Subgroups — C₂×#13130039 #16792576

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 246 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	#13130039	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718251	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×#1057	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
8	C₂³×#1055	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊#1057	C₄	1	4	yes	—
10	#11719119	C₄	1	8	yes	—
11	#11719119	C₂²	1	8	yes	—
12	C₂×C₄⋊#1057	C₄	1	4	yes	—
13	C₂×C₄×#1057	C₂²	1	4	yes	—
14	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
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	#11718251	C₂²	1	8	yes	complemented
21	C₈×#1057	C₂²	1	8	yes	complemented
22	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂²×#1057	C₂×C₄	1	8	yes	—
25	C₂²×C₈×C₁₃	C₈	1	8	yes	complemented
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
30	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
32	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
33	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
35	C₂²×#1055	C₈	1	8	yes	complemented
36	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
37	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
38	C₂²×#1055	C₂×C₄	1	4	yes	—
39	C₂²⋊#1057	C₂×C₄	1	16	yes	—
40	C₄⋊#1057	C₂×C₄	1	16	yes	—
41	C₄×#1057	C₂×C₄	1	8	yes	—
42	C₄×#1057	C₂³	1	8	yes	—
43	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
44	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
45	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
46	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
47	C₈×Dic₁₃	C₂³	1	2	yes	—
48	C₈×Dic₁₃	C₂³	1	2	yes	—
49	C₂×#1450	—	13	1	no	maximal, Sylow
50	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
52	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
54	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×Dic₁₃	—	2	8	no	—
58	C₂²×Dic₁₃	C₄²	1	2	yes	—
59	C₂²×Dic₁₃	C₄²	1	4	yes	—
60	C₂²×Dic₁₃	C₂²×C₄	1	4	yes	—
61	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
62	C₂×#1057	—	2	16	no	—
63	C₂×#1057	C₂²×C₄	1	16	yes	—
64	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
65	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
66	C₂×C₈×C₁₃	C₂×C₈	1	16	yes	complemented
67	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
69	C₄×Dic₁₃	C₄²	1	2	yes	—
70	C₄×Dic₁₃	C₄²	1	4	yes	—
71	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
72	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
74	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
75	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
76	C₂×#1055	C₂×C₈	1	4	yes	—
77	C₂×#1055	C₂×C₈	1	4	yes	—
78	C₂×#1055	C₂×C₈	1	16	yes	complemented
79	C₂×#1055	C₂²×C₄	1	2	yes	—
80	C₂×#1055	C₂²×C₄	1	2	yes	—
81	C₂×#431	—	13	2	no	—
82	C₂²×C₄×C₈	—	13	1	no	—
83	#1450	—	13	8	no	—
84	C₂×#322	—	13	2	no	—
85	C₂×C₈²	—	13	2	no	—
86	C₂³×C₁₃	—	2	4	no	—
87	C₂³×C₁₃	C₄×C₈	1	4	yes	—
88	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
89	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₄×C₈	1	8	yes	—
91	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
92	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
94	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
95	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
96	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
97	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
98	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
99	C₂×Dic₁₃	—	2	4	no	—
100	C₂×Dic₁₃	—	2	8	no	—
101	C₂×Dic₁₃	—	2	8	no	—
102	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
103	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
104	C₂×Dic₁₃	#131	1	8	yes	—
105	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
106	#1057	—	2	16	no	—
107	C₈×C₁₃	C₂²×C₈	1	4	yes	—
108	C₈×C₁₃	C₂²×C₈	1	4	yes	—
109	#1055	C₂²×C₈	1	4	yes	—
110	#1055	C₂²×C₈	1	4	yes	—
111	C₂³×C₈	—	13	1	no	—
112	C₂³×C₈	#261	1	1	yes	characteristic
113	C₂²×C₄²	—	13	1	no	—
114	#431	—	13	8	no	—
115	#431	—	13	8	no	—
116	C₂×C₄⋊C₈	—	13	4	no	—
117	C₂×C₂²⋊C₈	—	13	4	no	—
118	C₂×C₄×C₈	—	13	4	no	—
119	C₂×C₄×C₈	—	13	1	no	—
120	C₂×C₄×C₈	—	13	4	no	—
121	C₂×C₄×C₈	—	13	1	no	—
122	C₂×C₄×C₈	—	13	4	no	—
123	C₂×C₄×C₈	—	13	1	no	—
124	C₂×C₄×C₈	—	13	1	no	—
125	#322	—	13	8	no	—
126	C₈²	—	13	8	no	—
127	C₂²×C₁₃	—	2	4	no	—
128	C₂²×C₁₃	—	2	8	no	—
129	C₂²×C₁₃	C₂×C₄×C₈	1	4	yes	—
130	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
131	C₂²×C₁₃	#405	1	4	yes	—
132	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
133	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
134	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
135	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
136	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
137	Dic₁₃	—	2	4	no	—
138	Dic₁₃	#405	1	4	yes	—
139	Dic₁₃	C₂×#131	1	4	yes	—
140	C₂³×C₄	—	13	2	no	—
141	C₂³×C₄	C₂×#261	1	1	yes	characteristic
142	C₂²×C₈	—	13	8	no	—
143	C₂²×C₈	—	13	1	no	—
144	C₂²×C₈	—	13	1	no	—
145	C₂²×C₈	—	13	4	no	—
146	C₂²×C₈	—	13	8	no	—
147	C₂²×C₈	#1057	1	8	yes	complemented
148	C₂²×C₈	C₂×#261	1	1	yes	characteristic
149	C₂²×C₈	C₂×#261	1	4	yes	—
150	C₂²×C₈	C₂×#261	1	1	yes	characteristic
151	C₂×C₄²	—	13	2	no	—
152	C₂×C₄²	—	13	4	no	—
153	C₂×C₄²	—	13	2	no	—
154	C₂×C₄²	—	13	1	no	—
155	C₂×C₄²	—	13	1	no	—
156	C₂×C₄²	—	13	2	no	—
157	C₄⋊C₈	—	13	16	no	—
158	C₂²⋊C₈	—	13	16	no	—
159	C₄×C₈	—	13	8	no	—
160	C₄×C₈	—	13	8	no	—
161	C₄×C₈	—	13	2	no	—
162	C₄×C₈	—	13	2	no	—
163	C₄×C₈	—	13	2	no	—
164	C₄×C₈	—	13	4	no	—
165	C₄×C₈	—	13	2	no	—
166	C₄×C₈	—	13	4	no	—
167	C₂×C₁₃	—	2	4	no	—
168	C₂×C₁₃	#1450	1	4	yes	complemented
169	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
170	C₂×C₁₃	C₂×#405	1	2	yes	—
171	C₂⁴	C₄×#261	1	1	yes	characteristic
172	C₂²×C₄	—	13	2	no	—
173	C₂²×C₄	—	13	4	no	—
174	C₂²×C₄	—	13	4	no	—
175	C₂²×C₄	—	13	2	no	—
176	C₂²×C₄	—	26	8	no	—
177	C₂²×C₄	D₁₃⋊C₈	1	4	yes	—
178	C₂²×C₄	C₄×#261	1	2	yes	—
179	C₂²×C₄	C₄×#261	1	1	yes	characteristic
180	C₂²×C₄	C₂×#1057	1	4	yes	—
181	C₂²×C₄	C₂²×#261	1	2	yes	—
182	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
183	C₂×C₈	—	13	4	no	—
184	C₂×C₈	—	13	4	no	—
185	C₂×C₈	—	13	16	no	—
186	C₂×C₈	—	13	2	no	—
187	C₂×C₈	—	13	2	no	—
188	C₂×C₈	—	13	16	no	—
189	C₂×C₈	—	26	16	no	—
190	C₂×C₈	C₂×#1057	1	4	yes	—
191	C₂×C₈	C₂×#1057	1	4	yes	—
192	C₂×C₈	C₂×#1057	1	16	yes	complemented
193	C₂×C₈	C₂²×#261	1	2	yes	—
194	C₂×C₈	C₂²×#261	1	2	yes	—
195	C₄²	—	13	2	no	—
196	C₄²	—	13	4	no	—
197	C₄²	—	13	4	no	—
198	C₄²	—	13	2	no	—
199	C₄²	—	13	1	no	—
200	C₄²	—	13	1	no	—
201	C₄²	—	13	2	no	—
202	C₁₃	C₂×#1450	1	1	yes	characteristic, complemented, Sylow
203	C₂³	—	2	4	no	—
204	C₂³	C₄×#1057	1	4	yes	—
205	C₂³	C₂×C₄×#261	1	2	yes	—
206	C₂³	C₂×C₄×#261	1	1	yes	characteristic
207	C₂×C₄	—	13	8	no	—
208	C₂×C₄	—	13	2	no	—
209	C₂×C₄	—	13	2	no	—
210	C₂×C₄	—	13	4	no	—
211	C₂×C₄	—	26	8	no	—
212	C₂×C₄	—	26	8	no	—
213	C₂×C₄	—	26	4	no	—
214	C₂×C₄	C₄×#1057	1	8	yes	—
215	C₂×C₄	C₄×#1057	1	4	yes	—
216	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
217	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
218	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
219	C₂×C₄	C₂×C₄×#261	1	2	yes	—
220	C₂×C₄	C₂²×#1057	1	2	yes	—
221	C₂×C₄	C₂²×#1057	1	4	yes	—
222	C₂×C₄	C₂³×#261	1	1	yes	characteristic
223	C₈	—	13	4	no	—
224	C₈	—	13	4	no	—
225	C₈	—	26	16	no	—
226	C₈	C₂²×#1057	1	4	yes	—
227	C₈	C₂²×#1057	1	4	yes	—
228	C₂²	—	2	8	no	—
229	C₂²	—	2	4	no	—
230	C₂²	#11719089	1	4	yes	—
231	C₂²	C₂×C₄×#1057	1	4	yes	—
232	C₂²	C₂×C₄×#1057	1	2	yes	—
233	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
234	C₄	—	13	4	no	—
235	C₄	—	13	4	no	—
236	C₄	—	26	4	no	—
237	C₄	C₂×C₄×#1057	1	2	yes	—
238	C₄	C₂×C₄×#1057	1	4	yes	—
239	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
240	C₄	C₂³×#1057	1	1	yes	characteristic
241	C₂	—	2	4	no	—
242	C₂	#13130039	1	4	yes	direct product factor
243	C₂	C₂²×C₄×#1057	1	1	yes	characteristic
244	C₂	C₂×#11719089	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂×#1450
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #13130039	C₂	direct (N × H)
3. C₂×#11718251	C₂	semidirect
4. C₂×C₈×#1057	C₂	semidirect
20. #11718251	C₂²	semidirect
21. C₈×#1057	C₂²	semidirect
25. C₂²×C₈×C₁₃	C₈	semidirect
35. C₂²×#1055	C₈	semidirect
66. C₂×C₈×C₁₃	C₂×C₈	semidirect
78. C₂×#1055	C₂×C₈	semidirect
147. C₂²×C₈	#1057	semidirect
168. C₂×C₁₃	#1450	semidirect
192. C₂×C₈	C₂×#1057	semidirect
202. C₁₃	C₂×#1450	semidirect
242. C₂	#13130039	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
#13130039	2
C₂×#11718251	2
C₂×C₈×#1057	2
C₂²×C₈×Dic₁₃	2
C₂×#1450	13

Subgroups — C2×#13130039 #16792576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130039 #16792576