Subgroups — C₇₁×#61956 #31882828

Order 18176.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3300	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3296	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3285	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3250	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#3211	C₂	1	2	yes	maximal, complemented
18	C₇₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3108	C₂	1	2	yes	maximal, complemented
20	C₇₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#464×C₇₁	C₂	1	2	yes	maximal, complemented
23	C₇₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₇₁	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
27	#559×C₇₁	C₂²	1	1	yes	characteristic
28	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
29	#556×C₇₁	—	2	1	no	—
30	#556×C₇₁	C₂²	1	1	yes	characteristic
31	#556×C₇₁	C₂²	1	1	yes	characteristic, complemented
32	#555×C₇₁	—	2	1	no	—
33	#552×C₇₁	—	2	2	no	—
34	#552×C₇₁	C₂²	1	2	yes	complemented
35	#551×C₇₁	—	2	2	no	—
36	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
38	#548×C₇₁	C₂²	1	2	yes	—
39	#548×C₇₁	C₂²	1	2	yes	complemented
40	#547×C₇₁	—	2	1	no	—
41	#547×C₇₁	C₂²	1	1	yes	characteristic
42	#546×C₇₁	—	2	1	no	—
43	#546×C₇₁	C₂²	1	2	yes	—
44	D₄²×C₇₁	C₂²	1	1	yes	characteristic
45	#542×C₇₁	—	2	1	no	—
46	#538×C₇₁	—	2	2	no	—
47	#533×C₇₁	—	2	1	no	—
48	#533×C₇₁	C₂²	1	1	yes	characteristic, complemented
49	#532×C₇₁	C₂²	1	1	yes	characteristic
50	#529×C₇₁	—	2	2	no	—
51	#529×C₇₁	C₂²	1	1	yes	characteristic
52	#529×C₇₁	C₂²	1	2	yes	—
53	#529×C₇₁	C₂²	1	2	yes	complemented
54	C₂×#124×C₇₁	C₂²	1	2	yes	—
55	#518×C₇₁	—	2	1	no	—
56	C₄×#41×C₇₁	—	2	1	no	—
57	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	complemented
60	#495×C₇₁	C₂²	1	2	yes	—
61	#495×C₇₁	C₂²	1	2	yes	complemented
62	#494×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	#492×C₇₁	C₂²	1	1	yes	characteristic
64	#488×C₇₁	C₂²	1	2	yes	—
65	#488×C₇₁	C₂²	1	2	yes	complemented
66	#487×C₇₁	C₂²	1	1	yes	characteristic, complemented
67	#486×C₇₁	C₂²	1	1	yes	characteristic
68	#485×C₇₁	C₂²	1	1	yes	characteristic, complemented
69	#483×C₇₁	C₂²	1	2	yes	complemented
70	#482×C₇₁	C₂²	1	1	yes	characteristic
71	#480×C₇₁	C₂²	1	2	yes	—
72	#479×C₇₁	C₂²	1	2	yes	complemented
73	#479×C₇₁	C₂²	1	1	yes	characteristic, complemented
74	#479×C₇₁	C₂²	1	2	yes	complemented
75	#478×C₇₁	C₂²	1	2	yes	complemented
76	#478×C₇₁	C₂²	1	1	yes	characteristic, complemented
77	#475×C₇₁	C₂²	1	1	yes	characteristic, complemented
78	#474×C₇₁	C₂²	1	1	yes	characteristic
79	#467×C₇₁	C₂²	1	2	yes	complemented
80	#467×C₇₁	C₂²	1	2	yes	complemented
81	#466×C₇₁	C₂²	1	2	yes	—
82	#465×C₇₁	C₂²	1	2	yes	—
83	#465×C₇₁	C₂²	1	2	yes	—
84	#465×C₇₁	C₂²	1	2	yes	complemented
85	#464×C₇₁	C₂²	1	2	yes	—
86	#464×C₇₁	C₂²	1	1	yes	characteristic
87	#464×C₇₁	C₂²	1	2	yes	—
88	#464×C₇₁	C₂²	1	2	yes	—
89	#464×C₇₁	C₂²	1	2	yes	complemented
90	#464×C₇₁	C₂²	1	2	yes	complemented
91	#464×C₇₁	C₂²	1	2	yes	complemented
92	#464×C₇₁	C₂²	1	2	yes	complemented
93	#464×C₇₁	C₂²	1	2	yes	complemented
94	#464×C₇₁	C₂²	1	2	yes	complemented
95	#463×C₇₁	C₂²	1	1	yes	characteristic
96	#463×C₇₁	C₂²	1	2	yes	complemented
97	#463×C₇₁	C₂²	1	2	yes	complemented
98	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
99	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
100	#461×C₇₁	C₂²	1	1	yes	characteristic
101	#461×C₇₁	C₂²	1	1	yes	characteristic, complemented
102	#460×C₇₁	C₂²	1	1	yes	characteristic
103	#459×C₇₁	C₂²	1	1	yes	characteristic
104	#452×C₇₁	C₂²	1	2	yes	complemented
105	#452×C₇₁	C₂²	1	2	yes	complemented
106	#452×C₇₁	C₂²	1	1	yes	characteristic, complemented
107	#451×C₇₁	C₂²	1	2	yes	complemented
108	#451×C₇₁	C₂²	1	2	yes	complemented
109	#450×C₇₁	C₂²	1	2	yes	—
110	#449×C₇₁	C₂²	1	1	yes	characteristic
111	#448×C₇₁	C₂²	1	2	yes	—
112	#448×C₇₁	C₂²	1	2	yes	complemented
113	#447×C₇₁	C₂²	1	2	yes	—
114	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₇₁	C₂²	1	2	yes	complemented
127	C₈×D₄×C₇₁	C₂²	1	2	yes	complemented
128	#431×C₇₁	C₂²	1	1	yes	characteristic, complemented
129	#431×C₇₁	C₂²	1	2	yes	complemented
130	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	complemented
132	#416×C₇₁	C₂²	1	2	yes	complemented
133	C₂×#103×C₇₁	C₂²	1	2	yes	complemented
134	C₂×#102×C₇₁	C₂²	1	2	yes	—
135	C₂×#41×C₇₁	—	2	1	no	—
136	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₇₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₁	—	2	1	no	—
142	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
143	#135×C₇₁	—	4	4	no	—
144	C₂×Q₁₆×C₇₁	—	4	4	no	—
145	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₇₁	—	4	4	no	—
151	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
158	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₇₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
169	#127×C₇₁	C₂³	1	1	yes	characteristic
170	#126×C₇₁	—	2	2	no	—
171	#126×C₇₁	—	2	2	no	—
172	#126×C₇₁	—	2	2	no	—
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	1	no	—
175	#126×C₇₁	—	2	2	no	—
176	#125×C₇₁	—	2	2	no	—
177	#125×C₇₁	—	2	2	no	—
178	#125×C₇₁	—	2	1	no	—
179	#125×C₇₁	C₂³	1	1	yes	characteristic
180	#125×C₇₁	C₂³	1	2	yes	—
181	#124×C₇₁	—	2	1	no	—
182	#124×C₇₁	—	2	2	no	—
183	#124×C₇₁	—	2	2	no	—
184	#124×C₇₁	—	2	2	no	—
185	#124×C₇₁	—	2	2	no	—
186	#124×C₇₁	C₂³	1	1	yes	characteristic
187	#124×C₇₁	C₂³	1	2	yes	—
188	#124×C₇₁	C₂³	1	2	yes	—
189	#124×C₇₁	C₂³	1	2	yes	—
190	#124×C₇₁	C₂³	1	2	yes	—
191	#123×C₇₁	—	2	2	no	—
192	#123×C₇₁	—	2	1	no	—
193	#123×C₇₁	—	2	2	no	—
194	#123×C₇₁	—	2	2	no	—
195	#123×C₇₁	—	2	2	no	—
196	#123×C₇₁	—	2	2	no	—
197	#123×C₇₁	—	2	2	no	—
198	C₂²⋊Q₈×C₇₁	—	2	1	no	—
199	C₂²⋊Q₈×C₇₁	—	2	1	no	—
200	C₂²⋊Q₈×C₇₁	—	2	1	no	—
201	C₂²⋊Q₈×C₇₁	—	2	1	no	—
202	C₂²⋊Q₈×C₇₁	—	2	2	no	—
203	C₂²⋊Q₈×C₇₁	—	2	2	no	—
204	C₂²⋊Q₈×C₇₁	—	2	2	no	—
205	C₂²⋊Q₈×C₇₁	—	2	2	no	—
206	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
210	#121×C₇₁	—	2	2	no	—
211	#121×C₇₁	—	2	2	no	—
212	#121×C₇₁	—	2	1	no	—
213	#121×C₇₁	—	2	1	no	—
214	#121×C₇₁	—	2	1	no	—
215	#121×C₇₁	—	2	2	no	—
216	#121×C₇₁	C₂³	1	2	yes	—
217	#121×C₇₁	C₂³	1	2	yes	—
218	#121×C₇₁	C₂³	1	1	yes	characteristic
219	#120×C₇₁	—	2	2	no	—
220	#120×C₇₁	—	2	2	no	—
221	C₄×Q₈×C₇₁	—	2	1	no	—
222	C₄×Q₈×C₇₁	—	2	2	no	—
223	C₄×Q₈×C₇₁	—	2	2	no	—
224	C₄×Q₈×C₇₁	—	2	1	no	—
225	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₇₁	—	2	1	no	—
235	C₄×D₄×C₇₁	—	2	1	no	—
236	C₄×D₄×C₇₁	—	2	2	no	—
237	C₄×D₄×C₇₁	—	2	1	no	—
238	C₄×D₄×C₇₁	—	2	1	no	—
239	C₄×D₄×C₇₁	—	2	2	no	—
240	C₄×D₄×C₇₁	—	2	1	no	—
241	C₄×D₄×C₇₁	—	2	1	no	—
242	C₄×D₄×C₇₁	—	2	2	no	—
243	C₄×D₄×C₇₁	—	2	2	no	—
244	C₄×D₄×C₇₁	—	2	1	no	—
245	C₄×D₄×C₇₁	—	2	1	no	—
246	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
247	C₄×D₄×C₇₁	D₄	1	2	yes	—
248	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₇₁	C₂³	1	2	yes	—
251	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₇₁	C₂³	1	2	yes	—
254	#117×C₇₁	—	2	1	no	—
255	#117×C₇₁	—	2	1	no	—
256	#117×C₇₁	—	2	1	no	—
257	#117×C₇₁	—	2	2	no	—
258	#117×C₇₁	—	2	1	no	—
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	2	no	—
261	#117×C₇₁	—	2	2	no	—
262	#117×C₇₁	D₄	1	2	yes	—
263	#117×C₇₁	D₄	1	1	yes	characteristic
264	#117×C₇₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
266	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
270	C₂×C₄²×C₇₁	—	2	2	no	—
271	C₂×C₄²×C₇₁	—	2	1	no	—
272	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
274	#107×C₇₁	C₂³	1	1	yes	characteristic
275	#107×C₇₁	C₂³	1	2	yes	—
276	#107×C₇₁	C₂³	1	1	yes	characteristic
277	#106×C₇₁	C₂³	1	1	yes	characteristic
278	#106×C₇₁	C₂³	1	1	yes	characteristic
279	#106×C₇₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
287	#103×C₇₁	C₂³	1	1	yes	characteristic
288	#103×C₇₁	C₂³	1	2	yes	—
289	#103×C₇₁	C₂³	1	2	yes	—
290	#103×C₇₁	C₂³	1	2	yes	—
291	#103×C₇₁	C₂³	1	2	yes	—
292	#103×C₇₁	C₂³	1	1	yes	characteristic
293	#103×C₇₁	C₂³	1	1	yes	characteristic
294	#103×C₇₁	C₂³	1	2	yes	—
295	#103×C₇₁	C₂³	1	2	yes	—
296	#103×C₇₁	C₂³	1	2	yes	—
297	#103×C₇₁	C₂³	1	1	yes	characteristic
298	#102×C₇₁	C₂³	1	1	yes	characteristic
299	#102×C₇₁	C₂³	1	2	yes	—
300	#102×C₇₁	C₂³	1	2	yes	—
301	#102×C₇₁	C₂³	1	2	yes	—
302	#102×C₇₁	C₂³	1	2	yes	—
303	#102×C₇₁	C₂³	1	1	yes	characteristic
304	#102×C₇₁	C₂³	1	1	yes	characteristic
305	#102×C₇₁	C₂³	1	2	yes	—
306	#102×C₇₁	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₁	C₂³	1	2	yes	—
314	C₄×C₈×C₇₁	C₂³	1	2	yes	—
315	C₂⁴×C₇₁	—	2	2	no	—
316	#41×C₇₁	—	2	4	no	—
317	#41×C₇₁	—	2	2	no	—
318	#41×C₇₁	—	4	1	no	—
319	#41×C₇₁	—	4	2	no	—
320	#41×C₇₁	—	4	2	no	—
321	#41×C₇₁	—	4	4	no	—
322	C₂×Q₈×C₇₁	—	2	2	no	—
323	C₂×Q₈×C₇₁	—	2	1	no	—
324	C₂×Q₈×C₇₁	—	2	2	no	—
325	C₂×Q₈×C₇₁	—	2	4	no	—
326	C₂×Q₈×C₇₁	—	4	2	no	—
327	C₂×Q₈×C₇₁	—	4	2	no	—
328	C₂×Q₈×C₇₁	—	4	2	no	—
329	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₇₁	—	2	2	no	—
335	C₂×D₄×C₇₁	—	2	1	no	—
336	C₂×D₄×C₇₁	—	2	2	no	—
337	C₂×D₄×C₇₁	—	2	1	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	1	no	—
340	C₂×D₄×C₇₁	—	2	1	no	—
341	C₂×D₄×C₇₁	—	2	2	no	—
342	C₂×D₄×C₇₁	—	4	2	no	—
343	C₂×D₄×C₇₁	—	4	2	no	—
344	C₂×D₄×C₇₁	—	4	4	no	—
345	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇₁	—	2	2	no	—
351	C₂²×C₄×C₇₁	—	2	2	no	—
352	C₂²×C₄×C₇₁	—	2	2	no	—
353	C₂²×C₄×C₇₁	—	2	1	no	—
354	C₂²×C₄×C₇₁	—	2	1	no	—
355	C₂²×C₄×C₇₁	—	2	1	no	—
356	C₂²×C₄×C₇₁	—	2	1	no	—
357	C₂²×C₄×C₇₁	—	2	2	no	—
358	C₂²×C₄×C₇₁	—	2	2	no	—
359	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₇₁	—	2	2	no	—
366	Q₁₆×C₇₁	—	2	4	no	—
367	Q₁₆×C₇₁	—	4	2	no	—
368	Q₁₆×C₇₁	—	4	2	no	—
369	Q₁₆×C₇₁	—	4	2	no	—
370	SD₁₆×C₇₁	—	2	2	no	—
371	SD₁₆×C₇₁	—	2	4	no	—
372	SD₁₆×C₇₁	—	4	2	no	—
373	SD₁₆×C₇₁	—	4	2	no	—
374	SD₁₆×C₇₁	—	4	1	no	—
375	SD₁₆×C₇₁	—	4	2	no	—
376	SD₁₆×C₇₁	—	4	2	no	—
377	D₈×C₇₁	—	4	1	no	—
378	D₈×C₇₁	—	4	2	no	—
379	C₂×C₈×C₇₁	—	4	2	no	—
380	C₂×C₈×C₇₁	—	4	2	no	—
381	C₂×C₈×C₇₁	—	4	2	no	—
382	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₇₁	—	2	1	no	—
389	C₄⋊C₄×C₇₁	—	2	2	no	—
390	C₄⋊C₄×C₇₁	—	2	2	no	—
391	C₄⋊C₄×C₇₁	—	2	2	no	—
392	C₄⋊C₄×C₇₁	—	2	2	no	—
393	C₄⋊C₄×C₇₁	—	2	1	no	—
394	C₄⋊C₄×C₇₁	—	2	1	no	—
395	C₄⋊C₄×C₇₁	—	2	1	no	—
396	C₄⋊C₄×C₇₁	—	2	1	no	—
397	C₄⋊C₄×C₇₁	—	2	1	no	—
398	C₄⋊C₄×C₇₁	—	2	2	no	—
399	C₄⋊C₄×C₇₁	—	2	2	no	—
400	C₄⋊C₄×C₇₁	—	2	1	no	—
401	C₄⋊C₄×C₇₁	—	2	2	no	—
402	C₄⋊C₄×C₇₁	—	2	1	no	—
403	C₄⋊C₄×C₇₁	—	2	2	no	—
404	C₄⋊C₄×C₇₁	—	2	1	no	—
405	C₄⋊C₄×C₇₁	—	2	2	no	—
406	C₄⋊C₄×C₇₁	—	2	1	no	—
407	C₄⋊C₄×C₇₁	—	2	2	no	—
408	C₄⋊C₄×C₇₁	—	2	1	no	—
409	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₇₁	—	2	2	no	—
419	C₂²⋊C₄×C₇₁	—	2	2	no	—
420	C₂²⋊C₄×C₇₁	—	2	2	no	—
421	C₂²⋊C₄×C₇₁	—	2	1	no	—
422	C₂²⋊C₄×C₇₁	—	2	1	no	—
423	C₂²⋊C₄×C₇₁	—	2	2	no	—
424	C₂²⋊C₄×C₇₁	—	2	1	no	—
425	C₂²⋊C₄×C₇₁	—	2	1	no	—
426	C₂²⋊C₄×C₇₁	—	2	1	no	—
427	C₂²⋊C₄×C₇₁	—	2	2	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	2	no	—
430	C₂²⋊C₄×C₇₁	—	2	2	no	—
431	C₂²⋊C₄×C₇₁	—	2	2	no	—
432	C₂²⋊C₄×C₇₁	—	2	2	no	—
433	C₂²⋊C₄×C₇₁	—	2	1	no	—
434	C₂²⋊C₄×C₇₁	—	2	1	no	—
435	C₂²⋊C₄×C₇₁	—	2	2	no	—
436	C₂²⋊C₄×C₇₁	—	2	2	no	—
437	C₂²⋊C₄×C₇₁	—	2	2	no	—
438	C₂²⋊C₄×C₇₁	—	2	1	no	—
439	C₂²⋊C₄×C₇₁	—	2	2	no	—
440	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
443	C₄²×C₇₁	—	2	1	no	—
444	C₄²×C₇₁	—	2	1	no	—
445	C₄²×C₇₁	—	2	2	no	—
446	C₄²×C₇₁	—	2	2	no	—
447	C₄²×C₇₁	—	2	1	no	—
448	C₄²×C₇₁	—	2	2	no	—
449	C₄²×C₇₁	—	2	2	no	—
450	C₄²×C₇₁	—	2	1	no	—
451	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₇₁	C₂×D₄	1	2	yes	—
454	C₄²×C₇₁	C₂×D₄	1	2	yes	—
455	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₇₁	C₂⁴	1	2	yes	—
457	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₇₁	—	2	1	no	—
459	C₂³×C₇₁	—	2	1	no	—
460	C₂³×C₇₁	—	2	2	no	—
461	C₂³×C₇₁	—	4	4	no	—
462	C₂³×C₇₁	—	8	2	no	—
463	C₂³×C₇₁	—	8	2	no	—
464	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
465	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
466	Q₈×C₇₁	—	2	2	no	—
467	Q₈×C₇₁	—	2	1	no	—
468	Q₈×C₇₁	—	2	2	no	—
469	Q₈×C₇₁	—	2	2	no	—
470	Q₈×C₇₁	—	2	1	no	—
471	Q₈×C₇₁	—	2	2	no	—
472	Q₈×C₇₁	—	2	1	no	—
473	Q₈×C₇₁	—	2	2	no	—
474	Q₈×C₇₁	—	4	4	no	—
475	Q₈×C₇₁	—	4	2	no	—
476	Q₈×C₇₁	—	8	2	no	—
477	Q₈×C₇₁	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₇₁	—	2	4	no	—
479	D₄×C₇₁	—	2	1	no	—
480	D₄×C₇₁	—	2	2	no	—
481	D₄×C₇₁	—	2	1	no	—
482	D₄×C₇₁	—	2	1	no	—
483	D₄×C₇₁	—	2	1	no	—
484	D₄×C₇₁	—	2	2	no	—
485	D₄×C₇₁	—	4	2	no	—
486	D₄×C₇₁	—	4	4	no	—
487	D₄×C₇₁	—	4	4	no	—
488	D₄×C₇₁	—	4	2	no	—
489	D₄×C₇₁	—	8	1	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	1	no	—
492	D₄×C₇₁	—	8	2	no	—
493	D₄×C₇₁	#135	1	4	yes	complemented
494	C₂×C₄×C₇₁	—	2	4	no	—
495	C₂×C₄×C₇₁	—	2	1	no	—
496	C₂×C₄×C₇₁	—	2	2	no	—
497	C₂×C₄×C₇₁	—	2	2	no	—
498	C₂×C₄×C₇₁	—	2	1	no	—
499	C₂×C₄×C₇₁	—	2	2	no	—
500	C₂×C₄×C₇₁	—	2	1	no	—
501	C₂×C₄×C₇₁	—	2	1	no	—
502	C₂×C₄×C₇₁	—	2	1	no	—
503	C₂×C₄×C₇₁	—	2	2	no	—
504	C₂×C₄×C₇₁	—	2	1	no	—
505	C₂×C₄×C₇₁	—	2	2	no	—
506	C₂×C₄×C₇₁	—	2	1	no	—
507	C₂×C₄×C₇₁	—	2	1	no	—
508	C₂×C₄×C₇₁	—	2	2	no	—
509	C₂×C₄×C₇₁	—	4	2	no	—
510	C₂×C₄×C₇₁	—	4	1	no	—
511	C₂×C₄×C₇₁	—	4	2	no	—
512	C₂×C₄×C₇₁	—	4	4	no	—
513	C₂×C₄×C₇₁	—	4	2	no	—
514	C₂×C₄×C₇₁	—	4	4	no	—
515	C₂×C₄×C₇₁	—	4	2	no	—
516	C₂×C₄×C₇₁	—	4	2	no	—
517	C₂×C₄×C₇₁	—	8	2	no	—
518	C₂×C₄×C₇₁	—	8	2	no	—
519	C₂×C₄×C₇₁	—	8	2	no	—
520	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₇₁	—	2	2	no	—
530	C₈×C₇₁	—	2	1	no	—
531	C₈×C₇₁	—	2	2	no	—
532	C₈×C₇₁	—	2	1	no	—
533	C₈×C₇₁	—	2	1	no	—
534	C₈×C₇₁	—	2	1	no	—
535	C₂²×C₇₁	—	2	2	no	—
536	C₂²×C₇₁	—	2	2	no	—
537	C₂²×C₇₁	—	2	1	no	—
538	C₂²×C₇₁	—	2	1	no	—
539	C₂²×C₇₁	—	2	1	no	—
540	C₂²×C₇₁	—	4	1	no	—
541	C₂²×C₇₁	—	4	2	no	—
542	C₂²×C₇₁	—	4	1	no	—
543	C₂²×C₇₁	—	4	1	no	—
544	C₂²×C₇₁	—	4	2	no	—
545	C₂²×C₇₁	—	4	1	no	—
546	C₂²×C₇₁	—	4	1	no	—
547	C₂²×C₇₁	—	4	1	no	—
548	C₂²×C₇₁	—	4	2	no	—
549	C₂²×C₇₁	—	16	4	no	—
550	C₂²×C₇₁	C₂×#135	1	4	yes	—
551	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₇₁	—	2	1	no	—
553	C₄×C₇₁	—	2	2	no	—
554	C₄×C₇₁	—	2	1	no	—
555	C₄×C₇₁	—	2	1	no	—
556	C₄×C₇₁	—	2	2	no	—
557	C₄×C₇₁	—	2	2	no	—
558	C₄×C₇₁	—	2	1	no	—
559	C₄×C₇₁	—	2	2	no	—
560	C₄×C₇₁	—	4	1	no	—
561	C₄×C₇₁	—	4	1	no	—
562	C₄×C₇₁	—	4	2	no	—
563	C₄×C₇₁	—	4	2	no	—
564	C₄×C₇₁	—	4	1	no	—
565	C₄×C₇₁	—	4	1	no	—
566	C₄×C₇₁	—	4	1	no	—
567	C₄×C₇₁	—	4	2	no	—
568	C₄×C₇₁	C₂×#135	1	2	yes	—
569	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄×C₇₁	#585	1	1	yes	characteristic
571	#61956	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂×C₇₁	—	2	4	no	—
573	C₂×C₇₁	—	4	1	no	—
574	C₂×C₇₁	—	8	1	no	—
575	C₂×C₇₁	—	8	2	no	—
576	C₂×C₇₁	—	8	1	no	—
577	C₂×C₇₁	#3488	1	1	yes	characteristic
578	C₂×C₇₁	C₂²×#135	1	1	yes	characteristic
579	C₂×C₇₁	#3586	1	1	yes	characteristic
580	#3514	C₂×C₇₁	1	1	yes	characteristic, complemented
581	#3482	C₂×C₇₁	1	1	yes	characteristic, complemented
582	#3394	C₂×C₇₁	1	1	yes	characteristic, complemented
583	#3393	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3365	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3364	C₂×C₇₁	1	1	yes	characteristic, complemented
586	#3300	C₂×C₇₁	1	2	yes	complemented
587	#3298	C₂×C₇₁	1	1	yes	characteristic, complemented
588	#3296	C₂×C₇₁	1	2	yes	complemented
589	#3294	C₂×C₇₁	1	1	yes	characteristic, complemented
590	D₄×Q₁₆	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3285	C₂×C₇₁	1	2	yes	complemented
592	#3282	C₂×C₇₁	1	2	yes	complemented
593	D₄×SD₁₆	C₂×C₇₁	1	1	yes	characteristic, complemented
594	#3250	C₂×C₇₁	1	2	yes	complemented
595	#3248	C₂×C₇₁	1	1	yes	characteristic, complemented
596	#3211	C₂×C₇₁	1	2	yes	complemented
597	#3210	C₂×C₇₁	1	1	yes	characteristic, complemented
598	#3108	C₂×C₇₁	1	2	yes	complemented
599	#3102	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#3035	C₂×C₇₁	1	1	yes	characteristic, complemented
601	C₂×#464	C₂×C₇₁	1	2	yes	complemented
602	#2988	C₂×C₇₁	1	1	yes	characteristic, complemented
603	C₇₁	#61956	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×#135	C₂²×C₇₁	1	2	yes	complemented
605	C₂²×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
606	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
607	#559	C₂²×C₇₁	1	1	yes	characteristic
608	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
609	#556	—	2	1	no	—
610	#556	C₂²×C₇₁	1	1	yes	characteristic
611	#556	C₂²×C₇₁	1	1	yes	characteristic, complemented
612	#555	—	2	1	no	—
613	#552	—	2	2	no	—
614	#552	C₂²×C₇₁	1	2	yes	complemented
615	#551	—	2	2	no	—
616	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
618	#548	C₂²×C₇₁	1	2	yes	—
619	#548	C₂²×C₇₁	1	2	yes	complemented
620	#547	—	2	1	no	—
621	#547	C₂²×C₇₁	1	1	yes	characteristic
622	#546	—	2	1	no	—
623	#546	C₂²×C₇₁	1	2	yes	—
624	D₄²	C₂²×C₇₁	1	1	yes	characteristic
625	#542	—	2	1	no	—
626	#538	—	2	2	no	—
627	#533	—	2	1	no	—
628	#533	C₂²×C₇₁	1	1	yes	characteristic, complemented
629	#532	C₂²×C₇₁	1	1	yes	characteristic
630	#529	—	2	2	no	—
631	#529	C₂²×C₇₁	1	1	yes	characteristic
632	#529	C₂²×C₇₁	1	2	yes	—
633	#529	C₂²×C₇₁	1	2	yes	complemented
634	C₂×#124	C₂²×C₇₁	1	2	yes	—
635	#518	—	2	1	no	—
636	C₄×#41	—	2	1	no	—
637	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
638	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic, complemented
639	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	complemented
640	#495	C₂²×C₇₁	1	2	yes	—
641	#495	C₂²×C₇₁	1	2	yes	complemented
642	#494	C₂²×C₇₁	1	1	yes	characteristic, complemented
643	#492	C₂²×C₇₁	1	1	yes	characteristic
644	#488	C₂²×C₇₁	1	2	yes	—
645	#488	C₂²×C₇₁	1	2	yes	complemented
646	#487	C₂²×C₇₁	1	1	yes	characteristic, complemented
647	#486	C₂²×C₇₁	1	1	yes	characteristic
648	#485	C₂²×C₇₁	1	1	yes	characteristic, complemented
649	#483	C₂²×C₇₁	1	2	yes	complemented
650	#482	C₂²×C₇₁	1	1	yes	characteristic
651	#480	C₂²×C₇₁	1	2	yes	—
652	#479	C₂²×C₇₁	1	1	yes	characteristic, complemented
653	#479	C₂²×C₇₁	1	2	yes	complemented
654	#479	C₂²×C₇₁	1	2	yes	complemented
655	#478	C₂²×C₇₁	1	1	yes	characteristic, complemented
656	#478	C₂²×C₇₁	1	2	yes	complemented
657	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
658	#474	C₂²×C₇₁	1	1	yes	characteristic
659	#467	C₂²×C₇₁	1	2	yes	complemented
660	#467	C₂²×C₇₁	1	2	yes	complemented
661	#466	C₂²×C₇₁	1	2	yes	—
662	#465	C₂²×C₇₁	1	2	yes	—
663	#465	C₂²×C₇₁	1	2	yes	—
664	#465	C₂²×C₇₁	1	2	yes	complemented
665	#464	C₂²×C₇₁	1	1	yes	characteristic
666	#464	C₂²×C₇₁	1	2	yes	—
667	#464	C₂²×C₇₁	1	2	yes	—
668	#464	C₂²×C₇₁	1	2	yes	—
669	#464	C₂²×C₇₁	1	2	yes	complemented
670	#464	C₂²×C₇₁	1	2	yes	complemented
671	#464	C₂²×C₇₁	1	2	yes	complemented
672	#464	C₂²×C₇₁	1	2	yes	complemented
673	#464	C₂²×C₇₁	1	2	yes	complemented
674	#464	C₂²×C₇₁	1	2	yes	complemented
675	#463	C₂²×C₇₁	1	1	yes	characteristic
676	#463	C₂²×C₇₁	1	2	yes	complemented
677	#463	C₂²×C₇₁	1	2	yes	complemented
678	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
679	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
680	#461	C₂²×C₇₁	1	1	yes	characteristic
681	#461	C₂²×C₇₁	1	1	yes	characteristic, complemented
682	#460	C₂²×C₇₁	1	1	yes	characteristic
683	#459	C₂²×C₇₁	1	1	yes	characteristic
684	#452	C₂²×C₇₁	1	1	yes	characteristic, complemented
685	#452	C₂²×C₇₁	1	2	yes	complemented
686	#452	C₂²×C₇₁	1	2	yes	complemented
687	#451	C₂²×C₇₁	1	2	yes	complemented
688	#451	C₂²×C₇₁	1	2	yes	complemented
689	#450	C₂²×C₇₁	1	2	yes	—
690	#449	C₂²×C₇₁	1	1	yes	characteristic
691	#448	C₂²×C₇₁	1	2	yes	—
692	#448	C₂²×C₇₁	1	2	yes	complemented
693	#447	C₂²×C₇₁	1	2	yes	—
694	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
695	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
696	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
697	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
698	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
700	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
703	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
704	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
705	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
706	C₈×D₄	C₂²×C₇₁	1	2	yes	complemented
707	C₈×D₄	C₂²×C₇₁	1	2	yes	complemented
708	#431	C₂²×C₇₁	1	1	yes	characteristic, complemented
709	#431	C₂²×C₇₁	1	2	yes	complemented
710	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
711	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
712	#416	C₂²×C₇₁	1	2	yes	complemented
713	C₂×#103	C₂²×C₇₁	1	2	yes	complemented
714	C₂×#102	C₂²×C₇₁	1	2	yes	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
717	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₇₁	1	2	yes	—
719	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
720	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
723	#135	—	4	4	no	—
724	C₂×Q₁₆	—	4	4	no	—
725	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
730	C₂×SD₁₆	—	4	4	no	—
731	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₇₁	1	2	yes	—
739	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
742	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
749	#127	C₂³×C₇₁	1	1	yes	characteristic
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	1	no	—
755	#126	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	C₂³×C₇₁	1	1	yes	characteristic
760	#125	C₂³×C₇₁	1	2	yes	—
761	#124	—	2	1	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	C₂³×C₇₁	1	1	yes	characteristic
767	#124	C₂³×C₇₁	1	2	yes	—
768	#124	C₂³×C₇₁	1	2	yes	—
769	#124	C₂³×C₇₁	1	2	yes	—
770	#124	C₂³×C₇₁	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	1	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	C₂³×C₇₁	1	2	yes	—
797	#121	C₂³×C₇₁	1	1	yes	characteristic
798	#121	C₂³×C₇₁	1	2	yes	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
827	C₄×D₄	D₄×C₇₁	1	2	yes	—
828	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₇₁	1	2	yes	—
832	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₇₁	1	2	yes	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	D₄×C₇₁	1	2	yes	—
843	#117	D₄×C₇₁	1	1	yes	characteristic
844	#117	C₂³×C₇₁	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
853	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
854	#107	C₂³×C₇₁	1	1	yes	characteristic
855	#107	C₂³×C₇₁	1	2	yes	—
856	#107	C₂³×C₇₁	1	1	yes	characteristic
857	#106	C₂³×C₇₁	1	1	yes	characteristic
858	#106	C₂³×C₇₁	1	1	yes	characteristic
859	#106	C₂³×C₇₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
867	#103	C₂³×C₇₁	1	1	yes	characteristic
868	#103	C₂³×C₇₁	1	2	yes	—
869	#103	C₂³×C₇₁	1	2	yes	—
870	#103	C₂³×C₇₁	1	2	yes	—
871	#103	C₂³×C₇₁	1	2	yes	—
872	#103	C₂³×C₇₁	1	1	yes	characteristic
873	#103	C₂³×C₇₁	1	1	yes	characteristic
874	#103	C₂³×C₇₁	1	2	yes	—
875	#103	C₂³×C₇₁	1	2	yes	—
876	#103	C₂³×C₇₁	1	2	yes	—
877	#103	C₂³×C₇₁	1	1	yes	characteristic
878	#102	C₂³×C₇₁	1	1	yes	characteristic
879	#102	C₂³×C₇₁	1	2	yes	—
880	#102	C₂³×C₇₁	1	2	yes	—
881	#102	C₂³×C₇₁	1	2	yes	—
882	#102	C₂³×C₇₁	1	2	yes	—
883	#102	C₂³×C₇₁	1	1	yes	characteristic
884	#102	C₂³×C₇₁	1	1	yes	characteristic
885	#102	C₂³×C₇₁	1	2	yes	—
886	#102	C₂³×C₇₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₇₁	1	2	yes	—
894	C₄×C₈	C₂³×C₇₁	1	2	yes	—
895	C₂⁴	—	2	2	no	—
896	#41	—	2	4	no	—
897	#41	—	2	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	4	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	4	no	—
925	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
940	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
942	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
945	Q₁₆	—	2	2	no	—
946	Q₁₆	—	2	4	no	—
947	Q₁₆	—	4	2	no	—
948	Q₁₆	—	4	2	no	—
949	Q₁₆	—	4	2	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	1	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	4	1	no	—
958	D₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
966	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1035	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₇₁	1	2	yes	—
1037	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1045	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	4	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	H(5,𝔽₂)×C₇₁	1	2	yes	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	#135×C₇₁	1	4	yes	complemented
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₂×#135×C₇₁	1	4	yes	—
1131	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₂×#135×C₇₁	1	2	yes	—
1149	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
1150	C₄	#585×C₇₁	1	1	yes	characteristic
1151	C₂	—	2	4	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₇₁×#3488	1	1	yes	characteristic
1157	C₂	C₂²×#135×C₇₁	1	1	yes	characteristic
1158	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×#3514	C₂	semidirect
2. C₇₁×#3482	C₂	semidirect
3. C₇₁×#3394	C₂	semidirect
4. C₇₁×#3393	C₂	semidirect
5. C₇₁×#3365	C₂	semidirect
6. C₇₁×#3364	C₂	semidirect
7. C₇₁×#3300	C₂	semidirect
8. C₇₁×#3298	C₂	semidirect
9. C₇₁×#3296	C₂	semidirect
10. C₇₁×#3294	C₂	semidirect
11. D₄×Q₁₆×C₇₁	C₂	semidirect
12. C₇₁×#3285	C₂	semidirect
13. C₇₁×#3282	C₂	semidirect
14. D₄×SD₁₆×C₇₁	C₂	semidirect
15. C₇₁×#3250	C₂	semidirect
16. C₇₁×#3248	C₂	semidirect
17. C₇₁×#3211	C₂	semidirect
18. C₇₁×#3210	C₂	semidirect
19. C₇₁×#3108	C₂	semidirect
20. C₇₁×#3102	C₂	semidirect
21. C₇₁×#3035	C₂	semidirect
22. C₂×#464×C₇₁	C₂	semidirect
23. C₇₁×#2988	C₂	semidirect
24. C₂×#135×C₇₁	C₂²	semidirect
25. C₂²×Q₁₆×C₇₁	C₂²	semidirect
28. #557×C₇₁	C₂²	semidirect
31. #556×C₇₁	C₂²	semidirect
34. #552×C₇₁	C₂²	semidirect
39. #548×C₇₁	C₂²	semidirect
48. #533×C₇₁	C₂²	semidirect
53. #529×C₇₁	C₂²	semidirect
58. C₄×#41×C₇₁	C₂²	semidirect
59. C₂×C₄×Q₈×C₇₁	C₂²	semidirect
61. #495×C₇₁	C₂²	semidirect
62. #494×C₇₁	C₂²	semidirect
65. #488×C₇₁	C₂²	semidirect
66. #487×C₇₁	C₂²	semidirect
68. #485×C₇₁	C₂²	semidirect
69. #483×C₇₁	C₂²	semidirect
72. #479×C₇₁	C₂²	semidirect
73. #479×C₇₁	C₂²	semidirect
74. #479×C₇₁	C₂²	semidirect
75. #478×C₇₁	C₂²	semidirect
76. #478×C₇₁	C₂²	semidirect
77. #475×C₇₁	C₂²	semidirect
79. #467×C₇₁	C₂²	semidirect
80. #467×C₇₁	C₂²	semidirect
84. #465×C₇₁	C₂²	semidirect
89. #464×C₇₁	C₂²	semidirect
90. #464×C₇₁	C₂²	semidirect
91. #464×C₇₁	C₂²	semidirect
92. #464×C₇₁	C₂²	semidirect
93. #464×C₇₁	C₂²	semidirect
94. #464×C₇₁	C₂²	semidirect
96. #463×C₇₁	C₂²	semidirect
97. #463×C₇₁	C₂²	semidirect
98. #462×C₇₁	C₂²	semidirect
99. #462×C₇₁	C₂²	semidirect
101. #461×C₇₁	C₂²	semidirect
104. #452×C₇₁	C₂²	semidirect
105. #452×C₇₁	C₂²	semidirect
106. #452×C₇₁	C₂²	semidirect
107. #451×C₇₁	C₂²	semidirect
108. #451×C₇₁	C₂²	semidirect
112. #448×C₇₁	C₂²	semidirect
114. C₈×Q₈×C₇₁	C₂²	semidirect
115. C₈×Q₈×C₇₁	C₂²	semidirect
116. C₄×Q₁₆×C₇₁	C₂²	semidirect
117. C₄×Q₁₆×C₇₁	C₂²	semidirect
118. C₄×Q₁₆×C₇₁	C₂²	semidirect
120. C₄×SD₁₆×C₇₁	C₂²	semidirect
121. C₄×SD₁₆×C₇₁	C₂²	semidirect
122. C₄×SD₁₆×C₇₁	C₂²	semidirect
126. C₈×D₄×C₇₁	C₂²	semidirect
127. C₈×D₄×C₇₁	C₂²	semidirect
128. #431×C₇₁	C₂²	semidirect
129. #431×C₇₁	C₂²	semidirect
130. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
131. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
132. #416×C₇₁	C₂²	semidirect
133. C₂×#103×C₇₁	C₂²	semidirect
493. D₄×C₇₁	#135	semidirect
571. #61956	C₇₁	direct (N × H)
580. #3514	C₂×C₇₁	semidirect
581. #3482	C₂×C₇₁	semidirect
582. #3394	C₂×C₇₁	semidirect
583. #3393	C₂×C₇₁	semidirect
584. #3365	C₂×C₇₁	semidirect
585. #3364	C₂×C₇₁	semidirect
586. #3300	C₂×C₇₁	semidirect
587. #3298	C₂×C₇₁	semidirect
588. #3296	C₂×C₇₁	semidirect
589. #3294	C₂×C₇₁	semidirect
590. D₄×Q₁₆	C₂×C₇₁	semidirect
591. #3285	C₂×C₇₁	semidirect
592. #3282	C₂×C₇₁	semidirect
593. D₄×SD₁₆	C₂×C₇₁	semidirect
594. #3250	C₂×C₇₁	semidirect
595. #3248	C₂×C₇₁	semidirect
596. #3211	C₂×C₇₁	semidirect
597. #3210	C₂×C₇₁	semidirect
598. #3108	C₂×C₇₁	semidirect
599. #3102	C₂×C₇₁	semidirect
600. #3035	C₂×C₇₁	semidirect
601. C₂×#464	C₂×C₇₁	semidirect
602. #2988	C₂×C₇₁	semidirect
603. C₇₁	#61956	direct (N × H)
604. C₂×#135	C₂²×C₇₁	semidirect
605. C₂²×Q₁₆	C₂²×C₇₁	semidirect
608. #557	C₂²×C₇₁	semidirect
611. #556	C₂²×C₇₁	semidirect
614. #552	C₂²×C₇₁	semidirect
619. #548	C₂²×C₇₁	semidirect
628. #533	C₂²×C₇₁	semidirect
633. #529	C₂²×C₇₁	semidirect
638. C₄×#41	C₂²×C₇₁	semidirect
639. C₂×C₄×Q₈	C₂²×C₇₁	semidirect
641. #495	C₂²×C₇₁	semidirect
642. #494	C₂²×C₇₁	semidirect
645. #488	C₂²×C₇₁	semidirect
646. #487	C₂²×C₇₁	semidirect
648. #485	C₂²×C₇₁	semidirect
649. #483	C₂²×C₇₁	semidirect
652. #479	C₂²×C₇₁	semidirect
653. #479	C₂²×C₇₁	semidirect
654. #479	C₂²×C₇₁	semidirect
655. #478	C₂²×C₇₁	semidirect
656. #478	C₂²×C₇₁	semidirect
657. #475	C₂²×C₇₁	semidirect
659. #467	C₂²×C₇₁	semidirect
660. #467	C₂²×C₇₁	semidirect
664. #465	C₂²×C₇₁	semidirect
669. #464	C₂²×C₇₁	semidirect
670. #464	C₂²×C₇₁	semidirect
671. #464	C₂²×C₇₁	semidirect
672. #464	C₂²×C₇₁	semidirect
673. #464	C₂²×C₇₁	semidirect
674. #464	C₂²×C₇₁	semidirect
676. #463	C₂²×C₇₁	semidirect
677. #463	C₂²×C₇₁	semidirect
678. #462	C₂²×C₇₁	semidirect
679. #462	C₂²×C₇₁	semidirect
681. #461	C₂²×C₇₁	semidirect
684. #452	C₂²×C₇₁	semidirect
685. #452	C₂²×C₇₁	semidirect
686. #452	C₂²×C₇₁	semidirect
687. #451	C₂²×C₇₁	semidirect
688. #451	C₂²×C₇₁	semidirect
692. #448	C₂²×C₇₁	semidirect
694. C₈×Q₈	C₂²×C₇₁	semidirect
695. C₈×Q₈	C₂²×C₇₁	semidirect
696. C₄×Q₁₆	C₂²×C₇₁	semidirect
697. C₄×Q₁₆	C₂²×C₇₁	semidirect
698. C₄×Q₁₆	C₂²×C₇₁	semidirect
700. C₄×SD₁₆	C₂²×C₇₁	semidirect
701. C₄×SD₁₆	C₂²×C₇₁	semidirect
702. C₄×SD₁₆	C₂²×C₇₁	semidirect
706. C₈×D₄	C₂²×C₇₁	semidirect
707. C₈×D₄	C₂²×C₇₁	semidirect
708. #431	C₂²×C₇₁	semidirect
709. #431	C₂²×C₇₁	semidirect
710. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
711. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
712. #416	C₂²×C₇₁	semidirect
713. C₂×#103	C₂²×C₇₁	semidirect
1073. D₄	#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×#3514	2
C₇₁×#3482	2
C₇₁×#3394	2
C₇₁×#3393	2
C₇₁×#3365	2
C₇₁×#3364	2
C₇₁×#3300	2
C₇₁×#3298	2
C₇₁×#3296	2
C₇₁×#3294	2
D₄×Q₁₆×C₇₁	2
C₇₁×#3285	2
C₇₁×#3282	2
D₄×SD₁₆×C₇₁	2
C₇₁×#3250	2
C₇₁×#3248	2
C₇₁×#3211	2
C₇₁×#3210	2
C₇₁×#3108	2
C₇₁×#3102	2
C₇₁×#3035	2
C₂×#464×C₇₁	2
C₇₁×#2988	2
#61956	71

Subgroups — C71×#61956 #31882828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61956 #31882828