Subgroups — C₂×#13116439 #16015575

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 290 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×#11718369	C₂	1	1	yes	maximal, characteristic
3	#13116439	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718104	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6094	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88126	C₄	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
12	C₂×#88055	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₄	1	1	yes	characteristic
16	D₁₃×M₃₂	C₄	1	8	yes	complemented
17	D₁₃×M₃₂	C₂²	1	8	yes	—
18	C₂×#88038	C₄	1	4	yes	complemented
19	C₂×C₁₆×D₁₃	C₄	1	4	yes	complemented
20	#11718369	C₄	1	4	yes	—
21	#11718369	C₂²	1	4	yes	—
22	C₁₃×#347	C₂²	1	4	yes	complemented
23	#11718104	C₂²	1	8	yes	complemented
24	#11718058	C₂²	1	4	yes	complemented
25	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#6103	—	2	1	no	—
30	C₂×#6101	—	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×#6094	—	2	2	no	—
35	C₂×#6094	—	2	2	no	—
36	C₂×#6094	C₂×C₄	1	4	yes	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
41	C₂×C₈×D₁₃	C₂³	1	2	yes	—
42	#88126	—	2	2	no	—
43	#88126	C₂×C₄	1	4	yes	—
44	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
45	C₁₃×M₃₂	C₂³	1	4	yes	—
46	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
47	C₁₃×#97	C₂×C₄	1	2	yes	—
48	C₁₃×#97	C₂³	1	2	yes	—
49	#88055	C₂×C₄	1	2	yes	—
50	#88055	C₂³	1	2	yes	—
51	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
52	#88052	C₂×C₄	1	4	yes	—
53	#88052	C₂³	1	4	yes	—
54	C₂×#6090	C₂×C₄	1	4	yes	—
55	C₄×#1055	C₂×C₄	1	4	yes	—
56	#88038	C₂×C₄	1	16	yes	complemented
57	C₁₆×D₁₃	C₂×C₄	1	16	yes	complemented
58	C₂×#2110	—	13	1	no	maximal, Sylow
59	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×Dic₁₃	—	2	1	no	—
63	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
64	C₂×C₄×D₁₃	C₄²	1	2	yes	—
65	C₂×C₄×D₁₃	C₄²	1	2	yes	—
66	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
67	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
68	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
69	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
70	C₂×C₈×C₁₃	—	2	1	no	—
71	C₂×C₈×C₁₃	—	2	1	no	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
73	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
75	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
76	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₄²×C₁₃	—	2	1	no	—
78	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
79	#6103	—	2	4	no	—
80	#6101	—	2	4	no	—
81	C₄×Dic₁₃	—	2	1	no	—
82	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
83	C₂×#1055	—	2	1	no	—
84	C₂×#1055	—	2	1	no	—
85	C₂×#1055	C₄²	1	2	yes	—
86	C₂×#1055	C₄²	1	1	yes	characteristic
87	C₂×#1055	C₄²	1	1	yes	characteristic
88	C₂×#1055	C₂²×C₄	1	2	yes	—
89	C₂×#1055	C₂²×C₄	1	2	yes	—
90	#6094	—	2	8	no	—
91	C₈×D₁₃	C₄²	1	4	yes	—
92	C₈×D₁₃	C₄²	1	4	yes	—
93	C₈×D₁₃	C₂²×C₄	1	4	yes	—
94	C₈×D₁₃	C₂²×C₄	1	4	yes	—
95	C₁₃×C₁₆	C₂²×C₄	1	8	yes	—
96	#6090	C₂²×C₄	1	8	yes	—
97	C₂²×M₃₂	—	13	2	no	—
98	C₂×#405	—	13	1	no	—
99	#2110	—	13	8	no	—
100	C₂×#347	—	13	2	no	—
101	C₂×#347	—	13	1	no	—
102	C₂×#347	D₁₃	1	1	yes	characteristic, complemented
103	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
104	C₂²×D₁₃	—	4	2	no	—
105	C₂²×D₁₃	#97	1	2	yes	—
106	C₂²×D₁₃	#97	1	2	yes	—
107	C₂²×D₁₃	C₂×M₁₆	1	2	yes	—
108	C₂×C₄×C₁₃	—	2	2	no	—
109	C₂×C₄×C₁₃	—	4	2	no	—
110	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
112	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
114	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
116	C₂×Dic₁₃	—	2	2	no	—
117	C₂×Dic₁₃	—	4	2	no	—
118	C₂×Dic₁₃	#97	1	2	yes	—
119	C₂×Dic₁₃	#97	1	2	yes	—
120	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
121	C₄×D₁₃	#97	1	4	yes	—
122	C₄×D₁₃	#97	1	4	yes	—
123	C₄×D₁₃	C₂×C₄²	1	4	yes	—
124	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
125	C₈×C₁₃	—	2	2	no	—
126	C₈×C₁₃	C₂×C₄²	1	2	yes	—
127	C₈×C₁₃	C₂³×C₄	1	2	yes	—
128	#1055	—	2	2	no	—
129	#1055	C₂×C₄²	1	2	yes	—
130	#1055	C₂×C₄²	1	2	yes	—
131	C₂²×M₁₆	—	13	1	no	—
132	C₂³×C₈	—	13	1	no	—
133	C₂×#117	—	13	1	no	—
134	C₂×M₃₂	—	13	2	no	—
135	C₂×M₃₂	—	13	8	no	—
136	C₂×M₃₂	—	13	8	no	—
137	C₂×M₃₂	—	13	4	no	—
138	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
139	C₂²×C₁₆	—	13	4	no	—
140	#405	—	13	4	no	—
141	#405	—	13	4	no	—
142	C₂×#97	—	13	1	no	—
143	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
144	C₂×C₄×C₈	—	13	1	no	—
145	C₂×C₄×C₈	—	13	1	no	—
146	#347	—	13	8	no	—
147	#347	—	13	4	no	—
148	#347	C₂×D₁₃	1	4	yes	complemented
149	C₂²×C₁₃	—	2	2	no	—
150	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
151	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
152	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
153	C₂×D₁₃	—	2	4	no	—
154	C₂×D₁₃	—	4	2	no	—
155	C₂×D₁₃	—	4	2	no	—
156	C₂×D₁₃	C₂×#97	1	4	yes	—
157	C₄×C₁₃	—	4	2	no	—
158	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
159	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
160	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
161	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
162	Dic₁₃	—	4	2	no	—
163	Dic₁₃	C₂×#97	1	4	yes	—
164	C₂³×C₄	—	13	1	no	—
165	C₂×M₁₆	—	13	4	no	—
166	C₂×M₁₆	—	26	2	no	—
167	C₂×M₁₆	—	26	2	no	—
168	C₂²×C₈	—	13	1	no	—
169	C₂²×C₈	—	13	2	no	—
170	C₂²×C₈	—	13	2	no	—
171	C₂²×C₈	—	13	4	no	—
172	C₂²×C₈	—	13	2	no	—
173	C₂²×C₈	—	13	2	no	—
174	C₂²×C₈	—	13	1	no	—
175	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
176	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
177	#117	—	13	4	no	—
178	#117	—	26	2	no	—
179	C₂×C₄⋊C₄	—	26	1	no	—
180	C₂×C₂²⋊C₄	—	26	1	no	—
181	C₂×C₄²	—	13	1	no	—
182	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
183	M₃₂	—	13	4	no	—
184	M₃₂	—	13	4	no	—
185	M₃₂	—	13	16	no	—
186	M₃₂	C₄×D₁₃	1	4	yes	—
187	M₃₂	C₂²×D₁₃	1	4	yes	—
188	C₂×C₁₆	—	13	4	no	—
189	C₂×C₁₆	—	13	16	no	—
190	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
191	#97	—	13	2	no	—
192	#97	—	13	2	no	—
193	#97	C₄×D₁₃	1	2	yes	—
194	#97	C₂²×D₁₃	1	2	yes	—
195	C₄×C₈	—	13	4	no	—
196	C₄×C₈	—	13	4	no	—
197	C₂×C₁₃	—	2	1	no	—
198	C₂×C₁₃	—	2	1	no	—
199	C₂×C₁₃	#2110	1	2	yes	complemented
200	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
201	D₁₃	—	2	4	no	—
202	C₂⁴	—	13	1	no	—
203	C₂²×C₄	—	2	1	no	—
204	C₂²×C₄	—	13	1	no	—
205	C₂²×C₄	—	13	2	no	—
206	C₂²×C₄	—	13	2	no	—
207	C₂²×C₄	—	13	2	no	—
208	C₂²×C₄	—	13	2	no	—
209	C₂²×C₄	—	13	2	no	—
210	C₂²×C₄	—	13	2	no	—
211	C₂²×C₄	—	26	1	no	—
212	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
213	M₁₆	—	26	8	no	—
214	C₂×C₈	—	2	1	no	—
215	C₂×C₈	—	2	1	no	—
216	C₂×C₈	—	13	2	no	—
217	C₂×C₈	—	13	1	no	—
218	C₂×C₈	—	13	1	no	—
219	C₂×C₈	—	13	2	no	—
220	C₂×C₈	—	13	4	no	—
221	C₂×C₈	—	13	4	no	—
222	C₂×C₈	—	13	4	no	—
223	C₂×C₈	—	13	4	no	—
224	C₂×C₈	—	13	2	no	—
225	C₂×C₈	—	26	1	no	—
226	C₂×C₈	—	26	1	no	—
227	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
228	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
229	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
230	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
231	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
232	C₄⋊C₄	—	26	4	no	—
233	C₂²⋊C₄	—	26	4	no	—
234	C₄²	—	2	1	no	—
235	C₄²	—	13	2	no	—
236	C₄²	—	26	1	no	—
237	C₄²	C₂×C₄×D₁₃	1	2	yes	—
238	C₁₆	—	13	8	no	—
239	C₁₆	C₂×C₄×D₁₃	1	8	yes	—
240	C₁₃	C₂×#2110	1	1	yes	characteristic, complemented, Sylow
241	C₂³	—	13	2	no	—
242	C₂³	—	13	2	no	—
243	C₂³	—	13	2	no	—
244	C₂³	—	52	2	no	—
245	C₂³	M₁₆×D₁₃	1	1	yes	characteristic
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	13	2	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	13	2	no	—
251	C₂×C₄	—	13	4	no	—
252	C₂×C₄	—	13	4	no	—
253	C₂×C₄	—	13	4	no	—
254	C₂×C₄	—	13	4	no	—
255	C₂×C₄	—	26	2	no	—
256	C₂×C₄	—	52	2	no	—
257	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
258	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
259	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
260	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
261	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
262	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
263	C₈	—	2	2	no	—
264	C₈	—	13	2	no	—
265	C₈	—	13	2	no	—
266	C₈	—	26	2	no	—
267	C₈	C₄²×D₁₃	1	2	yes	—
268	C₈	C₂²×C₄×D₁₃	1	2	yes	—
269	C₂²	—	2	2	no	—
270	C₂²	—	13	4	no	—
271	C₂²	—	26	4	no	—
272	C₂²	—	52	2	no	—
273	C₂²	—	52	2	no	—
274	C₂²	D₁₃×#97	1	1	yes	characteristic
275	C₂²	D₁₃×#97	1	1	yes	characteristic
276	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
277	C₄	—	4	2	no	—
278	C₄	—	13	4	no	—
279	C₄	—	52	2	no	—
280	C₄	D₁₃×#97	1	1	yes	characteristic
281	C₄	D₁₃×#97	1	1	yes	characteristic
282	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
283	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
284	C₂	—	2	1	no	—
285	C₂	—	2	1	no	—
286	C₂	—	26	4	no	—
287	C₂	#13116439	1	2	yes	direct product factor
288	C₂	C₂×D₁₃×#97	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₃
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#347	C₂
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#347	D₁₃
hypocenter	C₁₃	C₂×#2110
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#347

Complements

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

N	H ≅ G/N	type
3. #13116439	C₂	direct (N × H)
4. C₂×#11718058	C₂	semidirect
5. C₂×#11718104	C₂	semidirect
6. C₂×C₁₃×#347	C₂	semidirect
16. D₁₃×M₃₂	C₄	semidirect
18. C₂×#88038	C₄	semidirect
19. C₂×C₁₆×D₁₃	C₄	semidirect
22. C₁₃×#347	C₂²	semidirect
23. #11718104	C₂²	semidirect
24. #11718058	C₂²	semidirect
56. #88038	C₂×C₄	semidirect
57. C₁₆×D₁₃	C₂×C₄	semidirect
102. C₂×#347	D₁₃	semidirect
148. #347	C₂×D₁₃	semidirect
199. C₂×C₁₃	#2110	semidirect
240. C₁₃	C₂×#2110	semidirect
287. C₂	#13116439	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×#11718369	2
#13116439	2
C₂×#11718058	2
C₂×#11718104	2
C₂×C₁₃×#347	2
C₂×#2110	13

Subgroups — C2×#13116439 #16015575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116439 #16015575