Subgroups — C₁₃₁×#35001 #45720885

Order 33536.

4298 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₃₁	C₂	1	4	yes	maximal, complemented
2	C₂²×#121×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2856×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#2656×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2539×C₁₃₁	C₂	1	8	yes	maximal, complemented
6	#2501×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#2433×C₁₃₁	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₁	C₂²	1	4	yes	—
10	C₂³×D₄×C₁₃₁	C₂²	1	2	yes	complemented
11	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
12	#534×C₁₃₁	—	2	32	no	—
13	C₂×#127×C₁₃₁	C₂²	1	4	yes	complemented
14	C₂×#123×C₁₃₁	C₂²	1	16	yes	complemented
15	C₂×#121×C₁₃₁	—	2	16	no	—
16	C₂×#121×C₁₃₁	C₂²	1	4	yes	—
17	C₂×#121×C₁₃₁	C₂²	1	4	yes	—
18	C₂×#121×C₁₃₁	C₂²	1	4	yes	complemented
19	C₂×#121×C₁₃₁	C₂²	1	16	yes	complemented
20	C₂×#121×C₁₃₁	C₂²	1	4	yes	complemented
21	C₂×#120×C₁₃₁	C₂²	1	16	yes	complemented
22	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
25	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	complemented
26	#399×C₁₃₁	C₂²	1	16	yes	complemented
27	#392×C₁₃₁	C₂²	1	16	yes	complemented
28	#390×C₁₃₁	C₂²	1	8	yes	complemented
29	#390×C₁₃₁	C₂²	1	16	yes	complemented
30	#384×C₁₃₁	C₂²	1	4	yes	complemented
31	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
32	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
33	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
34	C₂⁵×C₁₃₁	C₂³	1	4	yes	—
35	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₃₁	—	2	16	no	—
37	C₂²×D₄×C₁₃₁	—	2	32	no	—
38	C₂²×D₄×C₁₃₁	—	2	8	no	—
39	C₂²×D₄×C₁₃₁	—	4	8	no	—
40	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
41	C₂²×D₄×C₁₃₁	C₂³	1	8	yes	—
42	C₂²×D₄×C₁₃₁	C₂³	1	8	yes	—
43	C₂²×D₄×C₁₃₁	C₂³	1	16	yes	—
44	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃₁	—	4	4	no	—
46	C₂³×C₄×C₁₃₁	D₄	1	8	yes	complemented
47	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
53	#127×C₁₃₁	—	4	8	no	—
54	#123×C₁₃₁	—	2	64	no	—
55	#121×C₁₃₁	—	2	16	no	—
56	#121×C₁₃₁	—	2	16	no	—
57	#121×C₁₃₁	—	2	16	no	—
58	#121×C₁₃₁	—	2	16	no	—
59	#121×C₁₃₁	—	2	64	no	—
60	#120×C₁₃₁	—	2	64	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	16	yes	—
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₁₃₁	—	2	16	no	—
66	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	16	yes	complemented
67	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	32	yes	—
69	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₃₁	—	4	4	no	—
72	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
73	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
74	#95×C₁₃₁	C₂³	1	8	yes	—
75	C₂⁴×C₁₃₁	—	2	8	no	—
76	C₂⁴×C₁₃₁	—	2	16	no	—
77	C₂⁴×C₁₃₁	—	4	2	no	—
78	C₂⁴×C₁₃₁	—	4	2	no	—
79	C₂⁴×C₁₃₁	—	4	8	no	—
80	C₂⁴×C₁₃₁	—	4	8	no	—
81	C₂⁴×C₁₃₁	C₂×D₄	1	8	yes	—
82	C₂⁴×C₁₃₁	C₂×D₄	1	4	yes	—
83	C₂⁴×C₁₃₁	C₂⁴	1	8	yes	—
84	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
85	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
86	C₂×D₄×C₁₃₁	—	2	32	no	—
87	C₂×D₄×C₁₃₁	—	2	16	no	—
88	C₂×D₄×C₁₃₁	—	2	16	no	—
89	C₂×D₄×C₁₃₁	—	2	32	no	—
90	C₂×D₄×C₁₃₁	—	2	8	no	—
91	C₂×D₄×C₁₃₁	—	2	8	no	—
92	C₂×D₄×C₁₃₁	—	2	32	no	—
93	C₂×D₄×C₁₃₁	—	2	16	no	—
94	C₂×D₄×C₁₃₁	—	4	8	no	—
95	C₂×D₄×C₁₃₁	—	4	32	no	—
96	C₂×D₄×C₁₃₁	—	4	16	no	—
97	C₂×D₄×C₁₃₁	—	4	16	no	—
98	C₂×D₄×C₁₃₁	—	4	64	no	—
99	C₂²×C₄×C₁₃₁	—	2	4	no	—
100	C₂²×C₄×C₁₃₁	—	2	8	no	—
101	C₂²×C₄×C₁₃₁	—	2	8	no	—
102	C₂²×C₄×C₁₃₁	—	2	16	no	—
103	C₂²×C₄×C₁₃₁	—	4	16	no	—
104	C₂²×C₄×C₁₃₁	—	4	4	no	—
105	C₂²×C₄×C₁₃₁	—	4	4	no	—
106	C₂²×C₄×C₁₃₁	—	4	2	no	—
107	C₂²×C₄×C₁₃₁	—	4	4	no	—
108	C₂²×C₄×C₁₃₁	C₂×D₄	1	8	yes	—
109	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₃₁	C₂×D₄	1	8	yes	—
111	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	16	yes	complemented
113	C₂²×C₄×C₁₃₁	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₁₃₁	C₂⁴	1	8	yes	—
116	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₁₃₁	—	2	8	no	—
119	C₄⋊C₄×C₁₃₁	—	2	8	no	—
120	C₄⋊C₄×C₁₃₁	—	2	32	no	—
121	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
122	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
123	C₂²⋊C₄×C₁₃₁	—	2	64	no	—
124	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	32	yes	complemented
125	C₄²×C₁₃₁	—	2	8	no	—
126	C₄²×C₁₃₁	—	4	4	no	—
127	C₂³×C₁₃₁	—	2	2	no	—
128	C₂³×C₁₃₁	—	2	4	no	—
129	C₂³×C₁₃₁	—	2	2	no	—
130	C₂³×C₁₃₁	—	2	4	no	—
131	C₂³×C₁₃₁	—	2	8	no	—
132	C₂³×C₁₃₁	—	2	16	no	—
133	C₂³×C₁₃₁	—	2	16	no	—
134	C₂³×C₁₃₁	—	2	16	no	—
135	C₂³×C₁₃₁	—	4	4	no	—
136	C₂³×C₁₃₁	—	4	4	no	—
137	C₂³×C₁₃₁	—	4	16	no	—
138	C₂³×C₁₃₁	—	4	16	no	—
139	C₂³×C₁₃₁	—	4	16	no	—
140	C₂³×C₁₃₁	—	4	16	no	—
141	C₂³×C₁₃₁	—	8	32	no	—
142	C₂³×C₁₃₁	#127	1	16	yes	complemented
143	C₂³×C₁₃₁	C₂²×D₄	1	8	yes	—
144	C₂³×C₁₃₁	C₂²×D₄	1	4	yes	—
145	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
146	C₂³×C₁₃₁	C₂²×D₄	1	4	yes	—
147	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
148	D₄×C₁₃₁	—	4	16	no	—
149	D₄×C₁₃₁	—	4	32	no	—
150	D₄×C₁₃₁	—	4	32	no	—
151	D₄×C₁₃₁	—	4	16	no	—
152	D₄×C₁₃₁	—	8	32	no	—
153	C₂×C₄×C₁₃₁	—	2	8	no	—
154	C₂×C₄×C₁₃₁	—	2	2	no	—
155	C₂×C₄×C₁₃₁	—	2	4	no	—
156	C₂×C₄×C₁₃₁	—	2	8	no	—
157	C₂×C₄×C₁₃₁	—	2	8	no	—
158	C₂×C₄×C₁₃₁	—	2	16	no	—
159	C₂×C₄×C₁₃₁	—	2	8	no	—
160	C₂×C₄×C₁₃₁	—	2	16	no	—
161	C₂×C₄×C₁₃₁	—	4	8	no	—
162	C₂×C₄×C₁₃₁	—	4	4	no	—
163	C₂×C₄×C₁₃₁	—	4	16	no	—
164	C₂×C₄×C₁₃₁	—	4	16	no	—
165	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₁₃₁	C₂²×D₄	1	16	yes	—
167	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
170	C₂²×C₁₃₁	—	2	4	no	—
171	C₂²×C₁₃₁	—	2	2	no	—
172	C₂²×C₁₃₁	—	2	4	no	—
173	C₂²×C₁₃₁	—	2	2	no	—
174	C₂²×C₁₃₁	—	2	8	no	—
175	C₂²×C₁₃₁	—	2	16	no	—
176	C₂²×C₁₃₁	—	4	16	no	—
177	C₂²×C₁₃₁	—	4	8	no	—
178	C₂²×C₁₃₁	—	4	8	no	—
179	C₂²×C₁₃₁	—	4	8	no	—
180	C₂²×C₁₃₁	—	4	32	no	—
181	C₂²×C₁₃₁	—	8	32	no	—
182	C₂²×C₁₃₁	C₂×#127	1	8	yes	—
183	C₂²×C₁₃₁	C₂×#127	1	4	yes	—
184	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₁₃₁	C₂³×D₄	1	2	yes	—
186	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
187	C₂²×C₁₃₁	#585	1	2	yes	—
188	C₄×C₁₃₁	—	2	2	no	—
189	C₄×C₁₃₁	—	2	4	no	—
190	C₄×C₁₃₁	—	2	16	no	—
191	C₄×C₁₃₁	—	4	8	no	—
192	C₄×C₁₃₁	#534	1	4	yes	complemented
193	C₂×C₁₃₁	—	2	8	no	—
194	C₂×C₁₃₁	—	2	4	no	—
195	C₂×C₁₃₁	—	8	8	no	—
196	C₂×C₁₃₁	C₂²×#127	1	1	yes	characteristic
197	C₂×C₁₃₁	C₂×#534	1	1	yes	characteristic
198	C₂×C₁₃₁	#3449	1	1	yes	characteristic
199	C₂×C₁₃₁	#3496	1	4	yes	—
200	#35001	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₁₃₁	#35001	1	1	yes	characteristic, direct product factor, Sylow
202	C₂×#534	C₂×C₁₃₁	1	4	yes	complemented
203	C₂²×#121	C₂×C₁₃₁	1	2	yes	complemented
204	#2856	C₂×C₁₃₁	1	4	yes	complemented
205	#2656	C₂×C₁₃₁	1	4	yes	complemented
206	#2539	C₂×C₁₃₁	1	8	yes	complemented
207	#2501	C₂×C₁₃₁	1	4	yes	complemented
208	#2433	C₂×C₁₃₁	1	4	yes	complemented
209	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
210	C₂³×D₄	C₂²×C₁₃₁	1	4	yes	—
211	C₂³×D₄	C₂²×C₁₃₁	1	2	yes	complemented
212	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
213	#534	—	2	32	no	—
214	C₂×#127	C₂²×C₁₃₁	1	4	yes	complemented
215	C₂×#123	C₂²×C₁₃₁	1	16	yes	complemented
216	C₂×#121	—	2	16	no	—
217	C₂×#121	C₂²×C₁₃₁	1	4	yes	—
218	C₂×#121	C₂²×C₁₃₁	1	4	yes	—
219	C₂×#121	C₂²×C₁₃₁	1	4	yes	complemented
220	C₂×#121	C₂²×C₁₃₁	1	16	yes	complemented
221	C₂×#121	C₂²×C₁₃₁	1	4	yes	complemented
222	C₂×#120	C₂²×C₁₃₁	1	16	yes	complemented
223	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
224	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
225	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
226	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	complemented
227	#399	C₂²×C₁₃₁	1	16	yes	complemented
228	#392	C₂²×C₁₃₁	1	16	yes	complemented
229	#390	C₂²×C₁₃₁	1	8	yes	complemented
230	#390	C₂²×C₁₃₁	1	16	yes	complemented
231	#384	C₂²×C₁₃₁	1	4	yes	complemented
232	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
233	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
234	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
235	C₂⁵	C₂³×C₁₃₁	1	4	yes	—
236	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
237	C₂²×D₄	—	2	16	no	—
238	C₂²×D₄	—	2	32	no	—
239	C₂²×D₄	—	2	8	no	—
240	C₂²×D₄	—	4	8	no	—
241	C₂²×D₄	C₂³×C₁₃₁	1	8	yes	—
242	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
243	C₂²×D₄	C₂³×C₁₃₁	1	8	yes	—
244	C₂²×D₄	C₂³×C₁₃₁	1	16	yes	—
245	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
246	C₂³×C₄	—	4	4	no	—
247	C₂³×C₄	D₄×C₁₃₁	1	8	yes	complemented
248	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
249	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
250	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
254	#127	—	4	8	no	—
255	#123	—	2	64	no	—
256	#121	—	2	16	no	—
257	#121	—	2	16	no	—
258	#121	—	2	16	no	—
259	#121	—	2	16	no	—
260	#121	—	2	64	no	—
261	#120	—	2	64	no	—
262	C₂×C₄⋊C₄	—	2	8	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	16	yes	—
266	C₂×C₂²⋊C₄	—	2	16	no	—
267	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	16	yes	complemented
268	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	32	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
272	C₂×C₄²	—	4	4	no	—
273	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
274	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
275	#95	C₂³×C₁₃₁	1	8	yes	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	16	no	—
278	C₂⁴	—	4	2	no	—
279	C₂⁴	—	4	2	no	—
280	C₂⁴	—	4	8	no	—
281	C₂⁴	—	4	8	no	—
282	C₂⁴	C₂×D₄×C₁₃₁	1	8	yes	—
283	C₂⁴	C₂×D₄×C₁₃₁	1	4	yes	—
284	C₂⁴	C₂⁴×C₁₃₁	1	8	yes	—
285	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
286	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
287	C₂×D₄	—	2	32	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	16	no	—
290	C₂×D₄	—	2	32	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	32	no	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	—	4	32	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂×D₄	—	4	16	no	—
299	C₂×D₄	—	4	64	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	4	16	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	C₂×D₄×C₁₃₁	1	8	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃₁	1	8	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₁	1	16	yes	complemented
314	C₂²×C₄	C₂⁴×C₁₃₁	1	8	yes	—
315	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₁₃₁	1	8	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	32	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	—	2	16	no	—
324	C₂²⋊C₄	—	2	64	no	—
325	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	32	yes	complemented
326	C₄²	—	2	8	no	—
327	C₄²	—	4	4	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	16	no	—
334	C₂³	—	2	16	no	—
335	C₂³	—	2	16	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	16	no	—
340	C₂³	—	4	16	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	8	32	no	—
343	C₂³	#127×C₁₃₁	1	16	yes	complemented
344	C₂³	C₂²×D₄×C₁₃₁	1	8	yes	—
345	C₂³	C₂²×D₄×C₁₃₁	1	4	yes	—
346	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
347	C₂³	C₂²×D₄×C₁₃₁	1	4	yes	—
348	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
349	D₄	—	4	16	no	—
350	D₄	—	4	32	no	—
351	D₄	—	4	32	no	—
352	D₄	—	4	16	no	—
353	D₄	—	8	32	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	16	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃₁	1	16	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
369	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
370	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	16	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	32	no	—
382	C₂²	—	8	32	no	—
383	C₂²	C₂×#127×C₁₃₁	1	8	yes	—
384	C₂²	C₂×#127×C₁₃₁	1	4	yes	—
385	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
386	C₂²	C₂³×D₄×C₁₃₁	1	2	yes	—
387	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
388	C₂²	#585×C₁₃₁	1	2	yes	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	16	no	—
392	C₄	—	4	8	no	—
393	C₄	#534×C₁₃₁	1	4	yes	complemented
394	C₂	—	2	8	no	—
395	C₂	—	2	4	no	—
396	C₂	—	8	8	no	—
397	C₂	C₂²×#127×C₁₃₁	1	1	yes	characteristic
398	C₂	C₂×#534×C₁₃₁	1	1	yes	characteristic
399	C₂	#3449×C₁₃₁	1	1	yes	characteristic
400	C₂	#3496×C₁₃₁	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#534×C₁₃₁	C₂	semidirect
2. C₂²×#121×C₁₃₁	C₂	semidirect
3. #2856×C₁₃₁	C₂	semidirect
4. #2656×C₁₃₁	C₂	semidirect
5. #2539×C₁₃₁	C₂	semidirect
6. #2501×C₁₃₁	C₂	semidirect
7. #2433×C₁₃₁	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
10. C₂³×D₄×C₁₃₁	C₂²	semidirect
13. C₂×#127×C₁₃₁	C₂²	semidirect
14. C₂×#123×C₁₃₁	C₂²	semidirect
18. C₂×#121×C₁₃₁	C₂²	semidirect
19. C₂×#121×C₁₃₁	C₂²	semidirect
20. C₂×#121×C₁₃₁	C₂²	semidirect
21. C₂×#120×C₁₃₁	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
24. C₂²×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
25. C₂²×C₄²×C₁₃₁	C₂²	semidirect
26. #399×C₁₃₁	C₂²	semidirect
27. #392×C₁₃₁	C₂²	semidirect
28. #390×C₁₃₁	C₂²	semidirect
29. #390×C₁₃₁	C₂²	semidirect
30. #384×C₁₃₁	C₂²	semidirect
31. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
33. C₂×#95×C₁₃₁	C₂²	semidirect
46. C₂³×C₄×C₁₃₁	D₄	semidirect
66. C₂×C₂²⋊C₄×C₁₃₁	D₄	semidirect
112. C₂²×C₄×C₁₃₁	C₂×D₄	semidirect
124. C₂²⋊C₄×C₁₃₁	C₂×D₄	semidirect
142. C₂³×C₁₃₁	#127	semidirect
192. C₄×C₁₃₁	#534	semidirect
200. #35001	C₁₃₁	direct (N × H)
201. C₁₃₁	#35001	direct (N × H)
202. C₂×#534	C₂×C₁₃₁	semidirect
203. C₂²×#121	C₂×C₁₃₁	semidirect
204. #2856	C₂×C₁₃₁	semidirect
205. #2656	C₂×C₁₃₁	semidirect
206. #2539	C₂×C₁₃₁	semidirect
207. #2501	C₂×C₁₃₁	semidirect
208. #2433	C₂×C₁₃₁	semidirect
209. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
211. C₂³×D₄	C₂²×C₁₃₁	semidirect
214. C₂×#127	C₂²×C₁₃₁	semidirect
215. C₂×#123	C₂²×C₁₃₁	semidirect
219. C₂×#121	C₂²×C₁₃₁	semidirect
220. C₂×#121	C₂²×C₁₃₁	semidirect
221. C₂×#121	C₂²×C₁₃₁	semidirect
222. C₂×#120	C₂²×C₁₃₁	semidirect
223. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
225. C₂²×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
226. C₂²×C₄²	C₂²×C₁₃₁	semidirect
227. #399	C₂²×C₁₃₁	semidirect
228. #392	C₂²×C₁₃₁	semidirect
229. #390	C₂²×C₁₃₁	semidirect
230. #390	C₂²×C₁₃₁	semidirect
231. #384	C₂²×C₁₃₁	semidirect
232. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
233. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
234. C₂×#95	C₂²×C₁₃₁	semidirect
247. C₂³×C₄	D₄×C₁₃₁	semidirect
267. C₂×C₂²⋊C₄	D₄×C₁₃₁	semidirect
313. C₂²×C₄	C₂×D₄×C₁₃₁	semidirect
325. C₂²⋊C₄	C₂×D₄×C₁₃₁	semidirect
343. C₂³	#127×C₁₃₁	semidirect
393. C₄	#534×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₁₃₁	2
C₂²×#121×C₁₃₁	2
#2856×C₁₃₁	2
#2656×C₁₃₁	2
#2539×C₁₃₁	2
#2501×C₁₃₁	2
#2433×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
#35001	131

Subgroups — C131×#35001 #45720885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#35001 #45720885