Subgroups — C₂×#13116649 #16016043

Order 3328.

538 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718783	C₂	1	1	yes	maximal, characteristic
2	#13116649	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718103	C₂	1	2	yes	maximal, complemented
4	C₂×#11718145	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718104	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#349	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
8	C₂×#88180	C₄	1	1	yes	characteristic
9	C₂³×#1055	C₄	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	#11718783	C₄	1	4	yes	—
12	#11718783	C₂²	1	4	yes	—
13	C₂×#88055	C₄	1	1	yes	characteristic
14	C₂×#88055	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂×#88052	C₂²	1	2	yes	—
18	C₁₃×#349	C₂²	1	4	yes	—
19	#11718145	C₂²	1	4	yes	—
20	#11718104	C₂²	1	8	yes	complemented
21	#11718103	C₂²	1	8	yes	complemented
22	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×M₁₆	—	2	2	no	—
24	C₂×C₁₃×M₁₆	—	2	2	no	—
25	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
26	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
30	#88180	—	2	2	no	—
31	#88180	C₂×C₄	1	4	yes	—
32	C₂×C₄⋊Dic₁₃	—	2	1	no	—
33	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×#1055	—	2	2	no	—
36	C₂²×#1055	—	2	2	no	—
37	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
38	C₂²×#1055	C₂×C₄	1	4	yes	—
39	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
40	C₁₃×M₃₂	—	2	2	no	—
41	C₁₃×M₃₂	C₂³	1	4	yes	—
42	C₂×C₁₃×C₁₆	—	2	2	no	—
43	#88055	C₂×C₄	1	4	yes	—
44	#88055	C₂×C₄	1	2	yes	—
45	#88055	C₂³	1	2	yes	—
46	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
47	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
48	C₈×Dic₁₃	C₂³	1	2	yes	—
49	#88052	—	2	2	no	—
50	#88052	C₂³	1	4	yes	—
51	C₂×#6090	—	2	2	no	—
52	C₂×#2166	—	13	1	no	maximal, Sylow
53	C₂⁴×C₁₃	M₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	—	2	1	no	—
55	C₂²×C₄×C₁₃	—	2	1	no	—
56	C₂²×C₄×C₁₃	—	2	1	no	—
57	C₂²×C₄×C₁₃	—	2	1	no	—
58	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×Dic₁₃	—	2	1	no	—
63	C₂²×Dic₁₃	—	2	1	no	—
64	C₁₃×M₁₆	—	2	4	no	—
65	C₁₃×M₁₆	—	2	4	no	—
66	C₂×C₈×C₁₃	—	2	1	no	—
67	C₂×C₈×C₁₃	—	2	1	no	—
68	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
69	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₃	#41	1	2	yes	—
71	C₂×C₈×C₁₃	#41	1	2	yes	—
72	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
73	C₂²⋊Dic₁₃	—	2	4	no	—
74	C₄⋊Dic₁₃	—	2	4	no	—
75	C₄×Dic₁₃	—	2	1	no	—
76	C₄×Dic₁₃	—	2	1	no	—
77	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
78	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
79	C₂×#1055	—	2	1	no	—
80	C₂×#1055	—	2	1	no	—
81	C₂×#1055	—	2	8	no	—
82	C₂×#1055	M₁₆	1	2	yes	—
83	C₂×#1055	M₁₆	1	2	yes	—
84	C₂×#1055	C₂²×C₄	1	2	yes	—
85	C₂×#1055	C₂²×C₄	1	2	yes	—
86	C₁₃×C₁₆	—	2	4	no	—
87	#6090	—	2	4	no	—
88	C₂×#405	—	13	1	no	—
89	#2166	—	13	8	no	—
90	C₂×#364	—	13	2	no	—
91	C₂×#349	—	13	1	no	—
92	C₂×#349	D₁₃	1	1	yes	characteristic
93	C₂×#347	—	13	2	no	—
94	C₂³×C₁₃	—	2	1	no	—
95	C₂³×C₁₃	—	2	1	no	—
96	C₂³×C₁₃	—	4	2	no	—
97	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
98	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	2	1	no	—
101	C₂×C₄×C₁₃	—	2	2	no	—
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	2	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
108	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
112	C₂×Dic₁₃	—	2	2	no	—
113	C₂×Dic₁₃	—	2	2	no	—
114	C₂×Dic₁₃	—	4	2	no	—
115	C₂×Dic₁₃	—	4	2	no	—
116	C₈×C₁₃	—	2	2	no	—
117	C₈×C₁₃	#117	1	2	yes	—
118	C₈×C₁₃	C₂×#41	1	2	yes	—
119	#1055	—	2	2	no	—
120	#1055	C₂×M₁₆	1	4	yes	—
121	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
122	C₂³×C₈	—	13	1	no	—
123	C₂×#117	—	13	1	no	—
124	C₂×M₃₂	—	13	2	no	—
125	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
126	#405	—	13	4	no	—
127	#405	—	13	4	no	—
128	C₂×#97	—	13	1	no	—
129	C₂×#97	—	13	1	no	—
130	C₂×C₄×C₈	—	13	1	no	—
131	C₂×C₄×C₈	—	13	1	no	—
132	#364	—	13	8	no	—
133	#349	—	13	4	no	—
134	#349	C₂×D₁₃	1	4	yes	—
135	#347	—	13	8	no	—
136	C₂²×C₁₃	—	2	2	no	—
137	C₂²×C₁₃	—	2	2	no	—
138	C₂²×C₁₃	—	4	2	no	—
139	C₂²×C₁₃	—	4	2	no	—
140	C₂²×C₁₃	—	4	2	no	—
141	C₂²×C₁₃	#432	1	1	yes	characteristic
142	C₂²×C₁₃	#432	1	1	yes	characteristic
143	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
144	C₄×C₁₃	—	2	2	no	—
145	C₄×C₁₃	#432	1	1	yes	characteristic
146	C₄×C₁₃	#432	1	1	yes	characteristic
147	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
148	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
149	Dic₁₃	—	4	2	no	—
150	Dic₁₃	—	4	2	no	—
151	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
155	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
156	C₂²×C₈	—	13	1	no	—
157	C₂²×C₈	—	13	1	no	—
158	C₂²×C₈	—	13	4	no	—
159	C₂²×C₈	—	26	2	no	—
160	C₂²×C₈	—	26	2	no	—
161	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
163	#117	—	13	4	no	—
164	#117	—	26	2	no	—
165	C₂×C₄⋊C₄	—	26	1	no	—
166	C₂×C₂²⋊C₄	—	26	1	no	—
167	C₂×C₄²	—	13	1	no	—
168	C₂×C₄²	—	13	1	no	—
169	M₃₂	—	2	2	no	—
170	M₃₂	—	13	4	no	—
171	M₃₂	—	26	2	no	—
172	M₃₂	C₂²×D₁₃	1	4	yes	—
173	C₂×C₁₆	—	2	2	no	—
174	C₂×C₁₆	—	26	2	no	—
175	#97	—	13	4	no	—
176	#97	—	13	2	no	—
177	#97	—	13	2	no	—
178	C₄×C₈	—	13	4	no	—
179	C₄×C₈	—	13	2	no	—
180	C₄×C₈	—	13	2	no	—
181	C₂×C₁₃	—	2	1	no	—
182	C₂×C₁₃	—	2	1	no	—
183	C₂×C₁₃	—	4	2	no	—
184	C₂×C₁₃	#2166	1	2	yes	complemented
185	C₂×C₁₃	C₂×#432	1	1	yes	characteristic
186	C₂⁴	#6094	1	1	yes	characteristic
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	26	1	no	—
192	C₂²×C₄	—	26	1	no	—
193	C₂²×C₄	#6094	1	1	yes	characteristic
194	C₂²×C₄	#6094	1	2	yes	—
195	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
196	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
197	M₁₆	—	2	4	no	—
198	M₁₆	—	2	4	no	—
199	C₂×C₈	—	2	1	no	—
200	C₂×C₈	—	2	1	no	—
201	C₂×C₈	—	13	2	no	—
202	C₂×C₈	—	13	2	no	—
203	C₂×C₈	—	13	2	no	—
204	C₂×C₈	—	13	2	no	—
205	C₂×C₈	—	26	8	no	—
206	C₂×C₈	—	26	1	no	—
207	C₂×C₈	—	26	1	no	—
208	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
209	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
210	C₂×C₈	#6129	1	2	yes	—
211	C₂×C₈	#6129	1	2	yes	—
212	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
213	C₄⋊C₄	—	26	4	no	—
214	C₂²⋊C₄	—	26	4	no	—
215	C₄²	—	13	2	no	—
216	C₄²	—	13	2	no	—
217	C₄²	—	26	1	no	—
218	C₄²	—	26	1	no	—
219	C₁₆	—	2	4	no	—
220	C₁₆	—	26	4	no	—
221	C₁₃	C₂×#2166	1	1	yes	characteristic, complemented, Sylow
222	C₂³	—	2	1	no	—
223	C₂³	—	2	1	no	—
224	C₂³	—	4	2	no	—
225	C₂³	C₂×#6094	1	1	yes	characteristic
226	C₂³	C₂×#6094	1	2	yes	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	26	2	no	—
234	C₂×C₄	—	26	2	no	—
235	C₂×C₄	—	52	2	no	—
236	C₂×C₄	—	52	2	no	—
237	C₂×C₄	#88131	1	1	yes	characteristic
238	C₂×C₄	#88131	1	1	yes	characteristic
239	C₂×C₄	C₂×#6094	1	2	yes	—
240	C₂×C₄	C₂×#6094	1	1	yes	characteristic
241	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
242	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
243	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
244	C₈	—	2	2	no	—
245	C₈	—	13	4	no	—
246	C₈	—	26	2	no	—
247	C₈	#88131	1	2	yes	—
248	C₈	C₂×#6129	1	2	yes	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	#11718380	1	1	yes	characteristic
255	C₂²	#11718380	1	1	yes	characteristic
256	C₂²	C₂²×#6094	1	1	yes	characteristic
257	C₄	—	2	2	no	—
258	C₄	—	52	2	no	—
259	C₄	—	52	2	no	—
260	C₄	#11718380	1	1	yes	characteristic
261	C₄	#11718380	1	1	yes	characteristic
262	C₄	C₂×#88131	1	1	yes	characteristic
263	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	—	4	2	no	—
267	C₂	#13116649	1	2	yes	direct product factor
268	C₂	C₂×#11718380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88131
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#349	C₂
socle	C₂²×C₁₃	#432
prime radical	C₂⁴×C₁₃	M₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#349	D₁₃
hypocenter	C₁₃	C₂×#2166
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

Complements

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

N	H ≅ G/N	type
2. #13116649	C₂	direct (N × H)
3. C₂×#11718103	C₂	semidirect
5. C₂×#11718104	C₂	semidirect
20. #11718104	C₂²	semidirect
21. #11718103	C₂²	semidirect
184. C₂×C₁₃	#2166	semidirect
221. C₁₃	C₂×#2166	semidirect
267. C₂	#13116649	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×#11718783	2
#13116649	2
C₂×#11718103	2
C₂×#11718145	2
C₂×#11718104	2
C₂×C₁₃×#349	2
C₂×#2166	13

Subgroups — C2×#13116649 #16016043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116649 #16016043