Subgroups — C₁₃₁×#34386 #45720270

Order 33536.

2614 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2378×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2377×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2358×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2353×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2349×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2343×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2339×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2329×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2325×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2322×C₁₃₁	C₂	1	4	yes	maximal, complemented
12	#2319×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2318×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	C₂×#381×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	#525×C₁₃₁	C₄	1	16	yes	complemented
19	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
33	#391×C₁₃₁	C₂²	1	4	yes	complemented
34	#390×C₁₃₁	C₂²	1	4	yes	—
35	#389×C₁₃₁	C₂²	1	4	yes	complemented
36	#389×C₁₃₁	C₂²	1	4	yes	complemented
37	#388×C₁₃₁	C₂²	1	4	yes	—
38	#388×C₁₃₁	C₂²	1	4	yes	—
39	#388×C₁₃₁	C₂²	1	4	yes	complemented
40	#388×C₁₃₁	C₂²	1	4	yes	complemented
41	#387×C₁₃₁	C₂²	1	4	yes	complemented
42	#387×C₁₃₁	C₂²	1	4	yes	complemented
43	#387×C₁₃₁	C₂²	1	4	yes	complemented
44	#387×C₁₃₁	C₂²	1	4	yes	complemented
45	#386×C₁₃₁	C₂²	1	4	yes	—
46	#386×C₁₃₁	C₂²	1	4	yes	—
47	#386×C₁₃₁	C₂²	1	4	yes	—
48	#386×C₁₃₁	C₂²	1	4	yes	complemented
49	#385×C₁₃₁	C₂²	1	4	yes	—
50	#385×C₁₃₁	C₂²	1	4	yes	—
51	#385×C₁₃₁	C₂²	1	4	yes	complemented
52	#385×C₁₃₁	C₂²	1	4	yes	complemented
53	#383×C₁₃₁	C₂²	1	2	yes	complemented
54	#382×C₁₃₁	C₂²	1	2	yes	complemented
55	#381×C₁₃₁	C₂²	1	2	yes	—
56	#381×C₁₃₁	C₂²	1	2	yes	—
57	#381×C₁₃₁	C₂²	1	2	yes	—
58	#381×C₁₃₁	C₂²	1	2	yes	—
59	#381×C₁₃₁	C₂²	1	2	yes	complemented
60	#380×C₁₃₁	C₂²	1	1	yes	characteristic
61	#380×C₁₃₁	C₂²	1	1	yes	characteristic
62	#380×C₁₃₁	C₂²	1	2	yes	—
63	#380×C₁₃₁	C₂²	1	2	yes	—
64	#380×C₁₃₁	C₂²	1	2	yes	—
65	#380×C₁₃₁	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
69	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
70	#376×C₁₃₁	C₂²	1	2	yes	complemented
71	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
72	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
73	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
74	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
75	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂×#41×C₁₃₁	—	4	4	no	—
78	C₂×#41×C₁₃₁	C₂×C₄	1	8	yes	complemented
79	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₁	—	4	4	no	—
85	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
97	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
98	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
99	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
100	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
101	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
102	#120×C₁₃₁	C₂×C₄	1	16	yes	complemented
103	C₄×D₄×C₁₃₁	—	4	8	no	—
104	C₄×D₄×C₁₃₁	—	4	8	no	—
105	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
106	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
107	#117×C₁₃₁	C₂×C₄	1	8	yes	complemented
108	C₂×C₄⋊C₄×C₁₃₁	—	4	4	no	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
120	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
138	#95×C₁₃₁	C₂³	1	4	yes	—
139	#95×C₁₃₁	C₂³	1	4	yes	—
140	#95×C₁₃₁	C₂³	1	4	yes	—
141	#95×C₁₃₁	C₂³	1	4	yes	—
142	#95×C₁₃₁	C₂³	1	2	yes	—
143	#95×C₁₃₁	C₂³	1	4	yes	—
144	#95×C₁₃₁	C₂³	1	4	yes	—
145	#95×C₁₃₁	C₂³	1	2	yes	—
146	#95×C₁₃₁	C₂³	1	4	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	2	yes	—
149	#95×C₁₃₁	C₂³	1	2	yes	—
150	#95×C₁₃₁	C₂³	1	2	yes	—
151	#95×C₁₃₁	C₂³	1	2	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	C₂⁴×C₁₃₁	—	2	2	no	—
154	C₂⁴×C₁₃₁	—	2	4	no	—
155	C₂⁴×C₁₃₁	—	2	2	no	—
156	C₂⁴×C₁₃₁	—	4	2	no	—
157	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
158	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
160	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
162	#41×C₁₃₁	—	4	16	no	—
163	C₂×Q₈×C₁₃₁	—	4	2	no	—
164	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
165	C₂×D₄×C₁₃₁	—	2	4	no	—
166	C₂×D₄×C₁₃₁	—	2	8	no	—
167	C₂×D₄×C₁₃₁	—	2	4	no	—
168	C₂×D₄×C₁₃₁	—	4	4	no	—
169	C₂×D₄×C₁₃₁	—	4	2	no	—
170	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₁₃₁	—	2	4	no	—
175	C₂²×C₄×C₁₃₁	—	2	4	no	—
176	C₂²×C₄×C₁₃₁	—	2	8	no	—
177	C₂²×C₄×C₁₃₁	—	2	4	no	—
178	C₂²×C₄×C₁₃₁	—	2	4	no	—
179	C₂²×C₄×C₁₃₁	—	4	16	no	—
180	C₂²×C₄×C₁₃₁	—	4	2	no	—
181	C₂²×C₄×C₁₃₁	—	4	2	no	—
182	C₂²×C₄×C₁₃₁	—	4	2	no	—
183	C₂²×C₄×C₁₃₁	—	4	2	no	—
184	C₂²×C₄×C₁₃₁	—	4	4	no	—
185	C₂²×C₄×C₁₃₁	—	4	2	no	—
186	C₂²×C₄×C₁₃₁	—	4	4	no	—
187	C₂²×C₄×C₁₃₁	—	4	2	no	—
188	C₂²×C₄×C₁₃₁	—	4	4	no	—
189	C₂²×C₄×C₁₃₁	—	4	4	no	—
190	C₂²×C₄×C₁₃₁	—	4	2	no	—
191	C₂²×C₄×C₁₃₁	—	4	4	no	—
192	C₂²×C₄×C₁₃₁	—	4	4	no	—
193	C₂²×C₄×C₁₃₁	—	4	2	no	—
194	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
199	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₁₃₁	—	4	2	no	—
213	C₄⋊C₄×C₁₃₁	—	4	4	no	—
214	C₄⋊C₄×C₁₃₁	—	4	2	no	—
215	C₄⋊C₄×C₁₃₁	—	4	4	no	—
216	C₄⋊C₄×C₁₃₁	—	4	4	no	—
217	C₄⋊C₄×C₁₃₁	—	4	4	no	—
218	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
223	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
224	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
225	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
226	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
227	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
228	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
229	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
230	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
231	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
233	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
234	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
235	C₄²×C₁₃₁	—	4	4	no	—
236	C₄²×C₁₃₁	—	4	4	no	—
237	C₄²×C₁₃₁	—	4	4	no	—
238	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
239	C₂³×C₁₃₁	—	2	2	no	—
240	C₂³×C₁₃₁	—	2	1	no	—
241	C₂³×C₁₃₁	—	2	1	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	2	no	—
244	C₂³×C₁₃₁	—	2	8	no	—
245	C₂³×C₁₃₁	—	2	8	no	—
246	C₂³×C₁₃₁	—	2	1	no	—
247	C₂³×C₁₃₁	—	2	2	no	—
248	C₂³×C₁₃₁	—	2	2	no	—
249	C₂³×C₁₃₁	—	2	4	no	—
250	C₂³×C₁₃₁	—	2	2	no	—
251	C₂³×C₁₃₁	—	2	1	no	—
252	C₂³×C₁₃₁	—	2	4	no	—
253	C₂³×C₁₃₁	—	2	2	no	—
254	C₂³×C₁₃₁	—	4	4	no	—
255	C₂³×C₁₃₁	—	4	8	no	—
256	C₂³×C₁₃₁	—	4	8	no	—
257	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
258	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
259	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
260	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
261	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
262	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
263	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
264	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
265	Q₈×C₁₃₁	—	4	4	no	—
266	D₄×C₁₃₁	—	2	16	no	—
267	D₄×C₁₃₁	—	2	16	no	—
268	D₄×C₁₃₁	—	4	8	no	—
269	D₄×C₁₃₁	—	4	4	no	—
270	C₂×C₄×C₁₃₁	—	2	8	no	—
271	C₂×C₄×C₁₃₁	—	2	8	no	—
272	C₂×C₄×C₁₃₁	—	2	2	no	—
273	C₂×C₄×C₁₃₁	—	2	4	no	—
274	C₂×C₄×C₁₃₁	—	2	2	no	—
275	C₂×C₄×C₁₃₁	—	2	2	no	—
276	C₂×C₄×C₁₃₁	—	2	2	no	—
277	C₂×C₄×C₁₃₁	—	2	2	no	—
278	C₂×C₄×C₁₃₁	—	2	2	no	—
279	C₂×C₄×C₁₃₁	—	2	4	no	—
280	C₂×C₄×C₁₃₁	—	2	4	no	—
281	C₂×C₄×C₁₃₁	—	2	4	no	—
282	C₂×C₄×C₁₃₁	—	2	4	no	—
283	C₂×C₄×C₁₃₁	—	2	4	no	—
284	C₂×C₄×C₁₃₁	—	2	4	no	—
285	C₂×C₄×C₁₃₁	—	2	4	no	—
286	C₂×C₄×C₁₃₁	—	2	4	no	—
287	C₂×C₄×C₁₃₁	—	2	4	no	—
288	C₂×C₄×C₁₃₁	—	2	4	no	—
289	C₂×C₄×C₁₃₁	—	2	4	no	—
290	C₂×C₄×C₁₃₁	—	2	4	no	—
291	C₂×C₄×C₁₃₁	—	2	4	no	—
292	C₂×C₄×C₁₃₁	—	4	4	no	—
293	C₂×C₄×C₁₃₁	—	4	4	no	—
294	C₂×C₄×C₁₃₁	—	4	4	no	—
295	C₂×C₄×C₁₃₁	—	4	4	no	—
296	C₂×C₄×C₁₃₁	—	4	8	no	—
297	C₂×C₄×C₁₃₁	—	8	8	no	—
298	C₂×C₄×C₁₃₁	—	8	4	no	—
299	C₂×C₄×C₁₃₁	—	8	4	no	—
300	C₂×C₄×C₁₃₁	—	8	8	no	—
301	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
308	C₂²×C₁₃₁	—	2	2	no	—
309	C₂²×C₁₃₁	—	2	2	no	—
310	C₂²×C₁₃₁	—	2	2	no	—
311	C₂²×C₁₃₁	—	2	2	no	—
312	C₂²×C₁₃₁	—	2	4	no	—
313	C₂²×C₁₃₁	—	2	4	no	—
314	C₂²×C₁₃₁	—	2	4	no	—
315	C₂²×C₁₃₁	—	2	4	no	—
316	C₂²×C₁₃₁	—	2	2	no	—
317	C₂²×C₁₃₁	—	2	4	no	—
318	C₂²×C₁₃₁	—	2	4	no	—
319	C₂²×C₁₃₁	—	2	2	no	—
320	C₂²×C₁₃₁	—	2	2	no	—
321	C₂²×C₁₃₁	—	2	4	no	—
322	C₂²×C₁₃₁	—	4	16	no	—
323	C₂²×C₁₃₁	—	4	4	no	—
324	C₂²×C₁₃₁	—	4	2	no	—
325	C₂²×C₁₃₁	—	4	4	no	—
326	C₂²×C₁₃₁	—	4	2	no	—
327	C₂²×C₁₃₁	#518	1	4	yes	—
328	C₂²×C₁₃₁	#520	1	4	yes	—
329	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
330	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂²×C₁₃₁	#585	1	2	yes	—
334	C₄×C₁₃₁	—	2	2	no	—
335	C₄×C₁₃₁	—	2	2	no	—
336	C₄×C₁₃₁	—	2	2	no	—
337	C₄×C₁₃₁	—	2	2	no	—
338	C₄×C₁₃₁	—	2	4	no	—
339	C₄×C₁₃₁	—	2	4	no	—
340	C₄×C₁₃₁	—	2	4	no	—
341	C₄×C₁₃₁	—	4	4	no	—
342	C₄×C₁₃₁	—	4	4	no	—
343	C₄×C₁₃₁	—	4	4	no	—
344	C₄×C₁₃₁	—	4	4	no	—
345	C₂×C₁₃₁	—	2	4	no	—
346	C₂×C₁₃₁	—	2	4	no	—
347	C₂×C₁₃₁	—	4	4	no	—
348	C₂×C₁₃₁	—	4	2	no	—
349	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
350	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
351	C₂×C₁₃₁	#3428	1	1	yes	characteristic
352	C₂×C₁₃₁	#3534	1	2	yes	—
353	C₂×C₁₃₁	#3535	1	2	yes	—
354	#34386	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₁₃₁	#34386	1	1	yes	characteristic, direct product factor, Sylow
356	C₂×#525	C₂×C₁₃₁	1	1	yes	characteristic
357	#2378	C₂×C₁₃₁	1	2	yes	complemented
358	#2377	C₂×C₁₃₁	1	2	yes	complemented
359	#2358	C₂×C₁₃₁	1	4	yes	complemented
360	#2353	C₂×C₁₃₁	1	2	yes	complemented
361	#2349	C₂×C₁₃₁	1	2	yes	complemented
362	#2343	C₂×C₁₃₁	1	2	yes	complemented
363	#2339	C₂×C₁₃₁	1	2	yes	complemented
364	#2329	C₂×C₁₃₁	1	2	yes	complemented
365	#2325	C₂×C₁₃₁	1	2	yes	complemented
366	#2322	C₂×C₁₃₁	1	4	yes	complemented
367	#2319	C₂×C₁₃₁	1	2	yes	complemented
368	#2318	C₂×C₁₃₁	1	2	yes	complemented
369	C₂×#381	C₂×C₁₃₁	1	1	yes	characteristic, complemented
370	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
371	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
372	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
373	#525	C₄×C₁₃₁	1	16	yes	complemented
374	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
375	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
376	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
377	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
378	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
379	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
380	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
381	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
382	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
384	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
386	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
387	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
388	#391	C₂²×C₁₃₁	1	4	yes	complemented
389	#390	C₂²×C₁₃₁	1	4	yes	—
390	#389	C₂²×C₁₃₁	1	4	yes	complemented
391	#389	C₂²×C₁₃₁	1	4	yes	complemented
392	#388	C₂²×C₁₃₁	1	4	yes	—
393	#388	C₂²×C₁₃₁	1	4	yes	—
394	#388	C₂²×C₁₃₁	1	4	yes	complemented
395	#388	C₂²×C₁₃₁	1	4	yes	complemented
396	#387	C₂²×C₁₃₁	1	4	yes	complemented
397	#387	C₂²×C₁₃₁	1	4	yes	complemented
398	#387	C₂²×C₁₃₁	1	4	yes	complemented
399	#387	C₂²×C₁₃₁	1	4	yes	complemented
400	#386	C₂²×C₁₃₁	1	4	yes	—
401	#386	C₂²×C₁₃₁	1	4	yes	—
402	#386	C₂²×C₁₃₁	1	4	yes	—
403	#386	C₂²×C₁₃₁	1	4	yes	complemented
404	#385	C₂²×C₁₃₁	1	4	yes	—
405	#385	C₂²×C₁₃₁	1	4	yes	—
406	#385	C₂²×C₁₃₁	1	4	yes	complemented
407	#385	C₂²×C₁₃₁	1	4	yes	complemented
408	#383	C₂²×C₁₃₁	1	2	yes	complemented
409	#382	C₂²×C₁₃₁	1	2	yes	complemented
410	#381	C₂²×C₁₃₁	1	2	yes	—
411	#381	C₂²×C₁₃₁	1	2	yes	—
412	#381	C₂²×C₁₃₁	1	2	yes	—
413	#381	C₂²×C₁₃₁	1	2	yes	—
414	#381	C₂²×C₁₃₁	1	2	yes	complemented
415	#380	C₂²×C₁₃₁	1	1	yes	characteristic
416	#380	C₂²×C₁₃₁	1	1	yes	characteristic
417	#380	C₂²×C₁₃₁	1	2	yes	—
418	#380	C₂²×C₁₃₁	1	2	yes	—
419	#380	C₂²×C₁₃₁	1	2	yes	—
420	#380	C₂²×C₁₃₁	1	2	yes	complemented
421	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
422	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
425	#376	C₂²×C₁₃₁	1	2	yes	complemented
426	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
427	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
428	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
429	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
430	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
431	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
432	C₂×#41	—	4	4	no	—
433	C₂×#41	C₂×C₄×C₁₃₁	1	8	yes	complemented
434	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
435	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
436	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
437	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
438	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
439	C₂³×C₄	—	4	4	no	—
440	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
441	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
444	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
445	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
446	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
447	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
450	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
452	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
453	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
454	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
455	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
456	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
457	#120	C₂×C₄×C₁₃₁	1	16	yes	complemented
458	C₄×D₄	—	4	8	no	—
459	C₄×D₄	—	4	8	no	—
460	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
461	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
462	#117	C₂×C₄×C₁₃₁	1	8	yes	complemented
463	C₂×C₄⋊C₄	—	4	4	no	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
474	C₂×C₂²⋊C₄	—	4	4	no	—
475	C₂×C₂²⋊C₄	—	4	4	no	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
489	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
490	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
491	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
492	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
493	#95	C₂³×C₁₃₁	1	2	yes	—
494	#95	C₂³×C₁₃₁	1	2	yes	—
495	#95	C₂³×C₁₃₁	1	2	yes	—
496	#95	C₂³×C₁₃₁	1	2	yes	—
497	#95	C₂³×C₁₃₁	1	4	yes	—
498	#95	C₂³×C₁₃₁	1	2	yes	—
499	#95	C₂³×C₁₃₁	1	4	yes	—
500	#95	C₂³×C₁₃₁	1	4	yes	—
501	#95	C₂³×C₁₃₁	1	2	yes	—
502	#95	C₂³×C₁₃₁	1	4	yes	—
503	#95	C₂³×C₁₃₁	1	4	yes	—
504	#95	C₂³×C₁₃₁	1	4	yes	—
505	#95	C₂³×C₁₃₁	1	4	yes	—
506	#95	C₂³×C₁₃₁	1	4	yes	—
507	#95	C₂³×C₁₃₁	1	4	yes	—
508	C₂⁴	—	2	2	no	—
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	4	2	no	—
512	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
513	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
514	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
515	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
516	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
517	#41	—	4	16	no	—
518	C₂×Q₈	—	4	2	no	—
519	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	8	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	4	4	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
526	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
527	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
528	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	8	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	4	16	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
550	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
551	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
552	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
553	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
554	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
559	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
576	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
590	C₄²	—	4	4	no	—
591	C₄²	—	4	4	no	—
592	C₄²	—	4	4	no	—
593	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	4	8	no	—
611	C₂³	—	4	8	no	—
612	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
613	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
614	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
615	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
616	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
617	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
618	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
619	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
620	Q₈	—	4	4	no	—
621	D₄	—	2	16	no	—
622	D₄	—	2	16	no	—
623	D₄	—	4	4	no	—
624	D₄	—	4	8	no	—
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	—	8	8	no	—
654	C₂×C₄	—	8	4	no	—
655	C₂×C₄	—	8	8	no	—
656	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
657	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
658	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
659	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
660	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
661	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
662	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	4	16	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	#518×C₁₃₁	1	4	yes	—
683	C₂²	#520×C₁₃₁	1	4	yes	—
684	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
685	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
686	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
687	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
688	C₂²	#585×C₁₃₁	1	2	yes	—
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	4	no	—
694	C₄	—	2	4	no	—
695	C₄	—	2	4	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	4	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	4	no	—
700	C₂	—	2	4	no	—
701	C₂	—	2	4	no	—
702	C₂	—	4	2	no	—
703	C₂	—	4	4	no	—
704	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
705	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
706	C₂	#3428×C₁₃₁	1	1	yes	characteristic
707	C₂	#3534×C₁₃₁	1	2	yes	—
708	C₂	#3535×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#525×C₁₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2378×C₁₃₁	C₂	semidirect
3. #2377×C₁₃₁	C₂	semidirect
4. #2358×C₁₃₁	C₂	semidirect
5. #2353×C₁₃₁	C₂	semidirect
6. #2349×C₁₃₁	C₂	semidirect
7. #2343×C₁₃₁	C₂	semidirect
8. #2339×C₁₃₁	C₂	semidirect
9. #2329×C₁₃₁	C₂	semidirect
10. #2325×C₁₃₁	C₂	semidirect
11. #2322×C₁₃₁	C₂	semidirect
12. #2319×C₁₃₁	C₂	semidirect
13. #2318×C₁₃₁	C₂	semidirect
14. C₂×#381×C₁₃₁	C₂	semidirect
15. C₂×#380×C₁₃₁	C₂	semidirect
18. #525×C₁₃₁	C₄	semidirect
33. #391×C₁₃₁	C₂²	semidirect
35. #389×C₁₃₁	C₂²	semidirect
36. #389×C₁₃₁	C₂²	semidirect
39. #388×C₁₃₁	C₂²	semidirect
40. #388×C₁₃₁	C₂²	semidirect
41. #387×C₁₃₁	C₂²	semidirect
42. #387×C₁₃₁	C₂²	semidirect
43. #387×C₁₃₁	C₂²	semidirect
44. #387×C₁₃₁	C₂²	semidirect
48. #386×C₁₃₁	C₂²	semidirect
51. #385×C₁₃₁	C₂²	semidirect
52. #385×C₁₃₁	C₂²	semidirect
53. #383×C₁₃₁	C₂²	semidirect
54. #382×C₁₃₁	C₂²	semidirect
59. #381×C₁₃₁	C₂²	semidirect
65. #380×C₁₃₁	C₂²	semidirect
66. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
70. #376×C₁₃₁	C₂²	semidirect
75. C₂×#95×C₁₃₁	C₂²	semidirect
78. C₂×#41×C₁₃₁	C₂×C₄	semidirect
85. C₂³×C₄×C₁₃₁	C₂×C₄	semidirect
97. #123×C₁₃₁	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
99. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
100. #121×C₁₃₁	C₂×C₄	semidirect
101. #121×C₁₃₁	C₂×C₄	semidirect
102. #120×C₁₃₁	C₂×C₄	semidirect
105. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
106. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
107. #117×C₁₃₁	C₂×C₄	semidirect
354. #34386	C₁₃₁	direct (N × H)
355. C₁₃₁	#34386	direct (N × H)
357. #2378	C₂×C₁₃₁	semidirect
358. #2377	C₂×C₁₃₁	semidirect
359. #2358	C₂×C₁₃₁	semidirect
360. #2353	C₂×C₁₃₁	semidirect
361. #2349	C₂×C₁₃₁	semidirect
362. #2343	C₂×C₁₃₁	semidirect
363. #2339	C₂×C₁₃₁	semidirect
364. #2329	C₂×C₁₃₁	semidirect
365. #2325	C₂×C₁₃₁	semidirect
366. #2322	C₂×C₁₃₁	semidirect
367. #2319	C₂×C₁₃₁	semidirect
368. #2318	C₂×C₁₃₁	semidirect
369. C₂×#381	C₂×C₁₃₁	semidirect
370. C₂×#380	C₂×C₁₃₁	semidirect
373. #525	C₄×C₁₃₁	semidirect
388. #391	C₂²×C₁₃₁	semidirect
390. #389	C₂²×C₁₃₁	semidirect
391. #389	C₂²×C₁₃₁	semidirect
394. #388	C₂²×C₁₃₁	semidirect
395. #388	C₂²×C₁₃₁	semidirect
396. #387	C₂²×C₁₃₁	semidirect
397. #387	C₂²×C₁₃₁	semidirect
398. #387	C₂²×C₁₃₁	semidirect
399. #387	C₂²×C₁₃₁	semidirect
403. #386	C₂²×C₁₃₁	semidirect
406. #385	C₂²×C₁₃₁	semidirect
407. #385	C₂²×C₁₃₁	semidirect
408. #383	C₂²×C₁₃₁	semidirect
409. #382	C₂²×C₁₃₁	semidirect
414. #381	C₂²×C₁₃₁	semidirect
420. #380	C₂²×C₁₃₁	semidirect
421. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
424. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
425. #376	C₂²×C₁₃₁	semidirect
430. C₂×#95	C₂²×C₁₃₁	semidirect
433. C₂×#41	C₂×C₄×C₁₃₁	semidirect
440. C₂³×C₄	C₂×C₄×C₁₃₁	semidirect
452. #123	C₂×C₄×C₁₃₁	semidirect
453. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
454. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
455. #121	C₂×C₄×C₁₃₁	semidirect
456. #121	C₂×C₄×C₁₃₁	semidirect
457. #120	C₂×C₄×C₁₃₁	semidirect
460. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
461. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
462. #117	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₃₁	2
#2378×C₁₃₁	2
#2377×C₁₃₁	2
#2358×C₁₃₁	2
#2353×C₁₃₁	2
#2349×C₁₃₁	2
#2343×C₁₃₁	2
#2339×C₁₃₁	2
#2329×C₁₃₁	2
#2325×C₁₃₁	2
#2322×C₁₃₁	2
#2319×C₁₃₁	2
#2318×C₁₃₁	2
C₂×#381×C₁₃₁	2
C₂×#380×C₁₃₁	2
#34386	131

Subgroups — C131×#34386 #45720270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34386 #45720270