Subgroups — C₇₁×#61965 #31882837

Order 18176.

1888 conjugacy classes of subgroups.

The subgroup lattice has 890 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
2	Q₈×#41×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3333	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3314	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3278	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₇₁×#3254	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3216	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3112	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3037	C₂	1	2	yes	maximal, complemented
16	C₂×#460×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₇₁	C₂²	1	4	yes	complemented
19	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
20	#559×C₇₁	—	2	1	no	—
21	#559×C₇₁	C₂²	1	2	yes	—
22	Q₈²×C₇₁	C₂²	1	1	yes	characteristic, complemented
23	#557×C₇₁	—	2	1	no	—
24	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
25	#554×C₇₁	—	2	2	no	—
26	#554×C₇₁	—	2	1	no	—
27	#554×C₇₁	C₂²	1	2	yes	—
28	#554×C₇₁	C₂²	1	1	yes	characteristic, complemented
29	#550×C₇₁	—	2	1	no	—
30	#550×C₇₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₇₁	C₂²	1	2	yes	—
32	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
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	—	2	1	no	—
38	#533×C₇₁	—	2	2	no	—
39	#533×C₇₁	C₂²	1	1	yes	characteristic
40	#533×C₇₁	C₂²	1	1	yes	characteristic
41	#533×C₇₁	C₂²	1	2	yes	complemented
42	#532×C₇₁	C₂²	1	2	yes	—
43	#532×C₇₁	C₂²	1	2	yes	—
44	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
45	#518×C₇₁	—	2	1	no	—
46	C₄×#41×C₇₁	—	2	1	no	—
47	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	complemented
50	#497×C₇₁	C₂²	1	4	yes	complemented
51	#492×C₇₁	C₂²	1	2	yes	—
52	#489×C₇₁	C₂²	1	4	yes	complemented
53	#486×C₇₁	C₂²	1	2	yes	—
54	#484×C₇₁	C₂²	1	2	yes	—
55	#480×C₇₁	C₂²	1	4	yes	complemented
56	#477×C₇₁	C₂²	1	2	yes	complemented
57	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
58	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	#477×C₇₁	C₂²	1	2	yes	complemented
60	#474×C₇₁	C₂²	1	4	yes	complemented
61	#468×C₇₁	C₂²	1	4	yes	complemented
62	#468×C₇₁	C₂²	1	4	yes	complemented
63	#467×C₇₁	C₂²	1	4	yes	—
64	#464×C₇₁	C₂²	1	4	yes	complemented
65	#464×C₇₁	C₂²	1	4	yes	complemented
66	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
67	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	#462×C₇₁	C₂²	1	2	yes	complemented
69	#462×C₇₁	C₂²	1	2	yes	complemented
70	#461×C₇₁	C₂²	1	4	yes	complemented
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	—
75	#460×C₇₁	C₂²	1	2	yes	—
76	#460×C₇₁	C₂²	1	2	yes	—
77	#452×C₇₁	C₂²	1	4	yes	complemented
78	#452×C₇₁	C₂²	1	4	yes	complemented
79	#451×C₇₁	C₂²	1	2	yes	—
80	#450×C₇₁	C₂²	1	4	yes	—
81	#448×C₇₁	C₂²	1	4	yes	complemented
82	#446×C₇₁	C₂²	1	2	yes	complemented
83	#440×C₇₁	C₂²	1	4	yes	complemented
84	#440×C₇₁	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
86	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
87	#436×C₇₁	C₂²	1	2	yes	complemented
88	#435×C₇₁	C₂²	1	4	yes	—
89	#432×C₇₁	C₂²	1	2	yes	complemented
90	#431×C₇₁	C₂²	1	1	yes	characteristic
91	#423×C₇₁	C₂²	1	2	yes	complemented
92	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
93	#417×C₇₁	C₂²	1	4	yes	complemented
94	C₂×#102×C₇₁	C₂²	1	2	yes	—
95	C₂×#41×C₇₁	—	2	2	no	—
96	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₇₁	C₂³	1	4	yes	—
98	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₇₁	—	2	1	no	—
101	C₂²×D₄×C₇₁	—	2	1	no	—
102	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
103	#137×C₇₁	—	4	8	no	—
104	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
106	C₂×Q₁₆×C₇₁	C₂³	1	4	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×SD₁₆×C₇₁	C₂³	1	4	yes	—
112	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
113	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₇₁	—	2	2	no	—
115	C₄⋊Q₈×C₇₁	—	2	1	no	—
116	C₄⋊Q₈×C₇₁	—	2	1	no	—
117	C₄⋊Q₈×C₇₁	—	2	2	no	—
118	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
124	#127×C₇₁	—	2	2	no	—
125	#127×C₇₁	—	2	1	no	—
126	#127×C₇₁	—	2	1	no	—
127	#127×C₇₁	C₂³	1	2	yes	—
128	#127×C₇₁	C₂³	1	2	yes	—
129	#125×C₇₁	—	2	1	no	—
130	#125×C₇₁	—	2	2	no	—
131	#125×C₇₁	—	2	2	no	—
132	#125×C₇₁	—	2	1	no	—
133	#125×C₇₁	—	2	1	no	—
134	#125×C₇₁	—	2	1	no	—
135	#125×C₇₁	—	2	2	no	—
136	#124×C₇₁	—	2	2	no	—
137	#124×C₇₁	—	2	2	no	—
138	#124×C₇₁	C₂³	1	4	yes	—
139	#123×C₇₁	—	2	4	no	—
140	#123×C₇₁	—	2	4	no	—
141	C₂²⋊Q₈×C₇₁	—	2	1	no	—
142	C₂²⋊Q₈×C₇₁	—	2	1	no	—
143	C₂²⋊Q₈×C₇₁	—	2	2	no	—
144	C₂²⋊Q₈×C₇₁	—	2	2	no	—
145	C₂²⋊Q₈×C₇₁	—	2	2	no	—
146	C₂²⋊Q₈×C₇₁	—	2	2	no	—
147	C₂²⋊Q₈×C₇₁	—	2	2	no	—
148	C₂²⋊Q₈×C₇₁	—	2	2	no	—
149	C₂²⋊Q₈×C₇₁	—	2	2	no	—
150	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
153	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
154	#121×C₇₁	—	2	2	no	—
155	#121×C₇₁	—	2	2	no	—
156	#121×C₇₁	—	2	2	no	—
157	#121×C₇₁	—	2	4	no	—
158	#121×C₇₁	—	2	4	no	—
159	#121×C₇₁	C₂³	1	4	yes	—
160	#120×C₇₁	—	2	4	no	—
161	C₄×Q₈×C₇₁	—	2	1	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	2	no	—
166	C₄×Q₈×C₇₁	—	2	2	no	—
167	C₄×Q₈×C₇₁	—	2	1	no	—
168	C₄×Q₈×C₇₁	—	2	2	no	—
169	C₄×Q₈×C₇₁	—	2	1	no	—
170	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
171	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
176	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
179	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₇₁	—	2	2	no	—
181	C₄×D₄×C₇₁	—	2	1	no	—
182	C₄×D₄×C₇₁	—	2	2	no	—
183	C₄×D₄×C₇₁	—	2	1	no	—
184	C₄×D₄×C₇₁	—	2	2	no	—
185	C₄×D₄×C₇₁	—	2	2	no	—
186	C₄×D₄×C₇₁	—	2	2	no	—
187	C₄×D₄×C₇₁	—	2	2	no	—
188	C₄×D₄×C₇₁	—	2	2	no	—
189	C₄×D₄×C₇₁	D₄	1	2	yes	—
190	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
191	C₄×D₄×C₇₁	C₂³	1	4	yes	—
192	C₄×D₄×C₇₁	C₂³	1	2	yes	—
193	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
194	#117×C₇₁	—	2	1	no	—
195	#117×C₇₁	—	2	2	no	—
196	#117×C₇₁	—	2	1	no	—
197	#117×C₇₁	D₄	1	1	yes	characteristic
198	#117×C₇₁	D₄	1	2	yes	—
199	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
201	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
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	#107×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	#103×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	#97×C₇₁	C₂³	1	4	yes	—
229	C₄×C₈×C₇₁	C₂³	1	2	yes	—
230	C₂⁴×C₇₁	—	2	2	no	—
231	#41×C₇₁	—	2	4	no	—
232	#41×C₇₁	—	4	4	no	—
233	#41×C₇₁	—	4	4	no	—
234	#41×C₇₁	—	8	4	no	—
235	C₂×Q₈×C₇₁	—	2	2	no	—
236	C₂×Q₈×C₇₁	—	2	1	no	—
237	C₂×Q₈×C₇₁	—	2	1	no	—
238	C₂×Q₈×C₇₁	—	2	2	no	—
239	C₂×Q₈×C₇₁	—	2	1	no	—
240	C₂×Q₈×C₇₁	—	2	2	no	—
241	C₂×Q₈×C₇₁	—	2	4	no	—
242	C₂×Q₈×C₇₁	—	4	1	no	—
243	C₂×Q₈×C₇₁	—	4	2	no	—
244	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₇₁	—	2	4	no	—
250	C₂×D₄×C₇₁	—	2	4	no	—
251	C₂×D₄×C₇₁	—	2	2	no	—
252	C₂×D₄×C₇₁	—	2	2	no	—
253	C₂×D₄×C₇₁	—	2	2	no	—
254	C₂×D₄×C₇₁	—	2	2	no	—
255	C₂×D₄×C₇₁	—	2	2	no	—
256	C₂×D₄×C₇₁	—	4	2	no	—
257	C₂×D₄×C₇₁	—	4	2	no	—
258	C₂×D₄×C₇₁	—	4	4	no	—
259	C₂×D₄×C₇₁	—	8	2	no	—
260	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₇₁	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₇₁	—	2	2	no	—
264	C₂²×C₄×C₇₁	—	2	1	no	—
265	C₂²×C₄×C₇₁	—	2	2	no	—
266	C₂²×C₄×C₇₁	—	2	1	no	—
267	C₂²×C₄×C₇₁	—	2	4	no	—
268	C₂²×C₄×C₇₁	—	2	4	no	—
269	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
275	Q₁₆×C₇₁	—	2	4	no	—
276	Q₁₆×C₇₁	—	4	2	no	—
277	Q₁₆×C₇₁	—	4	4	no	—
278	SD₁₆×C₇₁	—	2	8	no	—
279	SD₁₆×C₇₁	—	4	4	no	—
280	SD₁₆×C₇₁	—	4	4	no	—
281	SD₁₆×C₇₁	—	4	4	no	—
282	M₁₆×C₇₁	—	4	4	no	—
283	C₂×C₈×C₇₁	—	4	2	no	—
284	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
285	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₇₁	—	2	1	no	—
288	C₄⋊C₄×C₇₁	—	2	2	no	—
289	C₄⋊C₄×C₇₁	—	2	1	no	—
290	C₄⋊C₄×C₇₁	—	2	1	no	—
291	C₄⋊C₄×C₇₁	—	2	2	no	—
292	C₄⋊C₄×C₇₁	—	2	2	no	—
293	C₄⋊C₄×C₇₁	—	2	1	no	—
294	C₄⋊C₄×C₇₁	—	2	2	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	2	no	—
299	C₄⋊C₄×C₇₁	—	2	1	no	—
300	C₄⋊C₄×C₇₁	—	2	2	no	—
301	C₄⋊C₄×C₇₁	—	2	1	no	—
302	C₄⋊C₄×C₇₁	—	2	1	no	—
303	C₄⋊C₄×C₇₁	—	2	2	no	—
304	C₄⋊C₄×C₇₁	—	2	2	no	—
305	C₄⋊C₄×C₇₁	—	2	1	no	—
306	C₄⋊C₄×C₇₁	—	2	2	no	—
307	C₄⋊C₄×C₇₁	—	2	2	no	—
308	C₄⋊C₄×C₇₁	—	2	2	no	—
309	C₄⋊C₄×C₇₁	—	2	2	no	—
310	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
318	C₂²⋊C₄×C₇₁	—	2	2	no	—
319	C₂²⋊C₄×C₇₁	—	2	2	no	—
320	C₂²⋊C₄×C₇₁	—	2	2	no	—
321	C₂²⋊C₄×C₇₁	—	2	2	no	—
322	C₂²⋊C₄×C₇₁	—	2	4	no	—
323	C₂²⋊C₄×C₇₁	—	2	4	no	—
324	C₂²⋊C₄×C₇₁	—	2	4	no	—
325	C₂²⋊C₄×C₇₁	—	2	4	no	—
326	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
329	C₄²×C₇₁	—	2	1	no	—
330	C₄²×C₇₁	—	2	1	no	—
331	C₄²×C₇₁	—	2	2	no	—
332	C₄²×C₇₁	—	2	2	no	—
333	C₄²×C₇₁	—	2	1	no	—
334	C₄²×C₇₁	—	2	2	no	—
335	C₄²×C₇₁	—	2	1	no	—
336	C₄²×C₇₁	—	2	2	no	—
337	C₄²×C₇₁	C₂×D₄	1	2	yes	—
338	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇₁	C₂×D₄	1	2	yes	—
340	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
342	C₄²×C₇₁	C₂⁴	1	2	yes	—
343	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
344	C₂³×C₇₁	—	2	4	no	—
345	C₂³×C₇₁	—	4	4	no	—
346	C₂³×C₇₁	—	8	2	no	—
347	C₂³×C₇₁	—	8	2	no	—
348	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
349	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₇₁	—	2	2	no	—
351	Q₈×C₇₁	—	2	1	no	—
352	Q₈×C₇₁	—	2	1	no	—
353	Q₈×C₇₁	—	2	2	no	—
354	Q₈×C₇₁	—	2	2	no	—
355	Q₈×C₇₁	—	2	2	no	—
356	Q₈×C₇₁	—	2	1	no	—
357	Q₈×C₇₁	—	2	2	no	—
358	Q₈×C₇₁	—	4	4	no	—
359	Q₈×C₇₁	—	4	2	no	—
360	Q₈×C₇₁	—	4	2	no	—
361	Q₈×C₇₁	—	8	2	no	—
362	Q₈×C₇₁	—	8	1	no	—
363	Q₈×C₇₁	H(5,𝔽₂)	1	2	yes	—
364	D₄×C₇₁	—	2	4	no	—
365	D₄×C₇₁	—	2	2	no	—
366	D₄×C₇₁	—	2	4	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	—	8	2	no	—
372	D₄×C₇₁	—	8	2	no	—
373	D₄×C₇₁	—	8	4	no	—
374	D₄×C₇₁	—	8	4	no	—
375	C₂×C₄×C₇₁	—	2	1	no	—
376	C₂×C₄×C₇₁	—	2	4	no	—
377	C₂×C₄×C₇₁	—	2	1	no	—
378	C₂×C₄×C₇₁	—	2	2	no	—
379	C₂×C₄×C₇₁	—	2	1	no	—
380	C₂×C₄×C₇₁	—	2	2	no	—
381	C₂×C₄×C₇₁	—	2	1	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	2	no	—
387	C₂×C₄×C₇₁	—	2	2	no	—
388	C₂×C₄×C₇₁	—	4	1	no	—
389	C₂×C₄×C₇₁	—	4	2	no	—
390	C₂×C₄×C₇₁	—	4	2	no	—
391	C₂×C₄×C₇₁	—	4	4	no	—
392	C₂×C₄×C₇₁	—	8	4	no	—
393	C₂×C₄×C₇₁	—	8	4	no	—
394	C₂×C₄×C₇₁	—	8	1	no	—
395	C₂×C₄×C₇₁	—	8	2	no	—
396	C₂×C₄×C₇₁	#137	1	4	yes	complemented
397	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
406	C₈×C₇₁	—	2	4	no	—
407	C₈×C₇₁	—	2	2	no	—
408	C₈×C₇₁	—	2	2	no	—
409	C₂²×C₇₁	—	2	1	no	—
410	C₂²×C₇₁	—	2	1	no	—
411	C₂²×C₇₁	—	2	2	no	—
412	C₂²×C₇₁	—	2	2	no	—
413	C₂²×C₇₁	—	2	2	no	—
414	C₂²×C₇₁	—	4	4	no	—
415	C₂²×C₇₁	—	4	4	no	—
416	C₂²×C₇₁	—	4	4	no	—
417	C₂²×C₇₁	—	16	4	no	—
418	C₂²×C₇₁	C₂×#137	1	2	yes	—
419	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
420	C₄×C₇₁	—	2	1	no	—
421	C₄×C₇₁	—	2	2	no	—
422	C₄×C₇₁	—	2	1	no	—
423	C₄×C₇₁	—	2	2	no	—
424	C₄×C₇₁	—	2	1	no	—
425	C₄×C₇₁	—	2	2	no	—
426	C₄×C₇₁	—	2	2	no	—
427	C₄×C₇₁	—	4	1	no	—
428	C₄×C₇₁	—	4	2	no	—
429	C₄×C₇₁	—	4	1	no	—
430	C₄×C₇₁	—	4	2	no	—
431	C₄×C₇₁	—	4	1	no	—
432	C₄×C₇₁	—	4	2	no	—
433	C₄×C₇₁	—	4	2	no	—
434	C₄×C₇₁	C₂×#137	1	2	yes	—
435	C₄×C₇₁	C₂×#137	1	2	yes	—
436	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₄×C₇₁	#585	1	1	yes	characteristic
438	#61965	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂×C₇₁	—	2	2	no	—
440	C₂×C₇₁	—	4	2	no	—
441	C₂×C₇₁	—	8	4	no	—
442	C₂×C₇₁	#3488	1	1	yes	characteristic
443	C₂×C₇₁	C₂²×#137	1	1	yes	characteristic
444	C₂×C₇₁	#3585	1	1	yes	characteristic
445	#3508	C₂×C₇₁	1	1	yes	characteristic
446	Q₈×#41	C₂×C₇₁	1	1	yes	characteristic, complemented
447	#3400	C₂×C₇₁	1	2	yes	complemented
448	#3375	C₂×C₇₁	1	2	yes	complemented
449	#3333	C₂×C₇₁	1	2	yes	complemented
450	#3314	C₂×C₇₁	1	4	yes	complemented
451	#3278	C₂×C₇₁	1	2	yes	complemented
452	#3266	C₂×C₇₁	1	4	yes	complemented
453	#3254	C₂×C₇₁	1	2	yes	complemented
454	#3249	C₂×C₇₁	1	1	yes	characteristic, complemented
455	#3216	C₂×C₇₁	1	2	yes	complemented
456	#3208	C₂×C₇₁	1	1	yes	characteristic, complemented
457	#3112	C₂×C₇₁	1	2	yes	complemented
458	#3104	C₂×C₇₁	1	1	yes	characteristic, complemented
459	#3037	C₂×C₇₁	1	2	yes	complemented
460	C₂×#460	C₂×C₇₁	1	1	yes	characteristic, complemented
461	#2989	C₂×C₇₁	1	1	yes	characteristic, complemented
462	C₇₁	#61965	1	1	yes	characteristic, direct product factor, Sylow
463	C₂×#137	C₂²×C₇₁	1	4	yes	complemented
464	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
465	#559	—	2	1	no	—
466	#559	C₂²×C₇₁	1	2	yes	—
467	Q₈²	C₂²×C₇₁	1	1	yes	characteristic, complemented
468	#557	—	2	1	no	—
469	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
470	#554	—	2	2	no	—
471	#554	—	2	1	no	—
472	#554	C₂²×C₇₁	1	2	yes	—
473	#554	C₂²×C₇₁	1	1	yes	characteristic, complemented
474	#550	—	2	1	no	—
475	#550	C₂²×C₇₁	1	2	yes	—
476	D₄×Q₈	C₂²×C₇₁	1	2	yes	—
477	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
478	#546	—	2	2	no	—
479	#546	C₂²×C₇₁	1	4	yes	—
480	#540	—	2	2	no	—
481	#535	—	2	1	no	—
482	#533	—	2	1	no	—
483	#533	—	2	2	no	—
484	#533	C₂²×C₇₁	1	1	yes	characteristic
485	#533	C₂²×C₇₁	1	1	yes	characteristic
486	#533	C₂²×C₇₁	1	2	yes	complemented
487	#532	C₂²×C₇₁	1	2	yes	—
488	#532	C₂²×C₇₁	1	2	yes	—
489	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
490	#518	—	2	1	no	—
491	C₄×#41	—	2	1	no	—
492	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
494	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	complemented
495	#497	C₂²×C₇₁	1	4	yes	complemented
496	#492	C₂²×C₇₁	1	2	yes	—
497	#489	C₂²×C₇₁	1	4	yes	complemented
498	#486	C₂²×C₇₁	1	2	yes	—
499	#484	C₂²×C₇₁	1	2	yes	—
500	#480	C₂²×C₇₁	1	4	yes	complemented
501	#477	C₂²×C₇₁	1	2	yes	complemented
502	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
503	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
504	#477	C₂²×C₇₁	1	2	yes	complemented
505	#474	C₂²×C₇₁	1	4	yes	complemented
506	#468	C₂²×C₇₁	1	4	yes	complemented
507	#468	C₂²×C₇₁	1	4	yes	complemented
508	#467	C₂²×C₇₁	1	4	yes	—
509	#464	C₂²×C₇₁	1	4	yes	complemented
510	#464	C₂²×C₇₁	1	4	yes	complemented
511	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
512	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
513	#462	C₂²×C₇₁	1	2	yes	complemented
514	#462	C₂²×C₇₁	1	2	yes	complemented
515	#461	C₂²×C₇₁	1	4	yes	complemented
516	#460	C₂²×C₇₁	1	2	yes	—
517	#460	C₂²×C₇₁	1	2	yes	—
518	#460	C₂²×C₇₁	1	2	yes	—
519	#460	C₂²×C₇₁	1	2	yes	—
520	#460	C₂²×C₇₁	1	2	yes	—
521	#460	C₂²×C₇₁	1	2	yes	—
522	#452	C₂²×C₇₁	1	4	yes	complemented
523	#452	C₂²×C₇₁	1	4	yes	complemented
524	#451	C₂²×C₇₁	1	2	yes	—
525	#450	C₂²×C₇₁	1	4	yes	—
526	#448	C₂²×C₇₁	1	4	yes	complemented
527	#446	C₂²×C₇₁	1	2	yes	complemented
528	#440	C₂²×C₇₁	1	4	yes	complemented
529	#440	C₂²×C₇₁	1	4	yes	complemented
530	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
531	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
532	#436	C₂²×C₇₁	1	2	yes	complemented
533	#435	C₂²×C₇₁	1	4	yes	—
534	#432	C₂²×C₇₁	1	2	yes	complemented
535	#431	C₂²×C₇₁	1	1	yes	characteristic
536	#423	C₂²×C₇₁	1	2	yes	complemented
537	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
538	#417	C₂²×C₇₁	1	4	yes	complemented
539	C₂×#102	C₂²×C₇₁	1	2	yes	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
542	C₂×#41	C₂³×C₇₁	1	4	yes	—
543	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
548	#137	—	4	8	no	—
549	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
550	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
551	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
552	C₂×SD₁₆	—	4	4	no	—
553	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
555	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
557	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
558	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
559	C₄⋊Q₈	—	2	2	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
569	#127	—	2	2	no	—
570	#127	—	2	1	no	—
571	#127	—	2	1	no	—
572	#127	C₂³×C₇₁	1	2	yes	—
573	#127	C₂³×C₇₁	1	2	yes	—
574	#125	—	2	1	no	—
575	#125	—	2	2	no	—
576	#125	—	2	2	no	—
577	#125	—	2	1	no	—
578	#125	—	2	1	no	—
579	#125	—	2	1	no	—
580	#125	—	2	2	no	—
581	#124	—	2	2	no	—
582	#124	—	2	2	no	—
583	#124	C₂³×C₇₁	1	4	yes	—
584	#123	—	2	4	no	—
585	#123	—	2	4	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
599	#121	—	2	2	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	—	2	4	no	—
603	#121	—	2	4	no	—
604	#121	C₂³×C₇₁	1	4	yes	—
605	#120	—	2	4	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
621	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
622	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
623	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
624	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	D₄×C₇₁	1	2	yes	—
635	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₇₁	1	4	yes	—
637	C₄×D₄	C₂³×C₇₁	1	2	yes	—
638	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
639	#117	—	2	1	no	—
640	#117	—	2	2	no	—
641	#117	—	2	1	no	—
642	#117	D₄×C₇₁	1	1	yes	characteristic
643	#117	D₄×C₇₁	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
648	C₂×C₂²⋊C₄	—	2	4	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	2	no	—
651	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
653	#107	C₂³×C₇₁	1	2	yes	—
654	#107	C₂³×C₇₁	1	2	yes	—
655	#107	C₂³×C₇₁	1	4	yes	—
656	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
658	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
659	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
660	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
661	#103	C₂³×C₇₁	1	2	yes	—
662	#103	C₂³×C₇₁	1	4	yes	—
663	#103	C₂³×C₇₁	1	2	yes	—
664	#103	C₂³×C₇₁	1	2	yes	—
665	#103	C₂³×C₇₁	1	2	yes	—
666	#103	C₂³×C₇₁	1	4	yes	—
667	#102	C₂³×C₇₁	1	4	yes	—
668	#102	C₂³×C₇₁	1	4	yes	—
669	#102	C₂³×C₇₁	1	4	yes	—
670	#102	C₂³×C₇₁	1	4	yes	—
671	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
673	#97	C₂³×C₇₁	1	4	yes	—
674	C₄×C₈	C₂³×C₇₁	1	2	yes	—
675	C₂⁴	—	2	2	no	—
676	#41	—	2	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	8	4	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	—	4	1	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
693	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	8	2	no	—
705	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₇₁	1	4	yes	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
715	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
720	Q₁₆	—	2	4	no	—
721	Q₁₆	—	4	2	no	—
722	Q₁₆	—	4	4	no	—
723	SD₁₆	—	2	8	no	—
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	M₁₆	—	4	4	no	—
728	C₂×C₈	—	4	2	no	—
729	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
730	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
756	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
757	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
758	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	1	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	2	no	—
782	C₄²	C₂×D₄×C₇₁	1	2	yes	—
783	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
784	C₄²	C₂×D₄×C₇₁	1	2	yes	—
785	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
786	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
787	C₄²	C₂⁴×C₇₁	1	2	yes	—
788	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
789	C₂³	—	2	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	2	no	—
793	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
794	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
795	Q₈	—	2	2	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	8	2	no	—
807	Q₈	—	8	1	no	—
808	Q₈	H(5,𝔽₂)×C₇₁	1	2	yes	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	4	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	D₄	—	8	4	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	#137×C₇₁	1	4	yes	complemented
842	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	4	no	—
860	C₂²	—	4	4	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	16	4	no	—
863	C₂²	C₂×#137×C₇₁	1	2	yes	—
864	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	C₂×#137×C₇₁	1	2	yes	—
880	C₄	C₂×#137×C₇₁	1	2	yes	—
881	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
882	C₄	#585×C₇₁	1	1	yes	characteristic
883	C₂	—	2	2	no	—
884	C₂	—	4	2	no	—
885	C₂	—	8	4	no	—
886	C₂	C₇₁×#3488	1	1	yes	characteristic
887	C₂	C₂²×#137×C₇₁	1	1	yes	characteristic
888	C₂	C₇₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₇₁×#3508	C₂
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
2. Q₈×#41×C₇₁	C₂	semidirect
3. C₇₁×#3400	C₂	semidirect
4. C₇₁×#3375	C₂	semidirect
5. C₇₁×#3333	C₂	semidirect
6. C₇₁×#3314	C₂	semidirect
7. C₇₁×#3278	C₂	semidirect
8. C₇₁×#3266	C₂	semidirect
9. C₇₁×#3254	C₂	semidirect
10. C₇₁×#3249	C₂	semidirect
11. C₇₁×#3216	C₂	semidirect
12. C₇₁×#3208	C₂	semidirect
13. C₇₁×#3112	C₂	semidirect
14. C₇₁×#3104	C₂	semidirect
15. C₇₁×#3037	C₂	semidirect
16. C₂×#460×C₇₁	C₂	semidirect
17. C₇₁×#2989	C₂	semidirect
18. C₂×#137×C₇₁	C₂²	semidirect
22. Q₈²×C₇₁	C₂²	semidirect
24. #557×C₇₁	C₂²	semidirect
28. #554×C₇₁	C₂²	semidirect
32. D₄×Q₈×C₇₁	C₂²	semidirect
41. #533×C₇₁	C₂²	semidirect
49. C₂×C₄×Q₈×C₇₁	C₂²	semidirect
50. #497×C₇₁	C₂²	semidirect
52. #489×C₇₁	C₂²	semidirect
55. #480×C₇₁	C₂²	semidirect
56. #477×C₇₁	C₂²	semidirect
57. #477×C₇₁	C₂²	semidirect
58. #477×C₇₁	C₂²	semidirect
59. #477×C₇₁	C₂²	semidirect
60. #474×C₇₁	C₂²	semidirect
61. #468×C₇₁	C₂²	semidirect
62. #468×C₇₁	C₂²	semidirect
64. #464×C₇₁	C₂²	semidirect
65. #464×C₇₁	C₂²	semidirect
66. #462×C₇₁	C₂²	semidirect
67. #462×C₇₁	C₂²	semidirect
68. #462×C₇₁	C₂²	semidirect
69. #462×C₇₁	C₂²	semidirect
70. #461×C₇₁	C₂²	semidirect
77. #452×C₇₁	C₂²	semidirect
78. #452×C₇₁	C₂²	semidirect
81. #448×C₇₁	C₂²	semidirect
82. #446×C₇₁	C₂²	semidirect
83. #440×C₇₁	C₂²	semidirect
84. #440×C₇₁	C₂²	semidirect
85. C₄×Q₁₆×C₇₁	C₂²	semidirect
86. C₄×Q₁₆×C₇₁	C₂²	semidirect
87. #436×C₇₁	C₂²	semidirect
89. #432×C₇₁	C₂²	semidirect
91. #423×C₇₁	C₂²	semidirect
93. #417×C₇₁	C₂²	semidirect
396. C₂×C₄×C₇₁	#137	semidirect
438. #61965	C₇₁	direct (N × H)
446. Q₈×#41	C₂×C₇₁	semidirect
447. #3400	C₂×C₇₁	semidirect
448. #3375	C₂×C₇₁	semidirect
449. #3333	C₂×C₇₁	semidirect
450. #3314	C₂×C₇₁	semidirect
451. #3278	C₂×C₇₁	semidirect
452. #3266	C₂×C₇₁	semidirect
453. #3254	C₂×C₇₁	semidirect
454. #3249	C₂×C₇₁	semidirect
455. #3216	C₂×C₇₁	semidirect
456. #3208	C₂×C₇₁	semidirect
457. #3112	C₂×C₇₁	semidirect
458. #3104	C₂×C₇₁	semidirect
459. #3037	C₂×C₇₁	semidirect
460. C₂×#460	C₂×C₇₁	semidirect
461. #2989	C₂×C₇₁	semidirect
462. C₇₁	#61965	direct (N × H)
463. C₂×#137	C₂²×C₇₁	semidirect
467. Q₈²	C₂²×C₇₁	semidirect
469. #557	C₂²×C₇₁	semidirect
473. #554	C₂²×C₇₁	semidirect
477. D₄×Q₈	C₂²×C₇₁	semidirect
486. #533	C₂²×C₇₁	semidirect
494. C₂×C₄×Q₈	C₂²×C₇₁	semidirect
495. #497	C₂²×C₇₁	semidirect
497. #489	C₂²×C₇₁	semidirect
500. #480	C₂²×C₇₁	semidirect
501. #477	C₂²×C₇₁	semidirect
502. #477	C₂²×C₇₁	semidirect
503. #477	C₂²×C₇₁	semidirect
504. #477	C₂²×C₇₁	semidirect
505. #474	C₂²×C₇₁	semidirect
506. #468	C₂²×C₇₁	semidirect
507. #468	C₂²×C₇₁	semidirect
509. #464	C₂²×C₇₁	semidirect
510. #464	C₂²×C₇₁	semidirect
511. #462	C₂²×C₇₁	semidirect
512. #462	C₂²×C₇₁	semidirect
513. #462	C₂²×C₇₁	semidirect
514. #462	C₂²×C₇₁	semidirect
515. #461	C₂²×C₇₁	semidirect
522. #452	C₂²×C₇₁	semidirect
523. #452	C₂²×C₇₁	semidirect
526. #448	C₂²×C₇₁	semidirect
527. #446	C₂²×C₇₁	semidirect
528. #440	C₂²×C₇₁	semidirect
529. #440	C₂²×C₇₁	semidirect
530. C₄×Q₁₆	C₂²×C₇₁	semidirect
531. C₄×Q₁₆	C₂²×C₇₁	semidirect
532. #436	C₂²×C₇₁	semidirect
534. #432	C₂²×C₇₁	semidirect
536. #423	C₂²×C₇₁	semidirect
538. #417	C₂²×C₇₁	semidirect
841. C₂×C₄	#137×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
Q₈×#41×C₇₁	2
C₇₁×#3400	2
C₇₁×#3375	2
C₇₁×#3333	2
C₇₁×#3314	2
C₇₁×#3278	2
C₇₁×#3266	2
C₇₁×#3254	2
C₇₁×#3249	2
C₇₁×#3216	2
C₇₁×#3208	2
C₇₁×#3112	2
C₇₁×#3104	2
C₇₁×#3037	2
C₂×#460×C₇₁	2
C₇₁×#2989	2
#61965	71

Subgroups — C71×#61965 #31882837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61965 #31882837