Subgroups — C₁₃₁×#33490 #45719374

Order 33536.

574 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2929×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2169×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2168×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2168×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₆×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2164×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2113×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2112×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊C₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	#525×C₁₃₁	C₄	1	1	yes	characteristic
13	C₂×M₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×M₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×M₃₂×C₁₃₁	C₂²	1	2	yes	complemented
16	C₂²×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
19	#435×C₁₃₁	C₄	1	2	yes	—
20	#435×C₁₃₁	C₄	1	2	yes	—
21	C₈×D₄×C₁₃₁	C₂²	1	2	yes	—
22	C₈×D₄×C₁₃₁	C₂²	1	2	yes	—
23	#424×C₁₃₁	C₄	1	1	yes	characteristic
24	#408×C₁₃₁	C₄	1	1	yes	characteristic
25	#407×C₁₃₁	C₄	1	1	yes	characteristic
26	#405×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
28	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
29	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
30	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
31	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
32	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
33	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
34	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
35	#346×C₁₃₁	C₂²	1	2	yes	complemented
36	C₄×C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
37	C₂×#41×C₁₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
39	#131×C₁₃₁	—	4	1	no	—
40	#131×C₁₃₁	—	4	1	no	—
41	C₂×M₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×M₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×M₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃₁	—	4	1	no	—
45	C₂²×C₈×C₁₃₁	—	4	1	no	—
46	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	#123×C₁₃₁	C₈	1	2	yes	—
54	C₂²⋊Q₈×C₁₃₁	C₈	1	1	yes	characteristic
55	C₂²⋊Q₈×C₁₃₁	C₈	1	1	yes	characteristic
56	#121×C₁₃₁	C₈	1	1	yes	characteristic
57	#121×C₁₃₁	C₈	1	1	yes	characteristic
58	#120×C₁₃₁	C₈	1	2	yes	—
59	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
61	#117×C₁₃₁	C₂×C₄	1	1	yes	characteristic
62	M₃₂×C₁₃₁	—	4	1	no	—
63	M₃₂×C₁₃₁	—	4	1	no	—
64	M₃₂×C₁₃₁	—	4	2	no	—
65	C₂×C₁₆×C₁₃₁	—	4	1	no	—
66	C₂×C₁₆×C₁₃₁	—	4	1	no	—
67	C₂×C₁₆×C₁₃₁	—	4	2	no	—
68	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
69	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
70	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
71	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
73	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
74	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
75	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
76	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
78	#97×C₁₃₁	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
80	C₂⁴×C₁₃₁	C₂×C₈	1	1	yes	characteristic
81	#41×C₁₃₁	—	4	1	no	—
82	#41×C₁₃₁	—	4	1	no	—
83	C₂×Q₈×C₁₃₁	C₂×C₈	1	1	yes	characteristic
84	C₂×D₄×C₁₃₁	C₂×C₈	1	2	yes	—
85	C₂×D₄×C₁₃₁	C₂×C₈	1	2	yes	—
86	C₂×D₄×C₁₃₁	C₂×C₈	1	2	yes	—
87	C₂×D₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₁	—	4	1	no	—
89	C₂²×C₄×C₁₃₁	—	4	1	no	—
90	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
97	M₁₆×C₁₃₁	—	4	1	no	—
98	M₁₆×C₁₃₁	—	4	2	no	—
99	M₁₆×C₁₃₁	—	4	1	no	—
100	C₂×C₈×C₁₃₁	—	2	1	no	—
101	C₂×C₈×C₁₃₁	—	2	1	no	—
102	C₂×C₈×C₁₃₁	—	2	2	no	—
103	C₂×C₈×C₁₃₁	—	2	1	no	—
104	C₂×C₈×C₁₃₁	—	2	1	no	—
105	C₂×C₈×C₁₃₁	—	2	2	no	—
106	C₂×C₈×C₁₃₁	—	2	1	no	—
107	C₂×C₈×C₁₃₁	—	2	1	no	—
108	C₂×C₈×C₁₃₁	—	4	1	no	—
109	C₂×C₈×C₁₃₁	—	4	1	no	—
110	C₂×C₈×C₁₃₁	—	4	1	no	—
111	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
118	C₄⋊C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
119	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
120	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
121	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
122	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
123	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
124	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
125	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
126	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
127	C₁₆×C₁₃₁	—	2	2	no	—
128	C₁₆×C₁₃₁	—	2	2	no	—
129	C₁₆×C₁₃₁	—	2	2	no	—
130	C₁₆×C₁₃₁	—	2	2	no	—
131	C₂³×C₁₃₁	—	2	2	no	—
132	C₂³×C₁₃₁	—	4	1	no	—
133	C₂³×C₁₃₁	—	4	1	no	—
134	C₂³×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
135	C₂³×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
136	C₂³×C₁₃₁	C₂²×C₈	1	2	yes	—
137	C₂³×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
138	Q₈×C₁₃₁	—	4	1	no	—
139	D₄×C₁₃₁	—	2	4	no	—
140	D₄×C₁₃₁	—	4	2	no	—
141	D₄×C₁₃₁	—	4	1	no	—
142	D₄×C₁₃₁	—	4	2	no	—
143	C₂×C₄×C₁₃₁	—	2	1	no	—
144	C₂×C₄×C₁₃₁	—	2	1	no	—
145	C₂×C₄×C₁₃₁	—	2	1	no	—
146	C₂×C₄×C₁₃₁	—	2	2	no	—
147	C₂×C₄×C₁₃₁	—	2	1	no	—
148	C₂×C₄×C₁₃₁	—	2	1	no	—
149	C₂×C₄×C₁₃₁	—	2	1	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	4	1	no	—
152	C₂×C₄×C₁₃₁	—	4	1	no	—
153	C₂×C₄×C₁₃₁	—	4	1	no	—
154	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
159	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
161	C₈×C₁₃₁	—	2	1	no	—
162	C₈×C₁₃₁	—	2	1	no	—
163	C₈×C₁₃₁	—	2	1	no	—
164	C₈×C₁₃₁	—	2	2	no	—
165	C₈×C₁₃₁	—	2	2	no	—
166	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
167	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂²×C₁₃₁	—	2	1	no	—
169	C₂²×C₁₃₁	—	2	1	no	—
170	C₂²×C₁₃₁	—	2	2	no	—
171	C₂²×C₁₃₁	—	2	1	no	—
172	C₂²×C₁₃₁	—	2	1	no	—
173	C₂²×C₁₃₁	—	2	1	no	—
174	C₂²×C₁₃₁	—	2	2	no	—
175	C₂²×C₁₃₁	—	2	1	no	—
176	C₂²×C₁₃₁	—	2	1	no	—
177	C₂²×C₁₃₁	—	2	1	no	—
178	C₂²×C₁₃₁	—	2	2	no	—
179	C₂²×C₁₃₁	—	4	4	no	—
180	C₂²×C₁₃₁	#504	1	2	yes	—
181	C₂²×C₁₃₁	C₂³×C₈	1	1	yes	characteristic
182	C₄×C₁₃₁	—	2	2	no	—
183	C₄×C₁₃₁	—	2	2	no	—
184	C₄×C₁₃₁	—	2	1	no	—
185	C₄×C₁₃₁	—	2	1	no	—
186	C₄×C₁₃₁	—	2	1	no	—
187	C₄×C₁₃₁	—	2	2	no	—
188	C₄×C₁₃₁	#518	1	1	yes	characteristic
189	C₄×C₁₃₁	#568	1	1	yes	characteristic
190	C₂×C₁₃₁	—	2	2	no	—
191	C₂×C₁₃₁	—	4	2	no	—
192	C₂×C₁₃₁	—	4	1	no	—
193	C₂×C₁₃₁	—	4	1	no	—
194	C₂×C₁₃₁	#2972	1	1	yes	characteristic
195	C₂×C₁₃₁	C₂×#504	1	1	yes	characteristic
196	C₂×C₁₃₁	#3407	1	1	yes	characteristic
197	#33490	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃₁	#33490	1	1	yes	characteristic, direct product factor, Sylow
199	#2929	C₂×C₁₃₁	1	1	yes	characteristic
200	#2169	C₂×C₁₃₁	1	2	yes	complemented
201	#2168	C₂×C₁₃₁	1	2	yes	complemented
202	#2168	C₂×C₁₃₁	1	2	yes	complemented
203	D₄×C₁₆	C₂×C₁₃₁	1	2	yes	complemented
204	#2164	C₂×C₁₃₁	1	2	yes	complemented
205	#2113	C₂×C₁₃₁	1	2	yes	complemented
206	#2112	C₂×C₁₃₁	1	1	yes	characteristic, complemented
207	C₂×C₂²⋊C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
208	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
210	#525	C₄×C₁₃₁	1	1	yes	characteristic
211	C₂×M₃₂	C₂²×C₁₃₁	1	1	yes	characteristic
212	C₂×M₃₂	C₂²×C₁₃₁	1	1	yes	characteristic
213	C₂×M₃₂	C₂²×C₁₃₁	1	2	yes	complemented
214	C₂²×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂²×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
216	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
217	#435	C₄×C₁₃₁	1	2	yes	—
218	#435	C₄×C₁₃₁	1	2	yes	—
219	C₈×D₄	C₂²×C₁₃₁	1	2	yes	—
220	C₈×D₄	C₂²×C₁₃₁	1	2	yes	—
221	#424	C₄×C₁₃₁	1	1	yes	characteristic
222	#408	C₄×C₁₃₁	1	1	yes	characteristic
223	#407	C₄×C₁₃₁	1	1	yes	characteristic
224	#405	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
226	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
227	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
228	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
229	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
230	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
231	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
232	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
233	#346	C₂²×C₁₃₁	1	2	yes	complemented
234	C₄×C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
235	C₂×#41	C₂×C₄×C₁₃₁	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
237	#131	—	4	1	no	—
238	#131	—	4	1	no	—
239	C₂×M₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
240	C₂×M₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
241	C₂×M₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
242	C₂²×C₈	—	4	1	no	—
243	C₂²×C₈	—	4	1	no	—
244	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
245	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
251	#123	C₈×C₁₃₁	1	2	yes	—
252	C₂²⋊Q₈	C₈×C₁₃₁	1	1	yes	characteristic
253	C₂²⋊Q₈	C₈×C₁₃₁	1	1	yes	characteristic
254	#121	C₈×C₁₃₁	1	1	yes	characteristic
255	#121	C₈×C₁₃₁	1	1	yes	characteristic
256	#120	C₈×C₁₃₁	1	2	yes	—
257	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
258	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
259	#117	C₂×C₄×C₁₃₁	1	1	yes	characteristic
260	M₃₂	—	4	1	no	—
261	M₃₂	—	4	1	no	—
262	M₃₂	—	4	2	no	—
263	C₂×C₁₆	—	4	1	no	—
264	C₂×C₁₆	—	4	1	no	—
265	C₂×C₁₆	—	4	2	no	—
266	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
267	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
268	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
269	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
270	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
271	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
272	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
273	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
274	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
275	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
276	#97	C₂×C₄×C₁₃₁	1	2	yes	—
277	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
278	C₂⁴	C₂×C₈×C₁₃₁	1	1	yes	characteristic
279	#41	—	4	1	no	—
280	#41	—	4	1	no	—
281	C₂×Q₈	C₂×C₈×C₁₃₁	1	1	yes	characteristic
282	C₂×D₄	C₂×C₈×C₁₃₁	1	2	yes	—
283	C₂×D₄	C₂×C₈×C₁₃₁	1	2	yes	—
284	C₂×D₄	C₂×C₈×C₁₃₁	1	2	yes	—
285	C₂×D₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
295	M₁₆	—	4	1	no	—
296	M₁₆	—	4	2	no	—
297	M₁₆	—	4	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
310	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
312	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
313	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
314	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
315	C₄⋊C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
316	C₄⋊C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
317	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
318	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
319	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
320	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
321	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
322	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
323	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
324	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
325	C₁₆	—	2	2	no	—
326	C₁₆	—	2	2	no	—
327	C₁₆	—	2	2	no	—
328	C₁₆	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
333	C₂³	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
334	C₂³	C₂²×C₈×C₁₃₁	1	2	yes	—
335	C₂³	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
336	Q₈	—	4	1	no	—
337	D₄	—	2	4	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
353	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
354	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
357	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
365	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	#504×C₁₃₁	1	2	yes	—
379	C₂²	C₂³×C₈×C₁₃₁	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	#518×C₁₃₁	1	1	yes	characteristic
387	C₄	#568×C₁₃₁	1	1	yes	characteristic
388	C₂	—	2	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	4	1	no	—
391	C₂	—	4	2	no	—
392	C₂	#2972×C₁₃₁	1	1	yes	characteristic
393	C₂	C₂×#504×C₁₃₁	1	1	yes	characteristic
394	C₂	#3407×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂³×C₈
prime radical	#525×C₁₃₁	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2169×C₁₃₁	C₂	semidirect
3. #2168×C₁₃₁	C₂	semidirect
4. #2168×C₁₃₁	C₂	semidirect
5. D₄×C₁₆×C₁₃₁	C₂	semidirect
6. #2164×C₁₃₁	C₂	semidirect
7. #2113×C₁₃₁	C₂	semidirect
8. #2112×C₁₃₁	C₂	semidirect
9. C₂×C₂²⋊C₁₆×C₁₃₁	C₂	semidirect
15. C₂×M₃₂×C₁₃₁	C₂²	semidirect
18. C₂²×C₁₆×C₁₃₁	C₂²	semidirect
27. C₄⋊C₁₆×C₁₃₁	C₂²	semidirect
28. C₄⋊C₁₆×C₁₃₁	C₂²	semidirect
33. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
34. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
35. #346×C₁₃₁	C₂²	semidirect
36. C₄×C₁₆×C₁₃₁	C₂²	semidirect
197. #33490	C₁₃₁	direct (N × H)
198. C₁₃₁	#33490	direct (N × H)
200. #2169	C₂×C₁₃₁	semidirect
201. #2168	C₂×C₁₃₁	semidirect
202. #2168	C₂×C₁₃₁	semidirect
203. D₄×C₁₆	C₂×C₁₃₁	semidirect
204. #2164	C₂×C₁₃₁	semidirect
205. #2113	C₂×C₁₃₁	semidirect
206. #2112	C₂×C₁₃₁	semidirect
207. C₂×C₂²⋊C₁₆	C₂×C₁₃₁	semidirect
213. C₂×M₃₂	C₂²×C₁₃₁	semidirect
216. C₂²×C₁₆	C₂²×C₁₃₁	semidirect
225. C₄⋊C₁₆	C₂²×C₁₃₁	semidirect
226. C₄⋊C₁₆	C₂²×C₁₃₁	semidirect
231. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect
232. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect
233. #346	C₂²×C₁₃₁	semidirect
234. C₄×C₁₆	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2929×C₁₃₁	2
#2169×C₁₃₁	2
#2168×C₁₃₁	2
D₄×C₁₆×C₁₃₁	2
#2164×C₁₃₁	2
#2113×C₁₃₁	2
#2112×C₁₃₁	2
C₂×C₂²⋊C₁₆×C₁₃₁	2
#33490	131

Subgroups — C131×#33490 #45719374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33490 #45719374