Subgroups — C₁₃₁×#23179 #45709063

Order 33536.

926 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3147×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#443×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2935×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1980×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1974×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1876×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	C₄×#108×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₁₃₁	C₂²	1	2	yes	—
10	C₂×#135×C₁₃₁	C₂²	1	2	yes	—
11	C₂×#131×C₁₃₁	C₂²	1	4	yes	—
12	#532×C₁₃₁	C₂²	1	2	yes	—
13	#495×C₁₃₁	C₄	1	2	yes	complemented
14	#495×C₁₃₁	C₄	1	2	yes	complemented
15	#494×C₁₃₁	C₄	1	1	yes	characteristic, complemented
16	#493×C₁₃₁	C₄	1	1	yes	characteristic, complemented
17	#492×C₁₃₁	C₄	1	2	yes	complemented
18	#443×C₁₃₁	—	2	8	no	—
19	#436×C₁₃₁	—	2	2	no	—
20	#435×C₁₃₁	—	2	4	no	—
21	C₈×D₄×C₁₃₁	—	2	2	no	—
22	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#104×C₁₃₁	C₂²	1	4	yes	—
26	C₂×#104×C₁₃₁	C₂²	1	4	yes	—
27	#408×C₁₃₁	C₂²	1	4	yes	—
28	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	#341×C₁₃₁	C₂²	1	2	yes	—
33	#336×C₁₃₁	C₂²	1	2	yes	—
34	C₂×#41×C₁₃₁	C₂³	1	4	yes	—
35	#135×C₁₃₁	—	2	4	no	—
36	#135×C₁₃₁	—	2	4	no	—
37	#135×C₁₃₁	—	4	2	no	—
38	#135×C₁₃₁	—	4	2	no	—
39	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
40	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
41	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
42	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
43	C₂×D₈×C₁₃₁	C₂×C₄	1	2	yes	—
44	C₂×D₈×C₁₃₁	C₂×C₄	1	2	yes	—
45	#131×C₁₃₁	—	2	8	no	—
46	#131×C₁₃₁	—	4	4	no	—
47	C₂×M₁₆×C₁₃₁	—	2	4	no	—
48	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₁	—	2	4	no	—
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
55	#127×C₁₃₁	C₂×C₄	1	2	yes	—
56	#124×C₁₃₁	C₂×C₄	1	4	yes	—
57	#121×C₁₃₁	—	2	2	no	—
58	#121×C₁₃₁	—	2	2	no	—
59	C₄×D₄×C₁₃₁	—	2	2	no	—
60	C₄×D₄×C₁₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	#108×C₁₃₁	—	2	2	no	—
65	#108×C₁₃₁	D₄	1	4	yes	complemented
66	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
67	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
68	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
69	#104×C₁₃₁	—	2	8	no	—
70	#104×C₁₃₁	—	4	4	no	—
71	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
73	#97×C₁₃₁	—	2	2	no	—
74	C₄×C₈×C₁₃₁	—	2	4	no	—
75	C₄×C₈×C₁₃₁	—	2	2	no	—
76	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
80	#95×C₁₃₁	—	2	1	no	—
81	#41×C₁₃₁	—	2	4	no	—
82	#41×C₁₃₁	—	2	4	no	—
83	#41×C₁₃₁	—	2	4	no	—
84	#41×C₁₃₁	—	2	4	no	—
85	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
86	C₂×D₄×C₁₃₁	—	2	4	no	—
87	C₂×D₄×C₁₃₁	—	2	2	no	—
88	C₂×D₄×C₁₃₁	—	2	2	no	—
89	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₃₁	—	2	2	no	—
91	C₂²×C₄×C₁₃₁	—	2	4	no	—
92	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
95	Q₁₆×C₁₃₁	—	2	4	no	—
96	Q₁₆×C₁₃₁	—	4	2	no	—
97	SD₁₆×C₁₃₁	—	2	8	no	—
98	SD₁₆×C₁₃₁	—	4	4	no	—
99	D₈×C₁₃₁	—	2	4	no	—
100	D₈×C₁₃₁	—	4	2	no	—
101	M₁₆×C₁₃₁	—	2	2	no	—
102	M₁₆×C₁₃₁	—	2	2	no	—
103	M₁₆×C₁₃₁	—	2	2	no	—
104	M₁₆×C₁₃₁	—	4	8	no	—
105	M₁₆×C₁₃₁	C₂×D₄	1	4	yes	—
106	C₂×C₈×C₁₃₁	—	2	2	no	—
107	C₂×C₈×C₁₃₁	—	2	2	no	—
108	C₂×C₈×C₁₃₁	—	2	2	no	—
109	C₂×C₈×C₁₃₁	—	2	1	no	—
110	C₂×C₈×C₁₃₁	—	2	1	no	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	4	8	no	—
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	1	yes	characteristic
116	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃₁	#41	1	2	yes	—
121	C₄⋊C₄×C₁₃₁	—	2	4	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
125	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
126	C₄²×C₁₃₁	—	2	2	no	—
127	C₄²×C₁₃₁	—	2	2	no	—
128	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
132	C₂³×C₁₃₁	—	2	4	no	—
133	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
134	Q₈×C₁₃₁	—	2	4	no	—
135	Q₈×C₁₃₁	—	2	4	no	—
136	D₄×C₁₃₁	—	2	4	no	—
137	D₄×C₁₃₁	—	2	4	no	—
138	D₄×C₁₃₁	—	4	4	no	—
139	D₄×C₁₃₁	—	4	4	no	—
140	D₄×C₁₃₁	—	4	4	no	—
141	D₄×C₁₃₁	—	8	2	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	2	4	no	—
144	C₂×C₄×C₁₃₁	—	2	4	no	—
145	C₂×C₄×C₁₃₁	—	4	1	no	—
146	C₂×C₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	4	2	no	—
148	C₂×C₄×C₁₃₁	—	4	4	no	—
149	C₂×C₄×C₁₃₁	—	4	4	no	—
150	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
160	C₈×C₁₃₁	—	2	1	no	—
161	C₈×C₁₃₁	—	2	1	no	—
162	C₈×C₁₃₁	—	2	2	no	—
163	C₈×C₁₃₁	—	2	2	no	—
164	C₈×C₁₃₁	—	2	4	no	—
165	C₈×C₁₃₁	—	4	2	no	—
166	C₈×C₁₃₁	C₄×D₄	1	2	yes	—
167	C₈×C₁₃₁	C₄×D₄	1	2	yes	—
168	C₂²×C₁₃₁	—	2	1	no	—
169	C₂²×C₁₃₁	—	2	1	no	—
170	C₂²×C₁₃₁	—	4	4	no	—
171	C₂²×C₁₃₁	—	4	4	no	—
172	C₂²×C₁₃₁	—	4	4	no	—
173	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
174	C₂²×C₁₃₁	#550	1	1	yes	characteristic
175	C₂²×C₁₃₁	#559	1	1	yes	characteristic
176	C₄×C₁₃₁	—	2	1	no	—
177	C₄×C₁₃₁	—	2	1	no	—
178	C₄×C₁₃₁	—	2	1	no	—
179	C₄×C₁₃₁	—	4	4	no	—
180	C₄×C₁₃₁	—	4	4	no	—
181	C₄×C₁₃₁	#443	1	2	yes	complemented
182	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
183	C₄×C₁₃₁	#518	1	1	yes	characteristic
184	C₄×C₁₃₁	D₄²	1	1	yes	characteristic
185	C₄×C₁₃₁	#550	1	1	yes	characteristic
186	C₂×C₁₃₁	—	2	1	no	—
187	C₂×C₁₃₁	—	2	1	no	—
188	C₂×C₁₃₁	—	8	4	no	—
189	C₂×C₁₃₁	#2366	1	1	yes	characteristic
190	C₂×C₁₃₁	C₂×#443	1	1	yes	characteristic
191	C₂×C₁₃₁	#2957	1	1	yes	characteristic
192	#23179	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₁	#23179	1	1	yes	characteristic, direct product factor, Sylow
194	#3147	C₂×C₁₃₁	1	1	yes	characteristic
195	C₂×#443	C₂×C₁₃₁	1	2	yes	complemented
196	#2935	C₂×C₁₃₁	1	2	yes	complemented
197	#1980	C₂×C₁₃₁	1	2	yes	complemented
198	#1974	C₂×C₁₃₁	1	2	yes	complemented
199	#1876	C₂×C₁₃₁	1	4	yes	complemented
200	C₄×#108	C₂×C₁₃₁	1	1	yes	characteristic, complemented
201	C₈×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
202	C₂×#135	C₂²×C₁₃₁	1	2	yes	—
203	C₂×#135	C₂²×C₁₃₁	1	2	yes	—
204	C₂×#131	C₂²×C₁₃₁	1	4	yes	—
205	#532	C₂²×C₁₃₁	1	2	yes	—
206	#495	C₄×C₁₃₁	1	2	yes	complemented
207	#495	C₄×C₁₃₁	1	2	yes	complemented
208	#494	C₄×C₁₃₁	1	1	yes	characteristic, complemented
209	#493	C₄×C₁₃₁	1	1	yes	characteristic, complemented
210	#492	C₄×C₁₃₁	1	2	yes	complemented
211	#443	—	2	8	no	—
212	#436	—	2	2	no	—
213	#435	—	2	4	no	—
214	C₈×D₄	—	2	2	no	—
215	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
216	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₂×#104	C₂²×C₁₃₁	1	4	yes	—
219	C₂×#104	C₂²×C₁₃₁	1	4	yes	—
220	#408	C₂²×C₁₃₁	1	4	yes	—
221	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
225	#341	C₂²×C₁₃₁	1	2	yes	—
226	#336	C₂²×C₁₃₁	1	2	yes	—
227	C₂×#41	C₂³×C₁₃₁	1	4	yes	—
228	#135	—	2	4	no	—
229	#135	—	2	4	no	—
230	#135	—	4	2	no	—
231	#135	—	4	2	no	—
232	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
233	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
234	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
235	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
236	C₂×D₈	C₂×C₄×C₁₃₁	1	2	yes	—
237	C₂×D₈	C₂×C₄×C₁₃₁	1	2	yes	—
238	#131	—	2	8	no	—
239	#131	—	4	4	no	—
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
242	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
243	C₂²×C₈	—	2	4	no	—
244	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
246	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
247	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
248	#127	C₂×C₄×C₁₃₁	1	2	yes	—
249	#124	C₂×C₄×C₁₃₁	1	4	yes	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
256	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
257	#108	—	2	2	no	—
258	#108	D₄×C₁₃₁	1	4	yes	complemented
259	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
260	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
261	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
262	#104	—	2	8	no	—
263	#104	—	4	4	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	#97	—	2	2	no	—
267	C₄×C₈	—	2	4	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
270	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
271	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
273	#95	—	2	1	no	—
274	#41	—	2	4	no	—
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	#41	—	2	4	no	—
278	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
286	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
288	Q₁₆	—	2	4	no	—
289	Q₁₆	—	4	2	no	—
290	SD₁₆	—	2	8	no	—
291	SD₁₆	—	4	4	no	—
292	D₈	—	2	4	no	—
293	D₈	—	4	2	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	2	no	—
297	M₁₆	—	4	8	no	—
298	M₁₆	C₂×D₄×C₁₃₁	1	4	yes	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	8	no	—
306	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
308	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
309	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
313	C₂×C₈	#41×C₁₃₁	1	2	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
322	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
325	C₂³	—	2	4	no	—
326	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
327	Q₈	—	2	4	no	—
328	Q₈	—	2	4	no	—
329	D₄	—	2	4	no	—
330	D₄	—	2	4	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	8	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
345	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
346	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
351	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
352	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	2	2	no	—
356	C₈	—	2	2	no	—
357	C₈	—	2	4	no	—
358	C₈	—	4	2	no	—
359	C₈	C₄×D₄×C₁₃₁	1	2	yes	—
360	C₈	C₄×D₄×C₁₃₁	1	2	yes	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
367	C₂²	#550×C₁₃₁	1	1	yes	characteristic
368	C₂²	#559×C₁₃₁	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	#443×C₁₃₁	1	2	yes	complemented
375	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
376	C₄	#518×C₁₃₁	1	1	yes	characteristic
377	C₄	D₄²×C₁₃₁	1	1	yes	characteristic
378	C₄	#550×C₁₃₁	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	8	4	no	—
382	C₂	#2366×C₁₃₁	1	1	yes	characteristic
383	C₂	C₂×#443×C₁₃₁	1	1	yes	characteristic
384	C₂	#2957×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×D₄
prime radical	#3147×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄⋊C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#443×C₁₃₁	C₂	semidirect
3. #2935×C₁₃₁	C₂	semidirect
4. #1980×C₁₃₁	C₂	semidirect
5. #1974×C₁₃₁	C₂	semidirect
6. #1876×C₁₃₁	C₂	semidirect
7. C₄×#108×C₁₃₁	C₂	semidirect
8. C₈×C₄⋊C₄×C₁₃₁	C₂	semidirect
13. #495×C₁₃₁	C₄	semidirect
14. #495×C₁₃₁	C₄	semidirect
15. #494×C₁₃₁	C₄	semidirect
16. #493×C₁₃₁	C₄	semidirect
17. #492×C₁₃₁	C₄	semidirect
65. #108×C₁₃₁	D₄	semidirect
181. C₄×C₁₃₁	#443	semidirect
192. #23179	C₁₃₁	direct (N × H)
193. C₁₃₁	#23179	direct (N × H)
195. C₂×#443	C₂×C₁₃₁	semidirect
196. #2935	C₂×C₁₃₁	semidirect
197. #1980	C₂×C₁₃₁	semidirect
198. #1974	C₂×C₁₃₁	semidirect
199. #1876	C₂×C₁₃₁	semidirect
200. C₄×#108	C₂×C₁₃₁	semidirect
201. C₈×C₄⋊C₄	C₂×C₁₃₁	semidirect
206. #495	C₄×C₁₃₁	semidirect
207. #495	C₄×C₁₃₁	semidirect
208. #494	C₄×C₁₃₁	semidirect
209. #493	C₄×C₁₃₁	semidirect
210. #492	C₄×C₁₃₁	semidirect
258. #108	D₄×C₁₃₁	semidirect
374. C₄	#443×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3147×C₁₃₁	2
C₂×#443×C₁₃₁	2
#2935×C₁₃₁	2
#1980×C₁₃₁	2
#1974×C₁₃₁	2
#1876×C₁₃₁	2
C₄×#108×C₁₃₁	2
C₈×C₄⋊C₄×C₁₃₁	2
#23179	131

Subgroups — C131×#23179 #45709063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23179 #45709063