Subgroups — C₂×#13116607 #16015929

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 362 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	1	yes	maximal, characteristic
2	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718521	C₂	1	1	yes	maximal, characteristic
4	#13116607	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718105	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718079	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×M₁₆×D₁₃	—	2	1	no	—
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88146	—	2	1	no	—
12	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
15	C₂×#88062	—	2	1	no	—
16	C₂×#88059	C₂²	1	1	yes	characteristic
17	C₂×#88057	C₂²	1	1	yes	characteristic
18	C₂×#88052	C₂²	1	1	yes	characteristic
19	C₂×#88047	—	2	1	no	—
20	D₁₃×M₃₂	C₄	1	4	yes	complemented
21	D₁₃×M₃₂	C₂²	1	4	yes	—
22	C₂×#88038	C₄	1	2	yes	complemented
23	C₂×C₁₆×D₁₃	C₄	1	2	yes	complemented
24	D₁₃×#108	—	2	2	no	—
25	D₁₃×#108	C₂²	1	4	yes	—
26	#11718521	—	2	2	no	—
27	#11718521	C₂²	1	4	yes	—
28	C₁₃×#365	C₂²	1	4	yes	complemented
29	#11718105	C₂²	1	4	yes	complemented
30	#11718086	C₂²	1	4	yes	complemented
31	#11718079	C₂²	1	4	yes	complemented
32	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
33	C₂×C₁₃×M₁₆	—	2	1	no	—
34	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₂×#6103	—	4	1	no	—
37	C₂×C₄⋊Dic₁₃	—	2	1	no	—
38	C₂×C₄×Dic₁₃	—	4	1	no	—
39	C₂×#6099	—	2	1	no	—
40	C₂²×#1055	D₄	1	1	yes	characteristic
41	M₁₆×D₁₃	—	2	4	no	—
42	M₁₆×D₁₃	—	4	2	no	—
43	C₂×#6094	—	4	1	no	—
44	C₂×C₈×D₁₃	—	4	1	no	—
45	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₁₃	D₄	1	2	yes	—
49	C₂×C₈×D₁₃	Q₈	1	2	yes	—
50	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
51	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂³	1	2	yes	—
53	#88146	—	2	4	no	—
54	#88146	—	4	2	no	—
55	C₁₃×M₃₂	C₂×C₄	1	2	yes	—
56	C₁₃×M₃₂	C₂³	1	2	yes	—
57	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
58	C₁₃×#108	—	2	1	no	—
59	C₁₃×#108	C₂³	1	2	yes	—
60	C₁₃×#106	—	2	1	no	—
61	C₁₃×#106	C₂³	1	2	yes	—
62	#88062	—	2	4	no	—
63	#88059	—	2	1	no	—
64	#88059	C₂³	1	2	yes	—
65	#88057	—	2	1	no	—
66	#88057	C₂³	1	2	yes	—
67	#88052	C₂×C₄	1	2	yes	—
68	#88052	C₂³	1	2	yes	—
69	C₂×#6090	C₂×C₄	1	2	yes	—
70	#88047	—	2	4	no	—
71	#88038	C₂×C₄	1	8	yes	complemented
72	C₁₆×D₁₃	C₂×C₄	1	8	yes	complemented
73	C₂×#2155	—	13	1	no	maximal, Sylow
74	C₂³×D₁₃	SD₁₆	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	—	4	1	no	—
76	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₁₃	—	4	1	no	—
78	C₂²×Dic₁₃	SD₁₆	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	2	yes	—
82	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
83	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
84	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
85	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
86	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
87	C₁₃×M₁₆	—	2	2	no	—
88	C₁₃×M₁₆	—	4	1	no	—
89	C₂×C₈×C₁₃	—	4	1	no	—
90	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
96	C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₁₃×C₄⋊C₄	—	4	1	no	—
98	#6103	—	4	4	no	—
99	C₄⋊Dic₁₃	—	2	2	no	—
100	C₄⋊Dic₁₃	—	4	1	no	—
101	C₄×Dic₁₃	—	4	4	no	—
102	#6099	—	2	2	no	—
103	#6099	—	4	1	no	—
104	C₂×#1055	—	4	1	no	—
105	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
106	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
107	C₂×#1055	C₄⋊C₄	1	2	yes	—
108	C₂×#1055	C₂×D₄	1	2	yes	—
109	#6094	—	4	4	no	—
110	C₈×D₁₃	—	4	4	no	—
111	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
112	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
113	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
114	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
115	C₈×D₁₃	C₂²×C₄	1	2	yes	—
116	C₈×D₁₃	C₂²×C₄	1	2	yes	—
117	C₈×D₁₃	C₂×Q₈	1	2	yes	—
118	C₈×D₁₃	C₂×Q₈	1	2	yes	—
119	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
120	#6090	C₂²×C₄	1	4	yes	—
121	C₂²×M₃₂	—	13	1	no	—
122	C₂²×#108	—	13	1	no	—
123	C₂×#427	—	13	1	no	—
124	#2155	—	13	8	no	—
125	C₂×#365	—	13	1	no	—
126	C₂×#365	—	13	1	no	—
127	C₂×#365	—	13	1	no	—
128	C₂×#365	D₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
130	C₂²×D₁₃	—	4	2	no	—
131	C₂²×D₁₃	#106	1	1	yes	characteristic
132	C₂²×D₁₃	#106	1	1	yes	characteristic
133	C₂²×D₁₃	#106	1	2	yes	—
134	C₂²×D₁₃	C₂×SD₁₆	1	2	yes	—
135	C₂×C₄×C₁₃	—	4	2	no	—
136	C₂×C₄×C₁₃	—	8	2	no	—
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×SD₁₆	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
143	C₂×Dic₁₃	—	4	2	no	—
144	C₂×Dic₁₃	—	8	2	no	—
145	C₂×Dic₁₃	#106	1	2	yes	—
146	C₂×Dic₁₃	#106	1	1	yes	characteristic
147	C₂×Dic₁₃	#106	1	1	yes	characteristic
148	C₂×Dic₁₃	C₂×SD₁₆	1	2	yes	—
149	C₄×D₁₃	#106	1	2	yes	—
150	C₄×D₁₃	#106	1	2	yes	—
151	C₄×D₁₃	#106	1	2	yes	—
152	C₄×D₁₃	#106	1	2	yes	—
153	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
154	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
155	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
156	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
157	C₈×C₁₃	—	4	2	no	—
158	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
162	#1055	—	4	2	no	—
163	#1055	C₂×C₄⋊C₄	1	2	yes	—
164	#1055	C₂×C₄⋊C₄	1	2	yes	—
165	C₂²×M₁₆	—	26	1	no	—
166	C₂³×C₈	—	13	1	no	—
167	C₂×#117	—	26	1	no	—
168	C₂×M₃₂	—	13	1	no	—
169	C₂×M₃₂	—	13	4	no	—
170	C₂×M₃₂	—	13	4	no	—
171	C₂×M₃₂	—	13	2	no	—
172	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
173	C₂²×C₁₆	—	13	2	no	—
174	C₂×#108	—	13	1	no	—
175	C₂×#108	—	13	4	no	—
176	C₂×#108	—	26	2	no	—
177	C₂×#108	—	26	1	no	—
178	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
179	#427	—	13	4	no	—
180	#427	—	26	2	no	—
181	C₂×#107	—	26	1	no	—
182	C₂×#106	—	13	1	no	—
183	C₂×#106	C₂×D₁₃	1	1	yes	characteristic
184	#365	—	13	4	no	—
185	#365	—	13	4	no	—
186	#365	—	13	4	no	—
187	#365	C₂×D₁₃	1	4	yes	complemented
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
190	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
191	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
192	C₂×D₁₃	—	2	2	no	—
193	C₂×D₁₃	—	2	2	no	—
194	C₂×D₁₃	—	4	2	no	—
195	C₂×D₁₃	—	4	2	no	—
196	C₂×D₁₃	C₂×#106	1	2	yes	—
197	C₂×D₁₃	C₂×#106	1	2	yes	—
198	C₄×C₁₃	—	8	2	no	—
199	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
200	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
201	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
203	Dic₁₃	—	8	2	no	—
204	Dic₁₃	C₂×#106	1	2	yes	—
205	Dic₁₃	C₂×#106	1	2	yes	—
206	C₂³×C₄	—	13	1	no	—
207	C₂×M₁₆	—	2	1	no	—
208	C₂×M₁₆	—	26	4	no	—
209	C₂×M₁₆	—	26	1	no	—
210	C₂×M₁₆	—	52	1	no	—
211	C₂×M₁₆	—	52	2	no	—
212	C₂²×C₈	—	13	1	no	—
213	C₂²×C₈	—	13	1	no	—
214	C₂²×C₈	—	13	2	no	—
215	C₂²×C₈	—	13	1	no	—
216	C₂²×C₈	—	13	2	no	—
217	C₂²×C₈	—	13	2	no	—
218	C₂²×C₈	—	13	1	no	—
219	C₂²×C₈	—	13	1	no	—
220	C₂²×C₈	—	13	2	no	—
221	C₂²×C₈	—	52	1	no	—
222	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
223	#117	—	26	4	no	—
224	#117	—	52	2	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	26	1	no	—
227	C₂×C₂²⋊C₄	—	52	1	no	—
228	C₂×C₄²	—	52	1	no	—
229	M₃₂	—	13	2	no	—
230	M₃₂	—	13	2	no	—
231	M₃₂	—	13	8	no	—
232	M₃₂	C₄×D₁₃	1	2	yes	—
233	M₃₂	C₂²×D₁₃	1	2	yes	—
234	C₂×C₁₆	—	13	2	no	—
235	C₂×C₁₆	—	13	8	no	—
236	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
237	#108	—	2	1	no	—
238	#108	—	13	2	no	—
239	#108	—	26	4	no	—
240	#108	—	26	1	no	—
241	#108	C₂²×D₁₃	1	2	yes	—
242	#107	—	26	4	no	—
243	#106	—	2	1	no	—
244	#106	—	13	2	no	—
245	#106	—	26	1	no	—
246	#106	C₂²×D₁₃	1	2	yes	—
247	C₂×C₁₃	—	2	1	no	—
248	C₂×C₁₃	—	2	1	no	—
249	C₂×C₁₃	#2155	1	2	yes	complemented
250	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
251	D₁₃	—	2	2	no	—
252	D₁₃	—	2	2	no	—
253	C₂⁴	—	13	1	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	—	13	1	no	—
256	C₂²×C₄	—	13	2	no	—
257	C₂²×C₄	—	13	1	no	—
258	C₂²×C₄	—	13	1	no	—
259	C₂²×C₄	—	13	2	no	—
260	C₂²×C₄	—	13	1	no	—
261	C₂²×C₄	—	13	2	no	—
262	C₂²×C₄	—	13	1	no	—
263	C₂²×C₄	—	13	2	no	—
264	C₂²×C₄	—	52	1	no	—
265	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
266	M₁₆	—	2	2	no	—
267	M₁₆	—	4	1	no	—
268	M₁₆	—	26	2	no	—
269	M₁₆	—	52	4	no	—
270	M₁₆	—	52	1	no	—
271	C₂×C₈	—	4	1	no	—
272	C₂×C₈	—	13	2	no	—
273	C₂×C₈	—	13	1	no	—
274	C₂×C₈	—	13	1	no	—
275	C₂×C₈	—	13	2	no	—
276	C₂×C₈	—	13	2	no	—
277	C₂×C₈	—	13	2	no	—
278	C₂×C₈	—	13	2	no	—
279	C₂×C₈	—	13	2	no	—
280	C₂×C₈	—	13	2	no	—
281	C₂×C₈	—	13	2	no	—
282	C₂×C₈	—	13	2	no	—
283	C₂×C₈	—	13	2	no	—
284	C₂×C₈	—	52	4	no	—
285	C₂×C₈	—	52	1	no	—
286	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
287	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
288	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
289	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
290	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
291	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	26	2	no	—
295	C₄⋊C₄	—	52	1	no	—
296	C₂²⋊C₄	—	52	4	no	—
297	C₄²	—	52	4	no	—
298	C₁₆	—	13	4	no	—
299	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
300	C₁₃	C₂×#2155	1	1	yes	characteristic, complemented, Sylow
301	C₂³	—	13	1	no	—
302	C₂³	—	13	1	no	—
303	C₂³	—	13	2	no	—
304	C₂³	—	13	2	no	—
305	C₂³	—	52	2	no	—
306	C₂³	SD₁₆×D₁₃	1	1	yes	characteristic
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	8	2	no	—
309	C₂×C₄	—	13	2	no	—
310	C₂×C₄	—	13	2	no	—
311	C₂×C₄	—	13	1	no	—
312	C₂×C₄	—	13	1	no	—
313	C₂×C₄	—	13	2	no	—
314	C₂×C₄	—	13	2	no	—
315	C₂×C₄	—	13	2	no	—
316	C₂×C₄	—	13	2	no	—
317	C₂×C₄	—	13	2	no	—
318	C₂×C₄	—	13	2	no	—
319	C₂×C₄	—	13	2	no	—
320	C₂×C₄	—	13	2	no	—
321	C₂×C₄	—	52	2	no	—
322	C₂×C₄	—	104	2	no	—
323	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
324	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
325	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
326	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
327	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
328	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
329	C₈	—	4	2	no	—
330	C₈	—	13	2	no	—
331	C₈	—	13	2	no	—
332	C₈	—	52	2	no	—
333	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
334	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
335	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
336	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
337	C₂²	—	2	2	no	—
338	C₂²	—	13	2	no	—
339	C₂²	—	13	2	no	—
340	C₂²	—	26	2	no	—
341	C₂²	—	26	2	no	—
342	C₂²	—	52	2	no	—
343	C₂²	—	52	2	no	—
344	C₂²	D₁₃×#106	1	1	yes	characteristic
345	C₂²	D₁₃×#106	1	1	yes	characteristic
346	C₂²	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
347	C₄	—	8	2	no	—
348	C₄	—	13	2	no	—
349	C₄	—	13	2	no	—
350	C₄	—	104	2	no	—
351	C₄	D₁₃×#106	1	1	yes	characteristic
352	C₄	D₁₃×#106	1	1	yes	characteristic
353	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
354	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
355	C₂	—	2	1	no	—
356	C₂	—	2	1	no	—
357	C₂	—	26	2	no	—
358	C₂	—	26	2	no	—
359	C₂	#13116607	1	2	yes	direct product factor
360	C₂	C₂×D₁₃×#106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₃×#106
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#365	C₂
socle	C₂²×C₁₃	C₂×#106
prime radical	C₂³×D₁₃	SD₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#365	D₁₃
hypocenter	C₁₃	C₂×#2155
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

Complements

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

N	H ≅ G/N	type
4. #13116607	C₂	direct (N × H)
5. C₂×#11718086	C₂	semidirect
6. C₂×#11718105	C₂	semidirect
7. C₂×#11718079	C₂	semidirect
8. C₂×C₁₃×#365	C₂	semidirect
20. D₁₃×M₃₂	C₄	semidirect
22. C₂×#88038	C₄	semidirect
23. C₂×C₁₆×D₁₃	C₄	semidirect
28. C₁₃×#365	C₂²	semidirect
29. #11718105	C₂²	semidirect
30. #11718086	C₂²	semidirect
31. #11718079	C₂²	semidirect
71. #88038	C₂×C₄	semidirect
72. C₁₆×D₁₃	C₂×C₄	semidirect
128. C₂×#365	D₁₃	semidirect
187. #365	C₂×D₁₃	semidirect
249. C₂×C₁₃	#2155	semidirect
300. C₁₃	C₂×#2155	semidirect
359. C₂	#13116607	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×D₁₃×#108	2
C₂×#11718521	2
#13116607	2
C₂×#11718086	2
C₂×#11718105	2
C₂×#11718079	2
C₂×C₁₃×#365	2
C₂×#2155	13

Subgroups — C2×#13116607 #16015929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116607 #16015929