Subgroups — C₂×#13130393 #16794930

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719129	C₂	1	2	yes	maximal
2	#13130393	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718256	C₂	1	2	yes	maximal, complemented
4	C₂×#11718254	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#6122	—	2	2	no	—
7	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂³×#1055	C₄	1	1	yes	characteristic
10	#11719129	—	2	4	no	—
11	#11719129	C₂²	1	8	yes	—
12	C₂×#88112	—	2	2	no	—
13	C₂×C₄⋊#1057	C₂²	1	4	yes	—
14	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
16	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₁₃	C₂²	1	4	yes	—
20	#11718256	C₂²	1	8	yes	complemented
21	#11718254	C₂²	1	8	yes	complemented
22	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×Dic₁₃	D₄	1	1	yes	characteristic
24	C₂³×Dic₁₃	Q₈	1	1	yes	characteristic
25	C₂×#6122	—	2	8	no	—
26	C₂×#6122	—	4	8	no	—
27	C₂²×#1057	—	2	4	no	—
28	C₂²×C₈×C₁₃	—	2	4	no	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
36	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
37	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
40	C₂²×#1055	—	2	4	no	—
41	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
42	C₂²×#1055	C₂×C₄	1	4	yes	—
43	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
44	#88112	—	2	8	no	—
45	C₄⋊#1057	—	2	4	no	—
46	C₄⋊#1057	C₂³	1	8	yes	—
47	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
48	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
49	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
50	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
51	C₈×Dic₁₃	C₂³	1	2	yes	—
52	C₈×Dic₁₃	C₂³	1	2	yes	—
53	C₂×#1567	—	13	1	no	maximal, Sylow
54	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×Dic₁₃	—	2	4	no	—
62	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
63	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
64	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×Dic₁₃	D₈	1	4	yes	—
67	C₂²×Dic₁₃	Q₁₆	1	4	yes	—
68	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
70	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
71	C₂²×Dic₁₃	C₂×Q₈	1	2	yes	—
72	#6122	—	4	16	no	—
73	C₂×#1057	—	2	8	no	—
74	C₂×#1057	—	4	8	no	—
75	C₂×C₈×C₁₃	—	2	2	no	—
76	C₂×C₈×C₁₃	—	2	8	no	—
77	C₂×C₈×C₁₃	M₁₆	1	4	yes	complemented
78	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
80	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
81	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
82	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
83	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
85	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
86	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
87	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
88	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
90	C₂×#1055	—	2	2	no	—
91	C₂×#1055	—	2	8	no	—
92	C₂×#1055	M₁₆	1	4	yes	complemented
93	C₂×#1055	C₂²×C₄	1	2	yes	—
94	C₂×#1055	C₂²×C₄	1	2	yes	—
95	C₂×#423	—	13	2	no	—
96	C₂²×C₄×C₈	—	13	1	no	—
97	#1567	—	13	8	no	—
98	C₂×#335	—	13	2	no	—
99	C₂×#335	—	13	2	no	—
100	C₂³×C₁₃	—	2	2	no	—
101	C₂³×C₁₃	—	2	2	no	—
102	C₂³×C₁₃	#107	1	4	yes	—
103	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
104	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	—	2	4	no	—
109	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
110	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
112	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
113	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
114	C₂×Dic₁₃	—	2	2	no	—
115	C₂×Dic₁₃	—	2	4	no	—
116	C₂×Dic₁₃	—	2	4	no	—
117	C₂×Dic₁₃	#107	1	8	yes	—
118	C₂×Dic₁₃	#107	1	4	yes	—
119	C₂×Dic₁₃	#108	1	4	yes	—
120	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
125	C₂×Dic₁₃	C₂×D₈	1	4	yes	—
126	C₂×Dic₁₃	C₂×Q₁₆	1	4	yes	—
127	C₂×Dic₁₃	C₂×Q₁₆	1	2	yes	—
128	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
129	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
130	#1057	—	4	8	no	—
131	C₈×C₁₃	—	2	2	no	—
132	C₈×C₁₃	C₂×M₁₆	1	4	yes	complemented
133	#1055	—	2	2	no	—
134	#1055	C₂×M₁₆	1	4	yes	complemented
135	C₂²×M₁₆	—	26	2	no	—
136	C₂³×C₈	—	13	1	no	—
137	C₂³×C₈	#261	1	1	yes	characteristic
138	C₂²×C₄²	—	13	1	no	—
139	#423	—	13	8	no	—
140	#423	—	26	4	no	—
141	C₂×C₄⋊C₈	—	13	4	no	—
142	C₂×C₄⋊C₈	—	26	2	no	—
143	C₂×C₄×C₈	—	13	1	no	—
144	C₂×C₄×C₈	—	13	1	no	—
145	C₂×C₄×C₈	—	13	4	no	—
146	C₂×C₄×C₈	—	13	1	no	—
147	C₂×C₄×C₈	—	13	4	no	—
148	C₂×C₄×C₈	—	13	1	no	—
149	#335	—	13	8	no	—
150	#335	—	13	8	no	—
151	C₂²×C₁₃	—	2	8	no	—
152	C₂²×C₁₃	—	2	2	no	—
153	C₂²×C₁₃	—	2	2	no	—
154	C₂²×C₁₃	#423	1	2	yes	—
155	C₂²×C₁₃	C₂×#107	1	4	yes	—
156	C₂²×C₁₃	C₂×#107	1	2	yes	—
157	C₂²×C₁₃	C₂×#108	1	2	yes	—
158	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₄×C₁₃	—	2	2	no	—
160	C₄×C₁₃	#423	1	2	yes	—
161	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
162	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
163	Dic₁₃	—	2	1	no	—
164	Dic₁₃	—	2	1	no	—
165	Dic₁₃	C₂×#107	1	2	yes	—
166	Dic₁₃	C₂×#107	1	4	yes	—
167	Dic₁₃	C₂×#108	1	4	yes	—
168	Dic₁₃	C₂²×D₈	1	1	yes	characteristic
169	Dic₁₃	C₂²×Q₁₆	1	1	yes	characteristic
170	C₂³×C₄	—	13	1	no	—
171	C₂³×C₄	—	13	1	no	—
172	C₂³×C₄	C₂×#261	1	1	yes	characteristic
173	C₂×M₁₆	—	26	8	no	—
174	C₂×M₁₆	—	52	8	no	—
175	C₂²×C₈	—	2	4	no	—
176	C₂²×C₈	—	13	1	no	—
177	C₂²×C₈	—	13	4	no	—
178	C₂²×C₈	—	13	1	no	—
179	C₂²×C₈	—	26	4	no	—
180	C₂²×C₈	—	26	4	no	—
181	C₂²×C₈	C₂×#261	1	1	yes	characteristic
182	C₂²×C₈	C₂×#261	1	4	yes	—
183	C₂²×C₈	C₂×#261	1	1	yes	characteristic
184	C₂×C₄²	—	13	1	no	—
185	C₂×C₄²	—	13	2	no	—
186	C₂×C₄²	—	13	2	no	—
187	C₂×C₄²	—	13	1	no	—
188	C₂×C₄²	—	13	2	no	—
189	C₂×C₄²	—	13	1	no	—
190	C₂×C₄²	—	13	1	no	—
191	C₂×C₄²	—	13	2	no	—
192	C₄⋊C₈	—	13	8	no	—
193	C₄⋊C₈	—	26	4	no	—
194	C₄⋊C₈	—	26	8	no	—
195	C₄×C₈	—	13	2	no	—
196	C₄×C₈	—	13	2	no	—
197	C₄×C₈	—	13	2	no	—
198	C₄×C₈	—	13	4	no	—
199	C₄×C₈	—	13	4	no	—
200	C₄×C₈	—	13	2	no	—
201	C₂×C₁₃	—	2	4	no	—
202	C₂×C₁₃	#1567	1	4	yes	complemented
203	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
204	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
205	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
206	C₂⁴	C₄⋊#261	1	1	yes	characteristic
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	13	4	no	—
210	C₂²×C₄	—	13	4	no	—
211	C₂²×C₄	—	13	2	no	—
212	C₂²×C₄	—	13	2	no	—
213	C₂²×C₄	—	13	1	no	—
214	C₂²×C₄	—	13	1	no	—
215	C₂²×C₄	—	13	1	no	—
216	C₂²×C₄	—	13	2	no	—
217	C₂²×C₄	—	13	2	no	—
218	C₂²×C₄	—	13	1	no	—
219	C₂²×C₄	—	26	4	no	—
220	C₂²×C₄	C₄⋊#261	1	2	yes	—
221	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
222	C₂²×C₄	C₂²×#261	1	2	yes	—
223	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
224	M₁₆	—	52	16	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	8	no	—
227	C₂×C₈	—	13	4	no	—
228	C₂×C₈	—	13	2	no	—
229	C₂×C₈	—	13	2	no	—
230	C₂×C₈	—	26	8	no	—
231	C₂×C₈	—	26	2	no	—
232	C₂×C₈	—	26	8	no	—
233	C₂×C₈	—	52	8	no	—
234	C₂×C₈	#6122	1	4	yes	complemented
235	C₂×C₈	C₂²×#261	1	2	yes	—
236	C₂×C₈	C₂²×#261	1	2	yes	—
237	C₄²	—	13	2	no	—
238	C₄²	—	13	1	no	—
239	C₄²	—	13	2	no	—
240	C₄²	—	13	2	no	—
241	C₄²	—	13	2	no	—
242	C₄²	—	13	2	no	—
243	C₄²	—	13	1	no	—
244	C₄²	—	13	1	no	—
245	C₄²	—	13	2	no	—
246	C₄²	—	13	1	no	—
247	C₁₃	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
248	C₂³	—	2	2	no	—
249	C₂³	—	2	2	no	—
250	C₂³	#88102	1	4	yes	—
251	C₂³	C₂×C₄⋊#261	1	2	yes	—
252	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	13	2	no	—
258	C₂×C₄	—	13	4	no	—
259	C₂×C₄	—	13	8	no	—
260	C₂×C₄	—	13	4	no	—
261	C₂×C₄	—	13	4	no	—
262	C₂×C₄	—	13	2	no	—
263	C₂×C₄	—	13	4	no	—
264	C₂×C₄	—	13	1	no	—
265	C₂×C₄	—	13	2	no	—
266	C₂×C₄	—	13	1	no	—
267	C₂×C₄	—	13	2	no	—
268	C₂×C₄	—	13	1	no	—
269	C₂×C₄	—	13	1	no	—
270	C₂×C₄	—	26	4	no	—
271	C₂×C₄	—	26	4	no	—
272	C₂×C₄	—	26	2	no	—
273	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
274	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
275	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
276	C₂×C₄	C₂×#6122	1	2	yes	—
277	C₂×C₄	C₂³×#261	1	1	yes	characteristic
278	C₈	—	2	2	no	—
279	C₈	—	13	4	no	—
280	C₈	—	26	2	no	—
281	C₈	—	52	8	no	—
282	C₈	C₂×#6122	1	4	yes	complemented
283	C₂²	—	2	8	no	—
284	C₂²	—	2	2	no	—
285	C₂²	—	2	2	no	—
286	C₂²	C₂×#88102	1	4	yes	—
287	C₂²	C₂×#88102	1	2	yes	—
288	C₂²	D₁₃⋊#108	1	2	yes	—
289	C₂²	#11719129	1	2	yes	—
290	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
291	C₄	—	2	2	no	—
292	C₄	—	13	1	no	—
293	C₄	—	13	1	no	—
294	C₄	—	13	2	no	—
295	C₄	—	13	4	no	—
296	C₄	—	13	4	no	—
297	C₄	—	26	1	no	—
298	C₄	—	26	1	no	—
299	C₄	#11719129	1	2	yes	—
300	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
301	C₄	C₂²×#6122	1	1	yes	characteristic
302	C₂	—	2	4	no	—
303	C₂	#13130393	1	4	yes	direct product factor
304	C₂	C₂×#11719129	1	1	yes	characteristic
305	C₂	C₂²×#88102	1	1	yes	characteristic
306	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂×#1567
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #13130393	C₂	direct (N × H)
3. C₂×#11718256	C₂	semidirect
4. C₂×#11718254	C₂	semidirect
20. #11718256	C₂²	semidirect
21. #11718254	C₂²	semidirect
77. C₂×C₈×C₁₃	M₁₆	semidirect
92. C₂×#1055	M₁₆	semidirect
132. C₈×C₁₃	C₂×M₁₆	semidirect
134. #1055	C₂×M₁₆	semidirect
202. C₂×C₁₃	#1567	semidirect
234. C₂×C₈	#6122	semidirect
247. C₁₃	C₂×#1567	semidirect
282. C₈	C₂×#6122	semidirect
303. C₂	#13130393	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×#11719129	2
#13130393	2
C₂×#11718256	2
C₂×#11718254	2
C₂²×C₈×Dic₁₃	2
C₂×#1567	13

Subgroups — C2×#13130393 #16794930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130393 #16794930