Subgroups — C₇₁×#61953 #31882825

Order 18176.

1932 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3396	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3304	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3297	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3287	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3282	C₂	1	4	yes	maximal, complemented
9	C₇₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×#460×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₇₁	C₂²	1	4	yes	complemented
19	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
20	#559×C₇₁	—	2	1	no	—
21	#559×C₇₁	—	2	1	no	—
22	#559×C₇₁	C₂²	1	2	yes	—
23	#559×C₇₁	C₂²	1	1	yes	characteristic, complemented
24	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
25	#556×C₇₁	—	2	1	no	—
26	#556×C₇₁	C₂²	1	1	yes	characteristic, complemented
27	#553×C₇₁	—	2	2	no	—
28	#553×C₇₁	C₂²	1	2	yes	—
29	#550×C₇₁	—	2	1	no	—
30	#550×C₇₁	C₂²	1	2	yes	—
31	#550×C₇₁	C₂²	1	1	yes	characteristic, complemented
32	#548×C₇₁	C₂²	1	2	yes	—
33	#546×C₇₁	—	2	2	no	—
34	#546×C₇₁	C₂²	1	4	yes	—
35	#540×C₇₁	—	2	2	no	—
36	#535×C₇₁	—	2	1	no	—
37	#533×C₇₁	C₂²	1	1	yes	characteristic
38	#532×C₇₁	—	2	1	no	—
39	#532×C₇₁	C₂²	1	2	yes	—
40	#532×C₇₁	C₂²	1	2	yes	—
41	#532×C₇₁	C₂²	1	1	yes	characteristic
42	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
43	#529×C₇₁	—	2	2	no	—
44	#529×C₇₁	C₂²	1	2	yes	complemented
45	#518×C₇₁	—	2	1	no	—
46	C₄×#41×C₇₁	—	2	1	no	—
47	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₇₁	C₂²	1	2	yes	complemented
49	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
50	#495×C₇₁	C₂²	1	4	yes	complemented
51	#493×C₇₁	C₂²	1	2	yes	—
52	#488×C₇₁	C₂²	1	4	yes	complemented
53	#486×C₇₁	C₂²	1	2	yes	—
54	#484×C₇₁	C₂²	1	2	yes	—
55	#482×C₇₁	C₂²	1	4	yes	complemented
56	#478×C₇₁	C₂²	1	4	yes	complemented
57	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
58	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	#476×C₇₁	C₂²	1	2	yes	complemented
60	#475×C₇₁	C₂²	1	2	yes	complemented
61	#466×C₇₁	C₂²	1	4	yes	complemented
62	#465×C₇₁	C₂²	1	4	yes	—
63	#465×C₇₁	C₂²	1	4	yes	complemented
64	#464×C₇₁	C₂²	1	4	yes	complemented
65	#463×C₇₁	C₂²	1	4	yes	complemented
66	#463×C₇₁	C₂²	1	4	yes	complemented
67	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
69	#461×C₇₁	C₂²	1	2	yes	complemented
70	#460×C₇₁	C₂²	1	2	yes	—
71	#460×C₇₁	C₂²	1	2	yes	—
72	#460×C₇₁	C₂²	1	2	yes	—
73	#460×C₇₁	C₂²	1	2	yes	—
74	#460×C₇₁	C₂²	1	2	yes	complemented
75	#459×C₇₁	C₂²	1	2	yes	—
76	#459×C₇₁	C₂²	1	2	yes	—
77	#452×C₇₁	C₂²	1	4	yes	complemented
78	#451×C₇₁	C₂²	1	2	yes	—
79	#449×C₇₁	C₂²	1	4	yes	complemented
80	#449×C₇₁	C₂²	1	4	yes	complemented
81	#447×C₇₁	C₂²	1	4	yes	—
82	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
84	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	complemented
86	C₄×D₈×C₇₁	C₂²	1	4	yes	complemented
87	C₈×D₄×C₇₁	C₂²	1	4	yes	—
88	C₈×D₄×C₇₁	C₂²	1	2	yes	complemented
89	#431×C₇₁	C₂²	1	1	yes	characteristic
90	#431×C₇₁	C₂²	1	2	yes	complemented
91	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	complemented
93	#416×C₇₁	C₂²	1	4	yes	complemented
94	C₂×#102×C₇₁	C₂²	1	2	yes	—
95	C₂×#41×C₇₁	—	2	1	no	—
96	C₂×#41×C₇₁	—	2	2	no	—
97	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₇₁	C₂³	1	2	yes	—
99	C₂×#41×C₇₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₇₁	—	2	1	no	—
102	C₂²×D₄×C₇₁	—	2	1	no	—
103	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
104	#135×C₇₁	—	4	8	no	—
105	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
106	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₇₁	—	4	4	no	—
108	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
111	C₂×D₈×C₇₁	C₂³	1	4	yes	—
112	C₂×D₈×C₇₁	C₂³	1	4	yes	—
113	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
114	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₇₁	—	2	1	no	—
116	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
119	#127×C₇₁	—	2	1	no	—
120	#127×C₇₁	—	2	2	no	—
121	#127×C₇₁	—	2	1	no	—
122	#127×C₇₁	—	2	1	no	—
123	#127×C₇₁	C₂³	1	2	yes	—
124	#127×C₇₁	C₂³	1	2	yes	—
125	#127×C₇₁	C₂³	1	1	yes	characteristic
126	#126×C₇₁	—	2	2	no	—
127	#126×C₇₁	—	2	2	no	—
128	#126×C₇₁	—	2	2	no	—
129	#125×C₇₁	—	2	2	no	—
130	#125×C₇₁	—	2	1	no	—
131	#125×C₇₁	C₂³	1	2	yes	—
132	#124×C₇₁	—	2	1	no	—
133	#124×C₇₁	—	2	2	no	—
134	#124×C₇₁	—	2	1	no	—
135	#124×C₇₁	—	2	2	no	—
136	#124×C₇₁	—	2	2	no	—
137	#124×C₇₁	—	2	1	no	—
138	#124×C₇₁	C₂³	1	2	yes	—
139	#124×C₇₁	C₂³	1	4	yes	—
140	#123×C₇₁	—	2	2	no	—
141	#123×C₇₁	—	2	2	no	—
142	#123×C₇₁	—	2	4	no	—
143	#123×C₇₁	—	2	4	no	—
144	#123×C₇₁	—	2	2	no	—
145	C₂²⋊Q₈×C₇₁	—	2	1	no	—
146	C₂²⋊Q₈×C₇₁	—	2	2	no	—
147	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
149	#121×C₇₁	—	2	2	no	—
150	#121×C₇₁	—	2	2	no	—
151	#121×C₇₁	—	2	2	no	—
152	#121×C₇₁	—	2	2	no	—
153	#121×C₇₁	—	2	2	no	—
154	#121×C₇₁	—	2	1	no	—
155	#121×C₇₁	—	2	2	no	—
156	#121×C₇₁	—	2	4	no	—
157	#121×C₇₁	—	2	4	no	—
158	#121×C₇₁	C₂³	1	2	yes	—
159	#121×C₇₁	C₂³	1	2	yes	—
160	#121×C₇₁	C₂³	1	4	yes	—
161	#120×C₇₁	—	2	4	no	—
162	C₄×Q₈×C₇₁	—	2	1	no	—
163	C₄×Q₈×C₇₁	—	2	1	no	—
164	C₄×Q₈×C₇₁	—	2	1	no	—
165	C₄×Q₈×C₇₁	—	2	1	no	—
166	C₄×Q₈×C₇₁	—	2	1	no	—
167	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₇₁	—	2	2	no	—
176	C₄×D₄×C₇₁	—	2	2	no	—
177	C₄×D₄×C₇₁	—	2	2	no	—
178	C₄×D₄×C₇₁	—	2	1	no	—
179	C₄×D₄×C₇₁	—	2	1	no	—
180	C₄×D₄×C₇₁	—	2	2	no	—
181	C₄×D₄×C₇₁	—	2	2	no	—
182	C₄×D₄×C₇₁	—	2	2	no	—
183	C₄×D₄×C₇₁	—	2	2	no	—
184	C₄×D₄×C₇₁	—	2	2	no	—
185	C₄×D₄×C₇₁	—	2	2	no	—
186	C₄×D₄×C₇₁	—	2	1	no	—
187	C₄×D₄×C₇₁	—	2	2	no	—
188	C₄×D₄×C₇₁	D₄	1	2	yes	—
189	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
190	C₄×D₄×C₇₁	C₂³	1	2	yes	—
191	C₄×D₄×C₇₁	C₂³	1	4	yes	—
192	C₄×D₄×C₇₁	C₂³	1	2	yes	—
193	C₄×D₄×C₇₁	C₂³	1	2	yes	—
194	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
195	#117×C₇₁	—	2	1	no	—
196	#117×C₇₁	—	2	2	no	—
197	#117×C₇₁	—	2	2	no	—
198	#117×C₇₁	D₄	1	1	yes	characteristic
199	#117×C₇₁	D₄	1	2	yes	—
200	#117×C₇₁	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
204	C₂×C₄²×C₇₁	—	2	1	no	—
205	C₂×C₄²×C₇₁	—	2	2	no	—
206	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
208	#107×C₇₁	C₂³	1	2	yes	—
209	#107×C₇₁	C₂³	1	2	yes	—
210	#106×C₇₁	C₂³	1	4	yes	—
211	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
215	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
216	#103×C₇₁	C₂³	1	2	yes	—
217	#103×C₇₁	C₂³	1	4	yes	—
218	#103×C₇₁	C₂³	1	2	yes	—
219	#103×C₇₁	C₂³	1	2	yes	—
220	#103×C₇₁	C₂³	1	2	yes	—
221	#102×C₇₁	C₂³	1	4	yes	—
222	#102×C₇₁	C₂³	1	4	yes	—
223	#102×C₇₁	C₂³	1	4	yes	—
224	#102×C₇₁	C₂³	1	4	yes	—
225	#102×C₇₁	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
228	C₄×C₈×C₇₁	C₂³	1	2	yes	—
229	C₄×C₈×C₇₁	C₂³	1	4	yes	—
230	C₂⁴×C₇₁	—	2	2	no	—
231	#41×C₇₁	—	2	4	no	—
232	#41×C₇₁	—	2	4	no	—
233	#41×C₇₁	—	4	2	no	—
234	#41×C₇₁	—	4	4	no	—
235	#41×C₇₁	—	4	4	no	—
236	#41×C₇₁	—	4	4	no	—
237	#41×C₇₁	—	8	4	no	—
238	C₂×Q₈×C₇₁	—	2	1	no	—
239	C₂×Q₈×C₇₁	—	2	1	no	—
240	C₂×Q₈×C₇₁	—	2	1	no	—
241	C₂×Q₈×C₇₁	—	2	2	no	—
242	C₂×Q₈×C₇₁	—	4	1	no	—
243	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₇₁	—	2	2	no	—
248	C₂×D₄×C₇₁	—	2	2	no	—
249	C₂×D₄×C₇₁	—	2	2	no	—
250	C₂×D₄×C₇₁	—	2	4	no	—
251	C₂×D₄×C₇₁	—	2	4	no	—
252	C₂×D₄×C₇₁	—	2	2	no	—
253	C₂×D₄×C₇₁	—	2	1	no	—
254	C₂×D₄×C₇₁	—	2	2	no	—
255	C₂×D₄×C₇₁	—	2	2	no	—
256	C₂×D₄×C₇₁	—	2	1	no	—
257	C₂×D₄×C₇₁	—	2	2	no	—
258	C₂×D₄×C₇₁	—	2	2	no	—
259	C₂×D₄×C₇₁	—	4	2	no	—
260	C₂×D₄×C₇₁	—	4	2	no	—
261	C₂×D₄×C₇₁	—	4	4	no	—
262	C₂×D₄×C₇₁	—	8	2	no	—
263	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₇₁	C₂⁴	1	4	yes	—
266	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇₁	—	2	1	no	—
268	C₂²×C₄×C₇₁	—	2	1	no	—
269	C₂²×C₄×C₇₁	—	2	2	no	—
270	C₂²×C₄×C₇₁	—	2	2	no	—
271	C₂²×C₄×C₇₁	—	2	2	no	—
272	C₂²×C₄×C₇₁	—	2	4	no	—
273	C₂²×C₄×C₇₁	—	2	4	no	—
274	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
280	Q₁₆×C₇₁	—	2	4	no	—
281	Q₁₆×C₇₁	—	4	2	no	—
282	SD₁₆×C₇₁	—	2	8	no	—
283	SD₁₆×C₇₁	—	4	4	no	—
284	SD₁₆×C₇₁	—	4	4	no	—
285	D₈×C₇₁	—	4	4	no	—
286	D₈×C₇₁	—	4	4	no	—
287	C₂×C₈×C₇₁	—	4	2	no	—
288	C₂×C₈×C₇₁	—	4	4	no	—
289	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
290	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
291	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₇₁	—	2	1	no	—
293	C₄⋊C₄×C₇₁	—	2	1	no	—
294	C₄⋊C₄×C₇₁	—	2	1	no	—
295	C₄⋊C₄×C₇₁	—	2	1	no	—
296	C₄⋊C₄×C₇₁	—	2	1	no	—
297	C₄⋊C₄×C₇₁	—	2	1	no	—
298	C₄⋊C₄×C₇₁	—	2	1	no	—
299	C₄⋊C₄×C₇₁	—	2	2	no	—
300	C₄⋊C₄×C₇₁	—	2	2	no	—
301	C₄⋊C₄×C₇₁	—	2	2	no	—
302	C₄⋊C₄×C₇₁	—	2	1	no	—
303	C₄⋊C₄×C₇₁	—	2	1	no	—
304	C₄⋊C₄×C₇₁	—	2	2	no	—
305	C₄⋊C₄×C₇₁	—	2	2	no	—
306	C₄⋊C₄×C₇₁	—	2	2	no	—
307	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₇₁	—	2	2	no	—
316	C₂²⋊C₄×C₇₁	—	2	2	no	—
317	C₂²⋊C₄×C₇₁	—	2	2	no	—
318	C₂²⋊C₄×C₇₁	—	2	4	no	—
319	C₂²⋊C₄×C₇₁	—	2	4	no	—
320	C₂²⋊C₄×C₇₁	—	2	2	no	—
321	C₂²⋊C₄×C₇₁	—	2	2	no	—
322	C₂²⋊C₄×C₇₁	—	2	2	no	—
323	C₂²⋊C₄×C₇₁	—	2	2	no	—
324	C₂²⋊C₄×C₇₁	—	2	4	no	—
325	C₂²⋊C₄×C₇₁	—	2	2	no	—
326	C₂²⋊C₄×C₇₁	—	2	2	no	—
327	C₂²⋊C₄×C₇₁	—	2	4	no	—
328	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
331	C₄²×C₇₁	—	2	1	no	—
332	C₄²×C₇₁	—	2	1	no	—
333	C₄²×C₇₁	—	2	2	no	—
334	C₄²×C₇₁	—	2	2	no	—
335	C₄²×C₇₁	—	2	1	no	—
336	C₄²×C₇₁	—	2	1	no	—
337	C₄²×C₇₁	—	2	2	no	—
338	C₄²×C₇₁	C₂×D₄	1	2	yes	—
339	C₄²×C₇₁	C₂×D₄	1	2	yes	—
340	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₇₁	C₂⁴	1	2	yes	—
343	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
344	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
345	C₂³×C₇₁	—	2	2	no	—
346	C₂³×C₇₁	—	2	4	no	—
347	C₂³×C₇₁	—	4	4	no	—
348	C₂³×C₇₁	—	8	2	no	—
349	C₂³×C₇₁	—	8	2	no	—
350	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
351	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₇₁	—	2	2	no	—
353	Q₈×C₇₁	—	2	1	no	—
354	Q₈×C₇₁	—	2	1	no	—
355	Q₈×C₇₁	—	2	2	no	—
356	Q₈×C₇₁	—	2	1	no	—
357	Q₈×C₇₁	—	2	2	no	—
358	Q₈×C₇₁	—	4	2	no	—
359	Q₈×C₇₁	—	4	2	no	—
360	Q₈×C₇₁	—	4	2	no	—
361	Q₈×C₇₁	H(5,𝔽₂)	1	2	yes	—
362	D₄×C₇₁	—	2	4	no	—
363	D₄×C₇₁	—	2	2	no	—
364	D₄×C₇₁	—	2	2	no	—
365	D₄×C₇₁	—	2	4	no	—
366	D₄×C₇₁	—	2	2	no	—
367	D₄×C₇₁	—	2	4	no	—
368	D₄×C₇₁	—	4	4	no	—
369	D₄×C₇₁	—	4	4	no	—
370	D₄×C₇₁	—	4	4	no	—
371	D₄×C₇₁	—	4	4	no	—
372	D₄×C₇₁	—	4	4	no	—
373	D₄×C₇₁	—	4	2	no	—
374	D₄×C₇₁	—	8	1	no	—
375	D₄×C₇₁	—	8	2	no	—
376	D₄×C₇₁	—	8	2	no	—
377	D₄×C₇₁	—	8	2	no	—
378	D₄×C₇₁	—	8	4	no	—
379	D₄×C₇₁	—	8	4	no	—
380	C₂×C₄×C₇₁	—	2	1	no	—
381	C₂×C₄×C₇₁	—	2	4	no	—
382	C₂×C₄×C₇₁	—	2	1	no	—
383	C₂×C₄×C₇₁	—	2	2	no	—
384	C₂×C₄×C₇₁	—	2	1	no	—
385	C₂×C₄×C₇₁	—	2	2	no	—
386	C₂×C₄×C₇₁	—	2	1	no	—
387	C₂×C₄×C₇₁	—	2	1	no	—
388	C₂×C₄×C₇₁	—	2	2	no	—
389	C₂×C₄×C₇₁	—	2	1	no	—
390	C₂×C₄×C₇₁	—	2	2	no	—
391	C₂×C₄×C₇₁	—	2	2	no	—
392	C₂×C₄×C₇₁	—	4	1	no	—
393	C₂×C₄×C₇₁	—	4	2	no	—
394	C₂×C₄×C₇₁	—	4	4	no	—
395	C₂×C₄×C₇₁	—	4	2	no	—
396	C₂×C₄×C₇₁	—	4	4	no	—
397	C₂×C₄×C₇₁	—	8	2	no	—
398	C₂×C₄×C₇₁	—	8	4	no	—
399	C₂×C₄×C₇₁	—	8	4	no	—
400	C₂×C₄×C₇₁	—	8	1	no	—
401	C₂×C₄×C₇₁	#135	1	4	yes	complemented
402	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
411	C₈×C₇₁	—	2	2	no	—
412	C₈×C₇₁	—	2	4	no	—
413	C₈×C₇₁	—	2	2	no	—
414	C₂²×C₇₁	—	2	1	no	—
415	C₂²×C₇₁	—	2	1	no	—
416	C₂²×C₇₁	—	2	2	no	—
417	C₂²×C₇₁	—	2	2	no	—
418	C₂²×C₇₁	—	2	2	no	—
419	C₂²×C₇₁	—	4	4	no	—
420	C₂²×C₇₁	—	4	2	no	—
421	C₂²×C₇₁	—	4	2	no	—
422	C₂²×C₇₁	—	4	4	no	—
423	C₂²×C₇₁	—	4	2	no	—
424	C₂²×C₇₁	—	4	4	no	—
425	C₂²×C₇₁	—	16	4	no	—
426	C₂²×C₇₁	C₂×#135	1	2	yes	—
427	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₇₁	—	2	1	no	—
429	C₄×C₇₁	—	2	2	no	—
430	C₄×C₇₁	—	2	1	no	—
431	C₄×C₇₁	—	2	2	no	—
432	C₄×C₇₁	—	2	1	no	—
433	C₄×C₇₁	—	2	2	no	—
434	C₄×C₇₁	—	2	2	no	—
435	C₄×C₇₁	—	4	1	no	—
436	C₄×C₇₁	—	4	2	no	—
437	C₄×C₇₁	—	4	1	no	—
438	C₄×C₇₁	—	4	1	no	—
439	C₄×C₇₁	—	4	2	no	—
440	C₄×C₇₁	—	4	2	no	—
441	C₄×C₇₁	C₂×#135	1	2	yes	—
442	C₄×C₇₁	C₂×#135	1	2	yes	—
443	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₄×C₇₁	#585	1	1	yes	characteristic
445	#61953	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂×C₇₁	—	2	2	no	—
447	C₂×C₇₁	—	4	2	no	—
448	C₂×C₇₁	—	8	2	no	—
449	C₂×C₇₁	—	8	4	no	—
450	C₂×C₇₁	#3488	1	1	yes	characteristic
451	C₂×C₇₁	C₂²×#135	1	1	yes	characteristic
452	C₂×C₇₁	#3585	1	1	yes	characteristic
453	#3508	C₂×C₇₁	1	1	yes	characteristic, complemented
454	#3480	C₂×C₇₁	1	1	yes	characteristic, complemented
455	#3396	C₂×C₇₁	1	2	yes	complemented
456	#3365	C₂×C₇₁	1	2	yes	complemented
457	#3304	C₂×C₇₁	1	2	yes	complemented
458	#3297	C₂×C₇₁	1	4	yes	complemented
459	#3287	C₂×C₇₁	1	2	yes	complemented
460	#3282	C₂×C₇₁	1	4	yes	complemented
461	#3247	C₂×C₇₁	1	2	yes	complemented
462	#3246	C₂×C₇₁	1	1	yes	characteristic, complemented
463	#3212	C₂×C₇₁	1	2	yes	complemented
464	#3205	C₂×C₇₁	1	1	yes	characteristic, complemented
465	#3106	C₂×C₇₁	1	2	yes	complemented
466	#3104	C₂×C₇₁	1	1	yes	characteristic, complemented
467	#3035	C₂×C₇₁	1	2	yes	complemented
468	C₂×#460	C₂×C₇₁	1	1	yes	characteristic, complemented
469	#2988	C₂×C₇₁	1	1	yes	characteristic, complemented
470	C₇₁	#61953	1	1	yes	characteristic, direct product factor, Sylow
471	C₂×#135	C₂²×C₇₁	1	4	yes	complemented
472	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
473	#559	—	2	1	no	—
474	#559	—	2	1	no	—
475	#559	C₂²×C₇₁	1	2	yes	—
476	#559	C₂²×C₇₁	1	1	yes	characteristic, complemented
477	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
478	#556	—	2	1	no	—
479	#556	C₂²×C₇₁	1	1	yes	characteristic, complemented
480	#553	—	2	2	no	—
481	#553	C₂²×C₇₁	1	2	yes	—
482	#550	—	2	1	no	—
483	#550	C₂²×C₇₁	1	2	yes	—
484	#550	C₂²×C₇₁	1	1	yes	characteristic, complemented
485	#548	C₂²×C₇₁	1	2	yes	—
486	#546	—	2	2	no	—
487	#546	C₂²×C₇₁	1	4	yes	—
488	#540	—	2	2	no	—
489	#535	—	2	1	no	—
490	#533	C₂²×C₇₁	1	1	yes	characteristic
491	#532	—	2	1	no	—
492	#532	C₂²×C₇₁	1	2	yes	—
493	#532	C₂²×C₇₁	1	2	yes	—
494	#532	C₂²×C₇₁	1	1	yes	characteristic
495	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
496	#529	—	2	2	no	—
497	#529	C₂²×C₇₁	1	2	yes	complemented
498	#518	—	2	1	no	—
499	C₄×#41	—	2	1	no	—
500	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
501	C₄×#41	C₂²×C₇₁	1	2	yes	complemented
502	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
503	#495	C₂²×C₇₁	1	4	yes	complemented
504	#493	C₂²×C₇₁	1	2	yes	—
505	#488	C₂²×C₇₁	1	4	yes	complemented
506	#486	C₂²×C₇₁	1	2	yes	—
507	#484	C₂²×C₇₁	1	2	yes	—
508	#482	C₂²×C₇₁	1	4	yes	complemented
509	#478	C₂²×C₇₁	1	4	yes	complemented
510	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
511	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
512	#476	C₂²×C₇₁	1	2	yes	complemented
513	#475	C₂²×C₇₁	1	2	yes	complemented
514	#466	C₂²×C₇₁	1	4	yes	complemented
515	#465	C₂²×C₇₁	1	4	yes	—
516	#465	C₂²×C₇₁	1	4	yes	complemented
517	#464	C₂²×C₇₁	1	4	yes	complemented
518	#463	C₂²×C₇₁	1	4	yes	complemented
519	#463	C₂²×C₇₁	1	4	yes	complemented
520	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
521	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
522	#461	C₂²×C₇₁	1	2	yes	complemented
523	#460	C₂²×C₇₁	1	2	yes	—
524	#460	C₂²×C₇₁	1	2	yes	—
525	#460	C₂²×C₇₁	1	2	yes	—
526	#460	C₂²×C₇₁	1	2	yes	—
527	#460	C₂²×C₇₁	1	2	yes	complemented
528	#459	C₂²×C₇₁	1	2	yes	—
529	#459	C₂²×C₇₁	1	2	yes	—
530	#452	C₂²×C₇₁	1	4	yes	complemented
531	#451	C₂²×C₇₁	1	2	yes	—
532	#449	C₂²×C₇₁	1	4	yes	complemented
533	#449	C₂²×C₇₁	1	4	yes	complemented
534	#447	C₂²×C₇₁	1	4	yes	—
535	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
536	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
537	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
538	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	complemented
539	C₄×D₈	C₂²×C₇₁	1	4	yes	complemented
540	C₈×D₄	C₂²×C₇₁	1	4	yes	—
541	C₈×D₄	C₂²×C₇₁	1	2	yes	complemented
542	#431	C₂²×C₇₁	1	1	yes	characteristic
543	#431	C₂²×C₇₁	1	2	yes	complemented
544	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
545	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
546	#416	C₂²×C₇₁	1	4	yes	complemented
547	C₂×#102	C₂²×C₇₁	1	2	yes	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
551	C₂×#41	C₂³×C₇₁	1	2	yes	—
552	C₂×#41	C₂³×C₇₁	1	4	yes	—
553	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
557	#135	—	4	8	no	—
558	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
559	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
560	C₂×SD₁₆	—	4	4	no	—
561	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
562	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
563	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
564	C₂×D₈	C₂³×C₇₁	1	4	yes	—
565	C₂×D₈	C₂³×C₇₁	1	4	yes	—
566	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
567	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
568	C₄⋊Q₈	—	2	1	no	—
569	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
572	#127	—	2	1	no	—
573	#127	—	2	2	no	—
574	#127	—	2	1	no	—
575	#127	—	2	1	no	—
576	#127	C₂³×C₇₁	1	2	yes	—
577	#127	C₂³×C₇₁	1	2	yes	—
578	#127	C₂³×C₇₁	1	1	yes	characteristic
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#126	—	2	2	no	—
582	#125	—	2	2	no	—
583	#125	—	2	1	no	—
584	#125	C₂³×C₇₁	1	2	yes	—
585	#124	—	2	1	no	—
586	#124	—	2	2	no	—
587	#124	—	2	1	no	—
588	#124	—	2	2	no	—
589	#124	—	2	2	no	—
590	#124	—	2	1	no	—
591	#124	C₂³×C₇₁	1	2	yes	—
592	#124	C₂³×C₇₁	1	4	yes	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	2	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	—	2	4	no	—
610	#121	—	2	4	no	—
611	#121	C₂³×C₇₁	1	2	yes	—
612	#121	C₂³×C₇₁	1	4	yes	—
613	#121	C₂³×C₇₁	1	2	yes	—
614	#120	—	2	4	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
623	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
625	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
626	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
627	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	D₄×C₇₁	1	2	yes	—
642	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
643	C₄×D₄	C₂³×C₇₁	1	2	yes	—
644	C₄×D₄	C₂³×C₇₁	1	2	yes	—
645	C₄×D₄	C₂³×C₇₁	1	4	yes	—
646	C₄×D₄	C₂³×C₇₁	1	2	yes	—
647	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
648	#117	—	2	1	no	—
649	#117	—	2	2	no	—
650	#117	—	2	2	no	—
651	#117	D₄×C₇₁	1	1	yes	characteristic
652	#117	D₄×C₇₁	1	2	yes	—
653	#117	C₂³×C₇₁	1	2	yes	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	—	2	4	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	2	no	—
659	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
661	#107	C₂³×C₇₁	1	2	yes	—
662	#107	C₂³×C₇₁	1	2	yes	—
663	#106	C₂³×C₇₁	1	4	yes	—
664	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
665	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
666	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
667	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
668	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
669	#103	C₂³×C₇₁	1	2	yes	—
670	#103	C₂³×C₇₁	1	4	yes	—
671	#103	C₂³×C₇₁	1	2	yes	—
672	#103	C₂³×C₇₁	1	2	yes	—
673	#103	C₂³×C₇₁	1	2	yes	—
674	#102	C₂³×C₇₁	1	4	yes	—
675	#102	C₂³×C₇₁	1	4	yes	—
676	#102	C₂³×C₇₁	1	4	yes	—
677	#102	C₂³×C₇₁	1	4	yes	—
678	#102	C₂³×C₇₁	1	4	yes	—
679	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
681	C₄×C₈	C₂³×C₇₁	1	2	yes	—
682	C₄×C₈	C₂³×C₇₁	1	4	yes	—
683	C₂⁴	—	2	2	no	—
684	#41	—	2	4	no	—
685	#41	—	2	4	no	—
686	#41	—	4	2	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	#41	—	8	4	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	4	1	no	—
696	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
697	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
698	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
699	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	8	2	no	—
716	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
717	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
718	C₂×D₄	C₂⁴×C₇₁	1	4	yes	—
719	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
728	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
730	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
733	Q₁₆	—	2	4	no	—
734	Q₁₆	—	4	2	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	4	4	no	—
737	SD₁₆	—	4	4	no	—
738	D₈	—	4	4	no	—
739	D₈	—	4	4	no	—
740	C₂×C₈	—	4	2	no	—
741	C₂×C₈	—	4	4	no	—
742	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
743	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
744	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
762	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
766	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
767	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
783	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	1	no	—
790	C₄²	—	2	2	no	—
791	C₄²	C₂×D₄×C₇₁	1	2	yes	—
792	C₄²	C₂×D₄×C₇₁	1	2	yes	—
793	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
794	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
795	C₄²	C₂⁴×C₇₁	1	2	yes	—
796	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
797	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
798	C₂³	—	2	2	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	8	2	no	—
802	C₂³	—	8	2	no	—
803	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
804	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
805	Q₈	—	2	2	no	—
806	Q₈	—	2	1	no	—
807	Q₈	—	2	1	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	1	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	4	2	no	—
812	Q₈	—	4	2	no	—
813	Q₈	—	4	2	no	—
814	Q₈	H(5,𝔽₂)×C₇₁	1	2	yes	—
815	D₄	—	2	4	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	4	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	4	4	no	—
826	D₄	—	4	2	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	2	no	—
829	D₄	—	8	1	no	—
830	D₄	—	8	4	no	—
831	D₄	—	8	4	no	—
832	D₄	—	8	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	8	4	no	—
851	C₂×C₄	—	8	4	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	#135×C₇₁	1	4	yes	complemented
855	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
863	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
864	C₈	—	2	2	no	—
865	C₈	—	2	4	no	—
866	C₈	—	2	2	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	4	no	—
878	C₂²	—	16	4	no	—
879	C₂²	C₂×#135×C₇₁	1	2	yes	—
880	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	2	no	—
894	C₄	C₂×#135×C₇₁	1	2	yes	—
895	C₄	C₂×#135×C₇₁	1	2	yes	—
896	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
897	C₄	#585×C₇₁	1	1	yes	characteristic
898	C₂	—	2	2	no	—
899	C₂	—	4	2	no	—
900	C₂	—	8	4	no	—
901	C₂	—	8	2	no	—
902	C₂	C₇₁×#3488	1	1	yes	characteristic
903	C₂	C₂²×#135×C₇₁	1	1	yes	characteristic
904	C₂	C₇₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₄×#41×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3508	C₂	semidirect
2. C₇₁×#3480	C₂	semidirect
3. C₇₁×#3396	C₂	semidirect
4. C₇₁×#3365	C₂	semidirect
5. C₇₁×#3304	C₂	semidirect
6. C₇₁×#3297	C₂	semidirect
7. C₇₁×#3287	C₂	semidirect
8. C₇₁×#3282	C₂	semidirect
9. C₇₁×#3247	C₂	semidirect
10. C₇₁×#3246	C₂	semidirect
11. C₇₁×#3212	C₂	semidirect
12. C₇₁×#3205	C₂	semidirect
13. C₇₁×#3106	C₂	semidirect
14. C₇₁×#3104	C₂	semidirect
15. C₇₁×#3035	C₂	semidirect
16. C₂×#460×C₇₁	C₂	semidirect
17. C₇₁×#2988	C₂	semidirect
18. C₂×#135×C₇₁	C₂²	semidirect
23. #559×C₇₁	C₂²	semidirect
24. #557×C₇₁	C₂²	semidirect
26. #556×C₇₁	C₂²	semidirect
31. #550×C₇₁	C₂²	semidirect
44. #529×C₇₁	C₂²	semidirect
48. C₄×#41×C₇₁	C₂²	semidirect
50. #495×C₇₁	C₂²	semidirect
52. #488×C₇₁	C₂²	semidirect
55. #482×C₇₁	C₂²	semidirect
56. #478×C₇₁	C₂²	semidirect
57. #477×C₇₁	C₂²	semidirect
58. #477×C₇₁	C₂²	semidirect
59. #476×C₇₁	C₂²	semidirect
60. #475×C₇₁	C₂²	semidirect
61. #466×C₇₁	C₂²	semidirect
63. #465×C₇₁	C₂²	semidirect
64. #464×C₇₁	C₂²	semidirect
65. #463×C₇₁	C₂²	semidirect
66. #463×C₇₁	C₂²	semidirect
67. #462×C₇₁	C₂²	semidirect
68. #462×C₇₁	C₂²	semidirect
69. #461×C₇₁	C₂²	semidirect
74. #460×C₇₁	C₂²	semidirect
77. #452×C₇₁	C₂²	semidirect
79. #449×C₇₁	C₂²	semidirect
80. #449×C₇₁	C₂²	semidirect
82. C₈×Q₈×C₇₁	C₂²	semidirect
83. C₄×Q₁₆×C₇₁	C₂²	semidirect
84. C₄×Q₁₆×C₇₁	C₂²	semidirect
85. C₄×SD₁₆×C₇₁	C₂²	semidirect
86. C₄×D₈×C₇₁	C₂²	semidirect
88. C₈×D₄×C₇₁	C₂²	semidirect
90. #431×C₇₁	C₂²	semidirect
92. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
93. #416×C₇₁	C₂²	semidirect
401. C₂×C₄×C₇₁	#135	semidirect
445. #61953	C₇₁	direct (N × H)
453. #3508	C₂×C₇₁	semidirect
454. #3480	C₂×C₇₁	semidirect
455. #3396	C₂×C₇₁	semidirect
456. #3365	C₂×C₇₁	semidirect
457. #3304	C₂×C₇₁	semidirect
458. #3297	C₂×C₇₁	semidirect
459. #3287	C₂×C₇₁	semidirect
460. #3282	C₂×C₇₁	semidirect
461. #3247	C₂×C₇₁	semidirect
462. #3246	C₂×C₇₁	semidirect
463. #3212	C₂×C₇₁	semidirect
464. #3205	C₂×C₇₁	semidirect
465. #3106	C₂×C₇₁	semidirect
466. #3104	C₂×C₇₁	semidirect
467. #3035	C₂×C₇₁	semidirect
468. C₂×#460	C₂×C₇₁	semidirect
469. #2988	C₂×C₇₁	semidirect
470. C₇₁	#61953	direct (N × H)
471. C₂×#135	C₂²×C₇₁	semidirect
476. #559	C₂²×C₇₁	semidirect
477. #557	C₂²×C₇₁	semidirect
479. #556	C₂²×C₇₁	semidirect
484. #550	C₂²×C₇₁	semidirect
497. #529	C₂²×C₇₁	semidirect
501. C₄×#41	C₂²×C₇₁	semidirect
503. #495	C₂²×C₇₁	semidirect
505. #488	C₂²×C₇₁	semidirect
508. #482	C₂²×C₇₁	semidirect
509. #478	C₂²×C₇₁	semidirect
510. #477	C₂²×C₇₁	semidirect
511. #477	C₂²×C₇₁	semidirect
512. #476	C₂²×C₇₁	semidirect
513. #475	C₂²×C₇₁	semidirect
514. #466	C₂²×C₇₁	semidirect
516. #465	C₂²×C₇₁	semidirect
517. #464	C₂²×C₇₁	semidirect
518. #463	C₂²×C₇₁	semidirect
519. #463	C₂²×C₇₁	semidirect
520. #462	C₂²×C₇₁	semidirect
521. #462	C₂²×C₇₁	semidirect
522. #461	C₂²×C₇₁	semidirect
527. #460	C₂²×C₇₁	semidirect
530. #452	C₂²×C₇₁	semidirect
532. #449	C₂²×C₇₁	semidirect
533. #449	C₂²×C₇₁	semidirect
535. C₈×Q₈	C₂²×C₇₁	semidirect
536. C₄×Q₁₆	C₂²×C₇₁	semidirect
537. C₄×Q₁₆	C₂²×C₇₁	semidirect
538. C₄×SD₁₆	C₂²×C₇₁	semidirect
539. C₄×D₈	C₂²×C₇₁	semidirect
541. C₈×D₄	C₂²×C₇₁	semidirect
543. #431	C₂²×C₇₁	semidirect
545. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
546. #416	C₂²×C₇₁	semidirect
854. C₂×C₄	#135×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3508	2
C₇₁×#3480	2
C₇₁×#3396	2
C₇₁×#3365	2
C₇₁×#3304	2
C₇₁×#3297	2
C₇₁×#3287	2
C₇₁×#3282	2
C₇₁×#3247	2
C₇₁×#3246	2
C₇₁×#3212	2
C₇₁×#3205	2
C₇₁×#3106	2
C₇₁×#3104	2
C₇₁×#3035	2
C₂×#460×C₇₁	2
C₇₁×#2988	2
#61953	71

Subgroups — C71×#61953 #31882825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61953 #31882825