Subgroups — C₂×#13130032 #16792566

Order 3328.

1182 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×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13130032	C₂	1	8	yes	maximal, direct product factor
4	C₂×#1057⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
7	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
8	C₂²×C₈×D₁₃	C₄	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×#1057	C₄	1	2	yes	—
11	C₂×C₄×#1057	C₄	1	2	yes	—
12	C₂×C₄×#1057	C₂²	1	2	yes	—
13	C₂×C₄×#1057	C₂²	1	2	yes	—
14	C₄×D₁₃⋊C₈	C₄	1	4	yes	—
15	C₄×D₁₃⋊C₈	C₄	1	4	yes	—
16	C₄×D₁₃⋊C₈	C₂²	1	4	yes	—
17	C₄×D₁₃⋊C₈	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
20	C₂×C₄×#1055	C₄	1	1	yes	characteristic
21	C₄×C₈×D₁₃	C₄	1	4	yes	—
22	C₄×C₈×D₁₃	C₂²	1	4	yes	—
23	#1057⋊C₈	C₂²	1	16	yes	complemented
24	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×#1057	C₂×C₄	1	4	yes	—
28	C₂²×#1057	C₂×C₄	1	4	yes	—
29	C₂×D₁₃⋊C₈	—	2	8	no	—
30	C₂×D₁₃⋊C₈	C₈	1	16	yes	complemented
31	C₂×D₁₃⋊C₈	C₂×C₄	1	8	yes	—
32	C₂×D₁₃⋊C₈	C₂×C₄	1	8	yes	—
33	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
38	C₂²×#1055	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	—	2	8	no	—
40	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
41	C₄²×D₁₃	C₂×C₄	1	2	yes	—
42	C₄²×D₁₃	C₂×C₄	1	2	yes	—
43	C₄²×D₁₃	C₂×C₄	1	2	yes	—
44	C₄²×D₁₃	C₂³	1	2	yes	—
45	C₄×#1057	C₂×C₄	1	4	yes	—
46	C₄×#1057	C₂×C₄	1	4	yes	—
47	C₄×#1057	C₂×C₄	1	8	yes	—
48	C₄×#1057	C₂×C₄	1	8	yes	—
49	C₄×#1057	C₂³	1	4	yes	—
50	C₄×#1057	C₂³	1	4	yes	—
51	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
52	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
53	C₈×Dic₁₃	C₂³	1	4	yes	—
54	C₄×#1055	C₂×C₄	1	4	yes	—
55	C₂²×#322	—	13	1	no	maximal, Sylow
56	C₂³×D₁₃	C₄²	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
61	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×D₁₃	C₄²	1	2	yes	—
64	C₂×C₄×D₁₃	C₄²	1	2	yes	—
65	C₂×C₄×D₁₃	C₄²	1	2	yes	—
66	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
67	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
68	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
69	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
70	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
71	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
72	C₂×#1057	—	2	8	no	—
73	C₂×#1057	C₂×C₈	1	16	yes	complemented
74	C₂×#1057	C₂²×C₄	1	8	yes	—
75	C₂×#1057	C₂²×C₄	1	8	yes	—
76	D₁₃⋊C₈	—	2	16	no	—
77	D₁₃⋊C₈	C₂×C₈	1	32	yes	complemented
78	C₂×C₈×C₁₃	—	2	4	no	—
79	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
80	C₄²×C₁₃	C₄²	1	2	yes	—
81	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
82	C₄×Dic₁₃	C₄²	1	2	yes	—
83	C₄×Dic₁₃	C₄²	1	2	yes	—
84	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
88	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
89	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
90	C₂×#1055	—	2	4	no	—
91	C₂×#1055	C₂²×C₄	1	4	yes	—
92	C₈×D₁₃	—	2	16	no	—
93	C₂²×C₄×C₈	—	13	1	no	—
94	C₂²×C₄×C₈	—	13	1	no	—
95	C₂²×C₄×C₈	—	13	1	no	—
96	C₂×#322	—	13	4	no	—
97	C₂×#322	—	13	8	no	—
98	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
99	C₂²×D₁₃	C₄×C₈	1	4	yes	—
100	C₂²×D₁₃	#97	1	4	yes	—
101	C₂²×D₁₃	#97	1	4	yes	—
102	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
103	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
104	C₂×C₄×C₁₃	#97	1	4	yes	—
105	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
106	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
107	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
109	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
110	C₂×Dic₁₃	#97	1	4	yes	—
111	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
112	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
113	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
114	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
115	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
116	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
117	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
118	C₄×D₁₃	C₄×C₈	1	8	yes	—
119	C₄×D₁₃	#97	1	8	yes	—
120	C₄×D₁₃	#97	1	8	yes	—
121	C₄×D₁₃	C₂²×C₈	1	8	yes	—
122	C₄×D₁₃	C₂×M₁₆	1	8	yes	—
123	C₄×D₁₃	C₂×M₁₆	1	8	yes	—
124	#1057	—	2	8	no	—
125	#1057	C₂²×C₈	1	16	yes	complemented
126	C₈×C₁₃	—	2	4	no	—
127	#1055	—	2	4	no	—
128	C₂³×C₈	—	13	2	no	—
129	C₂³×C₈	—	13	2	no	—
130	C₂³×C₈	—	13	2	no	—
131	C₂²×C₄²	—	13	1	no	—
132	C₂×C₄×C₈	—	13	4	no	—
133	C₂×C₄×C₈	—	13	4	no	—
134	C₂×C₄×C₈	—	13	4	no	—
135	C₂×C₄×C₈	—	13	4	no	—
136	C₂×C₄×C₈	—	13	2	no	—
137	C₂×C₄×C₈	—	13	2	no	—
138	C₂×C₄×C₈	—	13	2	no	—
139	C₂×C₄×C₈	—	13	2	no	—
140	C₂×C₄×C₈	—	13	2	no	—
141	C₂×C₄×C₈	—	13	1	no	—
142	C₂×C₄×C₈	—	13	4	no	—
143	C₂×C₄×C₈	—	13	4	no	—
144	C₂×C₄×C₈	#261	1	1	yes	characteristic
145	#322	—	13	16	no	—
146	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
147	C₂²×C₁₃	C₂×#97	1	2	yes	—
148	C₂²×C₁₃	C₂×#97	1	2	yes	—
149	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
150	C₂×D₁₃	#322	1	16	yes	complemented
151	C₂×D₁₃	C₂×C₄×C₈	1	4	yes	—
152	C₂×D₁₃	C₂×#97	1	4	yes	—
153	C₂×D₁₃	C₂×#97	1	4	yes	—
154	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
155	C₄×C₁₃	C₂×#97	1	2	yes	—
156	C₄×C₁₃	C₂×#97	1	4	yes	—
157	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
158	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
159	Dic₁₃	C₂×#97	1	2	yes	—
160	Dic₁₃	C₂×#97	1	4	yes	—
161	Dic₁₃	C₂³×C₈	1	2	yes	—
162	Dic₁₃	C₂²×M₁₆	1	2	yes	—
163	C₂³×C₄	—	13	1	no	—
164	C₂³×C₄	—	13	1	no	—
165	C₂³×C₄	—	13	1	no	—
166	C₂²×C₈	—	13	8	no	—
167	C₂²×C₈	—	13	4	no	—
168	C₂²×C₈	—	13	16	no	—
169	C₂²×C₈	—	13	8	no	—
170	C₂²×C₈	—	13	4	no	—
171	C₂²×C₈	—	13	2	no	—
172	C₂²×C₈	—	13	8	no	—
173	C₂²×C₈	—	26	8	no	—
174	C₂²×C₈	—	26	8	no	—
175	C₂²×C₈	C₂×#261	1	2	yes	—
176	C₂×C₄²	—	13	1	no	—
177	C₂×C₄²	—	13	1	no	—
178	C₂×C₄²	—	13	1	no	—
179	C₂×C₄²	—	13	2	no	—
180	C₂×C₄²	—	13	2	no	—
181	C₂×C₄²	—	13	2	no	—
182	C₂×C₄²	—	13	2	no	—
183	C₂×C₄²	C₂×#261	1	1	yes	characteristic
184	C₄×C₈	—	13	4	no	—
185	C₄×C₈	—	13	8	no	—
186	C₄×C₈	—	13	4	no	—
187	C₄×C₈	—	13	8	no	—
188	C₄×C₈	—	13	4	no	—
189	C₄×C₈	—	13	4	no	—
190	C₄×C₈	—	13	4	no	—
191	C₄×C₈	—	13	4	no	—
192	C₄×C₈	—	13	4	no	—
193	C₄×C₈	C₂×#261	1	4	yes	—
194	C₂×C₁₃	C₂×#322	1	4	yes	complemented
195	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
196	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
197	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
198	D₁₃	C₂×#322	1	8	yes	complemented
199	C₂⁴	—	13	1	no	—
200	C₂²×C₄	—	13	1	no	—
201	C₂²×C₄	—	13	1	no	—
202	C₂²×C₄	—	13	1	no	—
203	C₂²×C₄	—	13	8	no	—
204	C₂²×C₄	—	13	8	no	—
205	C₂²×C₄	—	13	8	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	—	13	2	no	—
212	C₂²×C₄	C₄×#261	1	1	yes	characteristic
213	C₂²×C₄	C₄×#261	1	1	yes	characteristic
214	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
215	C₂×C₈	—	2	4	no	—
216	C₂×C₈	—	13	8	no	—
217	C₂×C₈	—	13	32	no	—
218	C₂×C₈	—	13	16	no	—
219	C₂×C₈	—	13	8	no	—
220	C₂×C₈	—	13	4	no	—
221	C₂×C₈	—	26	16	no	—
222	C₂×C₈	—	26	16	no	—
223	C₂×C₈	—	26	8	no	—
224	C₂×C₈	—	26	4	no	—
225	C₂×C₈	C₂²×#261	1	4	yes	—
226	C₄²	—	13	1	no	—
227	C₄²	—	13	1	no	—
228	C₄²	—	13	2	no	—
229	C₄²	—	13	2	no	—
230	C₄²	—	13	2	no	—
231	C₄²	—	13	2	no	—
232	C₄²	—	13	1	no	—
233	C₄²	—	13	1	no	—
234	C₄²	C₄×#261	1	2	yes	—
235	C₄²	C₂²×#261	1	2	yes	—
236	C₁₃	C₂²×#322	1	1	yes	characteristic, complemented, Sylow
237	C₂³	—	13	4	no	—
238	C₂³	—	13	4	no	—
239	C₂³	—	13	4	no	—
240	C₂³	—	13	2	no	—
241	C₂³	C₂×C₄×#261	1	1	yes	characteristic
242	C₂×C₄	—	13	4	no	—
243	C₂×C₄	—	13	4	no	—
244	C₂×C₄	—	13	4	no	—
245	C₂×C₄	—	13	1	no	—
246	C₂×C₄	—	13	1	no	—
247	C₂×C₄	—	13	1	no	—
248	C₂×C₄	—	13	1	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	13	8	no	—
251	C₂×C₄	—	13	8	no	—
252	C₂×C₄	—	13	8	no	—
253	C₂×C₄	—	13	8	no	—
254	C₂×C₄	—	13	8	no	—
255	C₂×C₄	—	13	8	no	—
256	C₂×C₄	C₈×#261	1	4	yes	—
257	C₂×C₄	#88100	1	4	yes	—
258	C₂×C₄	D₁₃⋊M₁₆	1	4	yes	—
259	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
260	C₂×C₄	C₂×C₄×#261	1	2	yes	—
261	C₂×C₄	C₂×C₄×#261	1	2	yes	—
262	C₂×C₄	C₂³×#261	1	1	yes	characteristic
263	C₈	—	2	4	no	—
264	C₈	—	13	16	no	—
265	C₈	—	26	8	no	—
266	C₈	—	26	4	no	—
267	C₂²	—	13	16	no	—
268	C₂²	—	13	4	no	—
269	C₂²	—	13	4	no	—
270	C₂²	—	13	4	no	—
271	C₂²	#11719047	1	2	yes	—
272	C₂²	C₂×C₈×#261	1	2	yes	—
273	C₂²	C₂×#88100	1	2	yes	—
274	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
275	C₄	—	13	2	no	—
276	C₄	—	13	2	no	—
277	C₄	—	13	2	no	—
278	C₄	—	13	2	no	—
279	C₄	—	13	4	no	—
280	C₄	#11719047	1	2	yes	—
281	C₄	C₂×C₈×#261	1	4	yes	—
282	C₄	C₂×#88100	1	4	yes	—
283	C₄	C₂×D₁₃⋊M₁₆	1	2	yes	—
284	C₂	—	13	8	no	—
285	C₂	#13130032	1	4	yes	direct product factor
286	C₂	C₂²×C₈×#261	1	1	yes	characteristic
287	C₂	C₂²×#88100	1	1	yes	characteristic
288	C₂	C₂×#11719047	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂²×#322
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #13130032	C₂	direct (N × H)
4. C₂×#1057⋊C₈	C₂	semidirect
23. #1057⋊C₈	C₂²	semidirect
30. C₂×D₁₃⋊C₈	C₈	semidirect
73. C₂×#1057	C₂×C₈	semidirect
77. D₁₃⋊C₈	C₂×C₈	semidirect
125. #1057	C₂²×C₈	semidirect
150. C₂×D₁₃	#322	semidirect
194. C₂×C₁₃	C₂×#322	semidirect
198. D₁₃	C₂×#322	semidirect
236. C₁₃	C₂²×#322	semidirect
285. C₂	#13130032	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×C₄×D₁₃⋊C₈	2
#13130032	2
C₂×#1057⋊C₈	2
C₂×C₄×C₈×D₁₃	2
C₂²×#322	13

Subgroups — C2×#13130032 #16792566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130032 #16792566