Subgroups — C₂×#13130757 #16798168

Order 3328.

1182 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×#11719059	C₂	1	2	yes	maximal
2	#13130757	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718265	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊#261	—	2	2	no	—
6	C₂²×C₄⋊#261	—	2	2	no	—
7	C₂²×C₄⋊#261	C₂²	1	4	yes	—
8	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719059	—	2	4	no	—
11	#11719059	C₂²	1	8	yes	—
12	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
13	C₂×C₈×Dic₁₃	C₄	1	2	yes	complemented
14	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
15	C₄×C₈×D₁₃	C₄	1	4	yes	complemented
16	C₄×C₈×D₁₃	C₂²	1	4	yes	—
17	#11718265	C₂²	1	16	yes	—
18	C₂³×#261	—	2	4	no	—
19	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
21	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊#261	—	2	16	no	—
23	C₂×C₄⋊#261	—	2	4	no	—
24	C₂×C₄⋊#261	—	2	8	no	—
25	C₂×C₄⋊#261	—	2	8	no	—
26	C₂×C₄⋊#261	—	4	8	no	—
27	C₂×C₄⋊#261	—	4	8	no	—
28	C₂×C₄⋊#261	C₂³	1	8	yes	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
33	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
34	C₂²×#1055	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₁₃	—	2	8	no	—
36	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
37	C₂×C₈×D₁₃	C₂³	1	4	yes	—
38	C₄²×D₁₃	C₂×C₄	1	2	yes	—
39	C₄²×D₁₃	D₄	1	2	yes	—
40	C₄²×D₁₃	Q₈	1	2	yes	—
41	C₄²×D₁₃	C₂³	1	2	yes	—
42	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
43	C₈×Dic₁₃	C₂×C₄	1	8	yes	complemented
44	C₄×#1055	C₂×C₄	1	4	yes	complemented
45	C₂×#1834	—	13	1	no	maximal, Sylow
46	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×#261	—	2	8	no	—
48	C₂²×#261	—	4	8	no	—
49	C₂²×#261	—	4	8	no	—
50	C₂²×#261	—	4	8	no	—
51	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
58	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×D₁₃	D₈	1	4	yes	—
60	C₂×C₄×D₁₃	SD₁₆	1	8	yes	—
61	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
62	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
65	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
66	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₄×D₁₃	#41	1	8	yes	—
68	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
69	C₄⋊#261	—	2	16	no	—
70	C₄⋊#261	—	4	8	no	—
71	C₄⋊#261	—	4	16	no	—
72	C₄⋊#261	—	4	16	no	—
73	C₂×C₈×C₁₃	—	2	4	no	—
74	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
75	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
76	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
77	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
78	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
79	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
80	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
81	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
82	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
83	C₂×#1055	—	2	4	no	—
84	C₂×#1055	C₂²×C₄	1	4	yes	—
85	C₈×D₁₃	—	2	8	no	—
86	C₈×D₁₃	—	2	8	no	—
87	C₂²×C₄×C₈	—	13	1	no	—
88	C₂×#384	—	13	2	no	—
89	#1834	—	13	8	no	—
90	C₂×#340	—	13	4	no	—
91	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂²×D₁₃	#124	1	4	yes	—
94	C₂²×D₁₃	C₂×D₈	1	2	yes	—
95	C₂²×D₁₃	C₂×SD₁₆	1	4	yes	—
96	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
97	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
98	C₂×#261	—	4	8	no	—
99	C₂×#261	—	4	8	no	—
100	C₂×#261	—	4	8	no	—
101	C₂×#261	—	8	16	no	—
102	C₂×C₄×C₁₃	#106	1	4	yes	—
103	C₂×C₄×C₁₃	#107	1	4	yes	—
104	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
106	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
107	C₂×C₄×C₁₃	#117	1	4	yes	—
108	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
109	C₂×Dic₁₃	#106	1	4	yes	—
110	C₂×Dic₁₃	#107	1	4	yes	—
111	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
113	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
114	C₂×Dic₁₃	#125	1	4	yes	—
115	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
116	C₄×D₁₃	#106	1	8	yes	—
117	C₄×D₁₃	#107	1	8	yes	—
118	C₄×D₁₃	#117	1	4	yes	—
119	C₄×D₁₃	#124	1	4	yes	—
120	C₄×D₁₃	#125	1	4	yes	—
121	C₄×D₁₃	C₂×D₈	1	4	yes	—
122	C₄×D₁₃	C₂×SD₁₆	1	8	yes	—
123	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
124	C₄×D₁₃	C₂×#41	1	4	yes	—
125	C₈×C₁₃	—	2	4	no	—
126	#1055	—	2	4	no	—
127	C₂³×C₈	—	13	2	no	—
128	C₂²×C₄⋊C₄	—	13	4	no	—
129	C₂²×C₄⋊C₄	—	26	2	no	—
130	C₂²×C₄⋊C₄	—	26	2	no	—
131	C₂²×C₄²	—	13	1	no	—
132	C₂×C₄×C₈	—	13	2	no	—
133	C₂×C₄×C₈	—	13	1	no	—
134	C₂×C₄×C₈	—	13	4	no	—
135	C₂×C₄×C₈	—	13	4	no	—
136	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
137	#384	—	13	8	no	—
138	#384	—	26	4	no	—
139	#340	—	13	16	no	—
140	C₂²×C₁₃	#382	1	2	yes	—
141	C₂²×C₁₃	C₂×#106	1	2	yes	—
142	C₂²×C₁₃	C₂×#107	1	2	yes	—
143	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
144	C₂×D₁₃	#382	1	2	yes	—
145	C₂×D₁₃	C₂×#106	1	2	yes	—
146	C₂×D₁₃	C₂×#107	1	2	yes	—
147	C₂×D₁₃	#486	1	8	yes	—
148	C₂×D₁₃	#487	1	8	yes	—
149	C₂×D₁₃	C₂×#124	1	2	yes	—
150	C₂×D₁₃	C₂²×D₈	1	1	yes	characteristic
151	C₂×D₁₃	C₂²×SD₁₆	1	2	yes	—
152	C₂×D₁₃	C₂²×Q₁₆	1	1	yes	characteristic
153	#261	—	8	8	no	—
154	C₄×C₁₃	#382	1	2	yes	—
155	C₄×C₁₃	C₂×#106	1	4	yes	—
156	C₄×C₁₃	C₂×#107	1	4	yes	—
157	C₄×C₁₃	C₂×#117	1	2	yes	—
158	Dic₁₃	#382	1	2	yes	—
159	Dic₁₃	C₂×#106	1	4	yes	—
160	Dic₁₃	C₂×#107	1	4	yes	—
161	Dic₁₃	C₂×#125	1	2	yes	—
162	C₂³×C₄	—	13	1	no	—
163	C₂³×C₄	—	13	1	no	—
164	C₂³×C₄	—	13	1	no	—
165	C₂³×C₄	—	26	4	no	—
166	C₂²×C₈	—	13	2	no	—
167	C₂²×C₈	—	13	4	no	—
168	C₂²×C₈	—	13	4	no	—
169	C₂²×C₈	—	26	8	no	—
170	C₂²×C₈	C₂×#261	1	2	yes	—
171	C₂×C₄⋊C₄	—	13	8	no	—
172	C₂×C₄⋊C₄	—	26	16	no	—
173	C₂×C₄⋊C₄	—	26	4	no	—
174	C₂×C₄⋊C₄	—	26	8	no	—
175	C₂×C₄⋊C₄	—	26	8	no	—
176	C₂×C₄⋊C₄	—	52	8	no	—
177	C₂×C₄⋊C₄	—	52	8	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	2	no	—
184	C₂×C₄²	—	13	2	no	—
185	C₂×C₄²	C₂×#261	1	1	yes	characteristic
186	C₄×C₈	—	13	8	no	—
187	C₄×C₈	—	13	4	no	—
188	C₄×C₈	C₂×#261	1	4	yes	complemented
189	C₂×C₁₃	#1834	1	4	yes	complemented
190	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
191	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
192	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
193	D₁₃	#1834	1	4	yes	complemented
194	D₁₃	C₂×#486	1	2	yes	—
195	D₁₃	C₂×#487	1	2	yes	—
196	C₂⁴	—	13	1	no	—
197	C₂²×C₄	—	13	1	no	—
198	C₂²×C₄	—	13	1	no	—
199	C₂²×C₄	—	13	1	no	—
200	C₂²×C₄	—	13	8	no	—
201	C₂²×C₄	—	13	4	no	—
202	C₂²×C₄	—	13	4	no	—
203	C₂²×C₄	—	13	1	no	—
204	C₂²×C₄	—	13	2	no	—
205	C₂²×C₄	—	13	2	no	—
206	C₂²×C₄	—	13	2	no	—
207	C₂²×C₄	—	13	2	no	—
208	C₂²×C₄	—	13	1	no	—
209	C₂²×C₄	—	13	8	no	—
210	C₂²×C₄	—	13	1	no	—
211	C₂²×C₄	—	13	1	no	—
212	C₂²×C₄	—	26	8	no	—
213	C₂²×C₄	—	52	8	no	—
214	C₂²×C₄	—	52	8	no	—
215	C₂²×C₄	—	52	8	no	—
216	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
217	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
218	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
219	C₂×C₈	—	2	4	no	—
220	C₂×C₈	—	13	4	no	—
221	C₂×C₈	—	26	8	no	—
222	C₂×C₈	—	26	8	no	—
223	C₂×C₈	—	26	4	no	—
224	C₂×C₈	C₂²×#261	1	4	yes	—
225	C₄⋊C₄	—	26	16	no	—
226	C₄⋊C₄	—	52	8	no	—
227	C₄⋊C₄	—	52	16	no	—
228	C₄⋊C₄	—	52	16	no	—
229	C₄²	—	13	2	no	—
230	C₄²	—	13	2	no	—
231	C₄²	—	13	2	no	—
232	C₄²	—	13	2	no	—
233	C₄²	—	13	2	no	—
234	C₄²	—	13	2	no	—
235	C₄²	C₄⋊#261	1	2	yes	—
236	C₄²	C₂²×#261	1	2	yes	—
237	C₁₃	C₂×#1834	1	1	yes	characteristic, complemented, Sylow
238	C₂³	—	13	4	no	—
239	C₂³	—	13	4	no	—
240	C₂³	—	13	2	no	—
241	C₂³	—	13	2	no	—
242	C₂³	—	13	1	no	—
243	C₂³	—	13	1	no	—
244	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
245	C₂×C₄	—	13	4	no	—
246	C₂×C₄	—	13	4	no	—
247	C₂×C₄	—	13	4	no	—
248	C₂×C₄	—	13	1	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	13	2	no	—
251	C₂×C₄	—	13	1	no	—
252	C₂×C₄	—	13	4	no	—
253	C₂×C₄	—	13	4	no	—
254	C₂×C₄	—	13	8	no	—
255	C₂×C₄	—	13	8	no	—
256	C₂×C₄	—	13	4	no	—
257	C₂×C₄	—	13	8	no	—
258	C₂×C₄	—	13	4	no	—
259	C₂×C₄	—	13	4	no	—
260	C₂×C₄	—	13	4	no	—
261	C₂×C₄	—	52	8	no	—
262	C₂×C₄	—	52	8	no	—
263	C₂×C₄	—	52	8	no	—
264	C₂×C₄	—	104	16	no	—
265	C₂×C₄	#88101	1	4	yes	—
266	C₂×C₄	#88102	1	4	yes	—
267	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
268	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
269	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
270	C₂×C₄	#88237	1	4	yes	—
271	C₂×C₄	C₂³×#261	1	1	yes	characteristic
272	C₈	—	2	4	no	—
273	C₈	—	26	4	no	—
274	C₂²	—	13	8	no	—
275	C₂²	—	13	8	no	—
276	C₂²	—	13	2	no	—
277	C₂²	—	13	2	no	—
278	C₂²	—	13	2	no	—
279	C₂²	—	13	2	no	—
280	C₂²	—	13	1	no	—
281	C₂²	—	13	1	no	—
282	C₂²	—	13	2	no	—
283	C₂²	#11719060	1	2	yes	—
284	C₂²	C₂×#88101	1	2	yes	—
285	C₂²	C₂×#88102	1	2	yes	—
286	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
287	C₄	—	13	2	no	—
288	C₄	—	13	2	no	—
289	C₄	—	13	4	no	—
290	C₄	—	13	4	no	—
291	C₄	—	104	8	no	—
292	C₄	#11719060	1	2	yes	—
293	C₄	C₂×#88101	1	4	yes	—
294	C₄	C₂×#88102	1	4	yes	—
295	C₄	C₂×#88237	1	2	yes	—
296	C₂	—	13	2	no	—
297	C₂	—	13	4	no	—
298	C₂	—	13	2	no	—
299	C₂	#13130757	1	4	yes	direct product factor
300	C₂	C₂×#11719060	1	1	yes	characteristic
301	C₂	C₂²×#88101	1	1	yes	characteristic
302	C₂	C₂²×#88102	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1834
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130757	C₂	direct (N × H)
12. C₂×C₄×C₈×C₁₃	C₄	semidirect
13. C₂×C₈×Dic₁₃	C₄	semidirect
14. C₂×C₄×#1055	C₄	semidirect
15. C₄×C₈×D₁₃	C₄	semidirect
42. C₄×C₈×C₁₃	C₂×C₄	semidirect
43. C₈×Dic₁₃	C₂×C₄	semidirect
44. C₄×#1055	C₂×C₄	semidirect
136. C₂×C₄×C₈	#261	semidirect
188. C₄×C₈	C₂×#261	semidirect
189. C₂×C₁₃	#1834	semidirect
193. D₁₃	#1834	semidirect
237. C₁₃	C₂×#1834	semidirect
299. C₂	#13130757	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×#11719059	2
#13130757	2
C₂×#11718265	2
C₂×C₄×C₈×D₁₃	2
C₂×#1834	13

Subgroups — C2×#13130757 #16798168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130757 #16798168