Subgroups — D₁₃⋊#1567 #16794931

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#423	C₂	1	2	yes	maximal
2	#13130395	C₂	1	2	yes	maximal, complemented
3	#13130394	C₂	1	2	yes	maximal, complemented
4	#13130393	C₂	1	4	yes	maximal, complemented
5	D₁₃⋊#335	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₁₃⋊M₁₆	—	2	2	no	—
8	C₂²×C₈×D₁₃	C₄	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719129	—	2	2	no	—
11	#11719129	C₂²	1	4	yes	—
12	#11719053	—	2	2	no	—
13	#11719052	C₂²	1	4	yes	—
14	D₁₃⋊(C₄⋊C₈)	—	2	2	no	—
15	D₁₃⋊(C₄⋊C₈)	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
18	C₂×C₄×#1055	C₄	1	1	yes	characteristic
19	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
20	C₄×C₈×D₁₃	C₄	1	2	yes	—
21	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
22	C₄×C₈×D₁₃	C₂²	1	2	yes	—
23	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	#11718256	C₂²	1	8	yes	complemented
26	#11718254	C₂²	1	8	yes	complemented
27	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
30	C₂×#6122	—	2	4	no	—
31	D₁₃⋊M₁₆	—	4	8	no	—
32	C₂×#6118	—	2	4	no	—
33	C₂×D₁₃⋊C₈	—	2	4	no	—
34	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
39	C₂²×#1055	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₁₃	—	2	8	no	—
41	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
45	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₁₃	D₄	1	1	yes	characteristic
48	C₄²×D₁₃	D₄	1	1	yes	characteristic
49	C₄²×D₁₃	Q₈	1	1	yes	characteristic
50	C₄²×D₁₃	Q₈	1	1	yes	characteristic
51	C₄²×D₁₃	C₂³	1	1	yes	characteristic
52	C₄²×D₁₃	C₂³	1	1	yes	characteristic
53	#88112	—	2	4	no	—
54	#88112	—	2	4	no	—
55	C₄⋊#1057	—	2	4	no	—
56	C₄⋊#1057	C₂³	1	8	yes	—
57	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
61	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₈×Dic₁₃	C₂³	1	2	yes	—
63	C₈×Dic₁₃	C₂³	1	2	yes	—
64	C₄×#1055	C₂×C₄	1	1	yes	characteristic
65	C₄×#1055	C₂×C₄	1	2	yes	—
66	C₄×#1055	C₂×C₄	1	1	yes	characteristic
67	C₂×#1567	—	13	1	no	maximal, Sylow
68	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
75	C₂×C₄×D₁₃	—	2	4	no	—
76	C₂×C₄×D₁₃	—	2	4	no	—
77	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	D₈	1	4	yes	—
84	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
85	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
91	#6122	—	4	8	no	—
92	C₂×#1057	—	2	8	no	—
93	#6118	—	4	8	no	—
94	D₁₃⋊C₈	—	4	8	no	—
95	C₂×C₈×C₁₃	—	2	4	no	—
96	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
108	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
109	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
110	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
114	C₂×#1055	—	2	4	no	—
115	C₂×#1055	C₂²×C₄	1	2	yes	—
116	C₂×#1055	C₂²×C₄	1	2	yes	—
117	C₈×D₁₃	—	2	4	no	—
118	C₈×D₁₃	—	2	4	no	—
119	C₈×D₁₃	—	2	4	no	—
120	C₈×D₁₃	M₁₆	1	8	yes	complemented
121	C₂×#423	—	13	2	no	—
122	C₂²×C₄×C₈	—	13	1	no	—
123	#1567	—	13	4	no	—
124	#1567	—	13	2	no	—
125	#1567	—	13	2	no	—
126	C₂×#335	—	13	4	no	—
127	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂²×D₁₃	—	2	2	no	—
129	C₂²×D₁₃	—	2	2	no	—
130	C₂²×D₁₃	#107	1	4	yes	—
131	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	#107	1	4	yes	—
136	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
142	C₂×Dic₁₃	—	2	2	no	—
143	C₂×Dic₁₃	—	2	2	no	—
144	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
149	C₂×Dic₁₃	C₂×Q₁₆	1	2	yes	—
150	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
152	C₄×D₁₃	—	2	2	no	—
153	C₄×D₁₃	—	2	2	no	—
154	C₄×D₁₃	—	2	2	no	—
155	C₄×D₁₃	—	2	2	no	—
156	C₄×D₁₃	—	2	2	no	—
157	C₄×D₁₃	—	2	2	no	—
158	C₄×D₁₃	#107	1	4	yes	—
159	C₄×D₁₃	#107	1	4	yes	—
160	C₄×D₁₃	#108	1	4	yes	—
161	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
162	C₄×D₁₃	C₂×D₈	1	2	yes	—
163	C₄×D₁₃	C₂×D₈	1	2	yes	—
164	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
165	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
166	#1057	—	4	8	no	—
167	C₈×C₁₃	—	2	2	no	—
168	C₈×C₁₃	C₂×M₁₆	1	4	yes	complemented
169	#1055	—	2	2	no	—
170	#1055	C₂×M₁₆	1	4	yes	complemented
171	C₂²×M₁₆	—	26	2	no	—
172	C₂³×C₈	—	13	2	no	—
173	C₂²×C₄²	—	13	1	no	—
174	#423	—	13	4	no	—
175	#423	—	13	4	no	—
176	#423	—	26	2	no	—
177	#423	—	26	2	no	—
178	C₂×C₄⋊C₈	—	13	4	no	—
179	C₂×C₄⋊C₈	—	26	2	no	—
180	C₂×C₄×C₈	—	13	2	no	—
181	C₂×C₄×C₈	—	13	1	no	—
182	C₂×C₄×C₈	—	13	2	no	—
183	C₂×C₄×C₈	—	13	1	no	—
184	C₂×C₄×C₈	—	13	1	no	—
185	C₂×C₄×C₈	—	13	1	no	—
186	C₂×C₄×C₈	—	13	2	no	—
187	C₂×C₄×C₈	—	13	1	no	—
188	C₂×C₄×C₈	#261	1	1	yes	characteristic
189	#335	—	13	8	no	—
190	#335	—	13	8	no	—
191	C₂²×C₁₃	—	2	1	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	C₂×#107	1	2	yes	—
194	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₂×D₁₃	—	2	1	no	—
196	C₂×D₁₃	—	2	1	no	—
197	C₂×D₁₃	—	2	8	no	—
198	C₂×D₁₃	#423	1	2	yes	—
199	C₂×D₁₃	C₂×#107	1	2	yes	—
200	C₂×D₁₃	C₂×#107	1	2	yes	—
201	C₂×D₁₃	C₂×#108	1	2	yes	—
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	—	2	1	no	—
204	C₄×C₁₃	C₂×#107	1	2	yes	—
205	C₄×C₁₃	C₂×#107	1	2	yes	—
206	C₄×C₁₃	C₂×#108	1	2	yes	—
207	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
208	Dic₁₃	—	2	1	no	—
209	Dic₁₃	—	2	1	no	—
210	Dic₁₃	#423	1	2	yes	—
211	Dic₁₃	C₂×#107	1	2	yes	—
212	Dic₁₃	C₂×#108	1	2	yes	—
213	Dic₁₃	C₂²×D₈	1	1	yes	characteristic
214	Dic₁₃	C₂²×Q₁₆	1	1	yes	characteristic
215	C₂³×C₄	—	13	1	no	—
216	C₂³×C₄	—	13	1	no	—
217	C₂³×C₄	—	13	1	no	—
218	C₂×M₁₆	—	26	4	no	—
219	C₂×M₁₆	—	26	4	no	—
220	C₂×M₁₆	—	52	8	no	—
221	C₂²×C₈	—	13	2	no	—
222	C₂²×C₈	—	13	2	no	—
223	C₂²×C₈	—	13	2	no	—
224	C₂²×C₈	—	13	2	no	—
225	C₂²×C₈	—	13	2	no	—
226	C₂²×C₈	—	26	8	no	—
227	C₂²×C₈	—	26	4	no	—
228	C₂²×C₈	C₂×#261	1	2	yes	—
229	C₂×C₄²	—	13	1	no	—
230	C₂×C₄²	—	13	1	no	—
231	C₂×C₄²	—	13	1	no	—
232	C₂×C₄²	—	13	1	no	—
233	C₂×C₄²	—	13	1	no	—
234	C₂×C₄²	—	13	1	no	—
235	C₂×C₄²	—	13	1	no	—
236	C₂×C₄²	—	13	1	no	—
237	C₂×C₄²	—	13	1	no	—
238	C₂×C₄²	—	13	1	no	—
239	C₂×C₄²	—	13	1	no	—
240	C₂×C₄²	C₂×#261	1	1	yes	characteristic
241	C₄⋊C₈	—	13	8	no	—
242	C₄⋊C₈	—	26	4	no	—
243	C₄⋊C₈	—	26	4	no	—
244	C₄⋊C₈	—	26	4	no	—
245	C₄×C₈	—	13	2	no	—
246	C₄×C₈	—	13	2	no	—
247	C₄×C₈	—	13	2	no	—
248	C₄×C₈	—	13	2	no	—
249	C₄×C₈	—	13	1	no	—
250	C₄×C₈	—	13	1	no	—
251	C₄×C₈	—	13	2	no	—
252	C₄×C₈	C₂×#261	1	1	yes	characteristic
253	C₄×C₈	C₂×#261	1	1	yes	characteristic
254	C₄×C₈	C₂×#261	1	2	yes	—
255	C₂×C₁₃	—	2	2	no	—
256	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
257	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
258	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
259	D₁₃	—	2	2	no	—
260	D₁₃	#1567	1	4	yes	complemented
261	C₂⁴	—	13	1	no	—
262	C₂²×C₄	—	13	1	no	—
263	C₂²×C₄	—	13	4	no	—
264	C₂²×C₄	—	13	4	no	—
265	C₂²×C₄	—	13	1	no	—
266	C₂²×C₄	—	13	1	no	—
267	C₂²×C₄	—	13	1	no	—
268	C₂²×C₄	—	13	1	no	—
269	C₂²×C₄	—	13	1	no	—
270	C₂²×C₄	—	13	1	no	—
271	C₂²×C₄	—	13	1	no	—
272	C₂²×C₄	—	13	1	no	—
273	C₂²×C₄	—	13	1	no	—
274	C₂²×C₄	—	13	1	no	—
275	C₂²×C₄	—	13	1	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	26	4	no	—
280	C₂²×C₄	—	26	4	no	—
281	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
283	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
284	M₁₆	—	52	8	no	—
285	M₁₆	—	52	8	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	13	2	no	—
288	C₂×C₈	—	13	8	no	—
289	C₂×C₈	—	13	2	no	—
290	C₂×C₈	—	26	4	no	—
291	C₂×C₈	—	26	4	no	—
292	C₂×C₈	—	26	4	no	—
293	C₂×C₈	—	26	4	no	—
294	C₂×C₈	—	26	8	no	—
295	C₂×C₈	—	52	8	no	—
296	C₂×C₈	C₂²×#261	1	2	yes	—
297	C₂×C₈	C₂²×#261	1	2	yes	—
298	C₄²	—	13	1	no	—
299	C₄²	—	13	1	no	—
300	C₄²	—	13	1	no	—
301	C₄²	—	13	1	no	—
302	C₄²	—	13	1	no	—
303	C₄²	—	13	1	no	—
304	C₄²	—	13	1	no	—
305	C₄²	—	13	1	no	—
306	C₄²	—	13	1	no	—
307	C₄²	—	13	1	no	—
308	C₄²	—	13	1	no	—
309	C₄²	—	13	1	no	—
310	C₄²	C₄⋊#261	1	1	yes	characteristic
311	C₄²	C₄⋊#261	1	1	yes	characteristic
312	C₄²	C₂²×#261	1	1	yes	characteristic
313	C₄²	C₂²×#261	1	1	yes	characteristic
314	C₁₃	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
315	C₂³	—	13	1	no	—
316	C₂³	—	13	4	no	—
317	C₂³	—	13	1	no	—
318	C₂³	—	26	2	no	—
319	C₂³	—	26	2	no	—
320	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	13	2	no	—
324	C₂×C₄	—	13	2	no	—
325	C₂×C₄	—	13	1	no	—
326	C₂×C₄	—	13	1	no	—
327	C₂×C₄	—	13	1	no	—
328	C₂×C₄	—	13	1	no	—
329	C₂×C₄	—	13	2	no	—
330	C₂×C₄	—	13	2	no	—
331	C₂×C₄	—	13	4	no	—
332	C₂×C₄	—	13	4	no	—
333	C₂×C₄	—	13	2	no	—
334	C₂×C₄	—	13	2	no	—
335	C₂×C₄	—	13	4	no	—
336	C₂×C₄	—	13	4	no	—
337	C₂×C₄	—	13	1	no	—
338	C₂×C₄	—	13	1	no	—
339	C₂×C₄	—	26	2	no	—
340	C₂×C₄	—	26	2	no	—
341	C₂×C₄	—	26	2	no	—
342	C₂×C₄	—	26	2	no	—
343	C₂×C₄	—	26	2	no	—
344	C₂×C₄	—	26	2	no	—
345	C₂×C₄	—	26	2	no	—
346	C₂×C₄	—	26	2	no	—
347	C₂×C₄	#88102	1	4	yes	—
348	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
353	C₂×C₄	C₂³×#261	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	13	4	no	—
356	C₈	—	26	2	no	—
357	C₈	—	52	8	no	—
358	C₈	D₁₃⋊M₁₆	1	4	yes	complemented
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	13	2	no	—
362	C₂²	—	13	2	no	—
363	C₂²	—	13	2	no	—
364	C₂²	—	13	2	no	—
365	C₂²	—	26	8	no	—
366	C₂²	—	26	1	no	—
367	C₂²	—	26	1	no	—
368	C₂²	C₂×#88102	1	2	yes	—
369	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	13	2	no	—
373	C₄	—	13	1	no	—
374	C₄	—	13	1	no	—
375	C₄	—	13	2	no	—
376	C₄	—	13	2	no	—
377	C₄	—	26	1	no	—
378	C₄	—	26	1	no	—
379	C₄	C₂×#88102	1	2	yes	—
380	C₄	C₂×#88102	1	2	yes	—
381	C₄	D₁₃⋊#108	1	2	yes	—
382	C₄	C₂×D₁₃⋊M₁₆	1	2	yes	—
383	C₂	—	2	2	no	—
384	C₂	—	13	4	no	—
385	C₂	—	26	2	no	—
386	C₂	D₁₃⋊#423	1	1	yes	characteristic
387	C₂	C₂²×#88102	1	1	yes	characteristic
388	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
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×#1567
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130395	C₂	semidirect
3. #13130394	C₂	semidirect
4. #13130393	C₂	semidirect
5. D₁₃⋊#335	C₂	semidirect
25. #11718256	C₂²	semidirect
26. #11718254	C₂²	semidirect
120. C₈×D₁₃	M₁₆	semidirect
168. C₈×C₁₃	C₂×M₁₆	semidirect
170. #1055	C₂×M₁₆	semidirect
260. D₁₃	#1567	semidirect
314. C₁₃	C₂×#1567	semidirect
358. C₈	D₁₃⋊M₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#423	2
#13130395	2
#13130394	2
#13130393	2
D₁₃⋊#335	2
C₂×C₄×C₈×D₁₃	2
C₂×#1567	13

Subgroups — D13⋊#1567 #16794931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1567 #16794931