Subgroups — C₂×#2852×C₁₃₁ #45722501

Order 33536.

3354 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2852×C₁₃₁	C₂	1	16	yes	maximal, direct product factor
4	C₂×#388×C₁₃₁	C₂	1	3	yes	maximal, complemented
5	C₂×#387×C₁₃₁	C₂	1	3	yes	maximal, complemented
6	C₂×#386×C₁₃₁	C₂	1	3	yes	maximal
7	C₂×#385×C₁₃₁	C₂	1	3	yes	maximal, complemented
8	C₂×#383×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃₁	C₂²	1	3	yes	—
11	C₂×#126×C₁₃₁	—	2	8	no	—
12	C₂×#126×C₁₃₁	C₂²	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	3	yes	—
14	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	3	yes	—
15	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	3	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	3	yes	—
17	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	3	yes	—
18	C₂²×C₄²×C₁₃₁	—	2	8	no	—
19	C₂²×C₄²×C₁₃₁	C₂²	1	3	yes	—
20	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃₁	C₂²	1	8	yes	complemented
22	#388×C₁₃₁	C₂²	1	24	yes	complemented
23	#387×C₁₃₁	C₂²	1	24	yes	complemented
24	#386×C₁₃₁	C₂²	1	24	yes	—
25	#385×C₁₃₁	C₂²	1	24	yes	complemented
26	#383×C₁₃₁	C₂²	1	8	yes	complemented
27	C₂×#95×C₁₃₁	C₂²	1	3	yes	—
28	C₂×#95×C₁₃₁	C₂²	1	3	yes	—
29	C₂×#95×C₁₃₁	C₂²	1	3	yes	—
30	C₂×#95×C₁₃₁	C₂²	1	3	yes	—
31	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
32	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₁₃₁	—	2	12	no	—
34	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃₁	—	2	12	no	—
36	C₂³×C₄×C₁₃₁	—	2	12	no	—
37	C₂³×C₄×C₁₃₁	—	2	12	no	—
38	C₂³×C₄×C₁₃₁	C₂³	1	12	yes	—
39	C₂³×C₄×C₁₃₁	C₂³	1	3	yes	—
40	C₂³×C₄×C₁₃₁	C₂³	1	3	yes	—
41	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₁	C₂³	1	3	yes	—
43	C₂³×C₄×C₁₃₁	C₂³	1	3	yes	—
44	#126×C₁₃₁	—	2	32	no	—
45	C₂×C₄⋊C₄×C₁₃₁	—	2	12	no	—
46	C₂×C₄⋊C₄×C₁₃₁	—	2	12	no	—
47	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	12	yes	—
48	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	12	yes	—
49	C₂×C₂²⋊C₄×C₁₃₁	—	2	12	no	—
50	C₂×C₂²⋊C₄×C₁₃₁	—	2	12	no	—
51	C₂×C₂²⋊C₄×C₁₃₁	—	2	12	no	—
52	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	12	yes	—
53	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	12	yes	—
54	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	12	yes	—
55	C₂×C₄²×C₁₃₁	—	2	12	no	—
56	C₂×C₄²×C₁₃₁	—	2	32	no	—
57	C₂×C₄²×C₁₃₁	D₄	1	8	yes	complemented
58	C₂×C₄²×C₁₃₁	C₂³	1	12	yes	—
59	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
60	#95×C₁₃₁	C₂³	1	12	yes	—
61	#95×C₁₃₁	C₂³	1	12	yes	—
62	#95×C₁₃₁	C₂³	1	12	yes	—
63	#95×C₁₃₁	C₂³	1	12	yes	—
64	C₂⁴×C₁₃₁	—	2	2	no	—
65	C₂⁴×C₁₃₁	—	2	6	no	—
66	C₂⁴×C₁₃₁	—	2	2	no	—
67	C₂⁴×C₁₃₁	—	2	6	no	—
68	C₂⁴×C₁₃₁	—	2	6	no	—
69	C₂⁴×C₁₃₁	#41	1	12	yes	—
70	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
71	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
72	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
73	C₂×D₄×C₁₃₁	—	2	24	no	—
74	C₂×D₄×C₁₃₁	—	4	16	no	—
75	C₂²×C₄×C₁₃₁	—	2	96	no	—
76	C₂²×C₄×C₁₃₁	—	2	6	no	—
77	C₂²×C₄×C₁₃₁	—	2	24	no	—
78	C₂²×C₄×C₁₃₁	—	2	6	no	—
79	C₂²×C₄×C₁₃₁	—	2	6	no	—
80	C₂²×C₄×C₁₃₁	—	2	6	no	—
81	C₂²×C₄×C₁₃₁	—	2	24	no	—
82	C₂²×C₄×C₁₃₁	—	2	24	no	—
83	C₂²×C₄×C₁₃₁	—	2	6	no	—
84	C₂²×C₄×C₁₃₁	—	2	6	no	—
85	C₂²×C₄×C₁₃₁	—	2	6	no	—
86	C₂²×C₄×C₁₃₁	—	2	6	no	—
87	C₂²×C₄×C₁₃₁	—	2	6	no	—
88	C₂²×C₄×C₁₃₁	—	2	6	no	—
89	C₂²×C₄×C₁₃₁	—	2	6	no	—
90	C₂²×C₄×C₁₃₁	C₂×D₄	1	12	yes	—
91	C₂²×C₄×C₁₃₁	#41	1	12	yes	—
92	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
93	C₂²×C₄×C₁₃₁	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₁₃₁	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₁₃₁	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₁₃₁	C₂⁴	1	6	yes	—
97	C₄⋊C₄×C₁₃₁	—	2	24	no	—
98	C₄⋊C₄×C₁₃₁	—	2	24	no	—
99	C₂²⋊C₄×C₁₃₁	—	2	24	no	—
100	C₂²⋊C₄×C₁₃₁	—	2	24	no	—
101	C₂²⋊C₄×C₁₃₁	—	2	24	no	—
102	C₄²×C₁₃₁	—	2	24	no	—
103	C₄²×C₁₃₁	C₂×D₄	1	16	yes	complemented
104	C₂³×C₁₃₁	—	2	24	no	—
105	C₂³×C₁₃₁	—	2	24	no	—
106	C₂³×C₁₃₁	—	2	2	no	—
107	C₂³×C₁₃₁	—	2	6	no	—
108	C₂³×C₁₃₁	—	2	2	no	—
109	C₂³×C₁₃₁	—	2	6	no	—
110	C₂³×C₁₃₁	—	2	6	no	—
111	C₂³×C₁₃₁	—	4	12	no	—
112	C₂³×C₁₃₁	—	4	4	no	—
113	C₂³×C₁₃₁	—	4	12	no	—
114	C₂³×C₁₃₁	#126	1	16	yes	complemented
115	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
116	C₂³×C₁₃₁	C₂×#41	1	12	yes	—
117	C₂³×C₁₃₁	C₂×#41	1	6	yes	—
118	C₂³×C₁₃₁	C₂×#41	1	6	yes	—
119	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
120	D₄×C₁₃₁	—	4	16	no	—
121	C₂×C₄×C₁₃₁	—	2	96	no	—
122	C₂×C₄×C₁₃₁	—	2	24	no	—
123	C₂×C₄×C₁₃₁	—	2	24	no	—
124	C₂×C₄×C₁₃₁	—	2	6	no	—
125	C₂×C₄×C₁₃₁	—	2	6	no	—
126	C₂×C₄×C₁₃₁	—	2	6	no	—
127	C₂×C₄×C₁₃₁	—	2	6	no	—
128	C₂×C₄×C₁₃₁	—	2	6	no	—
129	C₂×C₄×C₁₃₁	—	2	6	no	—
130	C₂×C₄×C₁₃₁	—	2	6	no	—
131	C₂×C₄×C₁₃₁	—	2	6	no	—
132	C₂×C₄×C₁₃₁	—	2	6	no	—
133	C₂×C₄×C₁₃₁	—	2	6	no	—
134	C₂×C₄×C₁₃₁	—	2	6	no	—
135	C₂×C₄×C₁₃₁	—	4	12	no	—
136	C₂×C₄×C₁₃₁	—	4	4	no	—
137	C₂×C₄×C₁₃₁	—	4	12	no	—
138	C₂×C₄×C₁₃₁	C₂²×D₄	1	12	yes	—
139	C₂×C₄×C₁₃₁	C₂×#41	1	12	yes	—
140	C₂²×C₁₃₁	—	2	32	no	—
141	C₂²×C₁₃₁	—	2	12	no	—
142	C₂²×C₁₃₁	—	2	12	no	—
143	C₂²×C₁₃₁	—	4	6	no	—
144	C₂²×C₁₃₁	—	4	2	no	—
145	C₂²×C₁₃₁	—	4	6	no	—
146	C₂²×C₁₃₁	—	8	8	no	—
147	C₂²×C₁₃₁	#525	1	12	yes	—
148	C₂²×C₁₃₁	C₂×#126	1	4	yes	—
149	C₂²×C₁₃₁	C₂×#126	1	8	yes	complemented
150	C₂²×C₁₃₁	#529	1	12	yes	—
151	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
152	C₂²×C₁₃₁	C₂²×#41	1	3	yes	—
153	C₂²×C₁₃₁	C₂²×#41	1	3	yes	—
154	C₄×C₁₃₁	—	2	12	no	—
155	C₄×C₁₃₁	—	2	12	no	—
156	C₄×C₁₃₁	—	4	6	no	—
157	C₄×C₁₃₁	—	4	2	no	—
158	C₄×C₁₃₁	—	4	6	no	—
159	C₂×C₁₃₁	—	2	8	no	—
160	C₂×C₁₃₁	—	8	2	no	—
161	C₂×C₁₃₁	#2852	1	8	yes	direct product factor
162	C₂×C₁₃₁	C₂×#525	1	3	yes	—
163	C₂×C₁₃₁	C₂²×#126	1	1	yes	characteristic
164	C₂×C₁₃₁	C₂×#529	1	3	yes	—
165	C₂×#2852	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₁₃₁	C₂×#2852	1	1	yes	characteristic, direct product factor, Sylow
167	C₂²×#126	C₂×C₁₃₁	1	1	yes	characteristic, complemented
168	C₂³×C₄²	C₂×C₁₃₁	1	1	yes	characteristic, complemented
169	#2852	C₂×C₁₃₁	1	16	yes	direct product factor
170	C₂×#388	C₂×C₁₃₁	1	3	yes	complemented
171	C₂×#387	C₂×C₁₃₁	1	3	yes	complemented
172	C₂×#386	C₂×C₁₃₁	1	3	yes	—
173	C₂×#385	C₂×C₁₃₁	1	3	yes	complemented
174	C₂×#383	C₂×C₁₃₁	1	1	yes	characteristic, complemented
175	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
176	C₂⁴×C₄	C₂²×C₁₃₁	1	3	yes	—
177	C₂×#126	—	2	8	no	—
178	C₂×#126	C₂²×C₁₃₁	1	8	yes	complemented
179	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	3	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	3	yes	—
181	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	3	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	3	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	3	yes	—
184	C₂²×C₄²	—	2	8	no	—
185	C₂²×C₄²	C₂²×C₁₃₁	1	3	yes	—
186	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₃₁	1	8	yes	complemented
188	#388	C₂²×C₁₃₁	1	24	yes	complemented
189	#387	C₂²×C₁₃₁	1	24	yes	complemented
190	#386	C₂²×C₁₃₁	1	24	yes	—
191	#385	C₂²×C₁₃₁	1	24	yes	complemented
192	#383	C₂²×C₁₃₁	1	8	yes	complemented
193	C₂×#95	C₂²×C₁₃₁	1	3	yes	—
194	C₂×#95	C₂²×C₁₃₁	1	3	yes	—
195	C₂×#95	C₂²×C₁₃₁	1	3	yes	—
196	C₂×#95	C₂²×C₁₃₁	1	3	yes	—
197	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
198	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
199	C₂²×D₄	—	2	12	no	—
200	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
201	C₂³×C₄	—	2	12	no	—
202	C₂³×C₄	—	2	12	no	—
203	C₂³×C₄	—	2	12	no	—
204	C₂³×C₄	C₂³×C₁₃₁	1	3	yes	—
205	C₂³×C₄	C₂³×C₁₃₁	1	3	yes	—
206	C₂³×C₄	C₂³×C₁₃₁	1	12	yes	—
207	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₁₃₁	1	3	yes	—
209	C₂³×C₄	C₂³×C₁₃₁	1	3	yes	—
210	#126	—	2	32	no	—
211	C₂×C₄⋊C₄	—	2	12	no	—
212	C₂×C₄⋊C₄	—	2	12	no	—
213	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	12	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	12	yes	—
215	C₂×C₂²⋊C₄	—	2	12	no	—
216	C₂×C₂²⋊C₄	—	2	12	no	—
217	C₂×C₂²⋊C₄	—	2	12	no	—
218	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	12	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	12	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	12	yes	—
221	C₂×C₄²	—	2	12	no	—
222	C₂×C₄²	—	2	32	no	—
223	C₂×C₄²	D₄×C₁₃₁	1	8	yes	complemented
224	C₂×C₄²	C₂³×C₁₃₁	1	12	yes	—
225	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
226	#95	C₂³×C₁₃₁	1	12	yes	—
227	#95	C₂³×C₁₃₁	1	12	yes	—
228	#95	C₂³×C₁₃₁	1	12	yes	—
229	#95	C₂³×C₁₃₁	1	12	yes	—
230	C₂⁴	—	2	2	no	—
231	C₂⁴	—	2	6	no	—
232	C₂⁴	—	2	2	no	—
233	C₂⁴	—	2	6	no	—
234	C₂⁴	—	2	6	no	—
235	C₂⁴	#41×C₁₃₁	1	12	yes	—
236	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
237	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
238	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
239	C₂×D₄	—	2	24	no	—
240	C₂×D₄	—	4	16	no	—
241	C₂²×C₄	—	2	96	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	2	24	no	—
244	C₂²×C₄	—	2	6	no	—
245	C₂²×C₄	—	2	6	no	—
246	C₂²×C₄	—	2	6	no	—
247	C₂²×C₄	—	2	24	no	—
248	C₂²×C₄	—	2	24	no	—
249	C₂²×C₄	—	2	6	no	—
250	C₂²×C₄	—	2	6	no	—
251	C₂²×C₄	—	2	6	no	—
252	C₂²×C₄	—	2	6	no	—
253	C₂²×C₄	—	2	6	no	—
254	C₂²×C₄	—	2	6	no	—
255	C₂²×C₄	—	2	6	no	—
256	C₂²×C₄	C₂×D₄×C₁₃₁	1	12	yes	—
257	C₂²×C₄	#41×C₁₃₁	1	12	yes	—
258	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₁₃₁	1	6	yes	—
260	C₂²×C₄	C₂⁴×C₁₃₁	1	6	yes	—
261	C₂²×C₄	C₂⁴×C₁₃₁	1	6	yes	—
262	C₂²×C₄	C₂⁴×C₁₃₁	1	6	yes	—
263	C₄⋊C₄	—	2	24	no	—
264	C₄⋊C₄	—	2	24	no	—
265	C₂²⋊C₄	—	2	24	no	—
266	C₂²⋊C₄	—	2	24	no	—
267	C₂²⋊C₄	—	2	24	no	—
268	C₄²	—	2	24	no	—
269	C₄²	C₂×D₄×C₁₃₁	1	16	yes	complemented
270	C₂³	—	2	24	no	—
271	C₂³	—	2	24	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	6	no	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	6	no	—
276	C₂³	—	2	6	no	—
277	C₂³	—	4	12	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	4	12	no	—
280	C₂³	#126×C₁₃₁	1	16	yes	complemented
281	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
282	C₂³	C₂×#41×C₁₃₁	1	12	yes	—
283	C₂³	C₂×#41×C₁₃₁	1	6	yes	—
284	C₂³	C₂×#41×C₁₃₁	1	6	yes	—
285	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
286	D₄	—	4	16	no	—
287	C₂×C₄	—	2	96	no	—
288	C₂×C₄	—	2	24	no	—
289	C₂×C₄	—	2	24	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	2	6	no	—
292	C₂×C₄	—	2	6	no	—
293	C₂×C₄	—	2	6	no	—
294	C₂×C₄	—	2	6	no	—
295	C₂×C₄	—	2	6	no	—
296	C₂×C₄	—	2	6	no	—
297	C₂×C₄	—	2	6	no	—
298	C₂×C₄	—	2	6	no	—
299	C₂×C₄	—	2	6	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	4	12	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	12	no	—
304	C₂×C₄	C₂²×D₄×C₁₃₁	1	12	yes	—
305	C₂×C₄	C₂×#41×C₁₃₁	1	12	yes	—
306	C₂²	—	2	32	no	—
307	C₂²	—	2	12	no	—
308	C₂²	—	2	12	no	—
309	C₂²	—	4	6	no	—
310	C₂²	—	4	2	no	—
311	C₂²	—	4	6	no	—
312	C₂²	—	8	8	no	—
313	C₂²	#525×C₁₃₁	1	12	yes	—
314	C₂²	C₂×#126×C₁₃₁	1	4	yes	—
315	C₂²	C₂×#126×C₁₃₁	1	8	yes	complemented
316	C₂²	#529×C₁₃₁	1	12	yes	—
317	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
318	C₂²	C₂²×#41×C₁₃₁	1	3	yes	—
319	C₂²	C₂²×#41×C₁₃₁	1	3	yes	—
320	C₄	—	2	12	no	—
321	C₄	—	2	12	no	—
322	C₄	—	4	6	no	—
323	C₄	—	4	2	no	—
324	C₄	—	4	6	no	—
325	C₂	—	2	8	no	—
326	C₂	—	8	2	no	—
327	C₂	#2852×C₁₃₁	1	8	yes	direct product factor
328	C₂	C₂×#525×C₁₃₁	1	3	yes	—
329	C₂	C₂²×#126×C₁₃₁	1	1	yes	characteristic
330	C₂	C₂×#529×C₁₃₁	1	3	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
1. C₂²×#126×C₁₃₁	C₂	semidirect
2. C₂³×C₄²×C₁₃₁	C₂	semidirect
3. #2852×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×#383×C₁₃₁	C₂	semidirect
12. C₂×#126×C₁₃₁	C₂²	semidirect
21. C₂²×C₄²×C₁₃₁	C₂²	semidirect
22. #388×C₁₃₁	C₂²	semidirect
23. #387×C₁₃₁	C₂²	semidirect
25. #385×C₁₃₁	C₂²	semidirect
26. #383×C₁₃₁	C₂²	semidirect
57. C₂×C₄²×C₁₃₁	D₄	semidirect
103. C₄²×C₁₃₁	C₂×D₄	semidirect
114. C₂³×C₁₃₁	#126	semidirect
149. C₂²×C₁₃₁	C₂×#126	semidirect
161. C₂×C₁₃₁	#2852	direct (N × H)
165. C₂×#2852	C₁₃₁	direct (N × H)
166. C₁₃₁	C₂×#2852	direct (N × H)
167. C₂²×#126	C₂×C₁₃₁	semidirect
168. C₂³×C₄²	C₂×C₁₃₁	semidirect
169. #2852	C₂×C₁₃₁	direct (N × H)
170. C₂×#388	C₂×C₁₃₁	semidirect
171. C₂×#387	C₂×C₁₃₁	semidirect
173. C₂×#385	C₂×C₁₃₁	semidirect
174. C₂×#383	C₂×C₁₃₁	semidirect
178. C₂×#126	C₂²×C₁₃₁	semidirect
187. C₂²×C₄²	C₂²×C₁₃₁	semidirect
188. #388	C₂²×C₁₃₁	semidirect
189. #387	C₂²×C₁₃₁	semidirect
191. #385	C₂²×C₁₃₁	semidirect
192. #383	C₂²×C₁₃₁	semidirect
223. C₂×C₄²	D₄×C₁₃₁	semidirect
269. C₄²	C₂×D₄×C₁₃₁	semidirect
280. C₂³	#126×C₁₃₁	semidirect
315. C₂²	C₂×#126×C₁₃₁	semidirect
327. C₂	#2852×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×#126×C₁₃₁	2
C₂³×C₄²×C₁₃₁	2
#2852×C₁₃₁	2
C₂×#388×C₁₃₁	2
C₂×#387×C₁₃₁	2
C₂×#386×C₁₃₁	2
C₂×#385×C₁₃₁	2
C₂×#383×C₁₃₁	2
C₂×#2852	131

Subgroups — C2×#2852×C131 #45722501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2852×C₁₃₁ #45722501