Subgroups — C₂×#13129667 #16779028

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6118	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13129667	C₂	1	4	yes	maximal, direct product factor
4	C₂×#11718494	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6118	C₄	1	2	yes	—
6	C₂²×D₁₃⋊C₈	—	2	1	no	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88110	—	2	1	no	—
9	C₂×C₄×#1057	—	2	1	no	—
10	C₂×C₄×#1057	—	2	1	no	—
11	C₂×C₄×#1057	C₄	1	2	yes	—
12	C₄×#6118	—	2	1	no	—
13	C₄×#6118	—	2	1	no	—
14	C₄×#6118	C₄	1	2	yes	—
15	C₄×#6118	C₂²	1	2	yes	—
16	C₄×D₁₃⋊C₈	—	2	1	no	—
17	C₄×D₁₃⋊C₈	—	2	1	no	—
18	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
19	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
21	C₂×#88060	—	2	1	no	—
22	C₂×C₈×Dic₁₃	—	2	1	no	—
23	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic
24	#11718494	—	2	1	no	—
25	#11718494	—	2	1	no	—
26	#11718494	C₄	1	2	yes	—
27	#11718494	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
31	C₂²×#1057	—	2	2	no	—
32	C₂²×#1057	—	2	2	no	—
33	C₂×#6118	—	2	2	no	—
34	C₂×#6118	—	2	4	no	—
35	C₂×#6118	C₈	1	8	yes	complemented
36	C₂×#6118	C₂×C₄	1	4	yes	—
37	C₂×D₁₃⋊C₈	—	2	4	no	—
38	C₂×D₁₃⋊C₈	—	2	4	no	—
39	C₂×D₁₃⋊C₈	—	2	2	no	—
40	C₂×D₁₃⋊C₈	—	2	2	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
46	C₂²×#1055	—	2	1	no	—
47	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
53	C₄²×D₁₃	Q₈	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	1	yes	characteristic
55	#88110	—	2	2	no	—
56	#88110	—	2	2	no	—
57	C₄×#1057	—	2	2	no	—
58	C₄×#1057	—	2	2	no	—
59	C₄×#1057	—	2	2	no	—
60	C₄×#1057	—	2	2	no	—
61	C₄×#1057	—	2	2	no	—
62	C₄×#1057	C₂×C₄	1	4	yes	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	#88060	—	2	2	no	—
66	#88060	—	2	2	no	—
67	C₈×Dic₁₃	—	2	2	no	—
68	C₈×Dic₁₃	—	2	2	no	—
69	C₄⋊#1055	—	2	1	no	—
70	C₄⋊#1055	C₂×C₄	1	2	yes	—
71	C₂×#1278	—	13	1	no	maximal, Sylow
72	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃	—	2	2	no	—
80	C₂×C₄×D₁₃	—	2	2	no	—
81	C₂×C₄×D₁₃	—	2	4	no	—
82	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
83	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
92	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
93	C₂×C₄×D₁₃	C₂²×C₄	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×#1057	—	2	8	no	—
97	C₂×#1057	—	2	8	no	—
98	C₂×#1057	—	2	4	no	—
99	C₂×#1057	—	2	4	no	—
100	#6118	—	2	8	no	—
101	#6118	—	2	4	no	—
102	#6118	C₂×C₈	1	8	yes	complemented
103	D₁₃⋊C₈	—	2	8	no	—
104	D₁₃⋊C₈	—	2	4	no	—
105	D₁₃⋊C₈	—	2	4	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	4	2	no	—
108	C₄²×C₁₃	C₄²	1	1	yes	characteristic
109	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
113	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×#1055	—	2	2	no	—
125	C₂×#1055	—	4	2	no	—
126	C₂×#431	—	13	1	no	—
127	C₂×C₄×M₁₆	—	13	1	no	—
128	C₂²×C₄×C₈	—	13	1	no	—
129	#1278	—	13	4	no	—
130	C₂³×C₁₃	#95	1	1	yes	characteristic
131	C₂²×D₁₃	—	2	2	no	—
132	C₂²×D₁₃	—	2	2	no	—
133	C₂²×D₁₃	#95	1	1	yes	characteristic
134	C₂²×D₁₃	C₄⋊C₈	1	4	yes	—
135	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
141	C₂×C₄×C₁₃	#97	1	2	yes	—
142	C₂×C₄×C₁₃	#104	1	2	yes	—
143	C₂×C₄×C₁₃	#104	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×Dic₁₃	—	2	2	no	—
148	C₂×Dic₁₃	#95	1	1	yes	characteristic
149	C₂×Dic₁₃	#95	1	1	yes	characteristic
150	C₂×Dic₁₃	#95	1	1	yes	characteristic
151	C₂×Dic₁₃	C₂²⋊C₈	1	4	yes	—
152	C₂×Dic₁₃	#108	1	4	yes	—
153	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₄×D₁₃	—	2	2	no	—
157	C₄×D₁₃	—	2	2	no	—
158	C₄×D₁₃	—	2	1	no	—
159	C₄×D₁₃	—	2	1	no	—
160	C₄×D₁₃	—	2	1	no	—
161	C₄×D₁₃	—	2	1	no	—
162	C₄×D₁₃	—	2	2	no	—
163	C₄×D₁₃	—	2	2	no	—
164	C₄×D₁₃	—	2	2	no	—
165	C₄×D₁₃	—	2	2	no	—
166	C₄×D₁₃	C₄×C₈	1	2	yes	—
167	C₄×D₁₃	#97	1	2	yes	—
168	C₄×D₁₃	C₂²⋊C₈	1	4	yes	—
169	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
170	C₄×D₁₃	C₂²×C₈	1	2	yes	—
171	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
172	#1057	—	2	8	no	—
173	#1057	—	2	8	no	—
174	C₈×C₁₃	—	4	2	no	—
175	#1055	—	4	2	no	—
176	C₂²×M₁₆	—	13	2	no	—
177	C₂³×C₈	—	26	1	no	—
178	C₂²×C₄²	—	13	1	no	—
179	#431	—	13	2	no	—
180	#431	—	13	2	no	—
181	#431	—	26	1	no	—
182	#431	—	26	1	no	—
183	C₂×C₄⋊C₈	—	13	1	no	—
184	C₂×C₄⋊C₈	#261	1	1	yes	characteristic
185	C₂×C₂²⋊C₈	—	26	1	no	—
186	C₄×M₁₆	—	13	2	no	—
187	C₄×M₁₆	—	13	2	no	—
188	C₄×M₁₆	—	26	1	no	—
189	C₄×M₁₆	—	26	1	no	—
190	C₂×#97	—	26	1	no	—
191	C₂×C₄×C₈	—	13	2	no	—
192	C₂×C₄×C₈	—	13	2	no	—
193	C₂×C₄×C₈	—	13	2	no	—
194	C₂×C₄×C₈	—	26	1	no	—
195	C₂×C₄×C₈	—	26	1	no	—
196	C₂×C₄×C₈	—	26	1	no	—
197	C₂×C₄×C₈	—	26	1	no	—
198	C₂×C₄×C₈	—	26	1	no	—
199	C₂²×C₁₃	#336	1	2	yes	—
200	C₂²×C₁₃	#339	1	2	yes	—
201	C₂²×C₁₃	#341	1	2	yes	—
202	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
203	C₂×D₁₃	—	2	1	no	—
204	C₂×D₁₃	—	2	1	no	—
205	C₂×D₁₃	—	2	1	no	—
206	C₂×D₁₃	—	2	1	no	—
207	C₂×D₁₃	—	2	8	no	—
208	C₂×D₁₃	#336	1	2	yes	—
209	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	#336	1	2	yes	—
213	C₄×C₁₃	#339	1	2	yes	—
214	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
215	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
216	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
217	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
218	Dic₁₃	—	2	1	no	—
219	Dic₁₃	—	2	1	no	—
220	Dic₁₃	#336	1	2	yes	—
221	Dic₁₃	#341	1	2	yes	—
222	Dic₁₃	C₂×C₂²⋊C₈	1	2	yes	—
223	Dic₁₃	C₂×#108	1	2	yes	—
224	C₂³×C₄	—	13	1	no	—
225	C₂³×C₄	—	13	1	no	—
226	C₂³×C₄	—	13	1	no	—
227	C₂×M₁₆	—	13	4	no	—
228	C₂×M₁₆	—	13	8	no	—
229	C₂×M₁₆	—	26	2	no	—
230	C₂×M₁₆	—	26	4	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	26	2	no	—
233	C₂²×C₈	—	26	2	no	—
234	C₂²×C₈	—	26	2	no	—
235	C₂²×C₈	—	26	2	no	—
236	C₂²×C₈	—	26	4	no	—
237	C₂²×C₈	—	26	4	no	—
238	C₂²×C₈	—	26	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	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	13	1	no	—
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	C₂×#261	1	1	yes	characteristic
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	13	2	no	—
253	C₄⋊C₈	—	26	1	no	—
254	C₄⋊C₈	C₂×#261	1	2	yes	—
255	C₂²⋊C₈	—	26	2	no	—
256	C₂²⋊C₈	—	26	2	no	—
257	#97	—	26	2	no	—
258	#97	—	26	2	no	—
259	C₄×C₈	—	13	4	no	—
260	C₄×C₈	—	26	2	no	—
261	C₄×C₈	—	26	2	no	—
262	C₄×C₈	—	26	2	no	—
263	C₄×C₈	—	26	2	no	—
264	C₄×C₈	—	26	2	no	—
265	C₄×C₈	—	26	2	no	—
266	C₄×C₈	—	26	2	no	—
267	C₂×C₁₃	#1278	1	4	yes	complemented
268	C₂×C₁₃	C₂×#336	1	1	yes	characteristic
269	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
270	C₂×C₁₃	C₂×#341	1	1	yes	characteristic
271	D₁₃	—	2	2	no	—
272	D₁₃	—	2	2	no	—
273	C₂⁴	—	13	1	no	—
274	C₂²×C₄	—	13	1	no	—
275	C₂²×C₄	—	13	1	no	—
276	C₂²×C₄	—	13	4	no	—
277	C₂²×C₄	—	13	4	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	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	26	4	no	—
292	C₂²×C₄	—	26	2	no	—
293	C₂²×C₄	—	26	2	no	—
294	C₂²×C₄	C₄×#261	1	1	yes	characteristic
295	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
297	M₁₆	—	13	8	no	—
298	M₁₆	—	26	8	no	—
299	M₁₆	—	26	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	26	4	no	—
303	C₂×C₈	—	26	4	no	—
304	C₂×C₈	—	26	8	no	—
305	C₂×C₈	—	26	8	no	—
306	C₂×C₈	—	26	4	no	—
307	C₂×C₈	—	26	4	no	—
308	C₂×C₈	—	26	8	no	—
309	C₂×C₈	—	26	2	no	—
310	C₂×C₈	—	52	2	no	—
311	C₄²	—	13	1	no	—
312	C₄²	—	13	1	no	—
313	C₄²	—	13	1	no	—
314	C₄²	—	13	1	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	—	13	1	no	—
323	C₄²	C₄×#261	1	1	yes	characteristic
324	C₄²	C₄⋊#261	1	1	yes	characteristic
325	C₄²	C₂²⋊#261	1	1	yes	characteristic
326	C₄²	C₂²×#261	1	1	yes	characteristic
327	C₁₃	C₂×#1278	1	1	yes	characteristic, complemented, Sylow
328	C₂³	—	13	4	no	—
329	C₂³	—	13	1	no	—
330	C₂³	—	13	1	no	—
331	C₂³	—	26	2	no	—
332	C₂³	—	26	2	no	—
333	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
334	C₂×C₄	—	2	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	—	13	1	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	4	no	—
342	C₂×C₄	—	13	4	no	—
343	C₂×C₄	—	13	2	no	—
344	C₂×C₄	—	13	2	no	—
345	C₂×C₄	—	13	2	no	—
346	C₂×C₄	—	13	2	no	—
347	C₂×C₄	—	13	1	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	26	2	no	—
350	C₂×C₄	—	26	2	no	—
351	C₂×C₄	—	26	2	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	1	no	—
357	C₂×C₄	—	26	1	no	—
358	C₂×C₄	—	26	1	no	—
359	C₂×C₄	—	26	1	no	—
360	C₂×C₄	C₈×#261	1	2	yes	—
361	C₂×C₄	#88100	1	2	yes	—
362	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	#88116	1	2	yes	—
366	C₂×C₄	#88118	1	2	yes	—
367	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	26	8	no	—
372	C₈	—	26	8	no	—
373	C₈	—	52	2	no	—
374	C₂²	—	13	2	no	—
375	C₂²	—	13	2	no	—
376	C₂²	—	26	1	no	—
377	C₂²	—	26	1	no	—
378	C₂²	—	26	1	no	—
379	C₂²	—	26	1	no	—
380	C₂²	—	26	8	no	—
381	C₂²	#11718247	1	2	yes	—
382	C₂²	(C₂×#261)⋊C₈	1	2	yes	—
383	C₂²	#11718273	1	2	yes	—
384	C₂²	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	13	2	no	—
388	C₄	—	13	2	no	—
389	C₄	—	13	2	no	—
390	C₄	—	13	2	no	—
391	C₄	—	26	1	no	—
392	C₄	—	26	1	no	—
393	C₄	#11718247	1	2	yes	—
394	C₄	(C₂×#261)⋊C₈	1	2	yes	—
395	C₄	C₂×C₈×#261	1	1	yes	characteristic
396	C₄	C₂×#88100	1	1	yes	characteristic
397	C₄	C₂×#88116	1	1	yes	characteristic
398	C₄	C₂×#88118	1	1	yes	characteristic
399	C₂	—	26	2	no	—
400	C₂	—	26	2	no	—
401	C₂	#13129667	1	4	yes	direct product factor
402	C₂	C₂×(C₂×#261)⋊C₈	1	1	yes	characteristic
403	C₂	C₂×#11718247	1	1	yes	characteristic
404	C₂	C₂×#11718273	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₁₃×C₄⋊C₈	C₄
socle	C₂³×C₁₃	#95
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	C₂×#1278
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13129667	C₂	direct (N × H)
35. C₂×#6118	C₈	semidirect
102. #6118	C₂×C₈	semidirect
267. C₂×C₁₃	#1278	semidirect
327. C₁₃	C₂×#1278	semidirect
401. C₂	#13129667	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#6118	2
C₂×C₄×D₁₃⋊C₈	2
#13129667	2
C₂×#11718494	2
C₂×#1278	13

Subgroups — C2×#13129667 #16779028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129667 #16779028