Subgroups — C₂×D₁₃×#364 #16015913

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718103	C₂	1	2	yes	maximal, complemented
5	D₁₃×#364	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₄	1	1	yes	characteristic
16	D₁₃×M₃₂	—	2	4	no	—
17	D₁₃×M₃₂	C₂²	1	8	yes	—
18	C₂×#88038	—	2	2	no	—
19	C₂×C₁₆×D₁₃	—	2	2	no	—
20	C₄×C₈×D₁₃	C₄	1	4	yes	—
21	C₄×C₈×D₁₃	C₂²	1	4	yes	—
22	C₁₃×#364	C₂²	1	4	yes	complemented
23	#11718103	C₂²	1	8	yes	complemented
24	#11718055	C₂²	1	4	yes	complemented
25	C₂²×C₄×D₁₃	—	2	1	no	—
26	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₃	—	2	1	no	—
31	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
33	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×D₁₃	C₈	1	2	yes	—
35	C₂×C₈×D₁₃	C₈	1	4	yes	—
36	C₂×C₈×D₁₃	C₈	1	2	yes	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
39	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
40	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	D₄	1	2	yes	—
42	C₂×C₈×D₁₃	Q₈	1	2	yes	—
43	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
44	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
45	C₂×C₈×D₁₃	C₂³	1	2	yes	—
46	C₄²×D₁₃	—	2	2	no	—
47	C₄²×D₁₃	C₂×C₄	1	4	yes	—
48	C₁₃×M₃₂	—	2	2	no	—
49	C₁₃×M₃₂	C₂³	1	4	yes	—
50	C₂×C₁₃×C₁₆	—	2	2	no	—
51	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
52	C₄×C₈×C₁₃	C₂³	1	2	yes	—
53	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
54	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
55	C₈×Dic₁₃	C₂³	1	2	yes	—
56	#88052	—	2	2	no	—
57	#88052	C₂³	1	4	yes	—
58	C₂×#6090	—	2	2	no	—
59	C₄×#1055	C₂×C₄	1	4	yes	—
60	#88038	—	2	8	no	—
61	C₁₆×D₁₃	—	2	8	no	—
62	C₂²×#364	—	13	1	no	maximal, Sylow
63	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×Dic₁₃	—	2	1	no	—
67	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
68	C₂×C₄×D₁₃	—	2	8	no	—
69	C₂×C₄×D₁₃	—	2	4	no	—
70	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
72	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
74	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
75	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
76	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
77	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
78	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
79	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
80	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
85	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₄²×C₁₃	—	2	1	no	—
88	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
89	C₄×Dic₁₃	—	2	1	no	—
90	C₄×Dic₁₃	—	2	4	no	—
91	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
92	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
93	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
94	C₂×#1055	C₄⋊C₄	1	2	yes	—
95	C₂×#1055	C₂×C₈	1	2	yes	—
96	C₂×#1055	C₂×C₈	1	2	yes	—
97	C₂×#1055	C₂²×C₄	1	2	yes	—
98	C₂×#1055	C₂²×C₄	1	2	yes	—
99	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
100	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
101	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
102	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
103	C₈×D₁₃	C₂×C₈	1	8	yes	—
104	C₈×D₁₃	C₂×C₈	1	8	yes	—
105	C₈×D₁₃	C₂×D₄	1	2	yes	—
106	C₈×D₁₃	C₂×D₄	1	2	yes	—
107	C₈×D₁₃	C₂×Q₈	1	2	yes	—
108	C₈×D₁₃	C₂×Q₈	1	2	yes	—
109	C₁₃×C₁₆	—	2	4	no	—
110	#6090	—	2	4	no	—
111	C₂²×M₃₂	—	13	2	no	—
112	C₂²×C₄×C₈	—	13	1	no	—
113	C₂×#364	—	13	2	no	—
114	C₂×#364	—	13	1	no	—
115	C₂×#364	—	13	8	no	—
116	C₂×#364	D₁₃	1	1	yes	characteristic, direct product factor
117	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
118	C₂²×D₁₃	—	2	4	no	—
119	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
120	C₂²×D₁₃	C₄⋊C₈	1	2	yes	—
121	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
122	C₂²×D₁₃	C₂×M₁₆	1	2	yes	—
123	C₂×C₄×C₁₃	—	2	4	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
131	C₂×Dic₁₃	—	2	4	no	—
132	C₂×Dic₁₃	—	2	2	no	—
133	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
134	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
135	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
136	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
137	C₄×D₁₃	—	2	16	no	—
138	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
139	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
140	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
141	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
142	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₄×D₁₃	C₂²×C₈	1	2	yes	—
145	C₄×D₁₃	C₂²×C₈	1	2	yes	—
146	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₈×C₁₃	C₂²×C₈	1	4	yes	—
149	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
151	#1055	C₂×C₄⋊C₄	1	2	yes	—
152	#1055	C₂×C₄⋊C₄	1	2	yes	—
153	#1055	C₂²×C₈	1	4	yes	—
154	C₂³×C₈	—	13	1	no	—
155	C₂³×C₈	—	13	1	no	—
156	C₂²×C₄²	—	13	1	no	—
157	C₂×M₃₂	—	13	2	no	—
158	C₂×M₃₂	—	13	8	no	—
159	C₂×M₃₂	—	26	2	no	—
160	C₂×M₃₂	—	26	4	no	—
161	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
162	C₂²×C₁₆	—	26	2	no	—
163	C₂×C₄×C₈	—	13	1	no	—
164	C₂×C₄×C₈	—	13	1	no	—
165	C₂×C₄×C₈	—	13	1	no	—
166	C₂×C₄×C₈	—	13	4	no	—
167	C₂×C₄×C₈	—	13	4	no	—
168	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
169	#364	—	13	8	no	—
170	#364	—	13	4	no	—
171	#364	C₂×D₁₃	1	4	yes	direct product factor
172	C₂²×C₁₃	—	2	2	no	—
173	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
174	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
175	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
176	C₂×D₁₃	—	2	2	no	—
177	C₂×D₁₃	—	2	4	no	—
178	C₂×D₁₃	—	2	4	no	—
179	C₂×D₁₃	#364	1	4	yes	direct product factor
180	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
181	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
182	C₄×C₁₃	—	2	4	no	—
183	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
184	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
185	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
187	Dic₁₃	—	2	4	no	—
188	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
189	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
190	C₂³×C₄	—	13	1	no	—
191	C₂³×C₄	—	26	1	no	—
192	C₂²×C₈	—	13	1	no	—
193	C₂²×C₈	—	13	1	no	—
194	C₂²×C₈	—	13	2	no	—
195	C₂²×C₈	—	13	4	no	—
196	C₂²×C₈	—	13	2	no	—
197	C₂²×C₈	—	13	2	no	—
198	C₂²×C₈	—	13	4	no	—
199	C₂²×C₈	—	13	2	no	—
200	C₂²×C₈	—	13	1	no	—
201	C₂²×C₈	—	13	1	no	—
202	C₂²×C₈	—	13	2	no	—
203	C₂²×C₈	—	13	1	no	—
204	C₂²×C₈	—	13	1	no	—
205	C₂²×C₈	—	13	2	no	—
206	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
207	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
208	C₂×C₄²	—	13	1	no	—
209	C₂×C₄²	—	13	4	no	—
210	C₂×C₄²	—	26	2	no	—
211	C₂×C₄²	—	26	1	no	—
212	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
213	M₃₂	—	2	2	no	—
214	M₃₂	—	13	4	no	—
215	M₃₂	—	26	8	no	—
216	M₃₂	—	26	2	no	—
217	M₃₂	C₂²×D₁₃	1	4	yes	—
218	C₂×C₁₆	—	2	2	no	—
219	C₂×C₁₆	—	26	8	no	—
220	C₂×C₁₆	—	26	2	no	—
221	C₄×C₈	—	13	2	no	—
222	C₄×C₈	—	13	4	no	—
223	C₄×C₈	—	13	2	no	—
224	C₄×C₈	—	13	4	no	—
225	C₄×C₈	C₄×D₁₃	1	2	yes	—
226	C₄×C₈	C₂²×D₁₃	1	2	yes	—
227	C₂×C₁₃	—	2	1	no	—
228	C₂×C₁₃	—	2	1	no	—
229	C₂×C₁₃	C₂×#364	1	2	yes	complemented
230	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
231	D₁₃	—	2	2	no	—
232	D₁₃	C₂×#364	1	4	yes	direct product factor
233	C₂⁴	—	13	1	no	—
234	C₂²×C₄	—	2	1	no	—
235	C₂²×C₄	—	13	1	no	—
236	C₂²×C₄	—	13	2	no	—
237	C₂²×C₄	—	13	1	no	—
238	C₂²×C₄	—	13	1	no	—
239	C₂²×C₄	—	13	1	no	—
240	C₂²×C₄	—	13	2	no	—
241	C₂²×C₄	—	13	1	no	—
242	C₂²×C₄	—	13	2	no	—
243	C₂²×C₄	—	13	2	no	—
244	C₂²×C₄	—	26	4	no	—
245	C₂²×C₄	—	26	8	no	—
246	C₂²×C₄	—	26	1	no	—
247	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
248	C₂×C₈	—	13	2	no	—
249	C₂×C₈	—	13	1	no	—
250	C₂×C₈	—	13	1	no	—
251	C₂×C₈	—	13	2	no	—
252	C₂×C₈	—	13	2	no	—
253	C₂×C₈	—	13	2	no	—
254	C₂×C₈	—	13	2	no	—
255	C₂×C₈	—	13	2	no	—
256	C₂×C₈	—	13	2	no	—
257	C₂×C₈	—	13	2	no	—
258	C₂×C₈	—	13	2	no	—
259	C₂×C₈	—	13	8	no	—
260	C₂×C₈	—	13	8	no	—
261	C₂×C₈	—	13	2	no	—
262	C₂×C₈	—	13	2	no	—
263	C₂×C₈	—	13	2	no	—
264	C₂×C₈	—	13	2	no	—
265	C₂×C₈	C₈×D₁₃	1	2	yes	—
266	C₂×C₈	C₈×D₁₃	1	2	yes	—
267	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
268	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
269	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
270	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
271	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
272	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
273	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
274	C₄²	—	2	1	no	—
275	C₄²	—	13	2	no	—
276	C₄²	—	26	4	no	—
277	C₄²	—	26	1	no	—
278	C₄²	C₂×C₄×D₁₃	1	2	yes	—
279	C₁₆	—	2	4	no	—
280	C₁₆	—	26	4	no	—
281	C₁₃	C₂²×#364	1	1	yes	characteristic, complemented, Sylow
282	C₂³	—	13	1	no	—
283	C₂³	—	13	2	no	—
284	C₂³	—	13	2	no	—
285	C₂³	—	13	1	no	—
286	C₂³	—	26	4	no	—
287	C₂³	M₁₆×D₁₃	1	1	yes	characteristic
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	13	2	no	—
291	C₂×C₄	—	13	2	no	—
292	C₂×C₄	—	13	1	no	—
293	C₂×C₄	—	13	1	no	—
294	C₂×C₄	—	13	2	no	—
295	C₂×C₄	—	13	2	no	—
296	C₂×C₄	—	13	2	no	—
297	C₂×C₄	—	13	2	no	—
298	C₂×C₄	—	13	2	no	—
299	C₂×C₄	—	13	2	no	—
300	C₂×C₄	—	13	2	no	—
301	C₂×C₄	—	13	2	no	—
302	C₂×C₄	—	26	16	no	—
303	C₂×C₄	—	26	4	no	—
304	C₂×C₄	—	26	2	no	—
305	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
306	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
307	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
308	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
309	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
310	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
311	C₈	—	13	4	no	—
312	C₈	—	13	2	no	—
313	C₈	—	13	2	no	—
314	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
315	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
316	C₈	C₂×C₈×D₁₃	1	4	yes	—
317	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
318	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
319	C₂²	—	2	2	no	—
320	C₂²	—	13	2	no	—
321	C₂²	—	13	4	no	—
322	C₂²	—	13	2	no	—
323	C₂²	—	26	4	no	—
324	C₂²	—	26	4	no	—
325	C₂²	—	26	2	no	—
326	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
327	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
328	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
329	C₄	—	2	4	no	—
330	C₄	—	13	2	no	—
331	C₄	—	13	2	no	—
332	C₄	—	26	4	no	—
333	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
334	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
335	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
336	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
337	C₂	—	2	1	no	—
338	C₂	—	2	1	no	—
339	C₂	—	13	4	no	—
340	C₂	—	26	2	no	—
341	C₂	D₁₃×#364	1	2	yes	direct product factor
342	C₂	C₂×D₁₃×C₄⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#364	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#364	D₁₃
hypocenter	C₁₃	C₂²×#364
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
3. C₂×#11718055	C₂	semidirect
4. C₂×#11718103	C₂	semidirect
5. D₁₃×#364	C₂	direct (N × H)
6. C₂×C₁₃×#364	C₂	semidirect
22. C₁₃×#364	C₂²	semidirect
23. #11718103	C₂²	semidirect
24. #11718055	C₂²	semidirect
116. C₂×#364	D₁₃	direct (N × H)
171. #364	C₂×D₁₃	direct (N × H)
179. C₂×D₁₃	#364	direct (N × H)
229. C₂×C₁₃	C₂×#364	semidirect
232. D₁₃	C₂×#364	direct (N × H)
281. C₁₃	C₂²×#364	semidirect
341. C₂	D₁₃×#364	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×D₁₃×M₃₂	2
C₂×C₄×C₈×D₁₃	2
C₂×#11718055	2
C₂×#11718103	2
D₁₃×#364	2
C₂×C₁₃×#364	2
C₂²×#364	13

Subgroups — C2×D13×#364 #16015913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#364 #16015913