Subgroups — D₁₃⋊#1570 #16794976

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 394 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	1	yes	maximal, characteristic
2	C₂×D₁₃⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#13130404	C₂	1	4	yes	maximal, complemented
4	#13130403	C₂	1	4	yes	maximal, complemented
5	D₁₃⋊#334	C₂	1	4	yes	maximal, complemented
6	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
7	C₂×D₁₃⋊M₁₆	—	2	1	no	—
8	C₂²×D₁₃⋊C₈	—	2	1	no	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719129	—	2	1	no	—
11	#11719129	C₂²	1	2	yes	—
12	C₂×#88112	—	2	1	no	—
13	C₂×C₄⋊#1057	C₂²	1	2	yes	—
14	#11719053	—	2	1	no	—
15	#11719052	C₂²	1	2	yes	—
16	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
17	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
18	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
19	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
20	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
21	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
22	C₁₃×#431	C₄	1	1	yes	characteristic
23	#11718586	C₄	1	1	yes	characteristic
24	#11718494	C₂²	1	2	yes	—
25	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
26	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
27	#11718379	C₂²	1	2	yes	—
28	#11718346	C₄	1	2	yes	—
29	C₄×C₈×D₁₃	C₂²	1	2	yes	—
30	#11718255	C₂²	1	8	yes	complemented
31	#11718253	C₂²	1	8	yes	complemented
32	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
35	C₂×#6122	—	2	2	no	—
36	C₂²×#1057	—	2	2	no	—
37	D₁₃⋊M₁₆	—	4	4	no	—
38	C₂×#6118	—	2	2	no	—
39	C₂×D₁₃⋊C₈	—	2	2	no	—
40	C₂×D₁₃⋊C₈	—	2	2	no	—
41	C₂×D₁₃⋊C₈	—	2	2	no	—
42	C₂×D₁₃⋊C₈	—	4	4	no	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
48	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₁₃	D₄	1	1	yes	characteristic
51	C₄²×D₁₃	D₄	1	1	yes	characteristic
52	C₄²×D₁₃	Q₈	1	1	yes	characteristic
53	C₄²×D₁₃	Q₈	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	1	yes	characteristic
55	C₄²×D₁₃	C₂³	1	1	yes	characteristic
56	#88112	—	2	2	no	—
57	#88112	—	2	2	no	—
58	#88112	—	2	2	no	—
59	#88112	—	2	2	no	—
60	C₄⋊#1057	—	2	2	no	—
61	C₄⋊#1057	—	2	2	no	—
62	C₄⋊#1057	C₂³	1	4	yes	—
63	C₄⋊#1057	C₂³	1	4	yes	—
64	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
67	C₂²⋊#1055	C₂×C₄	1	2	yes	—
68	#88060	C₂×C₄	1	4	yes	—
69	#88054	C₂×C₄	1	4	yes	—
70	C₈×Dic₁₃	C₂³	1	4	yes	—
71	C₄⋊#1055	C₂×C₄	1	2	yes	—
72	C₄×#1055	C₂×C₄	1	2	yes	—
73	C₂×#1570	—	13	1	no	maximal, Sylow
74	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₄×D₁₃	—	2	4	no	—
82	C₂×C₄×D₁₃	—	4	2	no	—
83	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	SD₁₆	1	4	yes	—
90	C₂×C₄×D₁₃	SD₁₆	1	4	yes	—
91	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
97	#6122	—	4	4	no	—
98	C₂×#1057	—	2	4	no	—
99	C₂×#1057	—	2	4	no	—
100	C₂×#1057	—	4	4	no	—
101	#6118	—	4	4	no	—
102	D₁₃⋊C₈	—	4	4	no	—
103	D₁₃⋊C₈	—	4	4	no	—
104	D₁₃⋊C₈	—	4	4	no	—
105	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
106	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
116	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
117	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
118	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
119	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
122	C₂×#1055	C₂²×C₄	1	4	yes	—
123	C₈×D₁₃	—	2	8	no	—
124	C₂×#431	—	13	1	no	—
125	C₂×#423	—	13	1	no	—
126	C₂²×C₄⋊C₈	—	13	1	no	—
127	#1570	—	13	4	no	—
128	#1570	—	13	4	no	—
129	C₂×#334	—	13	4	no	—
130	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂²×D₁₃	—	2	2	no	—
132	C₂²×D₁₃	—	2	2	no	—
133	C₂²×D₁₃	#106	1	4	yes	—
134	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	4	1	no	—
138	C₂×C₄×C₁₃	#106	1	4	yes	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
145	C₂×Dic₁₃	—	2	2	no	—
146	C₂×Dic₁₃	—	4	1	no	—
147	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×Dic₁₃	C₂×SD₁₆	1	2	yes	—
152	C₂×Dic₁₃	C₂×SD₁₆	1	2	yes	—
153	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
155	C₄×D₁₃	—	2	2	no	—
156	C₄×D₁₃	—	2	2	no	—
157	C₄×D₁₃	—	2	2	no	—
158	C₄×D₁₃	—	2	2	no	—
159	C₄×D₁₃	—	2	2	no	—
160	C₄×D₁₃	—	4	1	no	—
161	C₄×D₁₃	—	4	1	no	—
162	C₄×D₁₃	#106	1	4	yes	—
163	C₄×D₁₃	#106	1	4	yes	—
164	C₄×D₁₃	#131	1	4	yes	—
165	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
166	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
167	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
168	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
169	#1057	—	4	4	no	—
170	#1057	—	4	4	no	—
171	C₈×C₁₃	—	2	4	no	—
172	#1055	—	2	4	no	—
173	C₂²×M₁₆	—	26	1	no	—
174	C₂³×C₈	—	26	1	no	—
175	C₂²×C₄²	—	13	1	no	—
176	#431	—	13	1	no	—
177	#431	—	13	2	no	—
178	#431	—	13	2	no	—
179	#431	—	13	2	no	—
180	#431	#261	1	1	yes	characteristic
181	#423	—	13	2	no	—
182	#423	—	13	2	no	—
183	#423	—	26	1	no	—
184	#423	—	26	1	no	—
185	C₂×C₄⋊C₈	—	13	2	no	—
186	C₂×C₄⋊C₈	—	13	2	no	—
187	C₂×C₄⋊C₈	—	13	2	no	—
188	C₂×C₄⋊C₈	—	13	2	no	—
189	C₂×C₄⋊C₈	—	13	2	no	—
190	C₂×C₄⋊C₈	—	26	1	no	—
191	C₂×C₄⋊C₈	—	26	1	no	—
192	C₂×C₄⋊C₈	—	26	1	no	—
193	C₂×C₄⋊C₈	—	26	1	no	—
194	C₂×C₂²⋊C₈	—	13	2	no	—
195	C₂×C₄×C₈	—	13	2	no	—
196	#334	—	13	8	no	—
197	#334	—	13	8	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	C₂×#106	1	2	yes	—
201	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂×D₁₃	—	2	1	no	—
203	C₂×D₁₃	—	2	1	no	—
204	C₂×D₁₃	—	2	8	no	—
205	C₂×D₁₃	#424	1	2	yes	—
206	C₂×D₁₃	C₂×#106	1	2	yes	—
207	C₂×D₁₃	C₂×#106	1	2	yes	—
208	C₂×D₁₃	#430	1	2	yes	—
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	C₂×#106	1	2	yes	—
213	C₄×C₁₃	C₂×#106	1	2	yes	—
214	C₄×C₁₃	C₂×#131	1	2	yes	—
215	Dic₁₃	—	2	1	no	—
216	Dic₁₃	—	2	1	no	—
217	Dic₁₃	—	2	1	no	—
218	Dic₁₃	#424	1	2	yes	—
219	Dic₁₃	C₂×#106	1	2	yes	—
220	Dic₁₃	C₂²×SD₁₆	1	1	yes	characteristic
221	Dic₁₃	C₂²×SD₁₆	1	1	yes	characteristic
222	C₂³×C₄	—	13	1	no	—
223	C₂³×C₄	—	13	1	no	—
224	C₂³×C₄	—	13	1	no	—
225	C₂×M₁₆	—	26	2	no	—
226	C₂×M₁₆	—	26	2	no	—
227	C₂×M₁₆	—	52	4	no	—
228	C₂²×C₈	—	13	4	no	—
229	C₂²×C₈	—	26	2	no	—
230	C₂²×C₈	—	26	2	no	—
231	C₂²×C₈	—	26	2	no	—
232	C₂²×C₈	—	26	2	no	—
233	C₂²×C₈	—	52	4	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	—	13	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	C₂×#261	1	1	yes	characteristic
246	C₄⋊C₈	—	13	4	no	—
247	C₄⋊C₈	—	13	4	no	—
248	C₄⋊C₈	—	13	4	no	—
249	C₄⋊C₈	—	13	2	no	—
250	C₄⋊C₈	—	26	2	no	—
251	C₄⋊C₈	—	26	2	no	—
252	C₄⋊C₈	—	26	2	no	—
253	C₄⋊C₈	—	26	2	no	—
254	C₄⋊C₈	—	26	2	no	—
255	C₄⋊C₈	—	26	2	no	—
256	C₄⋊C₈	C₂×#261	1	2	yes	—
257	C₂²⋊C₈	—	13	2	no	—
258	C₂²⋊C₈	—	13	4	no	—
259	C₂²⋊C₈	C₂×#261	1	2	yes	—
260	C₄×C₈	—	13	4	no	—
261	C₄×C₈	—	13	2	no	—
262	C₄×C₈	C₂×#261	1	2	yes	—
263	C₂×C₁₃	—	2	2	no	—
264	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
265	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
266	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
267	D₁₃	—	2	2	no	—
268	D₁₃	#1570	1	4	yes	complemented
269	C₂⁴	—	13	1	no	—
270	C₂²×C₄	—	13	1	no	—
271	C₂²×C₄	—	13	4	no	—
272	C₂²×C₄	—	13	4	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	—	13	1	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	26	4	no	—
288	C₂²×C₄	—	52	2	no	—
289	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
290	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
291	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
292	M₁₆	—	52	4	no	—
293	M₁₆	—	52	4	no	—
294	C₂×C₈	—	13	4	no	—
295	C₂×C₈	—	26	8	no	—
296	C₂×C₈	—	26	4	no	—
297	C₂×C₈	—	26	4	no	—
298	C₂×C₈	—	52	4	no	—
299	C₂×C₈	—	52	4	no	—
300	C₂×C₈	—	52	4	no	—
301	C₂×C₈	—	52	4	no	—
302	C₂×C₈	C₂²×#261	1	4	yes	—
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	—	13	1	no	—
311	C₄²	—	13	1	no	—
312	C₄²	—	13	1	no	—
313	C₄²	—	13	1	no	—
314	C₄²	—	13	1	no	—
315	C₄²	C₄⋊#261	1	1	yes	characteristic
316	C₄²	C₄⋊#261	1	1	yes	characteristic
317	C₄²	C₂²×#261	1	1	yes	characteristic
318	C₄²	C₂²×#261	1	1	yes	characteristic
319	C₁₃	C₂×#1570	1	1	yes	characteristic, complemented, Sylow
320	C₂³	—	13	1	no	—
321	C₂³	—	13	4	no	—
322	C₂³	—	13	1	no	—
323	C₂³	—	26	2	no	—
324	C₂³	—	26	2	no	—
325	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	13	2	no	—
329	C₂×C₄	—	13	2	no	—
330	C₂×C₄	—	13	1	no	—
331	C₂×C₄	—	13	1	no	—
332	C₂×C₄	—	13	1	no	—
333	C₂×C₄	—	13	2	no	—
334	C₂×C₄	—	13	2	no	—
335	C₂×C₄	—	13	2	no	—
336	C₂×C₄	—	13	2	no	—
337	C₂×C₄	—	13	4	no	—
338	C₂×C₄	—	13	4	no	—
339	C₂×C₄	—	13	4	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	1	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	—	26	2	no	—
348	C₂×C₄	—	26	2	no	—
349	C₂×C₄	—	52	1	no	—
350	C₂×C₄	—	52	1	no	—
351	C₂×C₄	—	52	1	no	—
352	C₂×C₄	#88101	1	4	yes	—
353	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
358	C₂×C₄	C₂³×#261	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	26	4	no	—
361	C₈	—	52	4	no	—
362	C₈	—	52	4	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	13	2	no	—
366	C₂²	—	13	2	no	—
367	C₂²	—	13	2	no	—
368	C₂²	—	13	2	no	—
369	C₂²	—	26	8	no	—
370	C₂²	—	26	1	no	—
371	C₂²	—	26	1	no	—
372	C₂²	C₂×#88101	1	2	yes	—
373	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	13	2	no	—
378	C₄	—	13	1	no	—
379	C₄	—	13	1	no	—
380	C₄	—	13	2	no	—
381	C₄	—	26	1	no	—
382	C₄	—	26	1	no	—
383	C₄	—	26	1	no	—
384	C₄	C₂×#88101	1	2	yes	—
385	C₄	C₂×#88101	1	2	yes	—
386	C₄	D₁₃⋊#131	1	2	yes	—
387	C₂	—	2	2	no	—
388	C₂	—	13	4	no	—
389	C₂	—	26	2	no	—
390	C₂	D₁₃⋊#424	1	1	yes	characteristic
391	C₂	C₂²×#88101	1	1	yes	characteristic
392	C₂	D₁₃⋊#430	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	C₁₃×#431	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	C₂×#1570
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130404	C₂	semidirect
4. #13130403	C₂	semidirect
5. D₁₃⋊#334	C₂	semidirect
30. #11718255	C₂²	semidirect
31. #11718253	C₂²	semidirect
268. D₁₃	#1570	semidirect
319. 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⋊#423	2
C₂×D₁₃⋊(C₄⋊C₈)	2
#13130404	2
#13130403	2
D₁₃⋊#334	2
D₁₃×#431	2
C₂×#1570	13

Subgroups — D13⋊#1570 #16794976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1570 #16794976