Subgroups — C₁₃₁×#36579 #45722463

Order 33536.

2388 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₁	C₂	1	2	yes	maximal
5	#2592×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2581×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2568×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2538×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2481×C₁₃₁	C₂	1	4	yes	maximal, complemented
10	#2469×C₁₃₁	C₂	1	4	yes	maximal, complemented
11	#2421×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2409×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2362×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2355×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#2352×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	C₄×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	#556×C₁₃₁	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₁	C₂²	1	4	yes	—
22	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃₁	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
42	#400×C₁₃₁	C₂²	1	4	yes	—
43	#400×C₁₃₁	C₂²	1	4	yes	—
44	#397×C₁₃₁	C₂²	1	4	yes	—
45	#396×C₁₃₁	C₂²	1	4	yes	—
46	#395×C₁₃₁	C₂²	1	4	yes	—
47	#393×C₁₃₁	C₂²	1	4	yes	—
48	#391×C₁₃₁	C₂²	1	2	yes	—
49	#391×C₁₃₁	C₂²	1	2	yes	—
50	#391×C₁₃₁	C₂²	1	2	yes	—
51	#391×C₁₃₁	C₂²	1	2	yes	—
52	#391×C₁₃₁	C₂²	1	2	yes	—
53	#390×C₁₃₁	C₂²	1	2	yes	—
54	#390×C₁₃₁	C₂²	1	1	yes	characteristic
55	#389×C₁₃₁	C₂²	1	2	yes	—
56	#389×C₁₃₁	C₂²	1	1	yes	characteristic
57	#389×C₁₃₁	C₂²	1	2	yes	—
58	#389×C₁₃₁	C₂²	1	2	yes	—
59	#388×C₁₃₁	C₂²	1	4	yes	—
60	#388×C₁₃₁	C₂²	1	2	yes	—
61	#388×C₁₃₁	C₂²	1	4	yes	—
62	#388×C₁₃₁	C₂²	1	4	yes	—
63	#388×C₁₃₁	C₂²	1	4	yes	—
64	#387×C₁₃₁	C₂²	1	4	yes	—
65	#387×C₁₃₁	C₂²	1	4	yes	—
66	#387×C₁₃₁	C₂²	1	4	yes	—
67	#387×C₁₃₁	C₂²	1	4	yes	—
68	#386×C₁₃₁	C₂²	1	2	yes	—
69	#386×C₁₃₁	C₂²	1	4	yes	—
70	#386×C₁₃₁	C₂²	1	4	yes	—
71	#385×C₁₃₁	C₂²	1	4	yes	—
72	#384×C₁₃₁	C₂²	1	1	yes	characteristic
73	#382×C₁₃₁	C₂²	1	2	yes	—
74	#382×C₁₃₁	C₂²	1	2	yes	—
75	#380×C₁₃₁	C₂²	1	2	yes	—
76	#380×C₁₃₁	C₂²	1	2	yes	—
77	#380×C₁₃₁	C₂²	1	1	yes	characteristic
78	#380×C₁₃₁	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
82	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
85	C₂²×Q₈×C₁₃₁	—	2	4	no	—
86	C₂²×Q₈×C₁₃₁	—	2	4	no	—
87	C₂²×Q₈×C₁₃₁	—	2	4	no	—
88	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
101	#126×C₁₃₁	—	2	16	no	—
102	#124×C₁₃₁	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
105	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
106	#121×C₁₃₁	—	2	4	no	—
107	C₄×Q₈×C₁₃₁	—	2	4	no	—
108	C₄×Q₈×C₁₃₁	—	2	4	no	—
109	C₄×Q₈×C₁₃₁	—	2	8	no	—
110	C₄×Q₈×C₁₃₁	—	2	4	no	—
111	C₄×Q₈×C₁₃₁	—	2	8	no	—
112	C₄×Q₈×C₁₃₁	—	2	8	no	—
113	C₄×Q₈×C₁₃₁	D₄	1	8	yes	complemented
114	C₄×D₄×C₁₃₁	—	2	8	no	—
115	C₄×D₄×C₁₃₁	—	2	4	no	—
116	#117×C₁₃₁	—	2	8	no	—
117	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
118	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₁	—	2	4	no	—
149	C₂×C₄²×C₁₃₁	—	2	8	no	—
150	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
161	#95×C₁₃₁	C₂³	1	4	yes	—
162	#95×C₁₃₁	C₂³	1	4	yes	—
163	#95×C₁₃₁	C₂³	1	4	yes	—
164	#95×C₁₃₁	C₂³	1	4	yes	—
165	#95×C₁₃₁	C₂³	1	4	yes	—
166	#95×C₁₃₁	C₂³	1	4	yes	—
167	#95×C₁₃₁	C₂³	1	4	yes	—
168	#95×C₁₃₁	C₂³	1	2	yes	—
169	#95×C₁₃₁	C₂³	1	2	yes	—
170	#95×C₁₃₁	C₂³	1	4	yes	—
171	#95×C₁₃₁	C₂³	1	4	yes	—
172	#95×C₁₃₁	C₂³	1	2	yes	—
173	#95×C₁₃₁	C₂³	1	4	yes	—
174	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₁₃₁	—	2	32	no	—
177	C₂×Q₈×C₁₃₁	—	2	4	no	—
178	C₂×Q₈×C₁₃₁	—	2	2	no	—
179	C₂×Q₈×C₁₃₁	—	2	4	no	—
180	C₂×Q₈×C₁₃₁	—	2	4	no	—
181	C₂×Q₈×C₁₃₁	—	2	4	no	—
182	C₂×Q₈×C₁₃₁	—	2	2	no	—
183	C₂×Q₈×C₁₃₁	—	2	2	no	—
184	C₂×Q₈×C₁₃₁	—	2	2	no	—
185	C₂×Q₈×C₁₃₁	—	2	4	no	—
186	C₂×Q₈×C₁₃₁	—	2	4	no	—
187	C₂×Q₈×C₁₃₁	C₂×D₄	1	4	yes	—
188	C₂×Q₈×C₁₃₁	#41	1	4	yes	—
189	C₂×D₄×C₁₃₁	—	2	4	no	—
190	C₂×D₄×C₁₃₁	—	2	4	no	—
191	C₂×D₄×C₁₃₁	—	2	4	no	—
192	C₂×D₄×C₁₃₁	—	2	2	no	—
193	C₂×D₄×C₁₃₁	—	2	2	no	—
194	C₂×D₄×C₁₃₁	—	2	2	no	—
195	C₂²×C₄×C₁₃₁	—	2	4	no	—
196	C₂²×C₄×C₁₃₁	—	2	2	no	—
197	C₂²×C₄×C₁₃₁	—	2	4	no	—
198	C₂²×C₄×C₁₃₁	—	2	2	no	—
199	C₂²×C₄×C₁₃₁	—	2	4	no	—
200	C₂²×C₄×C₁₃₁	—	2	2	no	—
201	C₂²×C₄×C₁₃₁	—	2	2	no	—
202	C₂²×C₄×C₁₃₁	—	2	4	no	—
203	C₂²×C₄×C₁₃₁	—	2	2	no	—
204	C₂²×C₄×C₁₃₁	—	2	4	no	—
205	C₂²×C₄×C₁₃₁	—	2	2	no	—
206	C₂²×C₄×C₁₃₁	—	2	4	no	—
207	C₂²×C₄×C₁₃₁	—	2	4	no	—
208	C₂²×C₄×C₁₃₁	—	2	4	no	—
209	C₂²×C₄×C₁₃₁	—	4	2	no	—
210	C₂²×C₄×C₁₃₁	—	4	1	no	—
211	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
212	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
213	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₁₃₁	—	2	4	no	—
229	C₄⋊C₄×C₁₃₁	—	2	4	no	—
230	C₄⋊C₄×C₁₃₁	—	2	4	no	—
231	C₄⋊C₄×C₁₃₁	—	2	4	no	—
232	C₄⋊C₄×C₁₃₁	—	2	2	no	—
233	C₄⋊C₄×C₁₃₁	—	2	4	no	—
234	C₄⋊C₄×C₁₃₁	—	2	2	no	—
235	C₄⋊C₄×C₁₃₁	—	2	8	no	—
236	C₄⋊C₄×C₁₃₁	—	2	4	no	—
237	C₄⋊C₄×C₁₃₁	—	2	4	no	—
238	C₄⋊C₄×C₁₃₁	—	2	2	no	—
239	C₄⋊C₄×C₁₃₁	—	2	4	no	—
240	C₄⋊C₄×C₁₃₁	—	2	4	no	—
241	C₄⋊C₄×C₁₃₁	—	2	8	no	—
242	C₄⋊C₄×C₁₃₁	—	2	8	no	—
243	C₄⋊C₄×C₁₃₁	—	2	2	no	—
244	C₄⋊C₄×C₁₃₁	—	4	2	no	—
245	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
246	C₄⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	—
247	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
250	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
255	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
256	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
257	C₄²×C₁₃₁	—	2	4	no	—
258	C₄²×C₁₃₁	—	2	2	no	—
259	C₄²×C₁₃₁	—	2	4	no	—
260	C₄²×C₁₃₁	—	2	2	no	—
261	C₄²×C₁₃₁	—	2	2	no	—
262	C₄²×C₁₃₁	—	2	4	no	—
263	C₄²×C₁₃₁	—	2	8	no	—
264	C₄²×C₁₃₁	—	2	4	no	—
265	C₄²×C₁₃₁	—	4	4	no	—
266	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
267	C₄²×C₁₃₁	C₂×D₄	1	8	yes	—
268	C₂³×C₁₃₁	—	2	1	no	—
269	C₂³×C₁₃₁	—	2	1	no	—
270	C₂³×C₁₃₁	—	2	1	no	—
271	C₂³×C₁₃₁	—	2	1	no	—
272	C₂³×C₁₃₁	—	2	2	no	—
273	C₂³×C₁₃₁	—	2	2	no	—
274	C₂³×C₁₃₁	—	2	2	no	—
275	C₂³×C₁₃₁	—	2	2	no	—
276	C₂³×C₁₃₁	—	2	2	no	—
277	C₂³×C₁₃₁	—	2	2	no	—
278	C₂³×C₁₃₁	—	2	2	no	—
279	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
280	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
281	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
282	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
283	Q₈×C₁₃₁	—	2	16	no	—
284	Q₈×C₁₃₁	—	2	8	no	—
285	Q₈×C₁₃₁	—	2	8	no	—
286	Q₈×C₁₃₁	—	4	8	no	—
287	D₄×C₁₃₁	—	4	8	no	—
288	D₄×C₁₃₁	—	4	4	no	—
289	C₂×C₄×C₁₃₁	—	2	16	no	—
290	C₂×C₄×C₁₃₁	—	2	1	no	—
291	C₂×C₄×C₁₃₁	—	2	2	no	—
292	C₂×C₄×C₁₃₁	—	2	1	no	—
293	C₂×C₄×C₁₃₁	—	2	2	no	—
294	C₂×C₄×C₁₃₁	—	2	2	no	—
295	C₂×C₄×C₁₃₁	—	2	2	no	—
296	C₂×C₄×C₁₃₁	—	2	1	no	—
297	C₂×C₄×C₁₃₁	—	2	1	no	—
298	C₂×C₄×C₁₃₁	—	2	2	no	—
299	C₂×C₄×C₁₃₁	—	2	1	no	—
300	C₂×C₄×C₁₃₁	—	2	2	no	—
301	C₂×C₄×C₁₃₁	—	2	1	no	—
302	C₂×C₄×C₁₃₁	—	2	8	no	—
303	C₂×C₄×C₁₃₁	—	2	8	no	—
304	C₂×C₄×C₁₃₁	—	2	2	no	—
305	C₂×C₄×C₁₃₁	—	2	2	no	—
306	C₂×C₄×C₁₃₁	—	2	1	no	—
307	C₂×C₄×C₁₃₁	—	2	4	no	—
308	C₂×C₄×C₁₃₁	—	2	2	no	—
309	C₂×C₄×C₁₃₁	—	2	2	no	—
310	C₂×C₄×C₁₃₁	—	2	4	no	—
311	C₂×C₄×C₁₃₁	—	2	4	no	—
312	C₂×C₄×C₁₃₁	—	2	2	no	—
313	C₂×C₄×C₁₃₁	—	2	2	no	—
314	C₂×C₄×C₁₃₁	—	2	4	no	—
315	C₂×C₄×C₁₃₁	—	2	2	no	—
316	C₂×C₄×C₁₃₁	—	2	2	no	—
317	C₂×C₄×C₁₃₁	—	2	2	no	—
318	C₂×C₄×C₁₃₁	—	2	1	no	—
319	C₂×C₄×C₁₃₁	—	2	2	no	—
320	C₂×C₄×C₁₃₁	—	2	4	no	—
321	C₂×C₄×C₁₃₁	—	2	2	no	—
322	C₂×C₄×C₁₃₁	—	2	4	no	—
323	C₂×C₄×C₁₃₁	—	2	1	no	—
324	C₂×C₄×C₁₃₁	—	2	2	no	—
325	C₂×C₄×C₁₃₁	—	4	8	no	—
326	C₂×C₄×C₁₃₁	—	4	4	no	—
327	C₂×C₄×C₁₃₁	—	4	8	no	—
328	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
329	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
334	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
335	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
336	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
337	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
340	C₂²×C₁₃₁	—	2	2	no	—
341	C₂²×C₁₃₁	—	2	2	no	—
342	C₂²×C₁₃₁	—	2	2	no	—
343	C₂²×C₁₃₁	—	2	2	no	—
344	C₂²×C₁₃₁	—	2	2	no	—
345	C₂²×C₁₃₁	—	2	2	no	—
346	C₂²×C₁₃₁	—	4	2	no	—
347	C₂²×C₁₃₁	—	4	2	no	—
348	C₂²×C₁₃₁	—	4	2	no	—
349	C₂²×C₁₃₁	—	4	2	no	—
350	C₂²×C₁₃₁	—	4	2	no	—
351	C₂²×C₁₃₁	—	4	2	no	—
352	C₂²×C₁₃₁	—	4	2	no	—
353	C₂²×C₁₃₁	#556	1	4	yes	complemented
354	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
355	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
356	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
357	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
359	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂²×C₁₃₁	#585	1	1	yes	characteristic
361	C₄×C₁₃₁	—	2	4	no	—
362	C₄×C₁₃₁	—	2	4	no	—
363	C₄×C₁₃₁	—	2	2	no	—
364	C₄×C₁₃₁	—	2	2	no	—
365	C₄×C₁₃₁	—	2	4	no	—
366	C₄×C₁₃₁	—	2	2	no	—
367	C₄×C₁₃₁	—	4	2	no	—
368	C₄×C₁₃₁	—	4	4	no	—
369	C₄×C₁₃₁	—	4	2	no	—
370	C₄×C₁₃₁	—	4	4	no	—
371	C₄×C₁₃₁	—	4	2	no	—
372	C₄×C₁₃₁	—	4	1	no	—
373	C₄×C₁₃₁	—	4	2	no	—
374	C₄×C₁₃₁	#525	1	4	yes	—
375	C₄×C₁₃₁	#548	1	4	yes	—
376	C₂×C₁₃₁	—	2	4	no	—
377	C₂×C₁₃₁	—	8	2	no	—
378	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
379	C₂×C₁₃₁	C₂×#548	1	1	yes	characteristic
380	C₂×C₁₃₁	C₂×#556	1	1	yes	characteristic
381	C₂×C₁₃₁	#3480	1	1	yes	characteristic
382	C₂×C₁₃₁	#3489	1	1	yes	characteristic
383	C₂×C₁₃₁	#3507	1	1	yes	characteristic
384	C₂×C₁₃₁	#3523	1	1	yes	characteristic
385	#36579	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₁₃₁	#36579	1	1	yes	characteristic, direct product factor, Sylow
387	C₂×#556	C₂×C₁₃₁	1	1	yes	characteristic, complemented
388	C₂²×C₄×Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
389	#2857	C₂×C₁₃₁	1	1	yes	characteristic, complemented
390	#2850	C₂×C₁₃₁	1	2	yes	—
391	#2592	C₂×C₁₃₁	1	2	yes	complemented
392	#2581	C₂×C₁₃₁	1	2	yes	complemented
393	#2568	C₂×C₁₃₁	1	1	yes	characteristic, complemented
394	#2538	C₂×C₁₃₁	1	1	yes	characteristic, complemented
395	#2481	C₂×C₁₃₁	1	4	yes	complemented
396	#2469	C₂×C₁₃₁	1	4	yes	complemented
397	#2421	C₂×C₁₃₁	1	2	yes	complemented
398	#2409	C₂×C₁₃₁	1	2	yes	complemented
399	#2362	C₂×C₁₃₁	1	2	yes	complemented
400	#2355	C₂×C₁₃₁	1	1	yes	characteristic, complemented
401	#2352	C₂×C₁₃₁	1	2	yes	complemented
402	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	2	yes	complemented
403	C₄×#121	C₂×C₁₃₁	1	1	yes	characteristic
404	C₂³×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
405	#556	—	2	8	no	—
406	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
407	C₂×#126	C₂²×C₁₃₁	1	4	yes	—
408	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
411	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
412	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
413	C₂×C₄×Q₈	—	2	8	no	—
414	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
415	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
419	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
420	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
423	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
424	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
426	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
427	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
428	#400	C₂²×C₁₃₁	1	4	yes	—
429	#400	C₂²×C₁₃₁	1	4	yes	—
430	#397	C₂²×C₁₃₁	1	4	yes	—
431	#396	C₂²×C₁₃₁	1	4	yes	—
432	#395	C₂²×C₁₃₁	1	4	yes	—
433	#393	C₂²×C₁₃₁	1	4	yes	—
434	#391	C₂²×C₁₃₁	1	2	yes	—
435	#391	C₂²×C₁₃₁	1	2	yes	—
436	#391	C₂²×C₁₃₁	1	2	yes	—
437	#391	C₂²×C₁₃₁	1	2	yes	—
438	#391	C₂²×C₁₃₁	1	2	yes	—
439	#390	C₂²×C₁₃₁	1	1	yes	characteristic
440	#390	C₂²×C₁₃₁	1	2	yes	—
441	#389	C₂²×C₁₃₁	1	1	yes	characteristic
442	#389	C₂²×C₁₃₁	1	2	yes	—
443	#389	C₂²×C₁₃₁	1	2	yes	—
444	#389	C₂²×C₁₃₁	1	2	yes	—
445	#388	C₂²×C₁₃₁	1	4	yes	—
446	#388	C₂²×C₁₃₁	1	4	yes	—
447	#388	C₂²×C₁₃₁	1	4	yes	—
448	#388	C₂²×C₁₃₁	1	4	yes	—
449	#388	C₂²×C₁₃₁	1	2	yes	—
450	#387	C₂²×C₁₃₁	1	4	yes	—
451	#387	C₂²×C₁₃₁	1	4	yes	—
452	#387	C₂²×C₁₃₁	1	4	yes	—
453	#387	C₂²×C₁₃₁	1	4	yes	—
454	#386	C₂²×C₁₃₁	1	4	yes	—
455	#386	C₂²×C₁₃₁	1	4	yes	—
456	#386	C₂²×C₁₃₁	1	2	yes	—
457	#385	C₂²×C₁₃₁	1	4	yes	—
458	#384	C₂²×C₁₃₁	1	1	yes	characteristic
459	#382	C₂²×C₁₃₁	1	2	yes	—
460	#382	C₂²×C₁₃₁	1	2	yes	—
461	#380	C₂²×C₁₃₁	1	2	yes	—
462	#380	C₂²×C₁₃₁	1	2	yes	—
463	#380	C₂²×C₁₃₁	1	2	yes	—
464	#380	C₂²×C₁₃₁	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
471	C₂²×Q₈	—	2	4	no	—
472	C₂²×Q₈	—	2	4	no	—
473	C₂²×Q₈	—	2	4	no	—
474	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
475	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
476	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
481	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
482	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
483	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
486	C₄⋊Q₈	—	2	4	no	—
487	#126	—	2	16	no	—
488	#124	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	C₂²⋊Q₈	—	2	8	no	—
491	C₂²⋊Q₈	—	2	8	no	—
492	#121	—	2	4	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	—	2	4	no	—
495	C₄×Q₈	—	2	8	no	—
496	C₄×Q₈	—	2	4	no	—
497	C₄×Q₈	—	2	8	no	—
498	C₄×Q₈	—	2	8	no	—
499	C₄×Q₈	D₄×C₁₃₁	1	8	yes	complemented
500	C₄×D₄	—	2	8	no	—
501	C₄×D₄	—	2	4	no	—
502	#117	—	2	8	no	—
503	C₂×C₄⋊C₄	—	2	4	no	—
504	C₂×C₄⋊C₄	—	2	8	no	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
534	C₂×C₄²	—	2	4	no	—
535	C₂×C₄²	—	2	8	no	—
536	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
537	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
538	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
540	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
541	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
543	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
545	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
547	#95	C₂³×C₁₃₁	1	2	yes	—
548	#95	C₂³×C₁₃₁	1	4	yes	—
549	#95	C₂³×C₁₃₁	1	4	yes	—
550	#95	C₂³×C₁₃₁	1	2	yes	—
551	#95	C₂³×C₁₃₁	1	4	yes	—
552	#95	C₂³×C₁₃₁	1	4	yes	—
553	#95	C₂³×C₁₃₁	1	4	yes	—
554	#95	C₂³×C₁₃₁	1	2	yes	—
555	#95	C₂³×C₁₃₁	1	4	yes	—
556	#95	C₂³×C₁₃₁	1	4	yes	—
557	#95	C₂³×C₁₃₁	1	4	yes	—
558	#95	C₂³×C₁₃₁	1	4	yes	—
559	#95	C₂³×C₁₃₁	1	4	yes	—
560	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
561	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
562	C₂×Q₈	—	2	32	no	—
563	C₂×Q₈	—	2	4	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	C₂×D₄×C₁₃₁	1	4	yes	—
574	C₂×Q₈	#41×C₁₃₁	1	4	yes	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
598	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	8	no	—
628	C₄⋊C₄	—	2	8	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
632	C₄⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	8	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	4	4	no	—
652	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
653	C₄²	C₂×D₄×C₁₃₁	1	8	yes	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
666	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
667	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
668	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
669	Q₈	—	2	16	no	—
670	Q₈	—	2	8	no	—
671	Q₈	—	2	8	no	—
672	Q₈	—	4	8	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	4	no	—
675	C₂×C₄	—	2	16	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	8	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
715	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
717	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
719	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
720	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
721	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
722	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
723	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
724	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
725	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	#556×C₁₃₁	1	4	yes	complemented
740	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
741	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
742	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
743	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
744	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
745	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
746	C₂²	#585×C₁₃₁	1	1	yes	characteristic
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	1	no	—
760	C₄	#525×C₁₃₁	1	4	yes	—
761	C₄	#548×C₁₃₁	1	4	yes	—
762	C₂	—	2	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
765	C₂	C₂×#548×C₁₃₁	1	1	yes	characteristic
766	C₂	C₂×#556×C₁₃₁	1	1	yes	characteristic
767	C₂	#3480×C₁₃₁	1	1	yes	characteristic
768	C₂	#3489×C₁₃₁	1	1	yes	characteristic
769	C₂	#3507×C₁₃₁	1	1	yes	characteristic
770	C₂	#3523×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#121×C₁₃₁	C₂²
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×#556×C₁₃₁	C₂	semidirect
2. C₂²×C₄×Q₈×C₁₃₁	C₂	semidirect
3. #2857×C₁₃₁	C₂	semidirect
5. #2592×C₁₃₁	C₂	semidirect
6. #2581×C₁₃₁	C₂	semidirect
7. #2568×C₁₃₁	C₂	semidirect
8. #2538×C₁₃₁	C₂	semidirect
9. #2481×C₁₃₁	C₂	semidirect
10. #2469×C₁₃₁	C₂	semidirect
11. #2421×C₁₃₁	C₂	semidirect
12. #2409×C₁₃₁	C₂	semidirect
13. #2362×C₁₃₁	C₂	semidirect
14. #2355×C₁₃₁	C₂	semidirect
15. #2352×C₁₃₁	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
113. C₄×Q₈×C₁₃₁	D₄	semidirect
353. C₂²×C₁₃₁	#556	semidirect
385. #36579	C₁₃₁	direct (N × H)
386. C₁₃₁	#36579	direct (N × H)
387. C₂×#556	C₂×C₁₃₁	semidirect
388. C₂²×C₄×Q₈	C₂×C₁₃₁	semidirect
389. #2857	C₂×C₁₃₁	semidirect
391. #2592	C₂×C₁₃₁	semidirect
392. #2581	C₂×C₁₃₁	semidirect
393. #2568	C₂×C₁₃₁	semidirect
394. #2538	C₂×C₁₃₁	semidirect
395. #2481	C₂×C₁₃₁	semidirect
396. #2469	C₂×C₁₃₁	semidirect
397. #2421	C₂×C₁₃₁	semidirect
398. #2409	C₂×C₁₃₁	semidirect
399. #2362	C₂×C₁₃₁	semidirect
400. #2355	C₂×C₁₃₁	semidirect
401. #2352	C₂×C₁₃₁	semidirect
402. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
499. C₄×Q₈	D₄×C₁₃₁	semidirect
739. C₂²	#556×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₁	2
C₂²×C₄×Q₈×C₁₃₁	2
#2857×C₁₃₁	2
#2850×C₁₃₁	2
#2592×C₁₃₁	2
#2581×C₁₃₁	2
#2568×C₁₃₁	2
#2538×C₁₃₁	2
#2481×C₁₃₁	2
#2469×C₁₃₁	2
#2421×C₁₃₁	2
#2409×C₁₃₁	2
#2362×C₁₃₁	2
#2355×C₁₃₁	2
#2352×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
C₄×#121×C₁₃₁	2
#36579	131

Subgroups — C131×#36579 #45722463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#36579 #45722463