Subgroups — C₂×#13130034 #16792569

Order 3328.

1046 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719049	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13130034	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718251	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×#1057	C₂	1	2	yes	maximal, complemented
6	C₂×#11718368	C₂	1	1	yes	maximal, characteristic
7	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
8	C₂²×#6094	C₄	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88112	C₄	1	2	yes	—
11	C₂×#88111	C₄	1	2	yes	—
12	C₂×C₄×#1057	C₄	1	2	yes	—
13	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
14	C₂×C₄×#1057	C₂²	1	2	yes	—
15	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
16	#11719049	C₄	1	4	yes	—
17	#11719049	C₂²	1	4	yes	—
18	C₄×D₁₃⋊C₈	C₄	1	4	yes	—
19	C₄×D₁₃⋊C₈	C₂²	1	4	yes	—
20	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
21	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
22	C₂×#88043	C₄	1	1	yes	characteristic
23	#11718368	C₄	1	4	yes	—
24	#11718368	C₂²	1	4	yes	—
25	#11718251	C₂²	1	8	yes	complemented
26	C₈×#1057	C₂²	1	8	yes	complemented
27	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1057	C₂×C₄	1	2	yes	—
31	C₂²×#1057	C₂×C₄	1	4	yes	—
32	C₂²×#1057	C₂×C₄	1	2	yes	—
33	C₂×D₁₃⋊C₈	—	2	8	no	—
34	C₂×D₁₃⋊C₈	C₂×C₄	1	8	yes	—
35	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
40	C₂²×#1055	C₂×C₄	1	2	yes	—
41	C₂×#6094	C₈	1	16	yes	complemented
42	C₂×#6094	C₂×C₄	1	8	yes	—
43	C₄²×D₁₃	C₂×C₄	1	2	yes	—
44	C₄²×D₁₃	C₂×C₄	1	2	yes	—
45	C₄²×D₁₃	C₂×C₄	1	2	yes	—
46	C₄²×D₁₃	C₂³	1	2	yes	—
47	#88112	C₂×C₄	1	8	yes	—
48	#88111	C₂×C₄	1	8	yes	—
49	C₄×#1057	C₂×C₄	1	2	yes	—
50	C₄×#1057	C₂×C₄	1	2	yes	—
51	C₄×#1057	C₂×C₄	1	8	yes	—
52	C₄×#1057	C₂×C₄	1	4	yes	—
53	C₄×#1057	C₂³	1	2	yes	—
54	C₄×#1057	C₂³	1	4	yes	—
55	C₄×#1057	C₂³	1	2	yes	—
56	C₁₃×#97	C₂×C₄	1	4	yes	—
57	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
58	C₈×Dic₁₃	C₂³	1	4	yes	—
59	#88043	C₂×C₄	1	4	yes	—
60	C₂×C₈×M₁₆	—	13	1	no	maximal, Sylow
61	C₂³×D₁₃	C₄²	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
66	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×D₁₃	—	2	4	no	—
69	C₂×C₄×D₁₃	—	2	4	no	—
70	C₂×C₄×D₁₃	C₄²	1	2	yes	—
71	C₂×C₄×D₁₃	C₄²	1	2	yes	—
72	C₂×C₄×D₁₃	C₄²	1	2	yes	—
73	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
74	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
75	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
76	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
77	C₂×#1057	—	2	4	no	—
78	C₂×#1057	—	2	8	no	—
79	C₂×#1057	M₁₆	1	8	yes	complemented
80	C₂×#1057	C₂²×C₄	1	4	yes	—
81	C₂×#1057	C₂²×C₄	1	8	yes	—
82	C₂×#1057	C₂²×C₄	1	4	yes	—
83	D₁₃⋊C₈	—	2	16	no	—
84	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	complemented
85	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
86	C₄²×C₁₃	C₄²	1	2	yes	—
87	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
88	C₄×Dic₁₃	C₄²	1	2	yes	—
89	C₄×Dic₁₃	C₄²	1	2	yes	—
90	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
94	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
95	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
96	C₂×#1055	C₂×C₈	1	8	yes	complemented
97	C₂×#1055	C₂²×C₄	1	4	yes	—
98	#6094	C₂×C₈	1	32	yes	complemented
99	C₂×#431	—	13	1	no	—
100	C₂×C₄×M₁₆	—	13	1	no	—
101	C₂²×C₄×C₈	—	13	1	no	—
102	C₈×M₁₆	—	13	8	no	—
103	C₂×#322	—	13	2	no	—
104	C₂×C₈²	—	13	2	no	—
105	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
106	C₂²×D₁₃	—	2	2	no	—
107	C₂²×D₁₃	—	2	2	no	—
108	C₂²×D₁₃	C₄×C₈	1	4	yes	—
109	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
110	C₂×C₄×C₁₃	—	2	2	no	—
111	C₂×C₄×C₁₃	—	2	2	no	—
112	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
113	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
114	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
116	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
117	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
118	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
119	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
120	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
121	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
122	C₂×Dic₁₃	#131	1	4	yes	—
123	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
124	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
125	C₄×D₁₃	—	2	4	no	—
126	C₄×D₁₃	—	2	4	no	—
127	C₄×D₁₃	—	2	4	no	—
128	C₄×D₁₃	—	2	4	no	—
129	C₄×D₁₃	C₄×C₈	1	8	yes	—
130	C₄×D₁₃	C₂²×C₈	1	8	yes	—
131	#1057	—	2	4	no	—
132	#1057	—	2	8	no	—
133	#1057	C₂×M₁₆	1	8	yes	complemented
134	C₈×C₁₃	C₂²×C₈	1	8	yes	complemented
135	#1055	C₂²×C₈	1	8	yes	complemented
136	C₂²×M₁₆	—	13	2	no	—
137	C₂³×C₈	—	13	2	no	—
138	C₂²×C₄²	—	13	1	no	—
139	#431	—	13	4	no	—
140	#431	—	13	4	no	—
141	C₂×C₄⋊C₈	—	13	2	no	—
142	C₂×C₂²⋊C₈	—	13	2	no	—
143	C₄×M₁₆	—	13	4	no	—
144	C₄×M₁₆	—	13	4	no	—
145	C₂×#97	—	13	1	no	—
146	C₂×#97	#261	1	1	yes	characteristic
147	C₂×C₄×C₈	—	13	4	no	—
148	C₂×C₄×C₈	—	13	4	no	—
149	C₂×C₄×C₈	—	13	1	no	—
150	C₂×C₄×C₈	—	13	1	no	—
151	C₂×C₄×C₈	—	13	2	no	—
152	C₂×C₄×C₈	—	13	2	no	—
153	C₂×C₄×C₈	—	13	2	no	—
154	#322	—	13	8	no	—
155	C₈²	—	13	8	no	—
156	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
157	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
158	C₂²×C₁₃	#405	1	2	yes	—
159	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
160	C₂×D₁₃	—	2	2	no	—
161	C₂×D₁₃	—	2	2	no	—
162	C₂×D₁₃	—	2	8	no	—
163	C₂×D₁₃	C₂×C₄×C₈	1	4	yes	—
164	C₄×C₁₃	—	2	2	no	—
165	C₄×C₁₃	—	2	2	no	—
166	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
167	C₄×C₁₃	C₂³×C₈	1	2	yes	—
168	Dic₁₃	C₂×C₄×C₈	1	4	yes	—
169	Dic₁₃	C₄×M₁₆	1	2	yes	—
170	Dic₁₃	#405	1	2	yes	—
171	Dic₁₃	C₂²×M₁₆	1	2	yes	—
172	Dic₁₃	C₂×#131	1	2	yes	—
173	C₂³×C₄	—	13	1	no	—
174	C₂³×C₄	—	13	1	no	—
175	C₂³×C₄	—	13	1	no	—
176	C₂×M₁₆	—	13	16	no	—
177	C₂×M₁₆	—	13	8	no	—
178	C₂²×C₈	—	13	2	no	—
179	C₂²×C₈	—	13	2	no	—
180	C₂²×C₈	—	13	8	no	—
181	C₂²×C₈	—	13	2	no	—
182	C₂²×C₈	—	13	4	no	—
183	C₂²×C₈	—	26	8	no	—
184	C₂²×C₈	C₂×#261	1	2	yes	—
185	C₂×C₄²	—	13	1	no	—
186	C₂×C₄²	—	13	1	no	—
187	C₂×C₄²	—	13	1	no	—
188	C₂×C₄²	—	13	2	no	—
189	C₂×C₄²	—	13	2	no	—
190	C₂×C₄²	—	13	2	no	—
191	C₂×C₄²	—	13	2	no	—
192	C₂×C₄²	C₂×#261	1	1	yes	characteristic
193	C₄⋊C₈	—	13	8	no	—
194	C₂²⋊C₈	—	13	8	no	—
195	#97	—	13	4	no	—
196	#97	C₂×#261	1	4	yes	—
197	C₄×C₈	—	13	2	no	—
198	C₄×C₈	—	13	8	no	—
199	C₄×C₈	—	13	2	no	—
200	C₄×C₈	—	13	4	no	—
201	C₄×C₈	—	13	2	no	—
202	C₄×C₈	—	13	4	no	—
203	C₄×C₈	—	13	2	no	—
204	C₄×C₈	—	13	4	no	—
205	C₄×C₈	—	13	4	no	—
206	C₂×C₁₃	C₈×M₁₆	1	4	yes	complemented
207	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
208	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
209	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
210	D₁₃	—	2	4	no	—
211	C₂⁴	—	13	1	no	—
212	C₂²×C₄	—	13	1	no	—
213	C₂²×C₄	—	13	1	no	—
214	C₂²×C₄	—	13	1	no	—
215	C₂²×C₄	—	13	8	no	—
216	C₂²×C₄	—	13	2	no	—
217	C₂²×C₄	—	13	2	no	—
218	C₂²×C₄	—	13	2	no	—
219	C₂²×C₄	—	13	2	no	—
220	C₂²×C₄	—	13	2	no	—
221	C₂²×C₄	—	13	2	no	—
222	C₂²×C₄	—	26	4	no	—
223	C₂²×C₄	—	26	4	no	—
224	C₂²×C₄	C₄×#261	1	1	yes	characteristic
225	C₂²×C₄	C₄×#261	1	1	yes	characteristic
226	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
227	M₁₆	—	13	32	no	—
228	C₂×C₈	—	13	4	no	—
229	C₂×C₈	—	13	8	no	—
230	C₂×C₈	—	13	8	no	—
231	C₂×C₈	—	13	4	no	—
232	C₂×C₈	—	13	4	no	—
233	C₂×C₈	—	13	8	no	—
234	C₂×C₈	—	26	16	no	—
235	C₂×C₈	—	26	4	no	—
236	C₂×C₈	—	26	8	no	—
237	C₂×C₈	D₁₃⋊C₈	1	8	yes	complemented
238	C₂×C₈	C₂²×#261	1	4	yes	—
239	C₄²	—	13	2	no	—
240	C₄²	—	13	1	no	—
241	C₄²	—	13	1	no	—
242	C₄²	—	13	2	no	—
243	C₄²	—	13	2	no	—
244	C₄²	—	13	2	no	—
245	C₄²	—	13	1	no	—
246	C₄²	—	13	1	no	—
247	C₄²	C₄×#261	1	2	yes	—
248	C₄²	C₂²×#261	1	2	yes	—
249	C₁₃	C₂×C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
250	C₂³	—	13	4	no	—
251	C₂³	—	13	2	no	—
252	C₂³	—	26	2	no	—
253	C₂³	—	26	2	no	—
254	C₂³	C₂×C₄×#261	1	1	yes	characteristic
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	13	4	no	—
258	C₂×C₄	—	13	4	no	—
259	C₂×C₄	—	13	4	no	—
260	C₂×C₄	—	13	1	no	—
261	C₂×C₄	—	13	1	no	—
262	C₂×C₄	—	13	2	no	—
263	C₂×C₄	—	13	1	no	—
264	C₂×C₄	—	13	1	no	—
265	C₂×C₄	—	13	8	no	—
266	C₂×C₄	—	13	8	no	—
267	C₂×C₄	—	26	4	no	—
268	C₂×C₄	—	26	4	no	—
269	C₂×C₄	—	26	4	no	—
270	C₂×C₄	—	26	4	no	—
271	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
272	C₂×C₄	C₂×C₄×#261	1	2	yes	—
273	C₂×C₄	C₂×C₄×#261	1	2	yes	—
274	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
275	C₂×C₄	C₂³×#261	1	1	yes	characteristic
276	C₈	—	13	8	no	—
277	C₈	—	13	8	no	—
278	C₈	—	26	4	no	—
279	C₈	—	26	8	no	—
280	C₈	C₂×D₁₃⋊C₈	1	8	yes	complemented
281	C₂²	—	13	4	no	—
282	C₂²	—	26	8	no	—
283	C₂²	—	26	2	no	—
284	C₂²	—	26	2	no	—
285	C₂²	C₄×D₁₃⋊C₈	1	2	yes	—
286	C₂²	M₁₆×#261	1	2	yes	—
287	C₂²	#11719099	1	2	yes	—
288	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
289	C₄	—	2	2	no	—
290	C₄	—	2	2	no	—
291	C₄	—	13	4	no	—
292	C₄	—	13	2	no	—
293	C₄	—	13	2	no	—
294	C₄	—	13	2	no	—
295	C₄	—	13	2	no	—
296	C₄	C₄×D₁₃⋊C₈	1	2	yes	—
297	C₄	C₂²×D₁₃⋊C₈	1	2	yes	—
298	C₂	—	26	4	no	—
299	C₂	#13130034	1	4	yes	direct product factor
300	C₂	C₂×C₄×D₁₃⋊C₈	1	1	yes	characteristic
301	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
302	C₂	C₂×#11719099	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#97	C₄
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×#97	#261
hypocenter	C₁₃	C₂×C₈×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
3. #13130034	C₂	direct (N × H)
4. C₂×#11718251	C₂	semidirect
5. C₂×C₈×#1057	C₂	semidirect
25. #11718251	C₂²	semidirect
26. C₈×#1057	C₂²	semidirect
41. C₂×#6094	C₈	semidirect
79. C₂×#1057	M₁₆	semidirect
84. C₂×C₈×C₁₃	C₂×C₈	semidirect
96. C₂×#1055	C₂×C₈	semidirect
98. #6094	C₂×C₈	semidirect
133. #1057	C₂×M₁₆	semidirect
134. C₈×C₁₃	C₂²×C₈	semidirect
135. #1055	C₂²×C₈	semidirect
206. C₂×C₁₃	C₈×M₁₆	semidirect
237. C₂×C₈	D₁₃⋊C₈	semidirect
249. C₁₃	C₂×C₈×M₁₆	semidirect
280. C₈	C₂×D₁₃⋊C₈	semidirect
299. C₂	#13130034	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×#11719049	2
C₂×C₄×D₁₃⋊C₈	2
#13130034	2
C₂×#11718251	2
C₂×C₈×#1057	2
C₂×#11718368	2
C₂×C₈×M₁₆	13

Subgroups — C2×#13130034 #16792569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130034 #16792569