Subgroups — C₂×#13112777 #15772059

Order 3328.

394 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718763	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic
3	#13112777	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88180	C₄	1	1	yes	characteristic
7	C₂²×#6099	C₄	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	—	2	1	no	—
9	#11718763	—	2	1	no	—
10	#11718763	—	2	1	no	—
11	#11718763	C₄	1	2	yes	—
12	#11718763	C₂²	1	2	yes	—
13	C₂×#88054	—	2	1	no	—
14	C₂×#88054	—	2	1	no	—
15	C₂²×#6090	—	2	1	no	—
16	C₁₃×C₂²⋊C₁₆	—	2	1	no	—
17	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
18	C₂²⋊#6090	—	2	1	no	—
19	C₂²⋊#6090	C₂²	1	2	yes	—
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	—	4	2	no	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
29	#88180	—	2	1	no	—
30	#88180	—	2	1	no	—
31	#88180	C₈	1	2	yes	—
32	#88180	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₁₃	C₈	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₃	C₈	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	—	2	1	no	—
36	C₂×#6099	—	2	1	no	—
37	C₂×#6099	—	4	2	no	—
38	C₂×#6099	C₂×C₄	1	2	yes	—
39	C₂²×#1055	—	2	1	no	—
40	C₂×C₁₃×C₁₆	—	2	2	no	—
41	C₂×C₁₃×C₁₆	—	4	2	no	—
42	#88054	—	2	2	no	—
43	#88054	—	2	2	no	—
44	#88054	—	2	2	no	—
45	#88054	—	2	2	no	—
46	C₂×#6090	—	2	2	no	—
47	C₂×#6090	—	4	2	no	—
48	C₂×#1323	—	13	1	no	maximal, Sylow
49	C₂⁴×C₁₃	M₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	—	2	2	no	—
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×Dic₁₃	—	2	1	no	—
59	C₂²×Dic₁₃	—	2	1	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₂×C₈×C₁₃	—	4	1	no	—
64	C₂×C₈×C₁₃	—	4	1	no	—
65	C₂×C₈×C₁₃	—	4	1	no	—
66	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂²⋊Dic₁₃	—	2	2	no	—
71	C₂²⋊Dic₁₃	—	2	2	no	—
72	C₄⋊Dic₁₃	—	2	1	no	—
73	C₄⋊Dic₁₃	—	2	1	no	—
74	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
75	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
76	C₄×Dic₁₃	—	2	2	no	—
77	C₄×Dic₁₃	—	2	2	no	—
78	#6099	—	4	2	no	—
79	#6099	—	4	2	no	—
80	C₂×#1055	—	2	2	no	—
81	C₂×#1055	—	4	2	no	—
82	C₁₃×C₁₆	—	4	2	no	—
83	#6090	—	4	2	no	—
84	C₂×#424	—	13	1	no	—
85	C₂×C₂²⋊C₁₆	—	13	1	no	—
86	C₂×C₂²⋊C₁₆	D₁₃	1	1	yes	characteristic
87	#1323	—	13	4	no	—
88	C₂³×C₁₃	—	2	2	no	—
89	C₂³×C₁₃	—	2	2	no	—
90	C₂³×C₁₃	—	2	2	no	—
91	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
92	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
93	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	1	no	—
98	C₂×C₄×C₁₃	—	2	1	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	2	1	no	—
101	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#99	1	2	yes	—
104	C₂×C₄×C₁₃	#101	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
107	C₂×Dic₁₃	—	2	2	no	—
108	C₂×Dic₁₃	—	2	2	no	—
109	C₂×Dic₁₃	—	4	2	no	—
110	C₂×Dic₁₃	—	4	2	no	—
111	C₈×C₁₃	—	2	1	no	—
112	C₈×C₁₃	—	2	1	no	—
113	C₈×C₁₃	—	2	1	no	—
114	C₈×C₁₃	—	2	1	no	—
115	#1055	—	4	2	no	—
116	C₂²×M₁₆	—	13	1	no	—
117	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
118	C₂×#117	—	13	1	no	—
119	C₂²×C₁₆	—	2	1	no	—
120	C₂²×C₁₆	—	26	1	no	—
121	#424	—	13	2	no	—
122	#424	—	13	2	no	—
123	#424	—	26	1	no	—
124	#424	—	26	1	no	—
125	C₂×C₄⋊C₈	—	26	1	no	—
126	C₂×C₄⋊C₈	—	26	1	no	—
127	C₂²⋊C₁₆	—	2	1	no	—
128	C₂²⋊C₁₆	—	13	2	no	—
129	C₂²⋊C₁₆	—	26	1	no	—
130	C₂²⋊C₁₆	C₂×D₁₃	1	2	yes	—
131	C₂²×C₁₃	—	2	1	no	—
132	C₂²×C₁₃	—	2	1	no	—
133	C₂²×C₁₃	—	2	1	no	—
134	C₂²×C₁₃	—	2	1	no	—
135	C₂²×C₁₃	—	2	1	no	—
136	C₂²×C₁₃	—	2	1	no	—
137	C₂²×C₁₃	—	4	4	no	—
138	C₂²×C₁₃	#324	1	2	yes	—
139	C₂²×C₁₃	#350	1	2	yes	—
140	C₂²×C₁₃	#350	1	2	yes	—
141	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
142	C₄×C₁₃	—	2	1	no	—
143	C₄×C₁₃	—	2	1	no	—
144	C₄×C₁₃	#324	1	2	yes	—
145	C₄×C₁₃	C₂×#99	1	1	yes	characteristic
146	C₄×C₁₃	C₂×#101	1	1	yes	characteristic
147	Dic₁₃	—	4	2	no	—
148	Dic₁₃	—	4	2	no	—
149	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
150	C₂×M₁₆	—	13	2	no	—
151	C₂×M₁₆	—	26	1	no	—
152	C₂×M₁₆	—	52	2	no	—
153	C₂²×C₈	—	4	2	no	—
154	C₂²×C₈	—	26	1	no	—
155	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
156	C₂²×C₈	D₅₂	1	1	yes	characteristic
157	C₂²×C₈	D₅₂	1	1	yes	characteristic
158	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
159	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
160	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
161	#117	—	13	2	no	—
162	#117	—	13	2	no	—
163	#117	—	26	1	no	—
164	#117	—	26	1	no	—
165	C₂×C₄⋊C₄	—	13	1	no	—
166	C₂×C₄⋊C₄	—	13	1	no	—
167	C₂×C₂²⋊C₄	—	26	1	no	—
168	C₂×C₄²	—	26	1	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	4	2	no	—
171	C₂×C₁₆	—	26	2	no	—
172	C₂×C₁₆	—	52	2	no	—
173	C₄⋊C₈	—	26	2	no	—
174	C₄⋊C₈	—	26	2	no	—
175	C₄⋊C₈	—	26	2	no	—
176	C₄⋊C₈	—	26	2	no	—
177	C₂×C₁₃	—	4	1	no	—
178	C₂×C₁₃	—	4	1	no	—
179	C₂×C₁₃	#1323	1	4	yes	complemented
180	C₂×C₁₃	C₂×#324	1	1	yes	characteristic
181	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
182	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
183	C₂⁴	#6094	1	1	yes	characteristic
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	26	1	no	—
187	C₂²×C₄	—	26	1	no	—
188	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
189	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
190	C₂²×C₄	#6094	1	1	yes	characteristic
191	C₂²×C₄	#6103	1	1	yes	characteristic
192	C₂²×C₄	#6103	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
194	M₁₆	—	52	2	no	—
195	M₁₆	—	52	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	26	2	no	—
203	C₂×C₈	—	52	2	no	—
204	C₂×C₈	#6103	1	1	yes	characteristic
205	C₂×C₈	#6103	1	1	yes	characteristic
206	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
207	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
208	C₄⋊C₄	—	13	2	no	—
209	C₄⋊C₄	—	13	2	no	—
210	C₄⋊C₄	—	26	1	no	—
211	C₄⋊C₄	—	26	1	no	—
212	C₂²⋊C₄	—	26	2	no	—
213	C₂²⋊C₄	—	26	2	no	—
214	C₄²	—	26	2	no	—
215	C₄²	—	26	2	no	—
216	C₁₆	—	4	2	no	—
217	C₁₆	—	52	2	no	—
218	C₁₃	C₂×#1323	1	1	yes	characteristic, complemented, Sylow
219	C₂³	—	2	2	no	—
220	C₂³	—	2	2	no	—
221	C₂³	—	2	2	no	—
222	C₂³	#88060	1	1	yes	characteristic
223	C₂³	#88060	1	1	yes	characteristic
224	C₂³	C₂×#6094	1	1	yes	characteristic
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	26	2	no	—
233	C₂×C₄	—	26	2	no	—
234	C₂×C₄	—	52	2	no	—
235	C₂×C₄	—	52	2	no	—
236	C₂×C₄	#88046	1	2	yes	—
237	C₂×C₄	#88060	1	1	yes	characteristic
238	C₂×C₄	#88060	1	1	yes	characteristic
239	C₂×C₄	#88064	1	2	yes	—
240	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
241	C₂×C₄	C₂×#6103	1	1	yes	characteristic
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	52	2	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	4	4	no	—
254	C₂²	#11718061	1	2	yes	—
255	C₂²	#11718100	1	2	yes	—
256	C₂²	#11718107	1	2	yes	—
257	C₂²	C₂×#88060	1	1	yes	characteristic
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	52	2	no	—
261	C₄	—	52	2	no	—
262	C₄	#11718061	1	2	yes	—
263	C₄	C₂×#88046	1	1	yes	characteristic
264	C₄	C₂×#88064	1	1	yes	characteristic
265	C₂	—	4	1	no	—
266	C₂	—	4	1	no	—
267	C₂	#13112777	1	4	yes	direct product factor
268	C₂	C₂×#11718061	1	1	yes	characteristic
269	C₂	C₂×#11718100	1	1	yes	characteristic
270	C₂	C₂×#11718107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#6103
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×C₂²⋊C₁₆	C₂
socle	C₂³×C₁₃	C₂²⋊C₈
prime radical	C₂⁴×C₁₃	M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₂²⋊C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1323
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
3. #13112777	C₂	direct (N × H)
179. C₂×C₁₃	#1323	semidirect
218. C₁₃	C₂×#1323	semidirect
267. C₂	#13112777	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×#11718763	2
C₂×C₂²⋊#6090	2
#13112777	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₂×#1323	13

Subgroups — C2×#13112777 #15772059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112777 #15772059