Subgroups — #16798334

Order 3328.

718 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	#13131517	C₂	1	2	yes	maximal
2	#13130777	C₂	1	1	yes	maximal, characteristic, complemented
3	#13130776	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130762	C₂	1	2	yes	maximal, complemented
5	#13130717	C₂	1	2	yes	maximal
6	#13130716	C₂	1	2	yes	maximal
7	#13130656	C₂	1	2	yes	maximal, complemented
8	C₄×#88104	C₂	1	2	yes	maximal, complemented
9	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
10	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	D₁₃×#117	C₂²	1	1	yes	characteristic
13	#11719127	C₂²	1	4	yes	—
14	C₂×#88104	C₂²	1	2	yes	—
15	C₂×#88104	C₂²	1	2	yes	—
16	C₂×#88104	C₂²	1	2	yes	—
17	C₂×#88103	C₂²	1	2	yes	—
18	#11719077	—	2	4	no	—
19	#11719068	—	2	4	no	—
20	#11719053	C₂²	1	2	yes	—
21	#11719052	C₂²	1	2	yes	—
22	C₄×#6118	C₂²	1	4	yes	—
23	C₁₃×#405	C₄	1	1	yes	characteristic
24	#11718783	C₄	1	1	yes	characteristic
25	#11718762	C₄	1	1	yes	characteristic
26	#11718658	C₄	1	1	yes	characteristic
27	#11718369	C₄	1	1	yes	characteristic
28	#11718369	C₄	1	1	yes	characteristic
29	D₁₃×#97	C₂²	1	1	yes	characteristic
30	D₁₃×#97	C₂²	1	1	yes	characteristic
31	#11718350	C₄	1	1	yes	characteristic
32	#11718350	C₄	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
35	#11718268	C₂²	1	4	yes	—
36	#11718268	C₂²	1	4	yes	—
37	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×#6118	C₂³	1	4	yes	—
39	C₂×#6118	C₂³	1	4	yes	—
40	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
43	#88180	C₂×C₄	1	1	yes	characteristic
44	C₂×#6099	C₂×C₄	1	1	yes	characteristic
45	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
46	M₁₆×D₁₃	—	2	2	no	—
47	M₁₆×D₁₃	—	2	2	no	—
48	C₂×#6094	C₂×C₄	1	1	yes	characteristic
49	C₂×#6094	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	—	2	2	no	—
51	C₂×C₈×D₁₃	—	2	2	no	—
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	#88146	D₄	1	2	yes	—
59	C₄⋊C₄×D₁₃	Q₈	1	2	yes	—
60	C₂²⋊C₄×D₁₃	Q₈	1	2	yes	—
61	#88131	D₄	1	2	yes	—
62	#88126	C₂×C₄	1	1	yes	characteristic
63	#88126	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	C₂²⋊#1057	—	2	4	no	—
67	#88112	—	2	4	no	—
68	#88111	—	2	4	no	—
69	#88110	—	2	4	no	—
70	C₄⋊#1057	—	2	4	no	—
71	C₄×#1057	—	2	4	no	—
72	#88104	—	2	4	no	—
73	#88104	—	2	4	no	—
74	#88104	—	2	4	no	—
75	#88103	—	2	4	no	—
76	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	#88055	C₂×C₄	1	1	yes	characteristic
81	#88055	C₂×C₄	1	1	yes	characteristic
82	#88055	C₂×C₄	1	1	yes	characteristic
83	#88055	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
88	#88043	C₂×C₄	1	1	yes	characteristic
89	#88043	C₂×C₄	1	1	yes	characteristic
90	C₄×#1055	C₂×C₄	1	1	yes	characteristic
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	#20828	—	13	1	no	maximal, Sylow
93	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	—	2	1	no	—
97	C₂×C₄×D₁₃	—	2	1	no	—
98	C₂×C₄×D₁₃	—	2	1	no	—
99	C₂×C₄×D₁₃	—	2	1	no	—
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
104	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
105	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
106	C₂×#1057	—	2	4	no	—
107	C₂×#1057	—	2	4	no	—
108	#6118	—	2	4	no	—
109	#6118	—	2	4	no	—
110	#6118	—	2	4	no	—
111	#6118	—	2	4	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
123	#6103	C₄⋊C₄	1	2	yes	—
124	#6103	C₄⋊C₄	1	2	yes	—
125	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
126	#6101	C₄⋊C₄	1	2	yes	—
127	#6101	C₄⋊C₄	1	2	yes	—
128	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
131	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
132	#6099	—	2	2	no	—
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
135	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
136	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
137	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
138	#6094	—	2	2	no	—
139	#6094	—	2	2	no	—
140	C₈×D₁₃	—	2	1	no	—
141	C₈×D₁₃	—	2	1	no	—
142	C₈×D₁₃	—	2	1	no	—
143	C₈×D₁₃	—	2	1	no	—
144	C₈×D₁₃	—	2	2	no	—
145	C₈×D₁₃	—	2	2	no	—
146	C₈×D₁₃	#41	1	2	yes	—
147	C₈×D₁₃	#41	1	2	yes	—
148	C₈×D₁₃	#41	1	2	yes	—
149	C₈×D₁₃	#41	1	2	yes	—
150	#2921	—	13	2	no	—
151	C₂×#405	—	13	1	no	—
152	#1848	—	13	1	no	—
153	#1848	—	13	1	no	—
154	#1838	—	13	2	no	—
155	#1811	—	13	2	no	—
156	#1810	—	13	2	no	—
157	#1778	—	13	2	no	—
158	C₄×#108	—	13	2	no	—
159	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×D₁₃	—	2	1	no	—
161	C₂²×D₁₃	—	2	1	no	—
162	C₂²×D₁₃	—	4	2	no	—
163	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×Dic₁₃	—	2	1	no	—
172	C₂×Dic₁₃	—	2	1	no	—
173	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
177	C₄×D₁₃	—	2	1	no	—
178	C₄×D₁₃	—	2	1	no	—
179	C₄×D₁₃	—	2	1	no	—
180	C₄×D₁₃	—	2	1	no	—
181	C₄×D₁₃	—	2	1	no	—
182	C₄×D₁₃	—	2	1	no	—
183	C₄×D₁₃	—	4	2	no	—
184	C₄×D₁₃	—	4	2	no	—
185	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
186	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
187	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
188	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
189	#1057	—	4	4	no	—
190	#1057	—	4	4	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	#117	1	2	yes	—
194	C₈×C₁₃	#117	1	2	yes	—
195	#1055	—	2	1	no	—
196	#1055	—	2	1	no	—
197	#1055	#117	1	2	yes	—
198	#1055	#117	1	2	yes	—
199	C₂²×M₁₆	—	13	1	no	—
200	C₂³×C₈	—	13	1	no	—
201	C₂×#117	—	13	1	no	—
202	#433	—	26	4	no	—
203	#433	—	26	4	no	—
204	C₂×#108	—	13	2	no	—
205	C₂×#108	—	13	2	no	—
206	C₂×#108	—	13	2	no	—
207	C₂×#108	—	13	2	no	—
208	#423	—	13	2	no	—
209	#423	—	13	2	no	—
210	#407	—	13	4	no	—
211	#405	—	13	1	no	—
212	#405	—	13	1	no	—
213	#405	—	13	1	no	—
214	#405	—	13	1	no	—
215	#405	—	13	1	no	—
216	#405	—	13	1	no	—
217	#405	—	13	1	no	—
218	#405	#261	1	1	yes	characteristic
219	C₄×M₁₆	—	13	4	no	—
220	C₂×#97	—	13	1	no	—
221	C₂×#97	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	#341	—	13	4	no	—
225	#341	—	13	4	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂×D₁₃	—	2	2	no	—
230	C₂×D₁₃	—	2	2	no	—
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	—	4	2	no	—
233	C₂×D₁₃	—	4	2	no	—
234	C₂×D₁₃	#533	1	1	yes	characteristic
235	C₂×D₁₃	#533	1	1	yes	characteristic
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
240	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
241	Dic₁₃	—	2	2	no	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	#532	1	1	yes	characteristic
245	Dic₁₃	#532	1	1	yes	characteristic
246	C₂³×C₄	—	13	1	no	—
247	C₂×M₁₆	—	13	1	no	—
248	C₂×M₁₆	—	13	1	no	—
249	C₂×M₁₆	—	13	1	no	—
250	C₂×M₁₆	—	13	4	no	—
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	26	2	no	—
253	C₂×M₁₆	—	26	2	no	—
254	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	26	2	no	—
263	C₂²×C₈	—	26	2	no	—
264	C₂²×C₈	C₂×#261	1	1	yes	characteristic
265	#117	—	13	1	no	—
266	#117	—	13	2	no	—
267	#117	—	13	2	no	—
268	#117	—	13	1	no	—
269	#117	—	13	1	no	—
270	#117	C₂×#261	1	1	yes	characteristic
271	C₂×C₄⋊C₄	—	13	2	no	—
272	C₂×C₂²⋊C₄	—	13	2	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	#108	—	26	4	no	—
276	#108	—	26	4	no	—
277	#108	—	26	4	no	—
278	#108	—	26	4	no	—
279	C₄⋊C₈	—	26	4	no	—
280	C₄⋊C₈	—	26	4	no	—
281	C₂²⋊C₈	—	26	4	no	—
282	C₂²⋊C₈	—	26	4	no	—
283	#97	—	13	1	no	—
284	#97	—	13	1	no	—
285	#97	—	13	1	no	—
286	#97	—	13	1	no	—
287	#97	—	13	1	no	—
288	#97	—	13	1	no	—
289	#97	—	26	4	no	—
290	#97	C₂×#261	1	1	yes	characteristic
291	#97	C₂×#261	1	1	yes	characteristic
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	—	26	4	no	—
299	C₄×C₈	C₂×#261	1	1	yes	characteristic
300	C₄×C₈	C₂×#261	1	1	yes	characteristic
301	C₂×C₁₃	—	4	1	no	—
302	C₂×C₁₃	#2285	1	1	yes	characteristic
303	C₂×C₁₃	#2916	1	2	yes	—
304	D₁₃	—	2	1	no	—
305	D₁₃	—	2	1	no	—
306	D₁₃	—	4	1	no	—
307	C₂⁴	—	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	2	no	—
314	C₂²×C₄	—	13	2	no	—
315	C₂²×C₄	—	26	1	no	—
316	C₂²×C₄	—	26	1	no	—
317	C₂²×C₄	—	26	1	no	—
318	C₂²×C₄	—	26	1	no	—
319	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
320	M₁₆	—	2	2	no	—
321	M₁₆	—	26	2	no	—
322	M₁₆	—	26	2	no	—
323	M₁₆	—	26	2	no	—
324	M₁₆	—	26	4	no	—
325	M₁₆	—	26	4	no	—
326	M₁₆	—	26	4	no	—
327	M₁₆	—	26	4	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	2	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	2	no	—
334	C₂×C₈	—	13	2	no	—
335	C₂×C₈	—	13	1	no	—
336	C₂×C₈	—	13	1	no	—
337	C₂×C₈	—	26	2	no	—
338	C₂×C₈	—	26	1	no	—
339	C₂×C₈	—	26	1	no	—
340	C₂×C₈	—	26	1	no	—
341	C₂×C₈	—	26	1	no	—
342	C₂×C₈	—	26	2	no	—
343	C₂×C₈	—	26	2	no	—
344	C₂×C₈	—	26	4	no	—
345	C₂×C₈	—	26	4	no	—
346	C₂×C₈	C₂²×#261	1	1	yes	characteristic
347	C₂×C₈	C₂²×#261	1	1	yes	characteristic
348	C₂×C₈	C₂²×#261	1	1	yes	characteristic
349	C₂×C₈	C₂²×#261	1	1	yes	characteristic
350	C₄⋊C₄	—	13	2	no	—
351	C₄⋊C₄	—	13	2	no	—
352	C₄⋊C₄	—	13	2	no	—
353	C₄⋊C₄	C₄⋊#261	1	2	yes	—
354	C₂²⋊C₄	—	13	2	no	—
355	C₂²⋊C₄	—	13	2	no	—
356	C₂²⋊C₄	—	13	2	no	—
357	C₂²⋊C₄	C₄⋊#261	1	2	yes	—
358	C₄²	—	13	2	no	—
359	C₄²	—	13	2	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	C₂²×#261	1	1	yes	characteristic
363	C₄²	C₂²×#261	1	1	yes	characteristic
364	C₁₃	#20828	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	13	1	no	—
366	C₂³	—	13	1	no	—
367	C₂³	—	26	1	no	—
368	C₂³	—	26	1	no	—
369	C₂³	—	52	2	no	—
370	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	2	no	—
379	C₂×C₄	—	13	2	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	26	1	no	—
382	C₂×C₄	—	26	1	no	—
383	C₂×C₄	—	26	1	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	26	1	no	—
386	C₂×C₄	—	26	1	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	—	26	1	no	—
389	C₂×C₄	—	52	2	no	—
390	C₂×C₄	—	52	2	no	—
391	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
392	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
393	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
394	C₂×C₄	C₂³×#261	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	13	2	no	—
398	C₈	—	13	2	no	—
399	C₈	—	26	1	no	—
400	C₈	—	26	1	no	—
401	C₈	—	52	4	no	—
402	C₈	—	52	4	no	—
403	C₈	#88237	1	2	yes	—
404	C₈	#88237	1	2	yes	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	13	1	no	—
408	C₂²	—	13	1	no	—
409	C₂²	—	26	2	no	—
410	C₂²	—	26	1	no	—
411	C₂²	—	26	2	no	—
412	C₂²	—	52	2	no	—
413	C₂²	—	52	2	no	—
414	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	13	1	no	—
419	C₄	—	13	1	no	—
420	C₄	—	26	1	no	—
421	C₄	—	26	2	no	—
422	C₄	—	26	2	no	—
423	C₄	C₂×#88237	1	1	yes	characteristic
424	C₄	C₂×#88237	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	26	1	no	—
427	C₂	—	26	1	no	—
428	C₂	—	52	1	no	—
429	C₂	#13131285	1	1	yes	characteristic
430	C₂	#13131498	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20828
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13130777	C₂	semidirect
3. #13130776	C₂	semidirect
4. #13130762	C₂	semidirect
7. #13130656	C₂	semidirect
8. C₄×#88104	C₂	semidirect
364. C₁₃	#20828	semidirect

Maximal subgroups

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

subgroup	index
#13131517	2
#13130777	2
#13130776	2
#13130762	2
#13130717	2
#13130716	2
#13130656	2
C₄×#88104	2
D₁₃×#405	2
#20828	13