Subgroups — C₁₃₁×#34218 #45720102

Order 33536.

3014 conjugacy classes of subgroups.

The subgroup lattice has 722 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	#2368×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2364×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2359×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	#2318×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	C₄×#120×C₁₃₁	C₂	1	4	yes	maximal, complemented
13	#2280×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2275×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	C₂²×#95×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₁	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
19	#525×C₁₃₁	C₄	1	16	yes	complemented
20	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
32	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
33	#391×C₁₃₁	C₂²	1	4	yes	complemented
34	#389×C₁₃₁	C₂²	1	4	yes	complemented
35	#388×C₁₃₁	C₂²	1	4	yes	complemented
36	#388×C₁₃₁	C₂²	1	4	yes	complemented
37	#387×C₁₃₁	C₂²	1	4	yes	complemented
38	#387×C₁₃₁	C₂²	1	4	yes	complemented
39	#387×C₁₃₁	C₂²	1	4	yes	complemented
40	#387×C₁₃₁	C₂²	1	4	yes	complemented
41	#386×C₁₃₁	C₂²	1	4	yes	—
42	#386×C₁₃₁	C₂²	1	4	yes	—
43	#386×C₁₃₁	C₂²	1	4	yes	—
44	#386×C₁₃₁	C₂²	1	4	yes	complemented
45	#385×C₁₃₁	C₂²	1	4	yes	—
46	#385×C₁₃₁	C₂²	1	4	yes	—
47	#385×C₁₃₁	C₂²	1	4	yes	—
48	#385×C₁₃₁	C₂²	1	4	yes	complemented
49	#383×C₁₃₁	C₂²	1	2	yes	complemented
50	#382×C₁₃₁	C₂²	1	2	yes	complemented
51	#381×C₁₃₁	C₂²	1	2	yes	—
52	#381×C₁₃₁	C₂²	1	2	yes	complemented
53	#380×C₁₃₁	C₂²	1	2	yes	—
54	#380×C₁₃₁	C₂²	1	1	yes	characteristic
55	#380×C₁₃₁	C₂²	1	1	yes	characteristic
56	#380×C₁₃₁	C₂²	1	2	yes	complemented
57	#379×C₁₃₁	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
59	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
60	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
61	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
67	#376×C₁₃₁	C₂²	1	2	yes	complemented
68	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
69	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
70	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
71	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
72	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
73	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
74	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
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	—	2	8	no	—
85	C₂³×C₄×C₁₃₁	—	4	4	no	—
86	C₂³×C₄×C₁₃₁	—	4	4	no	—
87	C₂³×C₄×C₁₃₁	—	4	4	no	—
88	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
89	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
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	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
101	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
102	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
103	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
104	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
105	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
106	#120×C₁₃₁	C₂×C₄	1	16	yes	complemented
107	C₄×D₄×C₁₃₁	—	2	16	no	—
108	C₄×D₄×C₁₃₁	—	4	8	no	—
109	C₄×D₄×C₁₃₁	—	4	8	no	—
110	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
111	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
112	#117×C₁₃₁	—	4	4	no	—
113	#117×C₁₃₁	C₂×C₄	1	8	yes	complemented
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	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	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	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×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
140	#95×C₁₃₁	C₂³	1	2	yes	—
141	#95×C₁₃₁	C₂³	1	4	yes	—
142	#95×C₁₃₁	C₂³	1	4	yes	—
143	#95×C₁₃₁	C₂³	1	4	yes	—
144	#95×C₁₃₁	C₂³	1	4	yes	—
145	#95×C₁₃₁	C₂³	1	4	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	2	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	#95×C₁₃₁	C₂³	1	4	yes	—
155	C₂⁴×C₁₃₁	—	2	4	no	—
156	C₂⁴×C₁₃₁	—	2	2	no	—
157	C₂⁴×C₁₃₁	—	2	4	no	—
158	C₂⁴×C₁₃₁	—	2	2	no	—
159	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
160	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
161	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
162	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
164	#41×C₁₃₁	—	4	16	no	—
165	C₂×Q₈×C₁₃₁	—	4	2	no	—
166	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	complemented
167	C₂×D₄×C₁₃₁	—	2	8	no	—
168	C₂×D₄×C₁₃₁	—	2	4	no	—
169	C₂×D₄×C₁₃₁	—	2	8	no	—
170	C₂×D₄×C₁₃₁	—	2	4	no	—
171	C₂×D₄×C₁₃₁	—	4	2	no	—
172	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
175	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	complemented
176	C₂²×C₄×C₁₃₁	—	2	4	no	—
177	C₂²×C₄×C₁₃₁	—	2	4	no	—
178	C₂²×C₄×C₁₃₁	—	2	4	no	—
179	C₂²×C₄×C₁₃₁	—	2	8	no	—
180	C₂²×C₄×C₁₃₁	—	2	8	no	—
181	C₂²×C₄×C₁₃₁	—	2	8	no	—
182	C₂²×C₄×C₁₃₁	—	2	8	no	—
183	C₂²×C₄×C₁₃₁	—	2	8	no	—
184	C₂²×C₄×C₁₃₁	—	4	16	no	—
185	C₂²×C₄×C₁₃₁	—	4	2	no	—
186	C₂²×C₄×C₁₃₁	—	4	2	no	—
187	C₂²×C₄×C₁₃₁	—	4	2	no	—
188	C₂²×C₄×C₁₃₁	—	4	2	no	—
189	C₂²×C₄×C₁₃₁	—	4	4	no	—
190	C₂²×C₄×C₁₃₁	—	4	4	no	—
191	C₂²×C₄×C₁₃₁	—	4	2	no	—
192	C₂²×C₄×C₁₃₁	—	4	2	no	—
193	C₂²×C₄×C₁₃₁	—	4	2	no	—
194	C₂²×C₄×C₁₃₁	—	4	2	no	—
195	C₂²×C₄×C₁₃₁	—	4	4	no	—
196	C₂²×C₄×C₁₃₁	—	4	4	no	—
197	C₂²×C₄×C₁₃₁	—	4	4	no	—
198	C₂²×C₄×C₁₃₁	—	4	32	no	—
199	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
203	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
206	C₂²×C₄×C₁₃₁	#41	1	8	yes	complemented
207	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
218	C₄⋊C₄×C₁₃₁	—	2	8	no	—
219	C₄⋊C₄×C₁₃₁	—	4	2	no	—
220	C₄⋊C₄×C₁₃₁	—	4	2	no	—
221	C₄⋊C₄×C₁₃₁	—	4	4	no	—
222	C₄⋊C₄×C₁₃₁	—	4	4	no	—
223	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	complemented
224	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	complemented
225	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
226	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
227	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
229	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
231	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
232	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
233	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
234	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
236	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
237	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
238	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
239	C₄²×C₁₃₁	—	2	8	no	—
240	C₄²×C₁₃₁	—	4	4	no	—
241	C₄²×C₁₃₁	—	4	4	no	—
242	C₄²×C₁₃₁	—	4	4	no	—
243	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	complemented
244	C₂³×C₁₃₁	—	2	16	no	—
245	C₂³×C₁₃₁	—	2	16	no	—
246	C₂³×C₁₃₁	—	2	8	no	—
247	C₂³×C₁₃₁	—	2	8	no	—
248	C₂³×C₁₃₁	—	2	8	no	—
249	C₂³×C₁₃₁	—	2	2	no	—
250	C₂³×C₁₃₁	—	2	2	no	—
251	C₂³×C₁₃₁	—	2	2	no	—
252	C₂³×C₁₃₁	—	2	2	no	—
253	C₂³×C₁₃₁	—	2	1	no	—
254	C₂³×C₁₃₁	—	2	1	no	—
255	C₂³×C₁₃₁	—	2	1	no	—
256	C₂³×C₁₃₁	—	2	1	no	—
257	C₂³×C₁₃₁	—	2	4	no	—
258	C₂³×C₁₃₁	—	2	2	no	—
259	C₂³×C₁₃₁	—	2	4	no	—
260	C₂³×C₁₃₁	—	2	2	no	—
261	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
262	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
263	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
264	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
265	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
266	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
267	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
268	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
269	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
270	Q₈×C₁₃₁	—	4	4	no	—
271	D₄×C₁₃₁	—	2	16	no	—
272	D₄×C₁₃₁	—	2	16	no	—
273	D₄×C₁₃₁	—	2	16	no	—
274	D₄×C₁₃₁	—	4	4	no	—
275	C₂×C₄×C₁₃₁	—	2	8	no	—
276	C₂×C₄×C₁₃₁	—	2	8	no	—
277	C₂×C₄×C₁₃₁	—	2	4	no	—
278	C₂×C₄×C₁₃₁	—	2	2	no	—
279	C₂×C₄×C₁₃₁	—	2	2	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	2	no	—
284	C₂×C₄×C₁₃₁	—	2	2	no	—
285	C₂×C₄×C₁₃₁	—	2	2	no	—
286	C₂×C₄×C₁₃₁	—	2	2	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	—	2	4	no	—
293	C₂×C₄×C₁₃₁	—	2	4	no	—
294	C₂×C₄×C₁₃₁	—	2	4	no	—
295	C₂×C₄×C₁₃₁	—	2	4	no	—
296	C₂×C₄×C₁₃₁	—	4	4	no	—
297	C₂×C₄×C₁₃₁	—	4	4	no	—
298	C₂×C₄×C₁₃₁	—	4	4	no	—
299	C₂×C₄×C₁₃₁	—	4	4	no	—
300	C₂×C₄×C₁₃₁	—	4	8	no	—
301	C₂×C₄×C₁₃₁	—	4	8	no	—
302	C₂×C₄×C₁₃₁	—	4	16	no	—
303	C₂×C₄×C₁₃₁	—	4	16	no	—
304	C₂×C₄×C₁₃₁	—	4	8	no	—
305	C₂×C₄×C₁₃₁	—	8	8	no	—
306	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₁₃₁	C₂×#41	1	8	yes	—
314	C₂²×C₁₃₁	—	2	32	no	—
315	C₂²×C₁₃₁	—	2	2	no	—
316	C₂²×C₁₃₁	—	2	2	no	—
317	C₂²×C₁₃₁	—	2	2	no	—
318	C₂²×C₁₃₁	—	2	2	no	—
319	C₂²×C₁₃₁	—	2	2	no	—
320	C₂²×C₁₃₁	—	2	2	no	—
321	C₂²×C₁₃₁	—	2	4	no	—
322	C₂²×C₁₃₁	—	2	4	no	—
323	C₂²×C₁₃₁	—	2	4	no	—
324	C₂²×C₁₃₁	—	2	4	no	—
325	C₂²×C₁₃₁	—	2	4	no	—
326	C₂²×C₁₃₁	—	2	4	no	—
327	C₂²×C₁₃₁	—	2	4	no	—
328	C₂²×C₁₃₁	—	2	4	no	—
329	C₂²×C₁₃₁	—	2	4	no	—
330	C₂²×C₁₃₁	—	4	4	no	—
331	C₂²×C₁₃₁	—	4	4	no	—
332	C₂²×C₁₃₁	C₄×#41	1	4	yes	—
333	C₂²×C₁₃₁	#518	1	4	yes	—
334	C₂²×C₁₃₁	#520	1	4	yes	—
335	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
336	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
337	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
338	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	C₄×C₁₃₁	—	2	4	no	—
341	C₄×C₁₃₁	—	2	2	no	—
342	C₄×C₁₃₁	—	2	2	no	—
343	C₄×C₁₃₁	—	2	2	no	—
344	C₄×C₁₃₁	—	2	2	no	—
345	C₄×C₁₃₁	—	2	4	no	—
346	C₄×C₁₃₁	—	2	4	no	—
347	C₄×C₁₃₁	—	2	8	no	—
348	C₄×C₁₃₁	—	4	4	no	—
349	C₄×C₁₃₁	—	4	4	no	—
350	C₄×C₁₃₁	—	4	4	no	—
351	C₂×C₁₃₁	—	2	4	no	—
352	C₂×C₁₃₁	—	2	4	no	—
353	C₂×C₁₃₁	—	2	4	no	—
354	C₂×C₁₃₁	—	4	4	no	—
355	C₂×C₁₃₁	C₂×C₄×#41	1	1	yes	characteristic
356	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
357	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
358	C₂×C₁₃₁	#3490	1	2	yes	—
359	C₂×C₁₃₁	#3492	1	2	yes	—
360	#34218	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₁₃₁	#34218	1	1	yes	characteristic, direct product factor, Sylow
362	C₂×#525	C₂×C₁₃₁	1	1	yes	characteristic
363	#2368	C₂×C₁₃₁	1	2	yes	complemented
364	#2364	C₂×C₁₃₁	1	2	yes	complemented
365	#2359	C₂×C₁₃₁	1	4	yes	complemented
366	#2353	C₂×C₁₃₁	1	2	yes	complemented
367	#2349	C₂×C₁₃₁	1	2	yes	complemented
368	#2343	C₂×C₁₃₁	1	2	yes	complemented
369	#2339	C₂×C₁₃₁	1	2	yes	complemented
370	#2329	C₂×C₁₃₁	1	2	yes	complemented
371	#2325	C₂×C₁₃₁	1	2	yes	complemented
372	#2318	C₂×C₁₃₁	1	2	yes	complemented
373	C₄×#120	C₂×C₁₃₁	1	4	yes	complemented
374	#2280	C₂×C₁₃₁	1	1	yes	characteristic, complemented
375	#2275	C₂×C₁₃₁	1	2	yes	complemented
376	C₂²×#95	C₂×C₁₃₁	1	1	yes	characteristic, complemented
377	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
378	C₂⁴×C₄	C₂²×C₁₃₁	1	2	yes	—
379	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
380	#525	C₄×C₁₃₁	1	16	yes	complemented
381	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
382	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
383	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
384	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
385	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
386	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
388	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
389	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
390	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
392	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
393	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
394	#391	C₂²×C₁₃₁	1	4	yes	complemented
395	#389	C₂²×C₁₃₁	1	4	yes	complemented
396	#388	C₂²×C₁₃₁	1	4	yes	complemented
397	#388	C₂²×C₁₃₁	1	4	yes	complemented
398	#387	C₂²×C₁₃₁	1	4	yes	complemented
399	#387	C₂²×C₁₃₁	1	4	yes	complemented
400	#387	C₂²×C₁₃₁	1	4	yes	complemented
401	#387	C₂²×C₁₃₁	1	4	yes	complemented
402	#386	C₂²×C₁₃₁	1	4	yes	—
403	#386	C₂²×C₁₃₁	1	4	yes	—
404	#386	C₂²×C₁₃₁	1	4	yes	—
405	#386	C₂²×C₁₃₁	1	4	yes	complemented
406	#385	C₂²×C₁₃₁	1	4	yes	—
407	#385	C₂²×C₁₃₁	1	4	yes	—
408	#385	C₂²×C₁₃₁	1	4	yes	—
409	#385	C₂²×C₁₃₁	1	4	yes	complemented
410	#383	C₂²×C₁₃₁	1	2	yes	complemented
411	#382	C₂²×C₁₃₁	1	2	yes	complemented
412	#381	C₂²×C₁₃₁	1	2	yes	—
413	#381	C₂²×C₁₃₁	1	2	yes	complemented
414	#380	C₂²×C₁₃₁	1	2	yes	—
415	#380	C₂²×C₁₃₁	1	1	yes	characteristic
416	#380	C₂²×C₁₃₁	1	1	yes	characteristic
417	#380	C₂²×C₁₃₁	1	2	yes	complemented
418	#379	C₂²×C₁₃₁	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
420	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
421	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
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	4	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
426	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
427	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
428	#376	C₂²×C₁₃₁	1	2	yes	complemented
429	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
430	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
431	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
432	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
433	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
434	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
435	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
436	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
437	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
438	C₂×#41	—	4	4	no	—
439	C₂×#41	C₂×C₄×C₁₃₁	1	8	yes	complemented
440	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
442	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
443	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
444	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
445	C₂³×C₄	—	2	8	no	—
446	C₂³×C₄	—	4	4	no	—
447	C₂³×C₄	—	4	4	no	—
448	C₂³×C₄	—	4	4	no	—
449	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
450	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
451	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
452	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
455	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
456	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
461	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
462	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
463	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
464	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
465	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
466	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
467	#120	C₂×C₄×C₁₃₁	1	16	yes	complemented
468	C₄×D₄	—	2	16	no	—
469	C₄×D₄	—	4	8	no	—
470	C₄×D₄	—	4	8	no	—
471	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
472	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
473	#117	—	4	4	no	—
474	#117	C₂×C₄×C₁₃₁	1	8	yes	complemented
475	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
496	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
497	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
498	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
499	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
500	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
501	#95	C₂³×C₁₃₁	1	2	yes	—
502	#95	C₂³×C₁₃₁	1	2	yes	—
503	#95	C₂³×C₁₃₁	1	2	yes	—
504	#95	C₂³×C₁₃₁	1	4	yes	—
505	#95	C₂³×C₁₃₁	1	4	yes	—
506	#95	C₂³×C₁₃₁	1	2	yes	—
507	#95	C₂³×C₁₃₁	1	2	yes	—
508	#95	C₂³×C₁₃₁	1	4	yes	—
509	#95	C₂³×C₁₃₁	1	2	yes	—
510	#95	C₂³×C₁₃₁	1	4	yes	—
511	#95	C₂³×C₁₃₁	1	4	yes	—
512	#95	C₂³×C₁₃₁	1	4	yes	—
513	#95	C₂³×C₁₃₁	1	4	yes	—
514	#95	C₂³×C₁₃₁	1	4	yes	—
515	#95	C₂³×C₁₃₁	1	4	yes	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	4	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
521	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
522	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
523	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
524	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
525	#41	—	4	16	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	complemented
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
534	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
535	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
536	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	complemented
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	4	16	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	32	no	—
560	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
561	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
562	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
563	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
564	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
565	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
566	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
567	C₂²×C₄	#41×C₁₃₁	1	8	yes	complemented
568	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
579	C₄⋊C₄	—	2	8	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	complemented
585	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	complemented
586	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
587	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
599	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
600	C₄²	—	2	8	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₄²	—	4	4	no	—
604	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	complemented
605	C₂³	—	2	16	no	—
606	C₂³	—	2	16	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
623	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
624	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
625	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
626	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
627	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
628	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
629	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
630	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
631	Q₈	—	4	4	no	—
632	D₄	—	2	16	no	—
633	D₄	—	2	16	no	—
634	D₄	—	2	16	no	—
635	D₄	—	4	4	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	8	no	—
662	C₂×C₄	—	4	8	no	—
663	C₂×C₄	—	4	16	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
668	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
670	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
671	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
672	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
674	C₂×C₄	C₂×#41×C₁₃₁	1	8	yes	—
675	C₂²	—	2	32	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	4	no	—
693	C₂²	C₄×#41×C₁₃₁	1	4	yes	—
694	C₂²	#518×C₁₃₁	1	4	yes	—
695	C₂²	#520×C₁₃₁	1	4	yes	—
696	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
698	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
699	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
700	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
701	C₄	—	2	4	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	8	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	4	no	—
716	C₂	C₂×C₄×#41×C₁₃₁	1	1	yes	characteristic
717	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
718	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
719	C₂	#3490×C₁₃₁	1	2	yes	—
720	C₂	#3492×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. #2368×C₁₃₁	C₂	semidirect
3. #2364×C₁₃₁	C₂	semidirect
4. #2359×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. #2318×C₁₃₁	C₂	semidirect
12. C₄×#120×C₁₃₁	C₂	semidirect
13. #2280×C₁₃₁	C₂	semidirect
14. #2275×C₁₃₁	C₂	semidirect
15. C₂²×#95×C₁₃₁	C₂	semidirect
19. #525×C₁₃₁	C₄	semidirect
33. #391×C₁₃₁	C₂²	semidirect
34. #389×C₁₃₁	C₂²	semidirect
35. #388×C₁₃₁	C₂²	semidirect
36. #388×C₁₃₁	C₂²	semidirect
37. #387×C₁₃₁	C₂²	semidirect
38. #387×C₁₃₁	C₂²	semidirect
39. #387×C₁₃₁	C₂²	semidirect
40. #387×C₁₃₁	C₂²	semidirect
44. #386×C₁₃₁	C₂²	semidirect
48. #385×C₁₃₁	C₂²	semidirect
49. #383×C₁₃₁	C₂²	semidirect
50. #382×C₁₃₁	C₂²	semidirect
52. #381×C₁₃₁	C₂²	semidirect
56. #380×C₁₃₁	C₂²	semidirect
58. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
59. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
67. #376×C₁₃₁	C₂²	semidirect
75. C₂×#95×C₁₃₁	C₂²	semidirect
78. C₂×#41×C₁₃₁	C₂×C₄	semidirect
88. C₂³×C₄×C₁₃₁	C₂×C₄	semidirect
101. #123×C₁₃₁	C₂×C₄	semidirect
102. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
103. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
104. #121×C₁₃₁	C₂×C₄	semidirect
105. #121×C₁₃₁	C₂×C₄	semidirect
106. #120×C₁₃₁	C₂×C₄	semidirect
110. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
111. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
113. #117×C₁₃₁	C₂×C₄	semidirect
166. C₂×Q₈×C₁₃₁	C₂²×C₄	semidirect
175. C₂×D₄×C₁₃₁	C₂²×C₄	semidirect
205. C₂²×C₄×C₁₃₁	C₂²×C₄	semidirect
206. C₂²×C₄×C₁₃₁	#41	semidirect
223. C₄⋊C₄×C₁₃₁	C₂²×C₄	semidirect
224. C₄⋊C₄×C₁₃₁	C₂²×C₄	semidirect
225. C₄⋊C₄×C₁₃₁	C₂²×C₄	semidirect
226. C₄⋊C₄×C₁₃₁	C₂²×C₄	semidirect
237. C₂²⋊C₄×C₁₃₁	C₂²×C₄	semidirect
238. C₂²⋊C₄×C₁₃₁	C₂²×C₄	semidirect
243. C₄²×C₁₃₁	C₂²×C₄	semidirect
360. #34218	C₁₃₁	direct (N × H)
361. C₁₃₁	#34218	direct (N × H)
363. #2368	C₂×C₁₃₁	semidirect
364. #2364	C₂×C₁₃₁	semidirect
365. #2359	C₂×C₁₃₁	semidirect
366. #2353	C₂×C₁₃₁	semidirect
367. #2349	C₂×C₁₃₁	semidirect
368. #2343	C₂×C₁₃₁	semidirect
369. #2339	C₂×C₁₃₁	semidirect
370. #2329	C₂×C₁₃₁	semidirect
371. #2325	C₂×C₁₃₁	semidirect
372. #2318	C₂×C₁₃₁	semidirect
373. C₄×#120	C₂×C₁₃₁	semidirect
374. #2280	C₂×C₁₃₁	semidirect
375. #2275	C₂×C₁₃₁	semidirect
376. C₂²×#95	C₂×C₁₃₁	semidirect
380. #525	C₄×C₁₃₁	semidirect
394. #391	C₂²×C₁₃₁	semidirect
395. #389	C₂²×C₁₃₁	semidirect
396. #388	C₂²×C₁₃₁	semidirect
397. #388	C₂²×C₁₃₁	semidirect
398. #387	C₂²×C₁₃₁	semidirect
399. #387	C₂²×C₁₃₁	semidirect
400. #387	C₂²×C₁₃₁	semidirect
401. #387	C₂²×C₁₃₁	semidirect
405. #386	C₂²×C₁₃₁	semidirect
409. #385	C₂²×C₁₃₁	semidirect
410. #383	C₂²×C₁₃₁	semidirect
411. #382	C₂²×C₁₃₁	semidirect
413. #381	C₂²×C₁₃₁	semidirect
417. #380	C₂²×C₁₃₁	semidirect
419. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
420. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
426. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
427. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
428. #376	C₂²×C₁₃₁	semidirect
436. C₂×#95	C₂²×C₁₃₁	semidirect
439. C₂×#41	C₂×C₄×C₁₃₁	semidirect
449. C₂³×C₄	C₂×C₄×C₁₃₁	semidirect
462. #123	C₂×C₄×C₁₃₁	semidirect
463. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
464. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
465. #121	C₂×C₄×C₁₃₁	semidirect
466. #121	C₂×C₄×C₁₃₁	semidirect
467. #120	C₂×C₄×C₁₃₁	semidirect
471. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
472. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
474. #117	C₂×C₄×C₁₃₁	semidirect
527. C₂×Q₈	C₂²×C₄×C₁₃₁	semidirect
536. C₂×D₄	C₂²×C₄×C₁₃₁	semidirect
566. C₂²×C₄	C₂²×C₄×C₁₃₁	semidirect
567. C₂²×C₄	#41×C₁₃₁	semidirect
584. C₄⋊C₄	C₂²×C₄×C₁₃₁	semidirect
585. C₄⋊C₄	C₂²×C₄×C₁₃₁	semidirect
586. C₄⋊C₄	C₂²×C₄×C₁₃₁	semidirect
587. C₄⋊C₄	C₂²×C₄×C₁₃₁	semidirect
598. C₂²⋊C₄	C₂²×C₄×C₁₃₁	semidirect
599. C₂²⋊C₄	C₂²×C₄×C₁₃₁	semidirect
604. C₄²	C₂²×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
#2368×C₁₃₁	2
#2364×C₁₃₁	2
#2359×C₁₃₁	2
#2353×C₁₃₁	2
#2349×C₁₃₁	2
#2343×C₁₃₁	2
#2339×C₁₃₁	2
#2329×C₁₃₁	2
#2325×C₁₃₁	2
#2318×C₁₃₁	2
C₄×#120×C₁₃₁	2
#2280×C₁₃₁	2
#2275×C₁₃₁	2
C₂²×#95×C₁₃₁	2
#34218	131

Subgroups — C131×#34218 #45720102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34218 #45720102