Subgroups — C₁₃₁×#29848 #45715732

Order 33536.

740 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#487×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#433×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2628×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2621×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2068×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2066×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2036×C₁₃₁	C₂	1	2	yes	maximal
8	#2035×C₁₃₁	C₂	1	2	yes	maximal
9	#1993×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1960×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1846×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
16	#487×C₁₃₁	—	2	4	no	—
17	#433×C₁₃₁	—	2	4	no	—
18	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
30	#400×C₁₃₁	—	2	1	no	—
31	#399×C₁₃₁	—	2	1	no	—
32	#398×C₁₃₁	—	2	1	no	—
33	#398×C₁₃₁	—	2	1	no	—
34	#397×C₁₃₁	—	2	1	no	—
35	#397×C₁₃₁	—	2	1	no	—
36	#395×C₁₃₁	—	2	1	no	—
37	#393×C₁₃₁	—	2	1	no	—
38	#391×C₁₃₁	C₂²	1	2	yes	—
39	#389×C₁₃₁	C₂²	1	2	yes	—
40	#382×C₁₃₁	C₂²	1	1	yes	characteristic
41	#382×C₁₃₁	C₂²	1	1	yes	characteristic
42	#380×C₁₃₁	C₂²	1	2	yes	—
43	#340×C₁₃₁	C₂²	1	2	yes	—
44	#340×C₁₃₁	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₁	—	2	1	no	—
46	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	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	1	yes	characteristic
52	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
54	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
55	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
56	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
57	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
58	#117×C₁₃₁	—	2	2	no	—
59	#117×C₁₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
76	#107×C₁₃₁	—	4	2	no	—
77	#106×C₁₃₁	—	4	2	no	—
78	C₄⋊C₈×C₁₃₁	—	2	2	no	—
79	C₄⋊C₈×C₁₃₁	—	2	2	no	—
80	#103×C₁₃₁	—	2	4	no	—
81	#103×C₁₃₁	—	2	4	no	—
82	#103×C₁₃₁	—	4	2	no	—
83	#103×C₁₃₁	—	4	2	no	—
84	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
85	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
86	#97×C₁₃₁	—	2	2	no	—
87	C₄×C₈×C₁₃₁	D₄	1	4	yes	—
88	#95×C₁₃₁	—	2	2	no	—
89	#95×C₁₃₁	—	2	2	no	—
90	#95×C₁₃₁	—	2	2	no	—
91	#95×C₁₃₁	—	2	1	no	—
92	#95×C₁₃₁	—	2	2	no	—
93	#95×C₁₃₁	—	2	1	no	—
94	#95×C₁₃₁	—	2	1	no	—
95	#95×C₁₃₁	—	2	1	no	—
96	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₁₃₁	—	2	2	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×Q₈×C₁₃₁	—	2	2	no	—
100	C₂×Q₈×C₁₃₁	—	2	2	no	—
101	C₂×Q₈×C₁₃₁	—	2	2	no	—
102	C₂×Q₈×C₁₃₁	—	2	2	no	—
103	C₂×Q₈×C₁₃₁	—	4	2	no	—
104	C₂×Q₈×C₁₃₁	—	8	2	no	—
105	C₂²×C₄×C₁₃₁	—	2	1	no	—
106	C₂²×C₄×C₁₃₁	—	2	1	no	—
107	C₂²×C₄×C₁₃₁	—	2	1	no	—
108	C₂²×C₄×C₁₃₁	—	2	1	no	—
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	—	2	1	no	—
111	C₂²×C₄×C₁₃₁	—	2	2	no	—
112	C₂²×C₄×C₁₃₁	—	2	2	no	—
113	C₂²×C₄×C₁₃₁	—	2	2	no	—
114	C₂²×C₄×C₁₃₁	—	2	2	no	—
115	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	—	2	1	no	—
125	C₂×C₈×C₁₃₁	—	2	1	no	—
126	C₂×C₈×C₁₃₁	—	2	1	no	—
127	C₂×C₈×C₁₃₁	—	2	1	no	—
128	C₂×C₈×C₁₃₁	—	2	1	no	—
129	C₂×C₈×C₁₃₁	—	2	1	no	—
130	C₂×C₈×C₁₃₁	—	2	1	no	—
131	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₁₃₁	—	2	2	no	—
134	C₄⋊C₄×C₁₃₁	—	2	2	no	—
135	C₄⋊C₄×C₁₃₁	—	2	2	no	—
136	C₄⋊C₄×C₁₃₁	—	2	2	no	—
137	C₄⋊C₄×C₁₃₁	—	2	2	no	—
138	C₄⋊C₄×C₁₃₁	—	2	2	no	—
139	C₄⋊C₄×C₁₃₁	—	2	2	no	—
140	C₄⋊C₄×C₁₃₁	—	2	2	no	—
141	C₄⋊C₄×C₁₃₁	—	4	4	no	—
142	C₄⋊C₄×C₁₃₁	—	4	2	no	—
143	C₄⋊C₄×C₁₃₁	—	4	2	no	—
144	C₄⋊C₄×C₁₃₁	—	4	2	no	—
145	C₄⋊C₄×C₁₃₁	—	8	2	no	—
146	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
147	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
148	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
149	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
150	C₄²×C₁₃₁	—	2	1	no	—
151	C₄²×C₁₃₁	—	2	1	no	—
152	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
153	C₄²×C₁₃₁	#41	1	2	yes	—
154	C₂³×C₁₃₁	—	2	1	no	—
155	C₂³×C₁₃₁	—	2	1	no	—
156	C₂³×C₁₃₁	—	2	1	no	—
157	C₂³×C₁₃₁	—	2	2	no	—
158	C₂³×C₁₃₁	—	2	2	no	—
159	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₃₁	—	4	2	no	—
161	Q₈×C₁₃₁	—	4	2	no	—
162	Q₈×C₁₃₁	—	4	2	no	—
163	Q₈×C₁₃₁	—	4	2	no	—
164	Q₈×C₁₃₁	—	8	4	no	—
165	C₂×C₄×C₁₃₁	—	2	2	no	—
166	C₂×C₄×C₁₃₁	—	2	2	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	2	1	no	—
171	C₂×C₄×C₁₃₁	—	2	1	no	—
172	C₂×C₄×C₁₃₁	—	2	2	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	4	1	no	—
175	C₂×C₄×C₁₃₁	—	4	1	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	—	4	1	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	2	no	—
180	C₂×C₄×C₁₃₁	—	4	2	no	—
181	C₂×C₄×C₁₃₁	—	4	2	no	—
182	C₂×C₄×C₁₃₁	—	4	2	no	—
183	C₂×C₄×C₁₃₁	—	4	2	no	—
184	C₂×C₄×C₁₃₁	—	4	2	no	—
185	C₂×C₄×C₁₃₁	—	4	2	no	—
186	C₂×C₄×C₁₃₁	—	4	2	no	—
187	C₂×C₄×C₁₃₁	—	4	2	no	—
188	C₂×C₄×C₁₃₁	—	4	2	no	—
189	C₂×C₄×C₁₃₁	—	4	2	no	—
190	C₂×C₄×C₁₃₁	#121	1	2	yes	—
191	C₂×C₄×C₁₃₁	#121	1	2	yes	—
192	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₁₃₁	—	2	2	no	—
199	C₈×C₁₃₁	—	2	2	no	—
200	C₈×C₁₃₁	—	4	1	no	—
201	C₈×C₁₃₁	—	4	1	no	—
202	C₂²×C₁₃₁	—	4	1	no	—
203	C₂²×C₁₃₁	—	4	2	no	—
204	C₂²×C₁₃₁	—	4	2	no	—
205	C₂²×C₁₃₁	—	4	1	no	—
206	C₂²×C₁₃₁	—	4	1	no	—
207	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
208	C₂²×C₁₃₁	#535	1	1	yes	characteristic
209	C₂²×C₁₃₁	#536	1	1	yes	characteristic
210	C₂²×C₁₃₁	#577	1	2	yes	—
211	C₂²×C₁₃₁	#578	1	2	yes	—
212	C₄×C₁₃₁	—	2	2	no	—
213	C₄×C₁₃₁	—	2	2	no	—
214	C₄×C₁₃₁	—	4	1	no	—
215	C₄×C₁₃₁	—	4	1	no	—
216	C₄×C₁₃₁	—	4	1	no	—
217	C₄×C₁₃₁	—	8	2	no	—
218	C₄×C₁₃₁	—	8	2	no	—
219	C₄×C₁₃₁	—	8	2	no	—
220	C₄×C₁₃₁	—	8	2	no	—
221	C₄×C₁₃₁	#537	1	1	yes	characteristic
222	C₄×C₁₃₁	#537	1	1	yes	characteristic
223	C₄×C₁₃₁	#542	1	1	yes	characteristic
224	C₄×C₁₃₁	#542	1	1	yes	characteristic
225	C₂×C₁₃₁	—	8	1	no	—
226	C₂×C₁₃₁	#2620	1	1	yes	characteristic
227	C₂×C₁₃₁	#3057	1	1	yes	characteristic
228	C₂×C₁₃₁	#3059	1	1	yes	characteristic
229	C₂×C₁₃₁	#3225	1	2	yes	—
230	C₂×C₁₃₁	#3242	1	2	yes	—
231	#29848	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃₁	#29848	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#487	C₂×C₁₃₁	1	1	yes	characteristic, complemented
234	C₂×#433	C₂×C₁₃₁	1	1	yes	characteristic
235	#2628	C₂×C₁₃₁	1	1	yes	characteristic
236	#2621	C₂×C₁₃₁	1	1	yes	characteristic
237	#2068	C₂×C₁₃₁	1	2	yes	complemented
238	#2066	C₂×C₁₃₁	1	2	yes	complemented
239	#2036	C₂×C₁₃₁	1	2	yes	—
240	#2035	C₂×C₁₃₁	1	2	yes	—
241	#1993	C₂×C₁₃₁	1	1	yes	characteristic, complemented
242	#1960	C₂×C₁₃₁	1	1	yes	characteristic, complemented
243	#1846	C₂×C₁₃₁	1	1	yes	characteristic, complemented
244	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
247	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
248	#487	—	2	4	no	—
249	#433	—	2	4	no	—
250	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
251	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
252	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
254	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
255	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
256	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
257	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
260	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
262	#400	—	2	1	no	—
263	#399	—	2	1	no	—
264	#398	—	2	1	no	—
265	#398	—	2	1	no	—
266	#397	—	2	1	no	—
267	#397	—	2	1	no	—
268	#395	—	2	1	no	—
269	#393	—	2	1	no	—
270	#391	C₂²×C₁₃₁	1	2	yes	—
271	#389	C₂²×C₁₃₁	1	2	yes	—
272	#382	C₂²×C₁₃₁	1	1	yes	characteristic
273	#382	C₂²×C₁₃₁	1	1	yes	characteristic
274	#380	C₂²×C₁₃₁	1	2	yes	—
275	#340	C₂²×C₁₃₁	1	2	yes	—
276	#340	C₂²×C₁₃₁	1	2	yes	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	4	2	no	—
289	C₂²⋊Q₈	—	4	2	no	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
308	#107	—	4	2	no	—
309	#106	—	4	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	4	no	—
313	#103	—	2	4	no	—
314	#103	—	4	2	no	—
315	#103	—	4	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	#97	—	2	2	no	—
319	C₄×C₈	D₄×C₁₃₁	1	4	yes	—
320	#95	—	2	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	8	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
385	C₄²	#41×C₁₃₁	1	2	yes	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	8	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	#121×C₁₃₁	1	2	yes	—
423	C₂×C₄	#121×C₁₃₁	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
426	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
429	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
440	C₂²	#535×C₁₃₁	1	1	yes	characteristic
441	C₂²	#536×C₁₃₁	1	1	yes	characteristic
442	C₂²	#577×C₁₃₁	1	2	yes	—
443	C₂²	#578×C₁₃₁	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	#537×C₁₃₁	1	1	yes	characteristic
454	C₄	#537×C₁₃₁	1	1	yes	characteristic
455	C₄	#542×C₁₃₁	1	1	yes	characteristic
456	C₄	#542×C₁₃₁	1	1	yes	characteristic
457	C₂	—	8	1	no	—
458	C₂	#2620×C₁₃₁	1	1	yes	characteristic
459	C₂	#3057×C₁₃₁	1	1	yes	characteristic
460	C₂	#3059×C₁₃₁	1	1	yes	characteristic
461	C₂	#3225×C₁₃₁	1	2	yes	—
462	C₂	#3242×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×#117×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#487×C₁₃₁	C₂	semidirect
5. #2068×C₁₃₁	C₂	semidirect
6. #2066×C₁₃₁	C₂	semidirect
9. #1993×C₁₃₁	C₂	semidirect
10. #1960×C₁₃₁	C₂	semidirect
11. #1846×C₁₃₁	C₂	semidirect
231. #29848	C₁₃₁	direct (N × H)
232. C₁₃₁	#29848	direct (N × H)
233. C₂×#487	C₂×C₁₃₁	semidirect
237. #2068	C₂×C₁₃₁	semidirect
238. #2066	C₂×C₁₃₁	semidirect
241. #1993	C₂×C₁₃₁	semidirect
242. #1960	C₂×C₁₃₁	semidirect
243. #1846	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#487×C₁₃₁	2
C₂×#433×C₁₃₁	2
#2628×C₁₃₁	2
#2621×C₁₃₁	2
#2068×C₁₃₁	2
#2066×C₁₃₁	2
#2036×C₁₃₁	2
#2035×C₁₃₁	2
#1993×C₁₃₁	2
#1960×C₁₃₁	2
#1846×C₁₃₁	2
#29848	131

Subgroups — C131×#29848 #45715732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29848 #45715732