Subgroups — C₂×#2853×C₁₃₁ #45722502

Order 33536.

3354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄²×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₁	C₂	1	16	yes	maximal, direct product factor
4	C₂×#388×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	C₂×#387×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	C₂×#386×C₁₃₁	C₂	1	2	yes	maximal
7	C₂×#385×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₂×#381×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃₁	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×#123×C₁₃₁	—	2	8	no	—
13	C₂×#123×C₁₃₁	C₂²	1	8	yes	—
14	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₃₁	—	2	8	no	—
21	C₂²×C₄²×C₁₃₁	C₂²	1	4	yes	—
22	C₂²×C₄²×C₁₃₁	C₂²	1	8	yes	complemented
23	#388×C₁₃₁	C₂²	1	32	yes	complemented
24	#387×C₁₃₁	C₂²	1	32	yes	complemented
25	#386×C₁₃₁	C₂²	1	16	yes	—
26	#385×C₁₃₁	C₂²	1	16	yes	complemented
27	#381×C₁₃₁	C₂²	1	8	yes	complemented
28	C₂×#95×C₁₃₁	C₂²	1	4	yes	—
29	C₂×#95×C₁₃₁	C₂²	1	4	yes	—
30	C₂×#95×C₁₃₁	C₂²	1	4	yes	—
31	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
32	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₁₃₁	—	2	4	no	—
34	C₂²×D₄×C₁₃₁	—	2	8	no	—
35	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃₁	—	2	8	no	—
37	C₂³×C₄×C₁₃₁	—	2	8	no	—
38	C₂³×C₄×C₁₃₁	—	2	16	no	—
39	C₂³×C₄×C₁₃₁	D₄	1	8	yes	—
40	C₂³×C₄×C₁₃₁	C₂³	1	8	yes	—
41	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
47	#123×C₁₃₁	—	2	32	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	16	no	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	16	yes	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	8	yes	—
52	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₁₃₁	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
57	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	16	yes	—
58	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
60	C₂×C₄²×C₁₃₁	—	2	16	no	—
61	C₂×C₄²×C₁₃₁	—	2	32	no	—
62	C₂×C₄²×C₁₃₁	C₂³	1	16	yes	—
63	#95×C₁₃₁	C₂³	1	16	yes	—
64	#95×C₁₃₁	C₂³	1	16	yes	—
65	#95×C₁₃₁	C₂³	1	16	yes	—
66	C₂⁴×C₁₃₁	—	2	8	no	—
67	C₂⁴×C₁₃₁	—	2	2	no	—
68	C₂⁴×C₁₃₁	—	2	8	no	—
69	C₂⁴×C₁₃₁	—	2	4	no	—
70	C₂⁴×C₁₃₁	C₂×D₄	1	4	yes	—
71	C₂⁴×C₁₃₁	#41	1	8	yes	—
72	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
73	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
74	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
75	C₂×D₄×C₁₃₁	—	2	8	no	—
76	C₂×D₄×C₁₃₁	—	2	16	no	—
77	C₂×D₄×C₁₃₁	—	4	16	no	—
78	C₂²×C₄×C₁₃₁	—	2	64	no	—
79	C₂²×C₄×C₁₃₁	—	2	32	no	—
80	C₂²×C₄×C₁₃₁	—	2	16	no	—
81	C₂²×C₄×C₁₃₁	—	2	8	no	—
82	C₂²×C₄×C₁₃₁	—	2	16	no	—
83	C₂²×C₄×C₁₃₁	—	2	8	no	—
84	C₂²×C₄×C₁₃₁	—	2	8	no	—
85	C₂²×C₄×C₁₃₁	—	2	32	no	—
86	C₂²×C₄×C₁₃₁	—	2	4	no	—
87	C₂²×C₄×C₁₃₁	—	2	2	no	—
88	C₂²×C₄×C₁₃₁	—	2	8	no	—
89	C₂²×C₄×C₁₃₁	—	2	8	no	—
90	C₂²×C₄×C₁₃₁	—	2	8	no	—
91	C₂²×C₄×C₁₃₁	—	2	8	no	—
92	C₂²×C₄×C₁₃₁	—	2	4	no	—
93	C₂²×C₄×C₁₃₁	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₁₃₁	C₂×D₄	1	16	yes	—
95	C₂²×C₄×C₁₃₁	#41	1	16	yes	—
96	C₂²×C₄×C₁₃₁	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₁₃₁	C₂⁴	1	8	yes	—
101	C₄⋊C₄×C₁₃₁	—	2	16	no	—
102	C₄⋊C₄×C₁₃₁	—	2	32	no	—
103	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
104	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
105	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
106	C₂²⋊C₄×C₁₃₁	—	2	32	no	—
107	C₄²×C₁₃₁	—	2	32	no	—
108	C₂³×C₁₃₁	—	2	16	no	—
109	C₂³×C₁₃₁	—	2	32	no	—
110	C₂³×C₁₃₁	—	2	8	no	—
111	C₂³×C₁₃₁	—	2	2	no	—
112	C₂³×C₁₃₁	—	2	8	no	—
113	C₂³×C₁₃₁	—	2	4	no	—
114	C₂³×C₁₃₁	—	4	4	no	—
115	C₂³×C₁₃₁	—	4	8	no	—
116	C₂³×C₁₃₁	—	4	16	no	—
117	C₂³×C₁₃₁	#123	1	16	yes	—
118	C₂³×C₁₃₁	C₂²×D₄	1	4	yes	—
119	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
120	C₂³×C₁₃₁	C₂×#41	1	8	yes	—
121	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
122	C₂³×C₁₃₁	C₂×#41	1	8	yes	—
123	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
124	D₄×C₁₃₁	—	4	16	no	—
125	C₂×C₄×C₁₃₁	—	2	64	no	—
126	C₂×C₄×C₁₃₁	—	2	32	no	—
127	C₂×C₄×C₁₃₁	—	2	16	no	—
128	C₂×C₄×C₁₃₁	—	2	32	no	—
129	C₂×C₄×C₁₃₁	—	2	8	no	—
130	C₂×C₄×C₁₃₁	—	2	8	no	—
131	C₂×C₄×C₁₃₁	—	2	8	no	—
132	C₂×C₄×C₁₃₁	—	2	4	no	—
133	C₂×C₄×C₁₃₁	—	2	2	no	—
134	C₂×C₄×C₁₃₁	—	2	8	no	—
135	C₂×C₄×C₁₃₁	—	2	8	no	—
136	C₂×C₄×C₁₃₁	—	2	8	no	—
137	C₂×C₄×C₁₃₁	—	2	8	no	—
138	C₂×C₄×C₁₃₁	—	2	4	no	—
139	C₂×C₄×C₁₃₁	—	4	4	no	—
140	C₂×C₄×C₁₃₁	—	4	8	no	—
141	C₂×C₄×C₁₃₁	—	4	16	no	—
142	C₂×C₄×C₁₃₁	C₂²×D₄	1	8	yes	—
143	C₂×C₄×C₁₃₁	C₂×#41	1	16	yes	—
144	C₂²×C₁₃₁	—	2	32	no	—
145	C₂²×C₁₃₁	—	2	8	no	—
146	C₂²×C₁₃₁	—	2	16	no	—
147	C₂²×C₁₃₁	—	4	2	no	—
148	C₂²×C₁₃₁	—	4	4	no	—
149	C₂²×C₁₃₁	—	4	8	no	—
150	C₂²×C₁₃₁	—	8	8	no	—
151	C₂²×C₁₃₁	C₂×#123	1	8	yes	—
152	C₂²×C₁₃₁	C₂×#123	1	4	yes	—
153	C₂²×C₁₃₁	#525	1	8	yes	—
154	C₂²×C₁₃₁	#529	1	16	yes	—
155	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
156	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
157	C₂²×C₁₃₁	C₂²×#41	1	4	yes	—
158	C₄×C₁₃₁	—	2	8	no	—
159	C₄×C₁₃₁	—	2	16	no	—
160	C₄×C₁₃₁	—	4	2	no	—
161	C₄×C₁₃₁	—	4	4	no	—
162	C₄×C₁₃₁	—	4	8	no	—
163	C₂×C₁₃₁	—	2	8	no	—
164	C₂×C₁₃₁	—	8	2	no	—
165	C₂×C₁₃₁	#2853	1	8	yes	direct product factor
166	C₂×C₁₃₁	C₂²×#123	1	1	yes	characteristic
167	C₂×C₁₃₁	C₂×#525	1	2	yes	—
168	C₂×C₁₃₁	C₂×#529	1	4	yes	—
169	C₂×#2853	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₁₃₁	C₂×#2853	1	1	yes	characteristic, direct product factor, Sylow
171	C₂²×#123	C₂×C₁₃₁	1	1	yes	characteristic
172	C₂³×C₄²	C₂×C₁₃₁	1	1	yes	characteristic, complemented
173	#2853	C₂×C₁₃₁	1	16	yes	direct product factor
174	C₂×#388	C₂×C₁₃₁	1	4	yes	complemented
175	C₂×#387	C₂×C₁₃₁	1	4	yes	complemented
176	C₂×#386	C₂×C₁₃₁	1	2	yes	—
177	C₂×#385	C₂×C₁₃₁	1	2	yes	complemented
178	C₂×#381	C₂×C₁₃₁	1	1	yes	characteristic, complemented
179	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
180	C₂⁴×C₄	C₂²×C₁₃₁	1	2	yes	—
181	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
182	C₂×#123	—	2	8	no	—
183	C₂×#123	C₂²×C₁₃₁	1	8	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
186	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
187	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
190	C₂²×C₄²	—	2	8	no	—
191	C₂²×C₄²	C₂²×C₁₃₁	1	4	yes	—
192	C₂²×C₄²	C₂²×C₁₃₁	1	8	yes	complemented
193	#388	C₂²×C₁₃₁	1	32	yes	complemented
194	#387	C₂²×C₁₃₁	1	32	yes	complemented
195	#386	C₂²×C₁₃₁	1	16	yes	—
196	#385	C₂²×C₁₃₁	1	16	yes	complemented
197	#381	C₂²×C₁₃₁	1	8	yes	complemented
198	C₂×#95	C₂²×C₁₃₁	1	4	yes	—
199	C₂×#95	C₂²×C₁₃₁	1	4	yes	—
200	C₂×#95	C₂²×C₁₃₁	1	4	yes	—
201	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
202	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
203	C₂²×D₄	—	2	4	no	—
204	C₂²×D₄	—	2	8	no	—
205	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
206	C₂³×C₄	—	2	8	no	—
207	C₂³×C₄	—	2	8	no	—
208	C₂³×C₄	—	2	16	no	—
209	C₂³×C₄	D₄×C₁₃₁	1	8	yes	—
210	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
211	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
212	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₁₃₁	1	8	yes	—
214	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
215	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
216	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
217	#123	—	2	32	no	—
218	C₂×C₄⋊C₄	—	2	8	no	—
219	C₂×C₄⋊C₄	—	2	16	no	—
220	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	8	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	16	yes	—
222	C₂×C₂²⋊C₄	—	2	4	no	—
223	C₂×C₂²⋊C₄	—	2	8	no	—
224	C₂×C₂²⋊C₄	—	2	8	no	—
225	C₂×C₂²⋊C₄	—	2	16	no	—
226	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
228	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	16	yes	—
230	C₂×C₄²	—	2	16	no	—
231	C₂×C₄²	—	2	32	no	—
232	C₂×C₄²	C₂³×C₁₃₁	1	16	yes	—
233	#95	C₂³×C₁₃₁	1	16	yes	—
234	#95	C₂³×C₁₃₁	1	16	yes	—
235	#95	C₂³×C₁₃₁	1	16	yes	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	2	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	C₂×D₄×C₁₃₁	1	4	yes	—
241	C₂⁴	#41×C₁₃₁	1	8	yes	—
242	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
243	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
244	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	2	16	no	—
247	C₂×D₄	—	4	16	no	—
248	C₂²×C₄	—	2	64	no	—
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	16	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	32	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	C₂×D₄×C₁₃₁	1	8	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃₁	1	16	yes	—
265	C₂²×C₄	#41×C₁₃₁	1	16	yes	—
266	C₂²×C₄	C₂⁴×C₁₃₁	1	8	yes	—
267	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₁₃₁	1	8	yes	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	32	no	—
273	C₂²⋊C₄	—	2	8	no	—
274	C₂²⋊C₄	—	2	16	no	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂²⋊C₄	—	2	32	no	—
277	C₄²	—	2	32	no	—
278	C₂³	—	2	16	no	—
279	C₂³	—	2	32	no	—
280	C₂³	—	2	8	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	4	4	no	—
285	C₂³	—	4	8	no	—
286	C₂³	—	4	16	no	—
287	C₂³	#123×C₁₃₁	1	16	yes	—
288	C₂³	C₂²×D₄×C₁₃₁	1	4	yes	—
289	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
290	C₂³	C₂×#41×C₁₃₁	1	8	yes	—
291	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
292	C₂³	C₂×#41×C₁₃₁	1	8	yes	—
293	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
294	D₄	—	4	16	no	—
295	C₂×C₄	—	2	64	no	—
296	C₂×C₄	—	2	32	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	2	32	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	8	no	—
311	C₂×C₄	—	4	16	no	—
312	C₂×C₄	C₂²×D₄×C₁₃₁	1	8	yes	—
313	C₂×C₄	C₂×#41×C₁₃₁	1	16	yes	—
314	C₂²	—	2	32	no	—
315	C₂²	—	2	8	no	—
316	C₂²	—	2	16	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	8	no	—
320	C₂²	—	8	8	no	—
321	C₂²	C₂×#123×C₁₃₁	1	8	yes	—
322	C₂²	C₂×#123×C₁₃₁	1	4	yes	—
323	C₂²	#525×C₁₃₁	1	8	yes	—
324	C₂²	#529×C₁₃₁	1	16	yes	—
325	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
326	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
327	C₂²	C₂²×#41×C₁₃₁	1	4	yes	—
328	C₄	—	2	8	no	—
329	C₄	—	2	16	no	—
330	C₄	—	4	2	no	—
331	C₄	—	4	4	no	—
332	C₄	—	4	8	no	—
333	C₂	—	2	8	no	—
334	C₂	—	8	2	no	—
335	C₂	#2853×C₁₃₁	1	8	yes	direct product factor
336	C₂	C₂²×#123×C₁₃₁	1	1	yes	characteristic
337	C₂	C₂×#525×C₁₃₁	1	2	yes	—
338	C₂	C₂×#529×C₁₃₁	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂³×D₄×C₁₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄²×C₁₃₁	C₂	semidirect
3. #2853×C₁₃₁	C₂	direct (N × H)
4. C₂×#388×C₁₃₁	C₂	semidirect
5. C₂×#387×C₁₃₁	C₂	semidirect
7. C₂×#385×C₁₃₁	C₂	semidirect
8. C₂×#381×C₁₃₁	C₂	semidirect
22. C₂²×C₄²×C₁₃₁	C₂²	semidirect
23. #388×C₁₃₁	C₂²	semidirect
24. #387×C₁₃₁	C₂²	semidirect
26. #385×C₁₃₁	C₂²	semidirect
27. #381×C₁₃₁	C₂²	semidirect
165. C₂×C₁₃₁	#2853	direct (N × H)
169. C₂×#2853	C₁₃₁	direct (N × H)
170. C₁₃₁	C₂×#2853	direct (N × H)
172. C₂³×C₄²	C₂×C₁₃₁	semidirect
173. #2853	C₂×C₁₃₁	direct (N × H)
174. C₂×#388	C₂×C₁₃₁	semidirect
175. C₂×#387	C₂×C₁₃₁	semidirect
177. C₂×#385	C₂×C₁₃₁	semidirect
178. C₂×#381	C₂×C₁₃₁	semidirect
192. C₂²×C₄²	C₂²×C₁₃₁	semidirect
193. #388	C₂²×C₁₃₁	semidirect
194. #387	C₂²×C₁₃₁	semidirect
196. #385	C₂²×C₁₃₁	semidirect
197. #381	C₂²×C₁₃₁	semidirect
335. C₂	#2853×C₁₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#123×C₁₃₁	2
C₂³×C₄²×C₁₃₁	2
#2853×C₁₃₁	2
C₂×#388×C₁₃₁	2
C₂×#387×C₁₃₁	2
C₂×#386×C₁₃₁	2
C₂×#385×C₁₃₁	2
C₂×#381×C₁₃₁	2
C₂×#2853	131

Subgroups — C2×#2853×C131 #45722502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2853×C₁₃₁ #45722502