Subgroups — C₂×#2469×C₁₃₁ #45720586

Order 33536.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₃₁	C₂	semidirect
3. #2469×C₁₃₁	C₂	direct (N × H)
4. C₂×#400×C₁₃₁	C₂	semidirect
6. C₂×#395×C₁₃₁	C₂	semidirect
8. C₂×#389×C₁₃₁	C₂	semidirect
13. C₂×#387×C₁₃₁	C₂	semidirect
14. C₂×#387×C₁₃₁	C₂	semidirect
15. C₂×#387×C₁₃₁	C₂	semidirect
16. C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	semidirect
21. C₂×C₄×Q₈×C₁₃₁	C₂²	semidirect
44. #400×C₁₃₁	C₂²	semidirect
46. #395×C₁₃₁	C₂²	semidirect
48. #389×C₁₃₁	C₂²	semidirect
53. #387×C₁₃₁	C₂²	semidirect
54. #387×C₁₃₁	C₂²	semidirect
55. #387×C₁₃₁	C₂²	semidirect
56. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
353. C₂×C₁₃₁	#2469	direct (N × H)
361. C₂×#2469	C₁₃₁	direct (N × H)
362. C₁₃₁	C₂×#2469	direct (N × H)
364. C₂²×C₄×Q₈	C₂×C₁₃₁	semidirect
365. #2469	C₂×C₁₃₁	direct (N × H)
366. C₂×#400	C₂×C₁₃₁	semidirect
368. C₂×#395	C₂×C₁₃₁	semidirect
370. C₂×#389	C₂×C₁₃₁	semidirect
375. C₂×#387	C₂×C₁₃₁	semidirect
376. C₂×#387	C₂×C₁₃₁	semidirect
377. C₂×#387	C₂×C₁₃₁	semidirect
378. C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	semidirect
383. C₂×C₄×Q₈	C₂²×C₁₃₁	semidirect
406. #400	C₂²×C₁₃₁	semidirect
408. #395	C₂²×C₁₃₁	semidirect
410. #389	C₂²×C₁₃₁	semidirect
415. #387	C₂²×C₁₃₁	semidirect
416. #387	C₂²×C₁₃₁	semidirect
417. #387	C₂²×C₁₃₁	semidirect
418. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
715. C₂	#2469×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#126×C₁₃₁	2
C₂²×C₄×Q₈×C₁₃₁	2
#2469×C₁₃₁	2
C₂×#400×C₁₃₁	2
C₂×#396×C₁₃₁	2
C₂×#395×C₁₃₁	2
C₂×#393×C₁₃₁	2
C₂×#389×C₁₃₁	2
C₂×#388×C₁₃₁	2
C₂×#387×C₁₃₁	2
C₂×C₄×C₄⋊C₄×C₁₃₁	2
C₂×#2469	131

Subgroups — C2×#2469×C131 #45720586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2469×C₁₃₁ #45720586