Subgroups — C₂×#13129676 #16779182

Order 3328.

678 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×#11719119	C₂	1	2	yes	maximal
2	#13129676	C₂	1	4	yes	maximal, direct product factor
3	C₂²×#88055	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂³×#1055	C₄	1	1	yes	characteristic
7	C₂×C₂²⋊#1057	C₄	1	4	yes	—
8	#11719119	—	2	2	no	—
9	#11719119	—	2	2	no	—
10	#11719119	C₄	1	4	yes	—
11	#11719119	C₂²	1	4	yes	—
12	C₂×C₄⋊#1057	—	2	2	no	—
13	C₂×C₄×#1057	—	2	2	no	—
14	C₂×#88055	—	2	2	no	—
15	C₂×#88055	—	2	2	no	—
16	C₂×#88055	C₄	1	2	yes	—
17	C₂×#88055	C₂²	1	2	yes	—
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
20	C₂²×#1057	—	2	4	no	—
21	C₂²×C₈×C₁₃	—	2	1	no	—
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₂²×C₈×C₁₃	—	2	2	no	—
24	C₂²×C₈×C₁₃	C₈	1	4	yes	complemented
25	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
31	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
32	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
33	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
35	C₂²×#1055	—	2	1	no	—
36	C₂²×#1055	—	2	1	no	—
37	C₂²×#1055	—	2	2	no	—
38	C₂²×#1055	C₈	1	4	yes	complemented
39	C₂²×#1055	C₂×C₄	1	2	yes	—
40	C₂²⋊#1057	—	2	4	no	—
41	C₂²⋊#1057	C₂×C₄	1	8	yes	—
42	C₄⋊#1057	—	2	4	no	—
43	C₄⋊#1057	—	2	4	no	—
44	C₄×#1057	—	2	4	no	—
45	C₄×#1057	—	2	4	no	—
46	#88055	—	2	4	no	—
47	#88055	—	2	4	no	—
48	C₂×#1281	—	13	1	no	maximal, Sylow
49	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
58	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×Dic₁₃	—	4	4	no	—
61	C₂²×Dic₁₃	C₄²	1	2	yes	—
62	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
65	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
66	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
67	C₂×#1057	—	2	8	no	—
68	C₂×#1057	—	4	8	no	—
69	C₂×C₈×C₁₃	—	2	4	no	—
70	C₂×C₈×C₁₃	—	2	4	no	—
71	C₂×C₈×C₁₃	—	2	2	no	—
72	C₂×C₈×C₁₃	—	2	2	no	—
73	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	complemented
74	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
75	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
76	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
77	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
80	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
81	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
82	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
83	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
84	C₂×#1055	—	2	4	no	—
85	C₂×#1055	—	2	4	no	—
86	C₂×#1055	—	2	2	no	—
87	C₂×#1055	—	2	2	no	—
88	C₂×#1055	C₂×C₈	1	4	yes	complemented
89	C₂×#431	—	13	2	no	—
90	C₂²×#97	—	13	1	no	—
91	#1281	—	13	4	no	—
92	C₂³×C₁₃	—	2	4	no	—
93	C₂³×C₁₃	#95	1	1	yes	characteristic
94	C₂³×C₁₃	#95	1	1	yes	characteristic
95	C₂³×C₁₃	C₄×C₈	1	2	yes	—
96	C₂³×C₁₃	#97	1	2	yes	—
97	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
101	C₂×C₄×C₁₃	#97	1	2	yes	—
102	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
103	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
104	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
105	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
106	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
107	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
108	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
109	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
110	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
113	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
114	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
116	C₂×Dic₁₃	—	2	4	no	—
117	C₂×Dic₁₃	—	2	4	no	—
118	C₂×Dic₁₃	—	4	2	no	—
119	C₂×Dic₁₃	—	4	2	no	—
120	C₂×Dic₁₃	—	4	2	no	—
121	C₂×Dic₁₃	—	4	2	no	—
122	C₂×Dic₁₃	#95	1	2	yes	—
123	C₂×Dic₁₃	#95	1	2	yes	—
124	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	2	yes	—
125	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
126	#1057	—	4	8	no	—
127	C₈×C₁₃	—	2	4	no	—
128	#1055	—	2	4	no	—
129	C₂³×C₈	—	13	1	no	—
130	C₂³×C₈	#261	1	1	yes	characteristic
131	C₂²×C₄²	—	13	1	no	—
132	#431	—	13	4	no	—
133	#431	—	13	4	no	—
134	#431	—	26	2	no	—
135	#431	—	26	2	no	—
136	C₂×C₄⋊C₈	—	26	2	no	—
137	C₂×C₂²⋊C₈	—	13	4	no	—
138	C₂×#97	—	13	2	no	—
139	C₂×#97	—	13	2	no	—
140	C₂×#97	—	26	2	no	—
141	C₂×#97	—	26	2	no	—
142	C₂×C₄×C₈	—	26	2	no	—
143	C₂²×C₁₃	—	2	4	no	—
144	C₂²×C₁₃	—	2	4	no	—
145	C₂²×C₁₃	—	2	2	no	—
146	C₂²×C₁₃	—	2	2	no	—
147	C₂²×C₁₃	#336	1	2	yes	—
148	C₂²×C₁₃	#336	1	2	yes	—
149	C₂²×C₁₃	#344	1	4	yes	—
150	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
151	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
152	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
153	C₄×C₁₃	#336	1	2	yes	—
154	C₄×C₁₃	#336	1	2	yes	—
155	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
156	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
157	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
158	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
159	Dic₁₃	—	2	2	no	—
160	Dic₁₃	—	2	2	no	—
161	Dic₁₃	—	2	2	no	—
162	Dic₁₃	—	2	2	no	—
163	C₂³×C₄	—	13	2	no	—
164	C₂³×C₄	C₂×#261	1	1	yes	characteristic
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	13	4	no	—
169	C₂²×C₈	—	13	2	no	—
170	C₂²×C₈	—	26	2	no	—
171	C₂²×C₈	—	26	1	no	—
172	C₂²×C₈	—	26	1	no	—
173	C₂²×C₈	—	26	4	no	—
174	C₂²×C₈	#1057	1	4	yes	complemented
175	C₂²×C₈	C₂×#261	1	2	yes	—
176	C₂×C₄²	—	13	2	no	—
177	C₂×C₄²	—	13	1	no	—
178	C₂×C₄²	—	13	1	no	—
179	C₂×C₄²	—	13	1	no	—
180	C₂×C₄²	—	13	1	no	—
181	C₂×C₄²	—	13	2	no	—
182	C₂×C₄²	—	13	2	no	—
183	C₂×C₄²	—	13	1	no	—
184	C₂×C₄²	—	13	1	no	—
185	C₄⋊C₈	—	26	4	no	—
186	C₄⋊C₈	—	26	4	no	—
187	C₂²⋊C₈	—	13	8	no	—
188	C₂²⋊C₈	—	26	4	no	—
189	#97	—	26	4	no	—
190	#97	—	26	4	no	—
191	C₄×C₈	—	26	4	no	—
192	C₄×C₈	—	26	4	no	—
193	C₂×C₁₃	—	2	2	no	—
194	C₂×C₁₃	—	2	1	no	—
195	C₂×C₁₃	—	2	1	no	—
196	C₂×C₁₃	#1281	1	4	yes	complemented
197	C₂×C₁₃	C₂×#336	1	1	yes	characteristic
198	C₂×C₁₃	C₂×#344	1	2	yes	—
199	C₂⁴	C₄×#261	1	1	yes	characteristic
200	C₂²×C₄	—	13	2	no	—
201	C₂²×C₄	—	13	2	no	—
202	C₂²×C₄	—	13	2	no	—
203	C₂²×C₄	—	13	2	no	—
204	C₂²×C₄	—	13	2	no	—
205	C₂²×C₄	—	13	2	no	—
206	C₂²×C₄	—	52	4	no	—
207	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
208	C₂²×C₄	#6118	1	2	yes	—
209	C₂²×C₄	C₄×#261	1	1	yes	characteristic
210	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
211	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
212	C₂²×C₄	C₂×#1057	1	2	yes	—
213	C₂²×C₄	#6122	1	2	yes	—
214	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
215	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
216	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
217	C₂×C₈	—	2	4	no	—
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	—	2	2	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	13	4	no	—
222	C₂×C₈	—	26	4	no	—
223	C₂×C₈	—	26	4	no	—
224	C₂×C₈	—	26	2	no	—
225	C₂×C₈	—	26	2	no	—
226	C₂×C₈	—	26	8	no	—
227	C₂×C₈	—	52	8	no	—
228	C₂×C₈	C₂×#1057	1	4	yes	complemented
229	C₄²	—	13	2	no	—
230	C₄²	—	13	2	no	—
231	C₄²	—	13	2	no	—
232	C₄²	—	13	2	no	—
233	C₄²	—	13	1	no	—
234	C₄²	—	13	1	no	—
235	C₄²	—	13	1	no	—
236	C₄²	—	13	1	no	—
237	C₄²	—	13	2	no	—
238	C₄²	—	13	2	no	—
239	C₁₃	C₂×#1281	1	1	yes	characteristic, complemented, Sylow
240	C₂³	—	2	4	no	—
241	C₂³	C₄×#1057	1	2	yes	—
242	C₂³	#88110	1	2	yes	—
243	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
244	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
245	C₂³	C₂×C₄×#261	1	1	yes	characteristic
246	C₂×C₄	—	13	2	no	—
247	C₂×C₄	—	13	2	no	—
248	C₂×C₄	—	13	2	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	26	4	no	—
251	C₂×C₄	—	26	4	no	—
252	C₂×C₄	—	52	2	no	—
253	C₂×C₄	—	52	2	no	—
254	C₂×C₄	—	52	2	no	—
255	C₂×C₄	—	52	2	no	—
256	C₂×C₄	C₄×#1057	1	2	yes	—
257	C₂×C₄	C₄⋊#1057	1	2	yes	—
258	C₂×C₄	C₄⋊#1057	1	2	yes	—
259	C₂×C₄	#88110	1	2	yes	—
260	C₂×C₄	#88111	1	2	yes	—
261	C₂×C₄	#88111	1	2	yes	—
262	C₂×C₄	#88112	1	2	yes	—
263	C₂×C₄	#88112	1	2	yes	—
264	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
265	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
266	C₂×C₄	C₂²⋊#1057	1	2	yes	—
267	C₂×C₄	C₂²⋊#1057	1	2	yes	—
268	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
269	C₂×C₄	C₂×#6118	1	1	yes	characteristic
270	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
271	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
272	C₂×C₄	C₂×#6122	1	1	yes	characteristic
273	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
274	C₈	—	2	4	no	—
275	C₈	—	26	4	no	—
276	C₈	—	52	8	no	—
277	C₂²	—	2	2	no	—
278	C₂²	—	2	2	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	2	4	no	—
281	C₂²	#11718266	1	4	yes	—
282	C₂²	#11718290	1	2	yes	—
283	C₂²	#11718290	1	2	yes	—
284	C₂²	C₂×C₄×#1057	1	1	yes	characteristic
285	C₂²	C₂×#88110	1	1	yes	characteristic
286	C₂²	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
287	C₄	—	26	2	no	—
288	C₄	—	26	2	no	—
289	C₄	—	26	2	no	—
290	C₄	—	26	2	no	—
291	C₄	#11718290	1	2	yes	—
292	C₄	#11718290	1	2	yes	—
293	C₄	C₂×C₄⋊#1057	1	1	yes	characteristic
294	C₄	C₂×#88111	1	1	yes	characteristic
295	C₄	C₂×#88112	1	1	yes	characteristic
296	C₄	C₂×C₂²⋊#1057	1	1	yes	characteristic
297	C₂	—	2	2	no	—
298	C₂	—	2	1	no	—
299	C₂	—	2	1	no	—
300	C₂	#13129676	1	4	yes	direct product factor
301	C₂	C₂×#11718290	1	1	yes	characteristic
302	C₂	C₂×#11718266	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#261
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂³×C₁₃	#95
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₂×C₄×Dic₁₃	C₂³
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂×#1281
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #13129676	C₂	direct (N × H)
24. C₂²×C₈×C₁₃	C₈	semidirect
38. C₂²×#1055	C₈	semidirect
73. C₂×C₈×C₁₃	C₂×C₈	semidirect
88. C₂×#1055	C₂×C₈	semidirect
174. C₂²×C₈	#1057	semidirect
196. C₂×C₁₃	#1281	semidirect
228. C₂×C₈	C₂×#1057	semidirect
239. C₁₃	C₂×#1281	semidirect
300. C₂	#13129676	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×#11719119	2
#13129676	2
C₂²×#88055	2
C₂×#1281	13

Subgroups — C2×#13129676 #16779182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129676 #16779182