Subgroups — C₇₁×#34308 #31855180

Order 18176.

3124 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₇₁	C₂	1	2	yes	maximal, complemented
3	C₇₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2361	C₂	1	2	yes	maximal, complemented
5	C₇₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₇₁×#2359	C₂	1	4	yes	maximal, complemented
7	D₄×C₄⋊C₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₄⋊C₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2344	C₂	1	2	yes	maximal, complemented
10	C₇₁×#2339	C₂	1	2	yes	maximal, complemented
11	C₇₁×#2323	C₂	1	2	yes	maximal, complemented
12	C₇₁×#2322	C₂	1	4	yes	maximal, complemented
13	C₄×C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#121×C₇₁	C₂	1	2	yes	maximal, complemented
15	C₇₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#389×C₇₁	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₇₁	C₂²	1	2	yes	—
19	#547×C₇₁	C₄	1	16	yes	complemented
20	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₇₁	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
23	C₂×#121×C₇₁	C₂²	1	2	yes	—
24	#520×C₇₁	—	2	16	no	—
25	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₁	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₇₁	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
35	C₂×#117×C₇₁	C₂²	1	2	yes	—
36	C₂×#117×C₇₁	C₂²	1	4	yes	—
37	C₂²×C₄⋊C₄×C₇₁	C₂²	1	4	yes	—
38	C₂²×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
41	C₂²×C₄²×C₇₁	C₂²	1	2	yes	—
42	#391×C₇₁	C₂²	1	2	yes	—
43	#391×C₇₁	C₂²	1	2	yes	—
44	#390×C₇₁	C₂²	1	1	yes	characteristic
45	#390×C₇₁	C₂²	1	1	yes	characteristic
46	#389×C₇₁	C₂²	1	1	yes	characteristic
47	#389×C₇₁	C₂²	1	2	yes	—
48	#389×C₇₁	C₂²	1	4	yes	—
49	#389×C₇₁	C₂²	1	2	yes	—
50	#389×C₇₁	C₂²	1	4	yes	—
51	#389×C₇₁	C₂²	1	2	yes	—
52	#389×C₇₁	C₂²	1	1	yes	characteristic
53	#389×C₇₁	C₂²	1	2	yes	—
54	#389×C₇₁	C₂²	1	2	yes	—
55	#388×C₇₁	C₂²	1	2	yes	—
56	#388×C₇₁	C₂²	1	2	yes	—
57	#388×C₇₁	C₂²	1	4	yes	—
58	#388×C₇₁	C₂²	1	4	yes	—
59	#387×C₇₁	C₂²	1	4	yes	—
60	#387×C₇₁	C₂²	1	4	yes	—
61	#387×C₇₁	C₂²	1	4	yes	—
62	#386×C₇₁	C₂²	1	4	yes	—
63	#386×C₇₁	C₂²	1	4	yes	—
64	#385×C₇₁	C₂²	1	4	yes	—
65	#385×C₇₁	C₂²	1	4	yes	—
66	#385×C₇₁	C₂²	1	4	yes	—
67	#384×C₇₁	C₂²	1	1	yes	characteristic
68	#381×C₇₁	C₂²	1	4	yes	—
69	#380×C₇₁	C₂²	1	2	yes	—
70	#380×C₇₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₇₁	C₂²	1	4	yes	—
83	C₂×#95×C₇₁	C₂²	1	4	yes	—
84	C₄³×C₇₁	C₂²	1	1	yes	characteristic
85	C₂×#41×C₇₁	—	2	8	no	—
86	C₂×#41×C₇₁	—	2	8	no	—
87	C₂×#41×C₇₁	C₂×C₄	1	16	yes	complemented
88	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₇₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
94	C₂³×C₄×C₇₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₇₁	C₂³	1	4	yes	—
97	C₂³×C₄×C₇₁	C₂³	1	4	yes	—
98	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
100	#123×C₇₁	C₂×C₄	1	32	yes	complemented
101	C₂²⋊Q₈×C₇₁	C₂×C₄	1	16	yes	complemented
102	#121×C₇₁	C₂×C₄	1	16	yes	complemented
103	C₄×Q₈×C₇₁	—	2	8	no	—
104	C₄×Q₈×C₇₁	—	2	8	no	—
105	C₄×D₄×C₇₁	—	2	8	no	—
106	C₄×D₄×C₇₁	—	2	4	no	—
107	C₄×D₄×C₇₁	—	2	16	no	—
108	C₄×D₄×C₇₁	—	2	16	no	—
109	C₄×D₄×C₇₁	—	4	4	no	—
110	C₄×D₄×C₇₁	C₂×C₄	1	8	yes	complemented
111	C₄×D₄×C₇₁	C₂×C₄	1	8	yes	complemented
112	C₄×D₄×C₇₁	D₄	1	8	yes	complemented
113	#117×C₇₁	—	2	16	no	—
114	#117×C₇₁	—	2	8	no	—
115	C₂×C₄⋊C₄×C₇₁	—	2	16	no	—
116	C₂×C₄⋊C₄×C₇₁	—	2	8	no	—
117	C₂×C₄⋊C₄×C₇₁	—	4	4	no	—
118	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	16	yes	complemented
119	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
148	C₂×C₄²×C₇₁	—	4	4	no	—
149	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
153	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
154	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
158	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
162	#95×C₇₁	C₂³	1	2	yes	—
163	#95×C₇₁	C₂³	1	4	yes	—
164	#95×C₇₁	C₂³	1	4	yes	—
165	#95×C₇₁	C₂³	1	4	yes	—
166	#95×C₇₁	C₂³	1	2	yes	—
167	#95×C₇₁	C₂³	1	2	yes	—
168	#95×C₇₁	C₂³	1	2	yes	—
169	#95×C₇₁	C₂³	1	4	yes	—
170	#95×C₇₁	C₂³	1	2	yes	—
171	#95×C₇₁	C₂³	1	4	yes	—
172	#95×C₇₁	C₂³	1	4	yes	—
173	#95×C₇₁	C₂³	1	2	yes	—
174	C₂⁴×C₇₁	C₂⁴	1	2	yes	—
175	C₂⁴×C₇₁	C₂⁴	1	2	yes	—
176	#41×C₇₁	—	2	64	no	—
177	C₂×Q₈×C₇₁	—	2	4	no	—
178	C₂×Q₈×C₇₁	—	2	4	no	—
179	C₂×Q₈×C₇₁	C₂²×C₄	1	8	yes	—
180	C₂×D₄×C₇₁	—	2	8	no	—
181	C₂×D₄×C₇₁	—	2	8	no	—
182	C₂×D₄×C₇₁	—	2	2	no	—
183	C₂×D₄×C₇₁	—	2	2	no	—
184	C₂×D₄×C₇₁	C₂²×C₄	1	4	yes	—
185	C₂×D₄×C₇₁	C₂²×C₄	1	16	yes	—
186	C₂×D₄×C₇₁	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₇₁	C₂×D₄	1	4	yes	—
188	C₂×D₄×C₇₁	#41	1	4	yes	—
189	C₂²×C₄×C₇₁	—	2	8	no	—
190	C₂²×C₄×C₇₁	—	2	8	no	—
191	C₂²×C₄×C₇₁	—	2	4	no	—
192	C₂²×C₄×C₇₁	—	2	4	no	—
193	C₂²×C₄×C₇₁	—	2	4	no	—
194	C₂²×C₄×C₇₁	—	2	4	no	—
195	C₂²×C₄×C₇₁	—	2	4	no	—
196	C₂²×C₄×C₇₁	—	2	8	no	—
197	C₂²×C₄×C₇₁	—	2	4	no	—
198	C₂²×C₄×C₇₁	—	2	8	no	—
199	C₂²×C₄×C₇₁	—	4	2	no	—
200	C₂²×C₄×C₇₁	—	4	2	no	—
201	C₂²×C₄×C₇₁	—	4	2	no	—
202	C₂²×C₄×C₇₁	—	4	4	no	—
203	C₂²×C₄×C₇₁	—	4	4	no	—
204	C₂²×C₄×C₇₁	—	4	4	no	—
205	C₂²×C₄×C₇₁	—	4	4	no	—
206	C₂²×C₄×C₇₁	C₂²×C₄	1	8	yes	—
207	C₂²×C₄×C₇₁	C₂²×C₄	1	16	yes	—
208	C₂²×C₄×C₇₁	C₂²×C₄	1	8	yes	—
209	C₂²×C₄×C₇₁	C₂×D₄	1	8	yes	—
210	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₇₁	—	2	8	no	—
226	C₄⋊C₄×C₇₁	—	2	4	no	—
227	C₄⋊C₄×C₇₁	—	2	8	no	—
228	C₄⋊C₄×C₇₁	—	2	8	no	—
229	C₄⋊C₄×C₇₁	—	2	4	no	—
230	C₄⋊C₄×C₇₁	—	2	4	no	—
231	C₄⋊C₄×C₇₁	—	2	2	no	—
232	C₄⋊C₄×C₇₁	—	2	2	no	—
233	C₄⋊C₄×C₇₁	—	2	4	no	—
234	C₄⋊C₄×C₇₁	—	2	2	no	—
235	C₄⋊C₄×C₇₁	—	4	4	no	—
236	C₄⋊C₄×C₇₁	—	4	2	no	—
237	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
238	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
239	C₄⋊C₄×C₇₁	C₂²×C₄	1	16	yes	—
240	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
241	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
242	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
243	C₂²⋊C₄×C₇₁	—	2	8	no	—
244	C₂²⋊C₄×C₇₁	—	2	4	no	—
245	C₂²⋊C₄×C₇₁	—	2	4	no	—
246	C₂²⋊C₄×C₇₁	—	2	4	no	—
247	C₂²⋊C₄×C₇₁	—	2	4	no	—
248	C₂²⋊C₄×C₇₁	—	4	2	no	—
249	C₂²⋊C₄×C₇₁	—	4	4	no	—
250	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
251	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
252	C₂²⋊C₄×C₇₁	C₂²×C₄	1	16	yes	—
253	C₂²⋊C₄×C₇₁	C₂×D₄	1	8	yes	—
254	C₄²×C₇₁	—	2	8	no	—
255	C₄²×C₇₁	—	2	8	no	—
256	C₄²×C₇₁	—	2	4	no	—
257	C₄²×C₇₁	—	2	2	no	—
258	C₄²×C₇₁	—	2	2	no	—
259	C₄²×C₇₁	—	2	4	no	—
260	C₄²×C₇₁	—	2	2	no	—
261	C₄²×C₇₁	—	2	2	no	—
262	C₄²×C₇₁	—	4	2	no	—
263	C₄²×C₇₁	—	4	2	no	—
264	C₄²×C₇₁	—	4	1	no	—
265	C₄²×C₇₁	C₂²×C₄	1	4	yes	—
266	C₄²×C₇₁	C₂×D₄	1	4	yes	—
267	C₂³×C₇₁	—	2	2	no	—
268	C₂³×C₇₁	—	2	2	no	—
269	C₂³×C₇₁	—	2	2	no	—
270	C₂³×C₇₁	—	2	2	no	—
271	C₂³×C₇₁	—	2	2	no	—
272	C₂³×C₇₁	—	2	2	no	—
273	C₂³×C₇₁	—	2	2	no	—
274	C₂³×C₇₁	—	2	2	no	—
275	C₂³×C₇₁	—	2	2	no	—
276	C₂³×C₇₁	—	2	2	no	—
277	C₂³×C₇₁	C₂³×C₄	1	4	yes	—
278	C₂³×C₇₁	C₂³×C₄	1	4	yes	—
279	C₂³×C₇₁	C₂²×D₄	1	4	yes	—
280	C₂³×C₇₁	C₂×#41	1	4	yes	—
281	C₂³×C₇₁	C₂⁵	1	1	yes	characteristic
282	Q₈×C₇₁	—	2	16	no	—
283	D₄×C₇₁	—	2	32	no	—
284	D₄×C₇₁	—	2	8	no	—
285	D₄×C₇₁	C₄×D₄	1	16	yes	complemented
286	C₂×C₄×C₇₁	—	2	32	no	—
287	C₂×C₄×C₇₁	—	2	4	no	—
288	C₂×C₄×C₇₁	—	2	2	no	—
289	C₂×C₄×C₇₁	—	2	1	no	—
290	C₂×C₄×C₇₁	—	2	2	no	—
291	C₂×C₄×C₇₁	—	2	4	no	—
292	C₂×C₄×C₇₁	—	2	1	no	—
293	C₂×C₄×C₇₁	—	2	1	no	—
294	C₂×C₄×C₇₁	—	2	2	no	—
295	C₂×C₄×C₇₁	—	2	2	no	—
296	C₂×C₄×C₇₁	—	2	1	no	—
297	C₂×C₄×C₇₁	—	2	1	no	—
298	C₂×C₄×C₇₁	—	2	1	no	—
299	C₂×C₄×C₇₁	—	2	2	no	—
300	C₂×C₄×C₇₁	—	2	1	no	—
301	C₂×C₄×C₇₁	—	2	1	no	—
302	C₂×C₄×C₇₁	—	2	2	no	—
303	C₂×C₄×C₇₁	—	2	16	no	—
304	C₂×C₄×C₇₁	—	2	16	no	—
305	C₂×C₄×C₇₁	—	2	2	no	—
306	C₂×C₄×C₇₁	—	2	4	no	—
307	C₂×C₄×C₇₁	—	2	2	no	—
308	C₂×C₄×C₇₁	—	2	1	no	—
309	C₂×C₄×C₇₁	—	2	2	no	—
310	C₂×C₄×C₇₁	—	2	2	no	—
311	C₂×C₄×C₇₁	—	2	4	no	—
312	C₂×C₄×C₇₁	—	2	2	no	—
313	C₂×C₄×C₇₁	—	2	1	no	—
314	C₂×C₄×C₇₁	—	2	2	no	—
315	C₂×C₄×C₇₁	—	2	2	no	—
316	C₂×C₄×C₇₁	—	2	2	no	—
317	C₂×C₄×C₇₁	—	2	1	no	—
318	C₂×C₄×C₇₁	—	2	2	no	—
319	C₂×C₄×C₇₁	—	2	4	no	—
320	C₂×C₄×C₇₁	—	4	8	no	—
321	C₂×C₄×C₇₁	—	4	8	no	—
322	C₂×C₄×C₇₁	—	8	8	no	—
323	C₂×C₄×C₇₁	—	8	8	no	—
324	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
326	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
327	C₂×C₄×C₇₁	C₂³×C₄	1	8	yes	—
328	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
335	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
336	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
337	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
338	C₂²×C₇₁	—	2	4	no	—
339	C₂²×C₇₁	—	2	4	no	—
340	C₂²×C₇₁	—	2	4	no	—
341	C₂²×C₇₁	—	2	4	no	—
342	C₂²×C₇₁	—	2	4	no	—
343	C₂²×C₇₁	—	2	4	no	—
344	C₂²×C₇₁	—	2	4	no	—
345	C₂²×C₇₁	—	2	4	no	—
346	C₂²×C₇₁	—	2	4	no	—
347	C₂²×C₇₁	—	4	2	no	—
348	C₂²×C₇₁	—	4	2	no	—
349	C₂²×C₇₁	—	4	2	no	—
350	C₂²×C₇₁	—	4	2	no	—
351	C₂²×C₇₁	C₂×C₄×D₄	1	8	yes	—
352	C₂²×C₇₁	C₂⁴×C₄	1	1	yes	characteristic
353	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₇₁	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
357	C₂²×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
358	C₂²×C₇₁	#585	1	1	yes	characteristic
359	C₄×C₇₁	—	2	4	no	—
360	C₄×C₇₁	—	2	8	no	—
361	C₄×C₇₁	—	2	4	no	—
362	C₄×C₇₁	—	2	2	no	—
363	C₄×C₇₁	—	2	2	no	—
364	C₄×C₇₁	—	2	4	no	—
365	C₄×C₇₁	—	2	2	no	—
366	C₄×C₇₁	—	2	2	no	—
367	C₄×C₇₁	—	4	4	no	—
368	C₄×C₇₁	—	4	2	no	—
369	C₄×C₇₁	—	4	2	no	—
370	C₄×C₇₁	—	4	1	no	—
371	C₄×C₇₁	—	4	2	no	—
372	C₄×C₇₁	C₂×C₄×D₄	1	4	yes	—
373	C₄×C₇₁	#520	1	4	yes	complemented
374	#34308	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂×C₇₁	—	2	8	no	—
376	C₂×C₇₁	—	4	4	no	—
377	C₂×C₇₁	C₂²×C₄×D₄	1	1	yes	characteristic
378	C₂×C₇₁	C₂×#520	1	1	yes	characteristic
379	C₂×C₇₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
380	C₂×C₇₁	#3496	1	1	yes	characteristic
381	C₂×C₇₁	#3499	1	1	yes	characteristic
382	C₂×C₇₁	#3515	1	1	yes	characteristic
383	C₂×C₇₁	#3520	1	1	yes	characteristic
384	C₂×#547	C₂×C₇₁	1	1	yes	characteristic
385	C₂×#520	C₂×C₇₁	1	2	yes	complemented
386	#2365	C₂×C₇₁	1	1	yes	characteristic, complemented
387	#2361	C₂×C₇₁	1	2	yes	complemented
388	#2360	C₂×C₇₁	1	2	yes	complemented
389	#2359	C₂×C₇₁	1	4	yes	complemented
390	D₄×C₄⋊C₄	C₂×C₇₁	1	1	yes	characteristic, complemented
391	D₄×C₄⋊C₄	C₂×C₇₁	1	1	yes	characteristic, complemented
392	#2344	C₂×C₇₁	1	2	yes	complemented
393	#2339	C₂×C₇₁	1	2	yes	complemented
394	#2323	C₂×C₇₁	1	2	yes	complemented
395	#2322	C₂×C₇₁	1	4	yes	complemented
396	C₄×C₄⋊Q₈	C₂×C₇₁	1	1	yes	characteristic, complemented
397	C₄×#121	C₂×C₇₁	1	2	yes	complemented
398	#2293	C₂×C₇₁	1	1	yes	characteristic, complemented
399	C₂×#389	C₂×C₇₁	1	2	yes	complemented
400	C₄²×D₄	C₂×C₇₁	1	1	yes	characteristic, complemented
401	C₇₁	#34308	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²×#41	C₂²×C₇₁	1	2	yes	—
403	#547	C₄×C₇₁	1	16	yes	complemented
404	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
405	C₂×#123	C₂²×C₇₁	1	4	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
407	C₂×#121	C₂²×C₇₁	1	2	yes	—
408	#520	—	2	16	no	—
409	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₇₁	1	4	yes	—
412	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₇₁	1	4	yes	—
415	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
419	C₂×#117	C₂²×C₇₁	1	2	yes	—
420	C₂×#117	C₂²×C₇₁	1	4	yes	—
421	C₂²×C₄⋊C₄	C₂²×C₇₁	1	4	yes	—
422	C₂²×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
423	C₂²×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
424	C₂²×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
425	C₂²×C₄²	C₂²×C₇₁	1	2	yes	—
426	#391	C₂²×C₇₁	1	2	yes	—
427	#391	C₂²×C₇₁	1	2	yes	—
428	#390	C₂²×C₇₁	1	1	yes	characteristic
429	#390	C₂²×C₇₁	1	1	yes	characteristic
430	#389	C₂²×C₇₁	1	2	yes	—
431	#389	C₂²×C₇₁	1	2	yes	—
432	#389	C₂²×C₇₁	1	4	yes	—
433	#389	C₂²×C₇₁	1	2	yes	—
434	#389	C₂²×C₇₁	1	1	yes	characteristic
435	#389	C₂²×C₇₁	1	2	yes	—
436	#389	C₂²×C₇₁	1	4	yes	—
437	#389	C₂²×C₇₁	1	2	yes	—
438	#389	C₂²×C₇₁	1	1	yes	characteristic
439	#388	C₂²×C₇₁	1	2	yes	—
440	#388	C₂²×C₇₁	1	4	yes	—
441	#388	C₂²×C₇₁	1	4	yes	—
442	#388	C₂²×C₇₁	1	2	yes	—
443	#387	C₂²×C₇₁	1	4	yes	—
444	#387	C₂²×C₇₁	1	4	yes	—
445	#387	C₂²×C₇₁	1	4	yes	—
446	#386	C₂²×C₇₁	1	4	yes	—
447	#386	C₂²×C₇₁	1	4	yes	—
448	#385	C₂²×C₇₁	1	4	yes	—
449	#385	C₂²×C₇₁	1	4	yes	—
450	#385	C₂²×C₇₁	1	4	yes	—
451	#384	C₂²×C₇₁	1	1	yes	characteristic
452	#381	C₂²×C₇₁	1	4	yes	—
453	#380	C₂²×C₇₁	1	2	yes	—
454	#380	C₂²×C₇₁	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
462	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₇₁	1	4	yes	—
467	C₂×#95	C₂²×C₇₁	1	4	yes	—
468	C₄³	C₂²×C₇₁	1	1	yes	characteristic
469	C₂×#41	—	2	8	no	—
470	C₂×#41	—	2	8	no	—
471	C₂×#41	C₂×C₄×C₇₁	1	16	yes	complemented
472	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
473	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₇₁	1	4	yes	—
475	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
477	C₂³×C₄	C₂³×C₇₁	1	4	yes	—
478	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
479	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
480	C₂³×C₄	C₂³×C₇₁	1	4	yes	—
481	C₂³×C₄	C₂³×C₇₁	1	4	yes	—
482	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
483	C₄⋊Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
484	#123	C₂×C₄×C₇₁	1	32	yes	complemented
485	C₂²⋊Q₈	C₂×C₄×C₇₁	1	16	yes	complemented
486	#121	C₂×C₄×C₇₁	1	16	yes	complemented
487	C₄×Q₈	—	2	8	no	—
488	C₄×Q₈	—	2	8	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	4	no	—
491	C₄×D₄	—	2	16	no	—
492	C₄×D₄	—	2	16	no	—
493	C₄×D₄	—	4	4	no	—
494	C₄×D₄	C₂×C₄×C₇₁	1	8	yes	complemented
495	C₄×D₄	C₂×C₄×C₇₁	1	8	yes	complemented
496	C₄×D₄	D₄×C₇₁	1	8	yes	complemented
497	#117	—	2	16	no	—
498	#117	—	2	8	no	—
499	C₂×C₄⋊C₄	—	2	16	no	—
500	C₂×C₄⋊C₄	—	2	8	no	—
501	C₂×C₄⋊C₄	—	4	4	no	—
502	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	16	yes	complemented
503	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
532	C₂×C₄²	—	4	4	no	—
533	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
534	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
535	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
536	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
538	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
543	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
544	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
546	#95	C₂³×C₇₁	1	2	yes	—
547	#95	C₂³×C₇₁	1	4	yes	—
548	#95	C₂³×C₇₁	1	4	yes	—
549	#95	C₂³×C₇₁	1	4	yes	—
550	#95	C₂³×C₇₁	1	2	yes	—
551	#95	C₂³×C₇₁	1	2	yes	—
552	#95	C₂³×C₇₁	1	2	yes	—
553	#95	C₂³×C₇₁	1	4	yes	—
554	#95	C₂³×C₇₁	1	2	yes	—
555	#95	C₂³×C₇₁	1	4	yes	—
556	#95	C₂³×C₇₁	1	4	yes	—
557	#95	C₂³×C₇₁	1	2	yes	—
558	C₂⁴	C₂⁴×C₇₁	1	2	yes	—
559	C₂⁴	C₂⁴×C₇₁	1	2	yes	—
560	#41	—	2	64	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	C₂²×C₄×C₇₁	1	8	yes	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	C₂²×C₄×C₇₁	1	4	yes	—
569	C₂×D₄	C₂²×C₄×C₇₁	1	16	yes	—
570	C₂×D₄	C₂²×C₄×C₇₁	1	4	yes	—
571	C₂×D₄	C₂×D₄×C₇₁	1	4	yes	—
572	C₂×D₄	#41×C₇₁	1	4	yes	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	C₂²×C₄×C₇₁	1	8	yes	—
591	C₂²×C₄	C₂²×C₄×C₇₁	1	16	yes	—
592	C₂²×C₄	C₂²×C₄×C₇₁	1	8	yes	—
593	C₂²×C₄	C₂×D₄×C₇₁	1	8	yes	—
594	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
602	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	4	4	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
622	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
623	C₄⋊C₄	C₂²×C₄×C₇₁	1	16	yes	—
624	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
625	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
626	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	4	no	—
634	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
635	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
636	C₂²⋊C₄	C₂²×C₄×C₇₁	1	16	yes	—
637	C₂²⋊C₄	C₂×D₄×C₇₁	1	8	yes	—
638	C₄²	—	2	8	no	—
639	C₄²	—	2	8	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	1	no	—
649	C₄²	C₂²×C₄×C₇₁	1	4	yes	—
650	C₄²	C₂×D₄×C₇₁	1	4	yes	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	C₂³×C₄×C₇₁	1	4	yes	—
662	C₂³	C₂³×C₄×C₇₁	1	4	yes	—
663	C₂³	C₂²×D₄×C₇₁	1	4	yes	—
664	C₂³	C₂×#41×C₇₁	1	4	yes	—
665	C₂³	C₂⁵×C₇₁	1	1	yes	characteristic
666	Q₈	—	2	16	no	—
667	D₄	—	2	32	no	—
668	D₄	—	2	8	no	—
669	D₄	C₄×D₄×C₇₁	1	16	yes	complemented
670	C₂×C₄	—	2	32	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	—	8	8	no	—
708	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
709	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
711	C₂×C₄	C₂³×C₄×C₇₁	1	8	yes	—
712	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
713	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
716	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
718	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
719	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
720	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
721	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	C₂×C₄×D₄×C₇₁	1	8	yes	—
736	C₂²	C₂⁴×C₄×C₇₁	1	1	yes	characteristic
737	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
738	C₂²	C₂²×#41×C₇₁	1	1	yes	characteristic
739	C₂²	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
740	C₂²	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
741	C₂²	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
742	C₂²	#585×C₇₁	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	8	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	C₂×C₄×D₄×C₇₁	1	4	yes	—
757	C₄	#520×C₇₁	1	4	yes	complemented
758	C₂	—	2	8	no	—
759	C₂	—	4	4	no	—
760	C₂	C₂²×C₄×D₄×C₇₁	1	1	yes	characteristic
761	C₂	C₂×#520×C₇₁	1	1	yes	characteristic
762	C₂	C₄×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
763	C₂	C₇₁×#3496	1	1	yes	characteristic
764	C₂	C₇₁×#3499	1	1	yes	characteristic
765	C₂	C₇₁×#3515	1	1	yes	characteristic
766	C₂	C₇₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇₁
Frattini, cosocle	C₂³	C₂⁵×C₇₁
prime radical	C₂×#547×C₇₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₇₁	C₂	semidirect
3. C₇₁×#2365	C₂	semidirect
4. C₇₁×#2361	C₂	semidirect
5. C₇₁×#2360	C₂	semidirect
6. C₇₁×#2359	C₂	semidirect
7. D₄×C₄⋊C₄×C₇₁	C₂	semidirect
8. D₄×C₄⋊C₄×C₇₁	C₂	semidirect
9. C₇₁×#2344	C₂	semidirect
10. C₇₁×#2339	C₂	semidirect
11. C₇₁×#2323	C₂	semidirect
12. C₇₁×#2322	C₂	semidirect
13. C₄×C₄⋊Q₈×C₇₁	C₂	semidirect
14. C₄×#121×C₇₁	C₂	semidirect
15. C₇₁×#2293	C₂	semidirect
16. C₂×#389×C₇₁	C₂	semidirect
17. C₄²×D₄×C₇₁	C₂	semidirect
19. #547×C₇₁	C₄	semidirect
87. C₂×#41×C₇₁	C₂×C₄	semidirect
99. C₄⋊Q₈×C₇₁	C₂×C₄	semidirect
100. #123×C₇₁	C₂×C₄	semidirect
101. C₂²⋊Q₈×C₇₁	C₂×C₄	semidirect
102. #121×C₇₁	C₂×C₄	semidirect
110. C₄×D₄×C₇₁	C₂×C₄	semidirect
111. C₄×D₄×C₇₁	C₂×C₄	semidirect
112. C₄×D₄×C₇₁	D₄	semidirect
118. C₂×C₄⋊C₄×C₇₁	C₂×C₄	semidirect
285. D₄×C₇₁	C₄×D₄	semidirect
373. C₄×C₇₁	#520	semidirect
374. #34308	C₇₁	direct (N × H)
385. C₂×#520	C₂×C₇₁	semidirect
386. #2365	C₂×C₇₁	semidirect
387. #2361	C₂×C₇₁	semidirect
388. #2360	C₂×C₇₁	semidirect
389. #2359	C₂×C₇₁	semidirect
390. D₄×C₄⋊C₄	C₂×C₇₁	semidirect
391. D₄×C₄⋊C₄	C₂×C₇₁	semidirect
392. #2344	C₂×C₇₁	semidirect
393. #2339	C₂×C₇₁	semidirect
394. #2323	C₂×C₇₁	semidirect
395. #2322	C₂×C₇₁	semidirect
396. C₄×C₄⋊Q₈	C₂×C₇₁	semidirect
397. C₄×#121	C₂×C₇₁	semidirect
398. #2293	C₂×C₇₁	semidirect
399. C₂×#389	C₂×C₇₁	semidirect
400. C₄²×D₄	C₂×C₇₁	semidirect
401. C₇₁	#34308	direct (N × H)
403. #547	C₄×C₇₁	semidirect
471. C₂×#41	C₂×C₄×C₇₁	semidirect
483. C₄⋊Q₈	C₂×C₄×C₇₁	semidirect
484. #123	C₂×C₄×C₇₁	semidirect
485. C₂²⋊Q₈	C₂×C₄×C₇₁	semidirect
486. #121	C₂×C₄×C₇₁	semidirect
494. C₄×D₄	C₂×C₄×C₇₁	semidirect
495. C₄×D₄	C₂×C₄×C₇₁	semidirect
496. C₄×D₄	D₄×C₇₁	semidirect
502. C₂×C₄⋊C₄	C₂×C₄×C₇₁	semidirect
669. D₄	C₄×D₄×C₇₁	semidirect
757. C₄	#520×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₇₁	2
C₂×#520×C₇₁	2
C₇₁×#2365	2
C₇₁×#2361	2
C₇₁×#2360	2
C₇₁×#2359	2
D₄×C₄⋊C₄×C₇₁	2
C₇₁×#2344	2
C₇₁×#2339	2
C₇₁×#2323	2
C₇₁×#2322	2
C₄×C₄⋊Q₈×C₇₁	2
C₄×#121×C₇₁	2
C₇₁×#2293	2
C₂×#389×C₇₁	2
C₄²×D₄×C₇₁	2
#34308	71

Subgroups — C71×#34308 #31855180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#34308 #31855180