Subgroups — C₇₁×#60918 #31881790

Order 18176.

1888 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×#533×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3255	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3254	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3252	C₂	1	4	yes	maximal, complemented
6	C₇₁×#3249	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3248	C₂	1	4	yes	maximal, complemented
8	C₇₁×#3246	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3079	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3078	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3056	C₂	1	4	yes	maximal, complemented
12	C₇₁×#3039	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3037	C₂	1	2	yes	maximal, complemented
14	C₂×#423×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#137×C₇₁	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₇₁	C₂²	1	2	yes	—
17	#533×C₇₁	—	2	1	no	—
18	#533×C₇₁	—	2	1	no	—
19	#533×C₇₁	—	2	1	no	—
20	#533×C₇₁	—	2	1	no	—
21	#533×C₇₁	C₂²	1	2	yes	—
22	#533×C₇₁	C₂²	1	2	yes	—
23	#533×C₇₁	C₂²	1	2	yes	—
24	#533×C₇₁	C₂²	1	2	yes	—
25	#533×C₇₁	C₂²	1	1	yes	characteristic
26	#533×C₇₁	C₂²	1	1	yes	characteristic
27	#533×C₇₁	C₂²	1	1	yes	characteristic
28	#532×C₇₁	C₂²	1	1	yes	characteristic
29	#532×C₇₁	C₂²	1	1	yes	characteristic
30	#532×C₇₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
33	#529×C₇₁	—	2	1	no	—
34	#529×C₇₁	—	2	1	no	—
35	#529×C₇₁	—	2	1	no	—
36	#529×C₇₁	—	2	1	no	—
37	#529×C₇₁	C₂²	1	2	yes	—
38	#529×C₇₁	C₂²	1	2	yes	—
39	C₂×#125×C₇₁	—	2	1	no	—
40	#525×C₇₁	—	2	1	no	—
41	#525×C₇₁	—	2	1	no	—
42	#525×C₇₁	C₂²	1	2	yes	—
43	C₂×C₂²⋊Q₈×C₇₁	—	2	1	no	—
44	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
45	C₄×#41×C₇₁	—	2	1	no	—
46	C₄×#41×C₇₁	—	2	1	no	—
47	C₄×#41×C₇₁	C₂²	1	2	yes	—
48	C₂×C₄×Q₈×C₇₁	—	2	1	no	—
49	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
50	C₂×#117×C₇₁	—	2	1	no	—
51	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
52	#479×C₇₁	C₂²	1	8	yes	complemented
53	#477×C₇₁	C₂²	1	4	yes	complemented
54	#477×C₇₁	C₂²	1	4	yes	complemented
55	#476×C₇₁	C₂²	1	4	yes	complemented
56	#475×C₇₁	C₂²	1	4	yes	complemented
57	#475×C₇₁	C₂²	1	4	yes	complemented
58	#474×C₇₁	C₂²	1	4	yes	complemented
59	#470×C₇₁	C₂²	1	8	yes	—
60	#468×C₇₁	C₂²	1	8	yes	—
61	#467×C₇₁	C₂²	1	8	yes	—
62	#465×C₇₁	C₂²	1	8	yes	—
63	#464×C₇₁	C₂²	1	8	yes	complemented
64	#462×C₇₁	C₂²	1	4	yes	complemented
65	#462×C₇₁	C₂²	1	4	yes	complemented
66	#462×C₇₁	C₂²	1	4	yes	complemented
67	#461×C₇₁	C₂²	1	4	yes	complemented
68	#461×C₇₁	C₂²	1	4	yes	complemented
69	#460×C₇₁	C₂²	1	4	yes	complemented
70	#428×C₇₁	C₂²	1	4	yes	—
71	#423×C₇₁	C₂²	1	2	yes	—
72	#423×C₇₁	C₂²	1	2	yes	—
73	#423×C₇₁	C₂²	1	2	yes	—
74	#423×C₇₁	C₂²	1	2	yes	—
75	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
76	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
77	#419×C₇₁	C₂²	1	4	yes	—
78	#417×C₇₁	C₂²	1	4	yes	—
79	C₂×#41×C₇₁	—	2	1	no	—
80	C₂×#41×C₇₁	—	2	1	no	—
81	C₂×#41×C₇₁	C₂³	1	2	yes	—
82	C₂²×Q₈×C₇₁	—	2	1	no	—
83	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
87	#137×C₇₁	—	4	8	no	—
88	C₂×Q₁₆×C₇₁	C₂³	1	8	yes	—
89	C₂×SD₁₆×C₇₁	C₂³	1	8	yes	—
90	C₂×M₁₆×C₇₁	—	4	4	no	—
91	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
92	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
93	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
94	C₄⋊Q₈×C₇₁	—	2	1	no	—
95	C₄⋊Q₈×C₇₁	—	2	1	no	—
96	C₄⋊Q₈×C₇₁	—	2	1	no	—
97	C₄⋊Q₈×C₇₁	—	2	1	no	—
98	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
105	#127×C₇₁	C₂³	1	1	yes	characteristic
106	#126×C₇₁	—	2	2	no	—
107	#126×C₇₁	—	2	2	no	—
108	#125×C₇₁	—	2	2	no	—
109	#125×C₇₁	—	2	2	no	—
110	#125×C₇₁	—	2	2	no	—
111	#125×C₇₁	—	2	2	no	—
112	#125×C₇₁	—	2	1	no	—
113	#125×C₇₁	—	2	1	no	—
114	#125×C₇₁	C₂³	1	2	yes	—
115	#124×C₇₁	—	2	1	no	—
116	#124×C₇₁	—	2	1	no	—
117	#124×C₇₁	C₂³	1	2	yes	—
118	#123×C₇₁	—	2	2	no	—
119	#123×C₇₁	—	2	2	no	—
120	#123×C₇₁	—	2	2	no	—
121	C₂²⋊Q₈×C₇₁	—	2	2	no	—
122	C₂²⋊Q₈×C₇₁	—	2	2	no	—
123	C₂²⋊Q₈×C₇₁	—	2	2	no	—
124	C₂²⋊Q₈×C₇₁	—	2	2	no	—
125	C₂²⋊Q₈×C₇₁	—	2	2	no	—
126	C₂²⋊Q₈×C₇₁	—	2	2	no	—
127	C₂²⋊Q₈×C₇₁	—	2	1	no	—
128	C₂²⋊Q₈×C₇₁	—	2	1	no	—
129	C₂²⋊Q₈×C₇₁	—	2	1	no	—
130	C₂²⋊Q₈×C₇₁	—	2	1	no	—
131	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
132	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
133	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
134	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
135	#121×C₇₁	—	2	1	no	—
136	#121×C₇₁	—	2	1	no	—
137	#121×C₇₁	—	2	1	no	—
138	#121×C₇₁	—	2	1	no	—
139	#121×C₇₁	C₂³	1	2	yes	—
140	#121×C₇₁	C₂³	1	2	yes	—
141	#120×C₇₁	—	2	2	no	—
142	C₄×Q₈×C₇₁	—	2	2	no	—
143	C₄×Q₈×C₇₁	—	2	2	no	—
144	C₄×Q₈×C₇₁	—	2	2	no	—
145	C₄×Q₈×C₇₁	—	2	2	no	—
146	C₄×Q₈×C₇₁	—	2	2	no	—
147	C₄×Q₈×C₇₁	—	2	2	no	—
148	C₄×Q₈×C₇₁	—	2	1	no	—
149	C₄×Q₈×C₇₁	—	2	1	no	—
150	C₄×Q₈×C₇₁	—	2	1	no	—
151	C₄×Q₈×C₇₁	—	2	1	no	—
152	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
153	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
156	C₄×D₄×C₇₁	—	2	2	no	—
157	C₄×D₄×C₇₁	—	2	2	no	—
158	C₄×D₄×C₇₁	—	2	2	no	—
159	C₄×D₄×C₇₁	—	2	2	no	—
160	C₄×D₄×C₇₁	—	2	2	no	—
161	C₄×D₄×C₇₁	—	2	2	no	—
162	C₄×D₄×C₇₁	—	2	1	no	—
163	C₄×D₄×C₇₁	—	2	1	no	—
164	C₄×D₄×C₇₁	—	2	1	no	—
165	C₄×D₄×C₇₁	—	2	1	no	—
166	C₄×D₄×C₇₁	C₂³	1	2	yes	—
167	C₄×D₄×C₇₁	C₂³	1	2	yes	—
168	#117×C₇₁	—	2	2	no	—
169	#117×C₇₁	—	2	2	no	—
170	#117×C₇₁	—	2	2	no	—
171	#117×C₇₁	—	2	2	no	—
172	#117×C₇₁	—	2	1	no	—
173	#117×C₇₁	—	2	1	no	—
174	#117×C₇₁	—	2	2	no	—
175	#117×C₇₁	—	2	2	no	—
176	#117×C₇₁	—	2	2	no	—
177	#117×C₇₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
185	C₂×C₄²×C₇₁	—	2	2	no	—
186	C₂×C₄²×C₇₁	—	2	2	no	—
187	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
199	#107×C₇₁	C₂³	1	8	yes	—
200	#106×C₇₁	C₂³	1	8	yes	—
201	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
202	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
203	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
204	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
205	#103×C₇₁	C₂³	1	8	yes	—
206	#103×C₇₁	C₂³	1	8	yes	—
207	#103×C₇₁	C₂³	1	8	yes	—
208	#102×C₇₁	C₂³	1	8	yes	—
209	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
210	#41×C₇₁	—	2	4	no	—
211	#41×C₇₁	—	2	4	no	—
212	#41×C₇₁	—	4	4	no	—
213	#41×C₇₁	—	4	4	no	—
214	C₂×Q₈×C₇₁	—	2	1	no	—
215	C₂×Q₈×C₇₁	—	2	1	no	—
216	C₂×Q₈×C₇₁	—	2	2	no	—
217	C₂×Q₈×C₇₁	—	2	2	no	—
218	C₂×Q₈×C₇₁	—	2	2	no	—
219	C₂×Q₈×C₇₁	—	2	4	no	—
220	C₂×Q₈×C₇₁	—	2	4	no	—
221	C₂×Q₈×C₇₁	—	4	4	no	—
222	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
224	C₂×D₄×C₇₁	—	2	2	no	—
225	C₂×D₄×C₇₁	—	2	2	no	—
226	C₂×D₄×C₇₁	—	2	2	no	—
227	C₂×D₄×C₇₁	—	2	1	no	—
228	C₂×D₄×C₇₁	—	2	1	no	—
229	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇₁	—	2	4	no	—
231	C₂²×C₄×C₇₁	—	2	2	no	—
232	C₂²×C₄×C₇₁	—	2	2	no	—
233	C₂²×C₄×C₇₁	—	2	2	no	—
234	C₂²×C₄×C₇₁	—	2	2	no	—
235	C₂²×C₄×C₇₁	—	2	2	no	—
236	C₂²×C₄×C₇₁	—	2	2	no	—
237	C₂²×C₄×C₇₁	—	2	2	no	—
238	C₂²×C₄×C₇₁	—	4	2	no	—
239	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
257	Q₁₆×C₇₁	—	4	8	no	—
258	SD₁₆×C₇₁	—	4	8	no	—
259	M₁₆×C₇₁	—	2	8	no	—
260	M₁₆×C₇₁	—	4	4	no	—
261	C₂×C₈×C₇₁	—	4	4	no	—
262	C₂×C₈×C₇₁	C₂⁴	1	8	yes	—
263	C₄⋊C₄×C₇₁	—	2	2	no	—
264	C₄⋊C₄×C₇₁	—	2	2	no	—
265	C₄⋊C₄×C₇₁	—	2	2	no	—
266	C₄⋊C₄×C₇₁	—	2	2	no	—
267	C₄⋊C₄×C₇₁	—	2	2	no	—
268	C₄⋊C₄×C₇₁	—	2	2	no	—
269	C₄⋊C₄×C₇₁	—	2	4	no	—
270	C₄⋊C₄×C₇₁	—	2	4	no	—
271	C₄⋊C₄×C₇₁	—	2	4	no	—
272	C₄⋊C₄×C₇₁	—	2	4	no	—
273	C₄⋊C₄×C₇₁	—	2	2	no	—
274	C₄⋊C₄×C₇₁	—	2	1	no	—
275	C₄⋊C₄×C₇₁	—	2	1	no	—
276	C₄⋊C₄×C₇₁	—	2	1	no	—
277	C₄⋊C₄×C₇₁	—	2	1	no	—
278	C₄⋊C₄×C₇₁	—	2	2	no	—
279	C₄⋊C₄×C₇₁	—	2	2	no	—
280	C₄⋊C₄×C₇₁	—	2	2	no	—
281	C₄⋊C₄×C₇₁	—	2	2	no	—
282	C₄⋊C₄×C₇₁	—	2	2	no	—
283	C₄⋊C₄×C₇₁	—	2	2	no	—
284	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₇₁	—	2	4	no	—
288	C₂²⋊C₄×C₇₁	—	2	4	no	—
289	C₂²⋊C₄×C₇₁	—	2	2	no	—
290	C₂²⋊C₄×C₇₁	—	2	2	no	—
291	C₂²⋊C₄×C₇₁	—	2	2	no	—
292	C₂²⋊C₄×C₇₁	—	2	2	no	—
293	C₂²⋊C₄×C₇₁	—	2	2	no	—
294	C₂²⋊C₄×C₇₁	—	2	2	no	—
295	C₂²⋊C₄×C₇₁	—	2	2	no	—
296	C₂²⋊C₄×C₇₁	—	2	2	no	—
297	C₂²⋊C₄×C₇₁	—	2	2	no	—
298	C₄²×C₇₁	—	2	2	no	—
299	C₄²×C₇₁	—	2	2	no	—
300	C₄²×C₇₁	—	2	4	no	—
301	C₄²×C₇₁	—	2	4	no	—
302	C₄²×C₇₁	—	2	2	no	—
303	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
316	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
317	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
319	C₂³×C₇₁	—	2	2	no	—
320	C₂³×C₇₁	—	2	2	no	—
321	C₂³×C₇₁	—	2	2	no	—
322	C₂³×C₇₁	—	4	1	no	—
323	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
324	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
325	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
326	Q₈×C₇₁	—	2	4	no	—
327	Q₈×C₇₁	—	2	2	no	—
328	Q₈×C₇₁	—	2	4	no	—
329	Q₈×C₇₁	—	2	2	no	—
330	Q₈×C₇₁	—	4	4	no	—
331	Q₈×C₇₁	—	4	2	no	—
332	Q₈×C₇₁	—	4	4	no	—
333	Q₈×C₇₁	—	4	2	no	—
334	Q₈×C₇₁	—	4	4	no	—
335	D₄×C₇₁	—	2	2	no	—
336	D₄×C₇₁	—	2	2	no	—
337	D₄×C₇₁	—	4	2	no	—
338	D₄×C₇₁	—	4	4	no	—
339	D₄×C₇₁	—	4	4	no	—
340	D₄×C₇₁	—	4	4	no	—
341	D₄×C₇₁	—	4	2	no	—
342	C₂×C₄×C₇₁	—	2	2	no	—
343	C₂×C₄×C₇₁	—	2	2	no	—
344	C₂×C₄×C₇₁	—	2	2	no	—
345	C₂×C₄×C₇₁	—	2	2	no	—
346	C₂×C₄×C₇₁	—	2	2	no	—
347	C₂×C₄×C₇₁	—	2	2	no	—
348	C₂×C₄×C₇₁	—	2	2	no	—
349	C₂×C₄×C₇₁	—	2	2	no	—
350	C₂×C₄×C₇₁	—	2	2	no	—
351	C₂×C₄×C₇₁	—	2	2	no	—
352	C₂×C₄×C₇₁	—	2	2	no	—
353	C₂×C₄×C₇₁	—	2	1	no	—
354	C₂×C₄×C₇₁	—	2	1	no	—
355	C₂×C₄×C₇₁	—	2	1	no	—
356	C₂×C₄×C₇₁	—	2	1	no	—
357	C₂×C₄×C₇₁	—	2	2	no	—
358	C₂×C₄×C₇₁	—	2	2	no	—
359	C₂×C₄×C₇₁	—	2	2	no	—
360	C₂×C₄×C₇₁	—	2	4	no	—
361	C₂×C₄×C₇₁	—	2	4	no	—
362	C₂×C₄×C₇₁	—	4	1	no	—
363	C₂×C₄×C₇₁	—	4	1	no	—
364	C₂×C₄×C₇₁	—	4	1	no	—
365	C₂×C₄×C₇₁	—	4	4	no	—
366	C₂×C₄×C₇₁	—	4	4	no	—
367	C₂×C₄×C₇₁	—	4	4	no	—
368	C₂×C₄×C₇₁	—	4	4	no	—
369	C₂×C₄×C₇₁	—	4	4	no	—
370	C₂×C₄×C₇₁	#137	1	4	yes	complemented
371	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
384	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
385	C₈×C₇₁	—	2	8	no	—
386	C₂²×C₇₁	—	2	1	no	—
387	C₂²×C₇₁	—	2	1	no	—
388	C₂²×C₇₁	—	2	1	no	—
389	C₂²×C₇₁	—	2	1	no	—
390	C₂²×C₇₁	—	2	1	no	—
391	C₂²×C₇₁	—	2	1	no	—
392	C₂²×C₇₁	—	2	1	no	—
393	C₂²×C₇₁	—	4	4	no	—
394	C₂²×C₇₁	—	4	2	no	—
395	C₂²×C₇₁	—	4	2	no	—
396	C₂²×C₇₁	—	4	2	no	—
397	C₂²×C₇₁	#537	1	2	yes	—
398	C₂²×C₇₁	C₂×#137	1	2	yes	—
399	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₇₁	—	2	1	no	—
401	C₄×C₇₁	—	2	1	no	—
402	C₄×C₇₁	—	2	1	no	—
403	C₄×C₇₁	—	2	1	no	—
404	C₄×C₇₁	—	2	1	no	—
405	C₄×C₇₁	—	2	1	no	—
406	C₄×C₇₁	—	2	1	no	—
407	C₄×C₇₁	—	4	2	no	—
408	C₄×C₇₁	—	4	4	no	—
409	C₄×C₇₁	—	4	2	no	—
410	C₄×C₇₁	—	4	2	no	—
411	C₄×C₇₁	—	4	4	no	—
412	C₄×C₇₁	#537	1	2	yes	—
413	C₄×C₇₁	C₂×#137	1	2	yes	—
414	C₄×C₇₁	C₂×#137	1	2	yes	—
415	C₄×C₇₁	#575	1	2	yes	—
416	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₄×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	#60918	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₇₁	—	2	2	no	—
420	C₂×C₇₁	—	2	2	no	—
421	C₂×C₇₁	—	4	1	no	—
422	C₂×C₇₁	—	8	2	no	—
423	C₂×C₇₁	C₂×#537	1	1	yes	characteristic
424	C₂×C₇₁	C₂²×#137	1	1	yes	characteristic
425	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
426	#3444	C₂×C₇₁	1	1	yes	characteristic
427	C₂×#533	C₂×C₇₁	1	1	yes	characteristic, complemented
428	#3255	C₂×C₇₁	1	2	yes	complemented
429	#3254	C₂×C₇₁	1	2	yes	complemented
430	#3252	C₂×C₇₁	1	4	yes	complemented
431	#3249	C₂×C₇₁	1	2	yes	complemented
432	#3248	C₂×C₇₁	1	4	yes	complemented
433	#3246	C₂×C₇₁	1	2	yes	complemented
434	#3079	C₂×C₇₁	1	2	yes	complemented
435	#3078	C₂×C₇₁	1	2	yes	complemented
436	#3056	C₂×C₇₁	1	4	yes	complemented
437	#3039	C₂×C₇₁	1	2	yes	complemented
438	#3037	C₂×C₇₁	1	2	yes	complemented
439	C₂×#423	C₂×C₇₁	1	1	yes	characteristic, complemented
440	C₇₁	#60918	1	1	yes	characteristic, direct product factor, Sylow
441	C₂×#137	C₂²×C₇₁	1	4	yes	—
442	C₂²×M₁₆	C₂²×C₇₁	1	2	yes	—
443	#533	—	2	1	no	—
444	#533	—	2	1	no	—
445	#533	—	2	1	no	—
446	#533	—	2	1	no	—
447	#533	C₂²×C₇₁	1	2	yes	—
448	#533	C₂²×C₇₁	1	2	yes	—
449	#533	C₂²×C₇₁	1	2	yes	—
450	#533	C₂²×C₇₁	1	2	yes	—
451	#533	C₂²×C₇₁	1	1	yes	characteristic
452	#533	C₂²×C₇₁	1	1	yes	characteristic
453	#533	C₂²×C₇₁	1	1	yes	characteristic
454	#532	C₂²×C₇₁	1	1	yes	characteristic
455	#532	C₂²×C₇₁	1	1	yes	characteristic
456	#532	C₂²×C₇₁	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
459	#529	—	2	1	no	—
460	#529	—	2	1	no	—
461	#529	—	2	1	no	—
462	#529	—	2	1	no	—
463	#529	C₂²×C₇₁	1	2	yes	—
464	#529	C₂²×C₇₁	1	2	yes	—
465	C₂×#125	—	2	1	no	—
466	#525	—	2	1	no	—
467	#525	—	2	1	no	—
468	#525	C₂²×C₇₁	1	2	yes	—
469	C₂×C₂²⋊Q₈	—	2	1	no	—
470	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
471	C₄×#41	—	2	1	no	—
472	C₄×#41	—	2	1	no	—
473	C₄×#41	C₂²×C₇₁	1	2	yes	—
474	C₂×C₄×Q₈	—	2	1	no	—
475	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
476	C₂×#117	—	2	1	no	—
477	C₂²×C₄²	C₂²×C₇₁	1	1	yes	characteristic
478	#479	C₂²×C₇₁	1	8	yes	complemented
479	#477	C₂²×C₇₁	1	4	yes	complemented
480	#477	C₂²×C₇₁	1	4	yes	complemented
481	#476	C₂²×C₇₁	1	4	yes	complemented
482	#475	C₂²×C₇₁	1	4	yes	complemented
483	#475	C₂²×C₇₁	1	4	yes	complemented
484	#474	C₂²×C₇₁	1	4	yes	complemented
485	#470	C₂²×C₇₁	1	8	yes	—
486	#468	C₂²×C₇₁	1	8	yes	—
487	#467	C₂²×C₇₁	1	8	yes	—
488	#465	C₂²×C₇₁	1	8	yes	—
489	#464	C₂²×C₇₁	1	8	yes	complemented
490	#462	C₂²×C₇₁	1	4	yes	complemented
491	#462	C₂²×C₇₁	1	4	yes	complemented
492	#462	C₂²×C₇₁	1	4	yes	complemented
493	#461	C₂²×C₇₁	1	4	yes	complemented
494	#461	C₂²×C₇₁	1	4	yes	complemented
495	#460	C₂²×C₇₁	1	4	yes	complemented
496	#428	C₂²×C₇₁	1	4	yes	—
497	#423	C₂²×C₇₁	1	2	yes	—
498	#423	C₂²×C₇₁	1	2	yes	—
499	#423	C₂²×C₇₁	1	2	yes	—
500	#423	C₂²×C₇₁	1	2	yes	—
501	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
502	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
503	#419	C₂²×C₇₁	1	4	yes	—
504	#417	C₂²×C₇₁	1	4	yes	—
505	C₂×#41	—	2	1	no	—
506	C₂×#41	—	2	1	no	—
507	C₂×#41	C₂³×C₇₁	1	2	yes	—
508	C₂²×Q₈	—	2	1	no	—
509	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
510	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
511	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
513	#137	—	4	8	no	—
514	C₂×Q₁₆	C₂³×C₇₁	1	8	yes	—
515	C₂×SD₁₆	C₂³×C₇₁	1	8	yes	—
516	C₂×M₁₆	—	4	4	no	—
517	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
518	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
519	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
531	#127	C₂³×C₇₁	1	1	yes	characteristic
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	2	no	—
538	#125	—	2	1	no	—
539	#125	—	2	1	no	—
540	#125	C₂³×C₇₁	1	2	yes	—
541	#124	—	2	1	no	—
542	#124	—	2	1	no	—
543	#124	C₂³×C₇₁	1	2	yes	—
544	#123	—	2	2	no	—
545	#123	—	2	2	no	—
546	#123	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
558	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
559	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
560	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
561	#121	—	2	1	no	—
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	—	2	1	no	—
565	#121	C₂³×C₇₁	1	2	yes	—
566	#121	C₂³×C₇₁	1	2	yes	—
567	#120	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
579	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
580	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
581	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	C₂³×C₇₁	1	2	yes	—
593	C₄×D₄	C₂³×C₇₁	1	2	yes	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	—	2	2	no	—
601	#117	—	2	2	no	—
602	#117	—	2	2	no	—
603	#117	C₂³×C₇₁	1	2	yes	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
610	C₂×C₂²⋊C₄	—	2	2	no	—
611	C₂×C₄²	—	2	2	no	—
612	C₂×C₄²	—	2	2	no	—
613	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
614	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
615	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
616	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
617	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
618	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
625	#107	C₂³×C₇₁	1	8	yes	—
626	#106	C₂³×C₇₁	1	8	yes	—
627	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
628	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
629	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
630	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
631	#103	C₂³×C₇₁	1	8	yes	—
632	#103	C₂³×C₇₁	1	8	yes	—
633	#103	C₂³×C₇₁	1	8	yes	—
634	#102	C₂³×C₇₁	1	8	yes	—
635	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	4	4	no	—
639	#41	—	4	4	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	4	4	no	—
648	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
649	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
683	Q₁₆	—	4	8	no	—
684	SD₁₆	—	4	8	no	—
685	M₁₆	—	2	8	no	—
686	M₁₆	—	4	4	no	—
687	C₂×C₈	—	4	4	no	—
688	C₂×C₈	C₂⁴×C₇₁	1	8	yes	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
711	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
730	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
741	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
742	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
743	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
744	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	4	1	no	—
749	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
750	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
751	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	4	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	4	4	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	#137×C₇₁	1	4	yes	complemented
797	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
808	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
809	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
810	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
811	C₈	—	2	8	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	#537×C₇₁	1	2	yes	—
824	C₂²	C₂×#137×C₇₁	1	2	yes	—
825	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	#537×C₇₁	1	2	yes	—
839	C₄	C₂×#137×C₇₁	1	2	yes	—
840	C₄	C₂×#137×C₇₁	1	2	yes	—
841	C₄	#575×C₇₁	1	2	yes	—
842	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
843	C₄	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×#537×C₇₁	1	1	yes	characteristic
849	C₂	C₂²×#137×C₇₁	1	1	yes	characteristic
850	C₂	C₂×#575×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₇₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂²×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#533×C₇₁	C₂	semidirect
3. C₇₁×#3255	C₂	semidirect
4. C₇₁×#3254	C₂	semidirect
5. C₇₁×#3252	C₂	semidirect
6. C₇₁×#3249	C₂	semidirect
7. C₇₁×#3248	C₂	semidirect
8. C₇₁×#3246	C₂	semidirect
9. C₇₁×#3079	C₂	semidirect
10. C₇₁×#3078	C₂	semidirect
11. C₇₁×#3056	C₂	semidirect
12. C₇₁×#3039	C₂	semidirect
13. C₇₁×#3037	C₂	semidirect
14. C₂×#423×C₇₁	C₂	semidirect
52. #479×C₇₁	C₂²	semidirect
53. #477×C₇₁	C₂²	semidirect
54. #477×C₇₁	C₂²	semidirect
55. #476×C₇₁	C₂²	semidirect
56. #475×C₇₁	C₂²	semidirect
57. #475×C₇₁	C₂²	semidirect
58. #474×C₇₁	C₂²	semidirect
63. #464×C₇₁	C₂²	semidirect
64. #462×C₇₁	C₂²	semidirect
65. #462×C₇₁	C₂²	semidirect
66. #462×C₇₁	C₂²	semidirect
67. #461×C₇₁	C₂²	semidirect
68. #461×C₇₁	C₂²	semidirect
69. #460×C₇₁	C₂²	semidirect
370. C₂×C₄×C₇₁	#137	semidirect
418. #60918	C₇₁	direct (N × H)
427. C₂×#533	C₂×C₇₁	semidirect
428. #3255	C₂×C₇₁	semidirect
429. #3254	C₂×C₇₁	semidirect
430. #3252	C₂×C₇₁	semidirect
431. #3249	C₂×C₇₁	semidirect
432. #3248	C₂×C₇₁	semidirect
433. #3246	C₂×C₇₁	semidirect
434. #3079	C₂×C₇₁	semidirect
435. #3078	C₂×C₇₁	semidirect
436. #3056	C₂×C₇₁	semidirect
437. #3039	C₂×C₇₁	semidirect
438. #3037	C₂×C₇₁	semidirect
439. C₂×#423	C₂×C₇₁	semidirect
440. C₇₁	#60918	direct (N × H)
478. #479	C₂²×C₇₁	semidirect
479. #477	C₂²×C₇₁	semidirect
480. #477	C₂²×C₇₁	semidirect
481. #476	C₂²×C₇₁	semidirect
482. #475	C₂²×C₇₁	semidirect
483. #475	C₂²×C₇₁	semidirect
484. #474	C₂²×C₇₁	semidirect
489. #464	C₂²×C₇₁	semidirect
490. #462	C₂²×C₇₁	semidirect
491. #462	C₂²×C₇₁	semidirect
492. #462	C₂²×C₇₁	semidirect
493. #461	C₂²×C₇₁	semidirect
494. #461	C₂²×C₇₁	semidirect
495. #460	C₂²×C₇₁	semidirect
796. 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×#3444	2
C₂×#533×C₇₁	2
C₇₁×#3255	2
C₇₁×#3254	2
C₇₁×#3252	2
C₇₁×#3249	2
C₇₁×#3248	2
C₇₁×#3246	2
C₇₁×#3079	2
C₇₁×#3078	2
C₇₁×#3056	2
C₇₁×#3039	2
C₇₁×#3037	2
C₂×#423×C₇₁	2
#60918	71

Subgroups — C71×#60918 #31881790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#60918 #31881790