Subgroups — C₇₁×#61950 #31882822

Order 18176.

1878 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3393	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3303	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3300	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3283	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3282	C₂	1	4	yes	maximal, complemented
9	C₇₁×#3248	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×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3107	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×#461×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	—
19	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
20	#556×C₇₁	C₂²	1	1	yes	characteristic
21	#556×C₇₁	C₂²	1	2	yes	complemented
22	#555×C₇₁	—	2	1	no	—
23	#555×C₇₁	C₂²	1	1	yes	characteristic
24	#554×C₇₁	—	2	1	no	—
25	#554×C₇₁	C₂²	1	1	yes	characteristic
26	#553×C₇₁	—	2	1	no	—
27	#553×C₇₁	—	2	2	no	—
28	#552×C₇₁	—	2	1	no	—
29	#552×C₇₁	C₂²	1	2	yes	—
30	#551×C₇₁	—	2	2	no	—
31	#548×C₇₁	C₂²	1	4	yes	—
32	#547×C₇₁	C₂²	1	1	yes	characteristic
33	#547×C₇₁	C₂²	1	2	yes	complemented
34	#546×C₇₁	C₂²	1	2	yes	—
35	#542×C₇₁	—	2	2	no	—
36	#537×C₇₁	—	2	1	no	—
37	#533×C₇₁	C₂²	1	1	yes	characteristic
38	#533×C₇₁	C₂²	1	2	yes	complemented
39	#532×C₇₁	C₂²	1	1	yes	characteristic
40	#532×C₇₁	C₂²	1	2	yes	complemented
41	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
42	#529×C₇₁	—	2	2	no	—
43	#529×C₇₁	C₂²	1	2	yes	—
44	#525×C₇₁	—	2	1	no	—
45	#520×C₇₁	—	2	1	no	—
46	C₄×#41×C₇₁	C₂²	1	2	yes	—
47	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
49	C₂×#117×C₇₁	—	2	1	no	—
50	#495×C₇₁	C₂²	1	4	yes	—
51	#494×C₇₁	C₂²	1	2	yes	complemented
52	#488×C₇₁	C₂²	1	4	yes	complemented
53	#487×C₇₁	C₂²	1	2	yes	complemented
54	#485×C₇₁	C₂²	1	4	yes	complemented
55	#480×C₇₁	C₂²	1	2	yes	—
56	#479×C₇₁	C₂²	1	4	yes	complemented
57	#476×C₇₁	C₂²	1	2	yes	complemented
58	#475×C₇₁	C₂²	1	2	yes	complemented
59	#474×C₇₁	C₂²	1	1	yes	characteristic
60	#474×C₇₁	C₂²	1	1	yes	characteristic
61	#467×C₇₁	C₂²	1	4	yes	complemented
62	#465×C₇₁	C₂²	1	4	yes	—
63	#465×C₇₁	C₂²	1	4	yes	—
64	#464×C₇₁	C₂²	1	4	yes	—
65	#464×C₇₁	C₂²	1	4	yes	complemented
66	#463×C₇₁	C₂²	1	4	yes	—
67	#462×C₇₁	C₂²	1	2	yes	complemented
68	#462×C₇₁	C₂²	1	2	yes	complemented
69	#461×C₇₁	C₂²	1	2	yes	—
70	#461×C₇₁	C₂²	1	2	yes	—
71	#461×C₇₁	C₂²	1	2	yes	—
72	#461×C₇₁	C₂²	1	2	yes	—
73	#461×C₇₁	C₂²	1	2	yes	complemented
74	#460×C₇₁	C₂²	1	2	yes	complemented
75	#459×C₇₁	C₂²	1	1	yes	characteristic
76	#459×C₇₁	C₂²	1	1	yes	characteristic
77	#452×C₇₁	C₂²	1	4	yes	—
78	#452×C₇₁	C₂²	1	4	yes	complemented
79	#451×C₇₁	C₂²	1	4	yes	—
80	#449×C₇₁	C₂²	1	4	yes	—
81	#447×C₇₁	C₂²	1	2	yes	—
82	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₇₁	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	—
85	C₄×D₈×C₇₁	C₂²	1	2	yes	—
86	C₄×D₈×C₇₁	C₂²	1	2	yes	—
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×#103×C₇₁	C₂²	1	2	yes	—
95	C₂×#41×C₇₁	—	2	1	no	—
96	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₇₁	C₂³	1	2	yes	—
98	C₂×#41×C₇₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇₁	—	2	1	no	—
102	#135×C₇₁	—	4	8	no	—
103	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₇₁	—	4	4	no	—
106	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
109	C₂×D₈×C₇₁	C₂³	1	2	yes	—
110	C₂×D₈×C₇₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
112	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₇₁	—	2	1	no	—
114	C₄⋊Q₈×C₇₁	—	2	1	no	—
115	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
120	#127×C₇₁	C₂³	1	1	yes	characteristic
121	#126×C₇₁	—	2	2	no	—
122	#126×C₇₁	—	2	4	no	—
123	#126×C₇₁	—	2	2	no	—
124	#126×C₇₁	—	2	2	no	—
125	#125×C₇₁	—	2	2	no	—
126	#125×C₇₁	—	2	1	no	—
127	#125×C₇₁	—	2	2	no	—
128	#125×C₇₁	C₂³	1	2	yes	—
129	#124×C₇₁	—	2	2	no	—
130	#124×C₇₁	—	2	4	no	—
131	#124×C₇₁	—	2	1	no	—
132	#124×C₇₁	C₂³	1	4	yes	—
133	#124×C₇₁	C₂³	1	2	yes	—
134	#123×C₇₁	—	2	2	no	—
135	#123×C₇₁	—	2	2	no	—
136	#123×C₇₁	—	2	2	no	—
137	#123×C₇₁	—	2	2	no	—
138	#123×C₇₁	—	2	4	no	—
139	C₂²⋊Q₈×C₇₁	—	2	1	no	—
140	C₂²⋊Q₈×C₇₁	—	2	1	no	—
141	C₂²⋊Q₈×C₇₁	—	2	2	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	4	no	—
146	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
148	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
149	#121×C₇₁	—	2	1	no	—
150	#121×C₇₁	—	2	1	no	—
151	#121×C₇₁	—	2	2	no	—
152	#121×C₇₁	—	2	4	no	—
153	#121×C₇₁	—	2	1	no	—
154	#121×C₇₁	—	2	2	no	—
155	#121×C₇₁	—	2	2	no	—
156	#121×C₇₁	—	2	2	no	—
157	#121×C₇₁	C₂³	1	2	yes	—
158	#121×C₇₁	C₂³	1	2	yes	—
159	#120×C₇₁	—	2	2	no	—
160	C₄×Q₈×C₇₁	—	2	2	no	—
161	C₄×Q₈×C₇₁	—	2	1	no	—
162	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
164	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₇₁	—	2	2	no	—
168	C₄×D₄×C₇₁	—	2	2	no	—
169	C₄×D₄×C₇₁	—	2	2	no	—
170	C₄×D₄×C₇₁	—	2	4	no	—
171	C₄×D₄×C₇₁	—	2	1	no	—
172	C₄×D₄×C₇₁	—	2	1	no	—
173	C₄×D₄×C₇₁	—	2	2	no	—
174	C₄×D₄×C₇₁	—	2	1	no	—
175	C₄×D₄×C₇₁	—	2	2	no	—
176	C₄×D₄×C₇₁	D₄	1	2	yes	—
177	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
178	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₇₁	C₂³	1	2	yes	—
181	C₄×D₄×C₇₁	C₂³	1	2	yes	—
182	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₇₁	C₂³	1	2	yes	—
185	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
186	#117×C₇₁	—	2	1	no	—
187	#117×C₇₁	—	2	2	no	—
188	#117×C₇₁	—	2	1	no	—
189	#117×C₇₁	—	2	1	no	—
190	#117×C₇₁	—	2	2	no	—
191	#117×C₇₁	—	2	2	no	—
192	#117×C₇₁	—	2	2	no	—
193	#117×C₇₁	—	2	2	no	—
194	#117×C₇₁	D₄	1	1	yes	characteristic
195	#117×C₇₁	D₄	1	2	yes	—
196	#117×C₇₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
198	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
202	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₇₁	—	2	2	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	4	yes	—
217	#103×C₇₁	C₂³	1	4	yes	—
218	#103×C₇₁	C₂³	1	4	yes	—
219	#103×C₇₁	C₂³	1	4	yes	—
220	#103×C₇₁	C₂³	1	4	yes	—
221	#102×C₇₁	C₂³	1	2	yes	—
222	#102×C₇₁	C₂³	1	4	yes	—
223	#102×C₇₁	C₂³	1	2	yes	—
224	#102×C₇₁	C₂³	1	2	yes	—
225	#102×C₇₁	C₂³	1	2	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	1	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	C₂×Q₈×C₇₁	—	2	1	no	—
238	C₂×Q₈×C₇₁	—	2	1	no	—
239	C₂×Q₈×C₇₁	—	2	2	no	—
240	C₂×Q₈×C₇₁	—	4	2	no	—
241	C₂×Q₈×C₇₁	—	4	2	no	—
242	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
244	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
245	C₂×D₄×C₇₁	—	2	2	no	—
246	C₂×D₄×C₇₁	—	2	2	no	—
247	C₂×D₄×C₇₁	—	2	2	no	—
248	C₂×D₄×C₇₁	—	2	2	no	—
249	C₂×D₄×C₇₁	—	2	4	no	—
250	C₂×D₄×C₇₁	—	2	1	no	—
251	C₂×D₄×C₇₁	—	2	1	no	—
252	C₂×D₄×C₇₁	—	2	1	no	—
253	C₂×D₄×C₇₁	—	4	1	no	—
254	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
257	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇₁	—	2	1	no	—
260	C₂²×C₄×C₇₁	—	2	2	no	—
261	C₂²×C₄×C₇₁	—	2	1	no	—
262	C₂²×C₄×C₇₁	—	2	2	no	—
263	C₂²×C₄×C₇₁	—	2	1	no	—
264	C₂²×C₄×C₇₁	—	2	2	no	—
265	C₂²×C₄×C₇₁	—	2	1	no	—
266	C₂²×C₄×C₇₁	—	2	1	no	—
267	C₂²×C₄×C₇₁	—	2	2	no	—
268	C₂²×C₄×C₇₁	—	2	4	no	—
269	C₂²×C₄×C₇₁	—	4	4	no	—
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	2	yes	—
273	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
276	Q₁₆×C₇₁	—	4	4	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	D₈×C₇₁	—	2	4	no	—
282	D₈×C₇₁	—	4	2	no	—
283	C₂×C₈×C₇₁	—	4	2	no	—
284	C₂×C₈×C₇₁	—	4	4	no	—
285	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
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	2	no	—
294	C₄⋊C₄×C₇₁	—	2	2	no	—
295	C₄⋊C₄×C₇₁	—	2	4	no	—
296	C₄⋊C₄×C₇₁	—	2	2	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	2	no	—
303	C₄⋊C₄×C₇₁	—	2	1	no	—
304	C₄⋊C₄×C₇₁	—	2	4	no	—
305	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₇₁	—	2	2	no	—
314	C₂²⋊C₄×C₇₁	—	2	4	no	—
315	C₂²⋊C₄×C₇₁	—	2	2	no	—
316	C₂²⋊C₄×C₇₁	—	2	2	no	—
317	C₂²⋊C₄×C₇₁	—	2	1	no	—
318	C₂²⋊C₄×C₇₁	—	2	2	no	—
319	C₂²⋊C₄×C₇₁	—	2	2	no	—
320	C₂²⋊C₄×C₇₁	—	2	1	no	—
321	C₂²⋊C₄×C₇₁	—	2	1	no	—
322	C₂²⋊C₄×C₇₁	—	2	1	no	—
323	C₂²⋊C₄×C₇₁	—	2	4	no	—
324	C₂²⋊C₄×C₇₁	—	2	2	no	—
325	C₂²⋊C₄×C₇₁	—	2	2	no	—
326	C₂²⋊C₄×C₇₁	—	2	4	no	—
327	C₂²⋊C₄×C₇₁	—	2	2	no	—
328	C₂²⋊C₄×C₇₁	—	2	2	no	—
329	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
332	C₄²×C₇₁	—	2	2	no	—
333	C₄²×C₇₁	—	2	2	no	—
334	C₄²×C₇₁	—	2	2	no	—
335	C₄²×C₇₁	—	2	4	no	—
336	C₄²×C₇₁	C₂×D₄	1	2	yes	—
337	C₄²×C₇₁	C₂×D₄	1	2	yes	—
338	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
341	C₄²×C₇₁	C₂⁴	1	2	yes	—
342	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
343	C₂³×C₇₁	—	2	1	no	—
344	C₂³×C₇₁	—	2	1	no	—
345	C₂³×C₇₁	—	2	2	no	—
346	C₂³×C₇₁	—	4	2	no	—
347	C₂³×C₇₁	—	4	2	no	—
348	C₂³×C₇₁	—	8	1	no	—
349	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
350	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₇₁	—	2	2	no	—
352	Q₈×C₇₁	—	2	4	no	—
353	Q₈×C₇₁	—	2	2	no	—
354	Q₈×C₇₁	—	2	2	no	—
355	Q₈×C₇₁	—	2	4	no	—
356	Q₈×C₇₁	—	4	2	no	—
357	Q₈×C₇₁	—	8	1	no	—
358	Q₈×C₇₁	—	8	2	no	—
359	D₄×C₇₁	—	2	4	no	—
360	D₄×C₇₁	—	2	2	no	—
361	D₄×C₇₁	—	2	2	no	—
362	D₄×C₇₁	—	2	1	no	—
363	D₄×C₇₁	—	2	1	no	—
364	D₄×C₇₁	—	2	1	no	—
365	D₄×C₇₁	—	2	2	no	—
366	D₄×C₇₁	—	4	2	no	—
367	D₄×C₇₁	—	4	2	no	—
368	D₄×C₇₁	—	4	4	no	—
369	D₄×C₇₁	—	4	4	no	—
370	D₄×C₇₁	—	4	2	no	—
371	D₄×C₇₁	—	8	2	no	—
372	D₄×C₇₁	—	8	4	no	—
373	D₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
374	C₂×C₄×C₇₁	—	2	4	no	—
375	C₂×C₄×C₇₁	—	2	1	no	—
376	C₂×C₄×C₇₁	—	2	2	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	2	no	—
382	C₂×C₄×C₇₁	—	2	2	no	—
383	C₂×C₄×C₇₁	—	2	4	no	—
384	C₂×C₄×C₇₁	—	2	1	no	—
385	C₂×C₄×C₇₁	—	4	2	no	—
386	C₂×C₄×C₇₁	—	4	1	no	—
387	C₂×C₄×C₇₁	—	4	4	no	—
388	C₂×C₄×C₇₁	—	4	2	no	—
389	C₂×C₄×C₇₁	—	4	2	no	—
390	C₂×C₄×C₇₁	—	4	2	no	—
391	C₂×C₄×C₇₁	—	4	2	no	—
392	C₂×C₄×C₇₁	—	4	2	no	—
393	C₂×C₄×C₇₁	—	4	4	no	—
394	C₂×C₄×C₇₁	—	8	2	no	—
395	C₂×C₄×C₇₁	—	8	4	no	—
396	C₂×C₄×C₇₁	—	8	2	no	—
397	C₂×C₄×C₇₁	#135	1	4	yes	complemented
398	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
402	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
407	C₈×C₇₁	—	2	2	no	—
408	C₈×C₇₁	—	2	4	no	—
409	C₈×C₇₁	—	2	2	no	—
410	C₂²×C₇₁	—	2	1	no	—
411	C₂²×C₇₁	—	2	1	no	—
412	C₂²×C₇₁	—	2	2	no	—
413	C₂²×C₇₁	—	2	2	no	—
414	C₂²×C₇₁	—	2	2	no	—
415	C₂²×C₇₁	—	2	2	no	—
416	C₂²×C₇₁	—	4	1	no	—
417	C₂²×C₇₁	—	4	1	no	—
418	C₂²×C₇₁	—	4	2	no	—
419	C₂²×C₇₁	—	4	1	no	—
420	C₂²×C₇₁	—	4	2	no	—
421	C₂²×C₇₁	—	4	1	no	—
422	C₂²×C₇₁	—	4	1	no	—
423	C₂²×C₇₁	—	4	2	no	—
424	C₂²×C₇₁	—	8	4	no	—
425	C₂²×C₇₁	C₂×#135	1	2	yes	—
426	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₇₁	—	2	1	no	—
428	C₄×C₇₁	—	2	2	no	—
429	C₄×C₇₁	—	2	1	no	—
430	C₄×C₇₁	—	2	2	no	—
431	C₄×C₇₁	—	2	1	no	—
432	C₄×C₇₁	—	2	2	no	—
433	C₄×C₇₁	—	4	2	no	—
434	C₄×C₇₁	—	4	2	no	—
435	C₄×C₇₁	—	4	4	no	—
436	C₄×C₇₁	—	4	1	no	—
437	C₄×C₇₁	—	4	1	no	—
438	C₄×C₇₁	—	4	2	no	—
439	C₄×C₇₁	C₂×#135	1	2	yes	—
440	C₄×C₇₁	C₂×#135	1	2	yes	—
441	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
442	C₄×C₇₁	#585	1	1	yes	characteristic
443	#61950	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂×C₇₁	—	2	2	no	—
445	C₂×C₇₁	—	4	2	no	—
446	C₂×C₇₁	—	4	2	no	—
447	C₂×C₇₁	—	8	2	no	—
448	C₂×C₇₁	—	8	1	no	—
449	C₂×C₇₁	#3488	1	1	yes	characteristic
450	C₂×C₇₁	C₂²×#135	1	1	yes	characteristic
451	C₂×C₇₁	#3586	1	1	yes	characteristic
452	#3511	C₂×C₇₁	1	1	yes	characteristic, complemented
453	#3475	C₂×C₇₁	1	1	yes	characteristic, complemented
454	#3393	C₂×C₇₁	1	2	yes	complemented
455	#3360	C₂×C₇₁	1	2	yes	complemented
456	#3303	C₂×C₇₁	1	2	yes	complemented
457	#3300	C₂×C₇₁	1	4	yes	complemented
458	#3283	C₂×C₇₁	1	2	yes	complemented
459	#3282	C₂×C₇₁	1	4	yes	complemented
460	#3248	C₂×C₇₁	1	2	yes	complemented
461	#3246	C₂×C₇₁	1	1	yes	characteristic, complemented
462	#3212	C₂×C₇₁	1	2	yes	complemented
463	#3209	C₂×C₇₁	1	1	yes	characteristic, complemented
464	#3107	C₂×C₇₁	1	2	yes	complemented
465	#3100	C₂×C₇₁	1	1	yes	characteristic, complemented
466	#3035	C₂×C₇₁	1	2	yes	complemented
467	C₂×#461	C₂×C₇₁	1	1	yes	characteristic, complemented
468	#2988	C₂×C₇₁	1	1	yes	characteristic, complemented
469	C₇₁	#61950	1	1	yes	characteristic, direct product factor, Sylow
470	C₂×#135	C₂²×C₇₁	1	4	yes	—
471	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
472	#556	C₂²×C₇₁	1	1	yes	characteristic
473	#556	C₂²×C₇₁	1	2	yes	complemented
474	#555	—	2	1	no	—
475	#555	C₂²×C₇₁	1	1	yes	characteristic
476	#554	—	2	1	no	—
477	#554	C₂²×C₇₁	1	1	yes	characteristic
478	#553	—	2	1	no	—
479	#553	—	2	2	no	—
480	#552	—	2	1	no	—
481	#552	C₂²×C₇₁	1	2	yes	—
482	#551	—	2	2	no	—
483	#548	C₂²×C₇₁	1	4	yes	—
484	#547	C₂²×C₇₁	1	1	yes	characteristic
485	#547	C₂²×C₇₁	1	2	yes	complemented
486	#546	C₂²×C₇₁	1	2	yes	—
487	#542	—	2	2	no	—
488	#537	—	2	1	no	—
489	#533	C₂²×C₇₁	1	1	yes	characteristic
490	#533	C₂²×C₇₁	1	2	yes	complemented
491	#532	C₂²×C₇₁	1	1	yes	characteristic
492	#532	C₂²×C₇₁	1	2	yes	complemented
493	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
494	#529	—	2	2	no	—
495	#529	C₂²×C₇₁	1	2	yes	—
496	#525	—	2	1	no	—
497	#520	—	2	1	no	—
498	C₄×#41	C₂²×C₇₁	1	2	yes	—
499	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
501	C₂×#117	—	2	1	no	—
502	#495	C₂²×C₇₁	1	4	yes	—
503	#494	C₂²×C₇₁	1	2	yes	complemented
504	#488	C₂²×C₇₁	1	4	yes	complemented
505	#487	C₂²×C₇₁	1	2	yes	complemented
506	#485	C₂²×C₇₁	1	4	yes	complemented
507	#480	C₂²×C₇₁	1	2	yes	—
508	#479	C₂²×C₇₁	1	4	yes	complemented
509	#476	C₂²×C₇₁	1	2	yes	complemented
510	#475	C₂²×C₇₁	1	2	yes	complemented
511	#474	C₂²×C₇₁	1	1	yes	characteristic
512	#474	C₂²×C₇₁	1	1	yes	characteristic
513	#467	C₂²×C₇₁	1	4	yes	complemented
514	#465	C₂²×C₇₁	1	4	yes	—
515	#465	C₂²×C₇₁	1	4	yes	—
516	#464	C₂²×C₇₁	1	4	yes	—
517	#464	C₂²×C₇₁	1	4	yes	complemented
518	#463	C₂²×C₇₁	1	4	yes	—
519	#462	C₂²×C₇₁	1	2	yes	complemented
520	#462	C₂²×C₇₁	1	2	yes	complemented
521	#461	C₂²×C₇₁	1	2	yes	—
522	#461	C₂²×C₇₁	1	2	yes	—
523	#461	C₂²×C₇₁	1	2	yes	—
524	#461	C₂²×C₇₁	1	2	yes	—
525	#461	C₂²×C₇₁	1	2	yes	complemented
526	#460	C₂²×C₇₁	1	2	yes	complemented
527	#459	C₂²×C₇₁	1	1	yes	characteristic
528	#459	C₂²×C₇₁	1	1	yes	characteristic
529	#452	C₂²×C₇₁	1	4	yes	—
530	#452	C₂²×C₇₁	1	4	yes	complemented
531	#451	C₂²×C₇₁	1	4	yes	—
532	#449	C₂²×C₇₁	1	4	yes	—
533	#447	C₂²×C₇₁	1	2	yes	—
534	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
535	C₄×Q₁₆	C₂²×C₇₁	1	4	yes	complemented
536	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	—
537	C₄×D₈	C₂²×C₇₁	1	2	yes	—
538	C₄×D₈	C₂²×C₇₁	1	2	yes	—
539	C₈×D₄	C₂²×C₇₁	1	4	yes	—
540	C₈×D₄	C₂²×C₇₁	1	2	yes	complemented
541	#431	C₂²×C₇₁	1	1	yes	characteristic
542	#431	C₂²×C₇₁	1	2	yes	complemented
543	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
544	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
545	#416	C₂²×C₇₁	1	4	yes	complemented
546	C₂×#103	C₂²×C₇₁	1	2	yes	—
547	C₂×#41	—	2	1	no	—
548	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
549	C₂×#41	C₂³×C₇₁	1	2	yes	—
550	C₂×#41	C₂³×C₇₁	1	4	yes	—
551	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
552	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
553	C₂³×C₄	—	2	1	no	—
554	#135	—	4	8	no	—
555	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
556	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
557	C₂×SD₁₆	—	4	4	no	—
558	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
559	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
561	C₂×D₈	C₂³×C₇₁	1	2	yes	—
562	C₂×D₈	C₂³×C₇₁	1	2	yes	—
563	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
564	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
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	C₂³×C₇₁	1	1	yes	characteristic
573	#126	—	2	2	no	—
574	#126	—	2	4	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#125	—	2	2	no	—
578	#125	—	2	1	no	—
579	#125	—	2	2	no	—
580	#125	C₂³×C₇₁	1	2	yes	—
581	#124	—	2	2	no	—
582	#124	—	2	4	no	—
583	#124	—	2	1	no	—
584	#124	C₂³×C₇₁	1	2	yes	—
585	#124	C₂³×C₇₁	1	4	yes	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	4	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
601	#121	—	2	1	no	—
602	#121	—	2	1	no	—
603	#121	—	2	2	no	—
604	#121	—	2	4	no	—
605	#121	—	2	1	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	C₂³×C₇₁	1	2	yes	—
610	#121	C₂³×C₇₁	1	2	yes	—
611	#120	—	2	2	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
616	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
617	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
618	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	4	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	D₄×C₇₁	1	2	yes	—
629	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₇₁	1	2	yes	—
635	C₄×D₄	C₂³×C₇₁	1	2	yes	—
636	C₄×D₄	C₂³×C₇₁	1	2	yes	—
637	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	—	2	1	no	—
641	#117	—	2	1	no	—
642	#117	—	2	2	no	—
643	#117	—	2	2	no	—
644	#117	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	D₄×C₇₁	1	1	yes	characteristic
647	#117	D₄×C₇₁	1	2	yes	—
648	#117	C₂³×C₇₁	1	2	yes	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	2	no	—
654	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	2	no	—
657	C₂×C₄²	—	2	2	no	—
658	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
660	#107	C₂³×C₇₁	1	2	yes	—
661	#107	C₂³×C₇₁	1	2	yes	—
662	#106	C₂³×C₇₁	1	4	yes	—
663	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
664	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
665	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
666	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
667	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
668	#103	C₂³×C₇₁	1	4	yes	—
669	#103	C₂³×C₇₁	1	4	yes	—
670	#103	C₂³×C₇₁	1	4	yes	—
671	#103	C₂³×C₇₁	1	4	yes	—
672	#103	C₂³×C₇₁	1	4	yes	—
673	#102	C₂³×C₇₁	1	2	yes	—
674	#102	C₂³×C₇₁	1	4	yes	—
675	#102	C₂³×C₇₁	1	2	yes	—
676	#102	C₂³×C₇₁	1	2	yes	—
677	#102	C₂³×C₇₁	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
680	C₄×C₈	C₂³×C₇₁	1	2	yes	—
681	C₄×C₈	C₂³×C₇₁	1	4	yes	—
682	C₂⁴	—	2	1	no	—
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	4	2	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
695	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
696	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
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	—	2	4	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
707	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
709	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
725	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
728	Q₁₆	—	4	4	no	—
729	Q₁₆	—	4	4	no	—
730	SD₁₆	—	2	8	no	—
731	SD₁₆	—	4	4	no	—
732	SD₁₆	—	4	4	no	—
733	D₈	—	2	4	no	—
734	D₈	—	4	2	no	—
735	C₂×C₈	—	4	2	no	—
736	C₂×C₈	—	4	4	no	—
737	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
738	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
739	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	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	—	2	1	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
759	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
760	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	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	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	4	no	—
788	C₄²	C₂×D₄×C₇₁	1	2	yes	—
789	C₄²	C₂×D₄×C₇₁	1	2	yes	—
790	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
791	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
792	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
793	C₄²	C₂⁴×C₇₁	1	2	yes	—
794	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	8	1	no	—
801	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
802	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
803	Q₈	—	2	2	no	—
804	Q₈	—	2	4	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	4	no	—
808	Q₈	—	4	2	no	—
809	Q₈	—	8	2	no	—
810	Q₈	—	8	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	1	no	—
816	D₄	—	2	1	no	—
817	D₄	—	2	2	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	2	no	—
823	D₄	—	8	4	no	—
824	D₄	—	8	2	no	—
825	D₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
826	C₂×C₄	—	2	4	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	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	8	4	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	—	8	2	no	—
849	C₂×C₄	#135×C₇₁	1	4	yes	complemented
850	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
851	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
858	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
859	C₈	—	2	2	no	—
860	C₈	—	2	4	no	—
861	C₈	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	8	4	no	—
877	C₂²	C₂×#135×C₇₁	1	2	yes	—
878	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
879	C₄	—	2	2	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	4	no	—
891	C₄	C₂×#135×C₇₁	1	2	yes	—
892	C₄	C₂×#135×C₇₁	1	2	yes	—
893	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
894	C₄	#585×C₇₁	1	1	yes	characteristic
895	C₂	—	2	2	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	2	no	—
898	C₂	—	8	1	no	—
899	C₂	—	8	2	no	—
900	C₂	C₇₁×#3488	1	1	yes	characteristic
901	C₂	C₂²×#135×C₇₁	1	1	yes	characteristic
902	C₂	C₇₁×#3586	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×#3511	C₂	semidirect
2. C₇₁×#3475	C₂	semidirect
3. C₇₁×#3393	C₂	semidirect
4. C₇₁×#3360	C₂	semidirect
5. C₇₁×#3303	C₂	semidirect
6. C₇₁×#3300	C₂	semidirect
7. C₇₁×#3283	C₂	semidirect
8. C₇₁×#3282	C₂	semidirect
9. C₇₁×#3248	C₂	semidirect
10. C₇₁×#3246	C₂	semidirect
11. C₇₁×#3212	C₂	semidirect
12. C₇₁×#3209	C₂	semidirect
13. C₇₁×#3107	C₂	semidirect
14. C₇₁×#3100	C₂	semidirect
15. C₇₁×#3035	C₂	semidirect
16. C₂×#461×C₇₁	C₂	semidirect
17. C₇₁×#2988	C₂	semidirect
21. #556×C₇₁	C₂²	semidirect
33. #547×C₇₁	C₂²	semidirect
38. #533×C₇₁	C₂²	semidirect
40. #532×C₇₁	C₂²	semidirect
51. #494×C₇₁	C₂²	semidirect
52. #488×C₇₁	C₂²	semidirect
53. #487×C₇₁	C₂²	semidirect
54. #485×C₇₁	C₂²	semidirect
56. #479×C₇₁	C₂²	semidirect
57. #476×C₇₁	C₂²	semidirect
58. #475×C₇₁	C₂²	semidirect
61. #467×C₇₁	C₂²	semidirect
65. #464×C₇₁	C₂²	semidirect
67. #462×C₇₁	C₂²	semidirect
68. #462×C₇₁	C₂²	semidirect
73. #461×C₇₁	C₂²	semidirect
74. #460×C₇₁	C₂²	semidirect
78. #452×C₇₁	C₂²	semidirect
82. C₈×Q₈×C₇₁	C₂²	semidirect
83. C₄×Q₁₆×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
397. C₂×C₄×C₇₁	#135	semidirect
443. #61950	C₇₁	direct (N × H)
452. #3511	C₂×C₇₁	semidirect
453. #3475	C₂×C₇₁	semidirect
454. #3393	C₂×C₇₁	semidirect
455. #3360	C₂×C₇₁	semidirect
456. #3303	C₂×C₇₁	semidirect
457. #3300	C₂×C₇₁	semidirect
458. #3283	C₂×C₇₁	semidirect
459. #3282	C₂×C₇₁	semidirect
460. #3248	C₂×C₇₁	semidirect
461. #3246	C₂×C₇₁	semidirect
462. #3212	C₂×C₇₁	semidirect
463. #3209	C₂×C₇₁	semidirect
464. #3107	C₂×C₇₁	semidirect
465. #3100	C₂×C₇₁	semidirect
466. #3035	C₂×C₇₁	semidirect
467. C₂×#461	C₂×C₇₁	semidirect
468. #2988	C₂×C₇₁	semidirect
469. C₇₁	#61950	direct (N × H)
473. #556	C₂²×C₇₁	semidirect
485. #547	C₂²×C₇₁	semidirect
490. #533	C₂²×C₇₁	semidirect
492. #532	C₂²×C₇₁	semidirect
503. #494	C₂²×C₇₁	semidirect
504. #488	C₂²×C₇₁	semidirect
505. #487	C₂²×C₇₁	semidirect
506. #485	C₂²×C₇₁	semidirect
508. #479	C₂²×C₇₁	semidirect
509. #476	C₂²×C₇₁	semidirect
510. #475	C₂²×C₇₁	semidirect
513. #467	C₂²×C₇₁	semidirect
517. #464	C₂²×C₇₁	semidirect
519. #462	C₂²×C₇₁	semidirect
520. #462	C₂²×C₇₁	semidirect
525. #461	C₂²×C₇₁	semidirect
526. #460	C₂²×C₇₁	semidirect
530. #452	C₂²×C₇₁	semidirect
534. C₈×Q₈	C₂²×C₇₁	semidirect
535. C₄×Q₁₆	C₂²×C₇₁	semidirect
540. C₈×D₄	C₂²×C₇₁	semidirect
542. #431	C₂²×C₇₁	semidirect
544. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
545. #416	C₂²×C₇₁	semidirect
849. 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×#3511	2
C₇₁×#3475	2
C₇₁×#3393	2
C₇₁×#3360	2
C₇₁×#3303	2
C₇₁×#3300	2
C₇₁×#3283	2
C₇₁×#3282	2
C₇₁×#3248	2
C₇₁×#3246	2
C₇₁×#3212	2
C₇₁×#3209	2
C₇₁×#3107	2
C₇₁×#3100	2
C₇₁×#3035	2
C₂×#461×C₇₁	2
C₇₁×#2988	2
#61950	71

Subgroups — C71×#61950 #31882822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61950 #31882822