	2	no	—
395	C₂×C₄	—	13	2	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
407	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
408	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
413	C₂×C₄	C₂³×#261	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	2	1	no	—
416	C₈	—	13	2	no	—
417	C₈	—	13	2	no	—
418	C₈	—	26	1	no	—
419	C₈	—	26	1	no	—
420	C₈	—	52	8	no	—
421	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
422	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	13	2	no	—
426	C₂²	—	13	2	no	—
427	C₂²	—	13	2	no	—
428	C₂²	—	13	2	no	—
429	C₂²	—	26	8	no	—
430	C₂²	—	26	1	no	—
431	C₂²	—	26	1	no	—
432	C₂²	D₁₃⋊(C₄⋊C₈)	1	2	yes	—
433	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	13	2	no	—
437	C₄	—	13	2	no	—
438	C₄	—	13	2	no	—
439	C₄	—	13	2	no	—
440	C₄	—	26	1	no	—
441	C₄	—	26	1	no	—
442	C₄	D₁₃⋊(C₄⋊C₈)	1	2	yes	—
443	C₄	#11719092	1	2	yes	—
444	C₄	D₁₃⋊#108	1	2	yes	—
445	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
446	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	13	4	no	—
449	C₂	—	26	2	no	—
450	C₂	C₂×D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
451	C₂	C₂×#11719092	1	1	yes	characteristic
452	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄⋊#261
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1564
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130386	C₂	semidirect
3. #13130385	C₂	semidirect
4. #13130384	C₂	semidirect
5. #13130383	C₂	semidirect
6. D₁₃⋊#335	C₂	semidirect
7. D₁₃⋊#334	C₂	semidirect
31. #11718256	C₂²	semidirect
32. #11718255	C₂²	semidirect
33. #11718254	C₂²	semidirect
34. #11718253	C₂²	semidirect
48. C₂×C₈×D₁₃	C₈	semidirect
114. C₂×C₈×C₁₃	C₂×C₈	semidirect
136. C₂×#1055	C₂×C₈	semidirect
147. C₈×D₁₃	C₂×C₈	semidirect
148. C₈×D₁₃	C₂×C₈	semidirect
312. D₁₃	#1564	semidirect
353. C₂×C₈	D₁₃⋊C₈	semidirect
374. C₁₃	C₂×#1564	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
#13130386	2
#13130385	2
#13130384	2
#13130383	2
D₁₃⋊#335	2
D₁₃⋊#334	2
C₂×C₄×C₈×D₁₃	2
C₂×#1564	13

Subgroups — D13⋊#1564 #16794906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1564 #16794906