Subgroups — C₇₁×#61938 #31882810

Order 18176.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3399	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3399	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3376	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3373	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3366	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3220	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3119	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#562×C₇₁	—	2	2	no	—
21	#559×C₇₁	C₂²	1	2	yes	—
22	#559×C₇₁	C₂²	1	2	yes	—
23	#559×C₇₁	C₂²	1	2	yes	complemented
24	#559×C₇₁	C₂²	1	1	yes	characteristic, complemented
25	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
26	#556×C₇₁	C₂²	1	2	yes	—
27	#555×C₇₁	—	2	1	no	—
28	#554×C₇₁	C₂²	1	2	yes	complemented
29	#553×C₇₁	—	2	2	no	—
30	#550×C₇₁	C₂²	1	2	yes	—
31	#550×C₇₁	C₂²	1	1	yes	characteristic, complemented
32	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
33	#548×C₇₁	—	2	1	no	—
34	#547×C₇₁	—	2	1	no	—
35	#547×C₇₁	—	2	1	no	—
36	#542×C₇₁	—	2	1	no	—
37	#542×C₇₁	C₂²	1	2	yes	—
38	#540×C₇₁	C₂²	1	2	yes	—
39	#539×C₇₁	—	2	2	no	—
40	#538×C₇₁	—	2	1	no	—
41	#538×C₇₁	—	2	1	no	—
42	#536×C₇₁	—	2	1	no	—
43	#535×C₇₁	C₂²	1	2	yes	—
44	#533×C₇₁	C₂²	1	1	yes	characteristic
45	#532×C₇₁	C₂²	1	1	yes	characteristic
46	#532×C₇₁	C₂²	1	1	yes	characteristic
47	#529×C₇₁	C₂²	1	1	yes	characteristic
48	#525×C₇₁	—	2	2	no	—
49	#520×C₇₁	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
51	#497×C₇₁	C₂²	1	1	yes	characteristic, complemented
52	#496×C₇₁	C₂²	1	2	yes	—
53	#496×C₇₁	C₂²	1	2	yes	—
54	#496×C₇₁	C₂²	1	1	yes	characteristic, complemented
55	#496×C₇₁	C₂²	1	2	yes	complemented
56	#495×C₇₁	C₂²	1	2	yes	—
57	#493×C₇₁	C₂²	1	2	yes	—
58	#491×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	#490×C₇₁	C₂²	1	2	yes	—
60	#490×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	#489×C₇₁	C₂²	1	2	yes	—
62	#489×C₇₁	C₂²	1	2	yes	complemented
63	#488×C₇₁	C₂²	1	2	yes	—
64	#486×C₇₁	C₂²	1	2	yes	—
65	#483×C₇₁	C₂²	1	1	yes	characteristic
66	#481×C₇₁	C₂²	1	2	yes	—
67	#480×C₇₁	C₂²	1	1	yes	characteristic
68	#479×C₇₁	C₂²	1	2	yes	complemented
69	#478×C₇₁	C₂²	1	2	yes	—
70	#478×C₇₁	C₂²	1	2	yes	complemented
71	#476×C₇₁	C₂²	1	2	yes	—
72	#476×C₇₁	C₂²	1	2	yes	complemented
73	#475×C₇₁	C₂²	1	2	yes	complemented
74	#464×C₇₁	C₂²	1	2	yes	—
75	#464×C₇₁	C₂²	1	2	yes	complemented
76	#464×C₇₁	C₂²	1	2	yes	complemented
77	#463×C₇₁	C₂²	1	2	yes	—
78	#463×C₇₁	C₂²	1	2	yes	—
79	#463×C₇₁	C₂²	1	2	yes	—
80	#463×C₇₁	C₂²	1	2	yes	—
81	#463×C₇₁	C₂²	1	2	yes	complemented
82	#463×C₇₁	C₂²	1	2	yes	complemented
83	#461×C₇₁	C₂²	1	2	yes	complemented
84	#460×C₇₁	C₂²	1	2	yes	—
85	#460×C₇₁	C₂²	1	2	yes	complemented
86	#459×C₇₁	C₂²	1	2	yes	—
87	#459×C₇₁	C₂²	1	2	yes	—
88	#459×C₇₁	C₂²	1	2	yes	—
89	#459×C₇₁	C₂²	1	2	yes	—
90	#459×C₇₁	C₂²	1	2	yes	complemented
91	#459×C₇₁	C₂²	1	2	yes	complemented
92	#452×C₇₁	C₂²	1	2	yes	—
93	#450×C₇₁	C₂²	1	1	yes	characteristic
94	#449×C₇₁	C₂²	1	2	yes	—
95	#449×C₇₁	C₂²	1	2	yes	—
96	#449×C₇₁	C₂²	1	2	yes	—
97	#447×C₇₁	C₂²	1	2	yes	—
98	#447×C₇₁	C₂²	1	1	yes	characteristic
99	#446×C₇₁	C₂²	1	2	yes	complemented
100	#446×C₇₁	C₂²	1	2	yes	complemented
101	#446×C₇₁	C₂²	1	2	yes	complemented
102	#446×C₇₁	C₂²	1	2	yes	complemented
103	#442×C₇₁	C₂²	1	2	yes	—
104	#442×C₇₁	C₂²	1	2	yes	—
105	#442×C₇₁	C₂²	1	2	yes	—
106	#442×C₇₁	C₂²	1	2	yes	complemented
107	#442×C₇₁	C₂²	1	2	yes	complemented
108	#441×C₇₁	C₂²	1	2	yes	complemented
109	#440×C₇₁	C₂²	1	2	yes	—
110	#440×C₇₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
114	C₄×D₈×C₇₁	C₂²	1	2	yes	complemented
115	#433×C₇₁	C₂²	1	2	yes	—
116	#433×C₇₁	C₂²	1	2	yes	—
117	#432×C₇₁	C₂²	1	1	yes	characteristic
118	#432×C₇₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₁	—	2	2	no	—
120	C₂×#41×C₇₁	—	2	1	no	—
121	C₂×#41×C₇₁	—	2	1	no	—
122	C₂×#41×C₇₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₇₁	—	2	1	no	—
124	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇₁	—	2	1	no	—
126	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
132	C₂×D₈×C₇₁	C₂³	1	2	yes	—
133	C₂×D₈×C₇₁	C₂³	1	2	yes	—
134	C₂×D₈×C₇₁	C₂³	1	2	yes	—
135	C₂×D₈×C₇₁	C₂³	1	2	yes	—
136	C₂×D₈×C₇₁	C₂³	1	2	yes	—
137	C₂×D₈×C₇₁	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₇₁	—	2	1	no	—
139	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
140	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
141	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
144	#127×C₇₁	C₂³	1	2	yes	—
145	#127×C₇₁	C₂³	1	1	yes	characteristic
146	#127×C₇₁	C₂³	1	2	yes	—
147	#127×C₇₁	C₂³	1	1	yes	characteristic
148	#127×C₇₁	C₂³	1	2	yes	—
149	#126×C₇₁	—	2	2	no	—
150	#126×C₇₁	—	2	2	no	—
151	#126×C₇₁	—	2	2	no	—
152	#126×C₇₁	—	2	1	no	—
153	#125×C₇₁	—	2	2	no	—
154	#125×C₇₁	D₄	1	2	yes	—
155	#125×C₇₁	C₂³	1	1	yes	characteristic
156	#125×C₇₁	C₂³	1	2	yes	—
157	#124×C₇₁	—	2	1	no	—
158	#124×C₇₁	—	2	2	no	—
159	#124×C₇₁	—	2	2	no	—
160	#124×C₇₁	—	2	2	no	—
161	#124×C₇₁	—	2	2	no	—
162	#124×C₇₁	—	2	1	no	—
163	#124×C₇₁	C₂³	1	2	yes	—
164	#124×C₇₁	C₂³	1	1	yes	characteristic
165	#124×C₇₁	C₂³	1	2	yes	—
166	#124×C₇₁	C₂³	1	2	yes	—
167	#124×C₇₁	C₂³	1	2	yes	—
168	#123×C₇₁	—	2	1	no	—
169	#123×C₇₁	—	2	2	no	—
170	#123×C₇₁	—	2	2	no	—
171	#123×C₇₁	—	2	2	no	—
172	#123×C₇₁	—	2	2	no	—
173	#123×C₇₁	—	2	2	no	—
174	#123×C₇₁	—	2	2	no	—
175	#123×C₇₁	—	2	2	no	—
176	#123×C₇₁	—	2	2	no	—
177	#123×C₇₁	—	2	2	no	—
178	#123×C₇₁	—	2	2	no	—
179	C₂²⋊Q₈×C₇₁	—	2	2	no	—
180	C₂²⋊Q₈×C₇₁	—	2	2	no	—
181	C₂²⋊Q₈×C₇₁	—	2	2	no	—
182	C₂²⋊Q₈×C₇₁	—	2	2	no	—
183	C₂²⋊Q₈×C₇₁	—	2	2	no	—
184	C₂²⋊Q₈×C₇₁	—	2	2	no	—
185	C₂²⋊Q₈×C₇₁	—	2	1	no	—
186	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
187	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
190	#121×C₇₁	—	2	1	no	—
191	#121×C₇₁	—	2	1	no	—
192	#121×C₇₁	—	2	1	no	—
193	#121×C₇₁	—	2	2	no	—
194	#121×C₇₁	—	2	2	no	—
195	#121×C₇₁	—	2	2	no	—
196	#121×C₇₁	—	2	2	no	—
197	#121×C₇₁	—	2	2	no	—
198	#121×C₇₁	—	2	2	no	—
199	#121×C₇₁	—	2	1	no	—
200	#121×C₇₁	—	2	2	no	—
201	#121×C₇₁	—	2	2	no	—
202	#121×C₇₁	C₂³	1	1	yes	characteristic
203	#121×C₇₁	C₂³	1	2	yes	—
204	#120×C₇₁	—	2	2	no	—
205	#120×C₇₁	—	2	2	no	—
206	C₄×Q₈×C₇₁	—	2	1	no	—
207	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₇₁	—	2	1	no	—
215	C₄×D₄×C₇₁	—	2	2	no	—
216	C₄×D₄×C₇₁	—	2	2	no	—
217	C₄×D₄×C₇₁	—	2	2	no	—
218	C₄×D₄×C₇₁	—	2	1	no	—
219	C₄×D₄×C₇₁	—	2	2	no	—
220	C₄×D₄×C₇₁	—	2	2	no	—
221	C₄×D₄×C₇₁	—	2	1	no	—
222	C₄×D₄×C₇₁	—	2	1	no	—
223	C₄×D₄×C₇₁	—	2	1	no	—
224	C₄×D₄×C₇₁	—	2	1	no	—
225	C₄×D₄×C₇₁	—	2	1	no	—
226	C₄×D₄×C₇₁	C₂³	1	2	yes	—
227	C₄×D₄×C₇₁	C₂³	1	2	yes	—
228	C₄×D₄×C₇₁	C₂³	1	2	yes	—
229	C₄×D₄×C₇₁	C₂³	1	2	yes	—
230	C₄×D₄×C₇₁	C₂³	1	2	yes	—
231	C₄×D₄×C₇₁	C₂³	1	2	yes	—
232	C₄×D₄×C₇₁	C₂³	1	2	yes	—
233	C₄×D₄×C₇₁	C₂³	1	2	yes	—
234	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
235	#117×C₇₁	—	2	2	no	—
236	#117×C₇₁	—	2	2	no	—
237	#117×C₇₁	—	2	1	no	—
238	#117×C₇₁	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
240	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
241	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
243	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
244	#107×C₇₁	C₂³	1	2	yes	—
245	#106×C₇₁	C₂³	1	2	yes	—
246	#106×C₇₁	C₂³	1	2	yes	—
247	#106×C₇₁	C₂³	1	2	yes	—
248	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
249	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
250	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
251	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
254	#103×C₇₁	C₂³	1	2	yes	—
255	#103×C₇₁	C₂³	1	2	yes	—
256	#103×C₇₁	C₂³	1	2	yes	—
257	#103×C₇₁	C₂³	1	2	yes	—
258	#103×C₇₁	C₂³	1	2	yes	—
259	#102×C₇₁	C₂³	1	2	yes	—
260	#102×C₇₁	C₂³	1	2	yes	—
261	#102×C₇₁	C₂³	1	2	yes	—
262	#102×C₇₁	C₂³	1	2	yes	—
263	#102×C₇₁	C₂³	1	2	yes	—
264	#102×C₇₁	C₂³	1	2	yes	—
265	#102×C₇₁	C₂³	1	2	yes	—
266	#102×C₇₁	C₂³	1	2	yes	—
267	#102×C₇₁	C₂³	1	2	yes	—
268	#102×C₇₁	C₂³	1	2	yes	—
269	#102×C₇₁	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
273	#97×C₇₁	C₂³	1	2	yes	—
274	#97×C₇₁	C₂³	1	1	yes	characteristic
275	#97×C₇₁	C₂³	1	1	yes	characteristic
276	#97×C₇₁	C₂³	1	2	yes	—
277	#97×C₇₁	C₂³	1	2	yes	—
278	C₄×C₈×C₇₁	C₂³	1	2	yes	—
279	C₄×C₈×C₇₁	C₂³	1	2	yes	—
280	C₂⁴×C₇₁	—	2	1	no	—
281	#41×C₇₁	—	4	2	no	—
282	#41×C₇₁	—	4	2	no	—
283	#41×C₇₁	—	8	2	no	—
284	#41×C₇₁	—	8	4	no	—
285	#41×C₇₁	—	8	2	no	—
286	C₂×Q₈×C₇₁	—	2	1	no	—
287	C₂×Q₈×C₇₁	—	2	2	no	—
288	C₂×Q₈×C₇₁	—	8	2	no	—
289	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
290	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₇₁	—	2	2	no	—
295	C₂×D₄×C₇₁	—	2	1	no	—
296	C₂×D₄×C₇₁	—	2	2	no	—
297	C₂×D₄×C₇₁	—	2	1	no	—
298	C₂×D₄×C₇₁	—	2	1	no	—
299	C₂×D₄×C₇₁	—	2	1	no	—
300	C₂×D₄×C₇₁	—	2	2	no	—
301	C₂×D₄×C₇₁	—	2	2	no	—
302	C₂×D₄×C₇₁	—	2	1	no	—
303	C₂×D₄×C₇₁	—	2	1	no	—
304	C₂×D₄×C₇₁	—	2	2	no	—
305	C₂×D₄×C₇₁	—	2	2	no	—
306	C₂×D₄×C₇₁	—	2	2	no	—
307	C₂×D₄×C₇₁	—	2	2	no	—
308	C₂×D₄×C₇₁	—	4	2	no	—
309	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
310	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
311	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
312	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇₁	—	2	1	no	—
314	C₂²×C₄×C₇₁	—	2	2	no	—
315	C₂²×C₄×C₇₁	—	2	2	no	—
316	C₂²×C₄×C₇₁	—	2	1	no	—
317	C₂²×C₄×C₇₁	—	2	2	no	—
318	C₂²×C₄×C₇₁	—	2	2	no	—
319	C₂²×C₄×C₇₁	—	2	2	no	—
320	C₂²×C₄×C₇₁	—	2	2	no	—
321	C₂²×C₄×C₇₁	—	2	2	no	—
322	C₂²×C₄×C₇₁	—	2	2	no	—
323	C₂²×C₄×C₇₁	—	2	2	no	—
324	C₂²×C₄×C₇₁	—	8	2	no	—
325	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
328	Q₁₆×C₇₁	—	4	2	no	—
329	SD₁₆×C₇₁	—	4	2	no	—
330	SD₁₆×C₇₁	—	4	2	no	—
331	SD₁₆×C₇₁	—	4	2	no	—
332	SD₁₆×C₇₁	—	4	2	no	—
333	SD₁₆×C₇₁	—	4	2	no	—
334	D₈×C₇₁	—	4	2	no	—
335	D₈×C₇₁	—	4	2	no	—
336	D₈×C₇₁	—	4	2	no	—
337	D₈×C₇₁	—	4	2	no	—
338	D₈×C₇₁	—	4	2	no	—
339	D₈×C₇₁	—	4	2	no	—
340	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
341	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
342	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
343	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₇₁	—	2	1	no	—
345	C₄⋊C₄×C₇₁	—	2	1	no	—
346	C₄⋊C₄×C₇₁	—	2	2	no	—
347	C₄⋊C₄×C₇₁	—	2	2	no	—
348	C₄⋊C₄×C₇₁	—	2	2	no	—
349	C₄⋊C₄×C₇₁	—	2	2	no	—
350	C₄⋊C₄×C₇₁	—	2	1	no	—
351	C₄⋊C₄×C₇₁	—	2	1	no	—
352	C₄⋊C₄×C₇₁	—	2	1	no	—
353	C₄⋊C₄×C₇₁	—	2	1	no	—
354	C₄⋊C₄×C₇₁	—	2	1	no	—
355	C₄⋊C₄×C₇₁	—	2	2	no	—
356	C₄⋊C₄×C₇₁	—	2	2	no	—
357	C₄⋊C₄×C₇₁	—	2	1	no	—
358	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
371	C₂²⋊C₄×C₇₁	—	2	1	no	—
372	C₂²⋊C₄×C₇₁	—	2	2	no	—
373	C₂²⋊C₄×C₇₁	—	2	2	no	—
374	C₂²⋊C₄×C₇₁	—	2	2	no	—
375	C₂²⋊C₄×C₇₁	—	2	2	no	—
376	C₂²⋊C₄×C₇₁	—	2	2	no	—
377	C₂²⋊C₄×C₇₁	—	2	2	no	—
378	C₂²⋊C₄×C₇₁	—	2	1	no	—
379	C₂²⋊C₄×C₇₁	—	2	1	no	—
380	C₂²⋊C₄×C₇₁	—	2	2	no	—
381	C₂²⋊C₄×C₇₁	—	2	1	no	—
382	C₂²⋊C₄×C₇₁	—	2	2	no	—
383	C₂²⋊C₄×C₇₁	—	2	2	no	—
384	C₂²⋊C₄×C₇₁	—	2	2	no	—
385	C₂²⋊C₄×C₇₁	—	2	2	no	—
386	C₂²⋊C₄×C₇₁	—	2	2	no	—
387	C₂²⋊C₄×C₇₁	—	2	2	no	—
388	C₂²⋊C₄×C₇₁	—	2	1	no	—
389	C₂²⋊C₄×C₇₁	—	2	2	no	—
390	C₂²⋊C₄×C₇₁	—	2	2	no	—
391	C₂²⋊C₄×C₇₁	—	2	2	no	—
392	C₂²⋊C₄×C₇₁	—	2	2	no	—
393	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
395	C₄²×C₇₁	—	2	2	no	—
396	C₄²×C₇₁	—	2	2	no	—
397	C₄²×C₇₁	—	2	1	no	—
398	C₄²×C₇₁	—	2	2	no	—
399	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₇₁	C₂⁴	1	2	yes	—
402	C₄²×C₇₁	C₂⁴	1	2	yes	—
403	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
404	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
405	C₂³×C₇₁	—	2	1	no	—
406	C₂³×C₇₁	—	2	2	no	—
407	C₂³×C₇₁	—	2	2	no	—
408	C₂³×C₇₁	—	2	2	no	—
409	C₂³×C₇₁	—	4	2	no	—
410	C₂³×C₇₁	—	8	1	no	—
411	C₂³×C₇₁	—	8	1	no	—
412	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
413	Q₈×C₇₁	—	2	2	no	—
414	Q₈×C₇₁	—	2	2	no	—
415	Q₈×C₇₁	—	2	2	no	—
416	Q₈×C₇₁	—	4	1	no	—
417	Q₈×C₇₁	—	4	2	no	—
418	Q₈×C₇₁	—	4	1	no	—
419	Q₈×C₇₁	—	4	2	no	—
420	Q₈×C₇₁	—	8	2	no	—
421	D₄×C₇₁	—	2	2	no	—
422	D₄×C₇₁	—	2	2	no	—
423	D₄×C₇₁	—	2	2	no	—
424	D₄×C₇₁	—	2	2	no	—
425	D₄×C₇₁	—	2	2	no	—
426	D₄×C₇₁	—	2	2	no	—
427	D₄×C₇₁	—	2	2	no	—
428	D₄×C₇₁	—	4	2	no	—
429	D₄×C₇₁	—	4	2	no	—
430	D₄×C₇₁	—	4	2	no	—
431	D₄×C₇₁	—	4	4	no	—
432	D₄×C₇₁	—	8	1	no	—
433	D₄×C₇₁	—	8	1	no	—
434	D₄×C₇₁	—	8	2	no	—
435	D₄×C₇₁	—	8	2	no	—
436	D₄×C₇₁	—	8	2	no	—
437	D₄×C₇₁	—	8	2	no	—
438	D₄×C₇₁	—	8	2	no	—
439	D₄×C₇₁	—	8	2	no	—
440	D₄×C₇₁	—	8	1	no	—
441	D₄×C₇₁	—	8	2	no	—
442	C₂×C₄×C₇₁	—	2	2	no	—
443	C₂×C₄×C₇₁	—	2	1	no	—
444	C₂×C₄×C₇₁	—	2	2	no	—
445	C₂×C₄×C₇₁	—	2	2	no	—
446	C₂×C₄×C₇₁	—	2	1	no	—
447	C₂×C₄×C₇₁	—	2	2	no	—
448	C₂×C₄×C₇₁	—	2	1	no	—
449	C₂×C₄×C₇₁	—	4	1	no	—
450	C₂×C₄×C₇₁	—	4	1	no	—
451	C₂×C₄×C₇₁	—	4	4	no	—
452	C₂×C₄×C₇₁	—	4	2	no	—
453	C₂×C₄×C₇₁	—	4	4	no	—
454	C₂×C₄×C₇₁	—	8	2	no	—
455	C₂×C₄×C₇₁	—	8	2	no	—
456	C₂×C₄×C₇₁	—	8	2	no	—
457	C₂×C₄×C₇₁	—	8	2	no	—
458	C₂×C₄×C₇₁	—	8	2	no	—
459	C₂×C₄×C₇₁	—	8	2	no	—
460	C₂×C₄×C₇₁	—	8	2	no	—
461	C₂×C₄×C₇₁	—	8	1	no	—
462	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
472	C₈×C₇₁	—	2	2	no	—
473	C₈×C₇₁	—	2	2	no	—
474	C₈×C₇₁	—	2	2	no	—
475	C₈×C₇₁	—	2	2	no	—
476	C₂²×C₇₁	—	2	1	no	—
477	C₂²×C₇₁	—	2	1	no	—
478	C₂²×C₇₁	—	2	1	no	—
479	C₂²×C₇₁	—	4	1	no	—
480	C₂²×C₇₁	—	4	2	no	—
481	C₂²×C₇₁	—	4	2	no	—
482	C₂²×C₇₁	—	4	2	no	—
483	C₂²×C₇₁	—	4	2	no	—
484	C₂²×C₇₁	—	4	2	no	—
485	C₂²×C₇₁	—	4	1	no	—
486	C₂²×C₇₁	—	4	2	no	—
487	C₂²×C₇₁	—	4	2	no	—
488	C₂²×C₇₁	—	4	2	no	—
489	C₂²×C₇₁	—	4	2	no	—
490	C₂²×C₇₁	—	4	1	no	—
491	C₂²×C₇₁	—	8	4	no	—
492	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₇₁	—	2	1	no	—
494	C₄×C₇₁	—	2	1	no	—
495	C₄×C₇₁	—	2	1	no	—
496	C₄×C₇₁	—	2	1	no	—
497	C₄×C₇₁	—	2	2	no	—
498	C₄×C₇₁	—	2	2	no	—
499	C₄×C₇₁	—	2	2	no	—
500	C₄×C₇₁	—	2	2	no	—
501	C₄×C₇₁	—	2	1	no	—
502	C₄×C₇₁	—	4	2	no	—
503	C₄×C₇₁	—	4	1	no	—
504	C₄×C₇₁	—	4	1	no	—
505	C₄×C₇₁	—	4	2	no	—
506	C₄×C₇₁	—	4	2	no	—
507	C₄×C₇₁	—	4	1	no	—
508	C₄×C₇₁	#585	1	2	yes	—
509	#61938	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
510	C₂×C₇₁	—	4	1	no	—
511	C₂×C₇₁	—	8	1	no	—
512	C₂×C₇₁	—	8	2	no	—
513	C₂×C₇₁	—	8	2	no	—
514	C₂×C₇₁	—	8	2	no	—
515	C₂×C₇₁	#3487	1	1	yes	characteristic
516	C₂×C₇₁	#3585	1	1	yes	characteristic
517	C₂×C₇₁	#3585	1	1	yes	characteristic
518	#3554	C₂×C₇₁	1	1	yes	characteristic, complemented
519	#3506	C₂×C₇₁	1	1	yes	characteristic, complemented
520	#3403	C₂×C₇₁	1	2	yes	complemented
521	#3401	C₂×C₇₁	1	2	yes	complemented
522	#3399	C₂×C₇₁	1	2	yes	complemented
523	#3399	C₂×C₇₁	1	2	yes	complemented
524	#3376	C₂×C₇₁	1	2	yes	complemented
525	#3373	C₂×C₇₁	1	2	yes	complemented
526	#3371	C₂×C₇₁	1	2	yes	complemented
527	#3366	C₂×C₇₁	1	2	yes	complemented
528	#3224	C₂×C₇₁	1	2	yes	complemented
529	#3220	C₂×C₇₁	1	2	yes	complemented
530	#3219	C₂×C₇₁	1	1	yes	characteristic, complemented
531	#3214	C₂×C₇₁	1	1	yes	characteristic, complemented
532	#3125	C₂×C₇₁	1	2	yes	complemented
533	#3119	C₂×C₇₁	1	2	yes	complemented
534	#3114	C₂×C₇₁	1	1	yes	characteristic, complemented
535	#3109	C₂×C₇₁	1	1	yes	characteristic, complemented
536	#2987	C₂×C₇₁	1	1	yes	characteristic, complemented
537	C₇₁	#61938	1	1	yes	characteristic, direct product factor, Sylow
538	#562	—	2	2	no	—
539	#559	C₂²×C₇₁	1	2	yes	—
540	#559	C₂²×C₇₁	1	2	yes	—
541	#559	C₂²×C₇₁	1	2	yes	complemented
542	#559	C₂²×C₇₁	1	1	yes	characteristic, complemented
543	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
544	#556	C₂²×C₇₁	1	2	yes	—
545	#555	—	2	1	no	—
546	#554	C₂²×C₇₁	1	2	yes	complemented
547	#553	—	2	2	no	—
548	#550	C₂²×C₇₁	1	2	yes	—
549	#550	C₂²×C₇₁	1	1	yes	characteristic, complemented
550	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
551	#548	—	2	1	no	—
552	#547	—	2	1	no	—
553	#547	—	2	1	no	—
554	#542	—	2	1	no	—
555	#542	C₂²×C₇₁	1	2	yes	—
556	#540	C₂²×C₇₁	1	2	yes	—
557	#539	—	2	2	no	—
558	#538	—	2	1	no	—
559	#538	—	2	1	no	—
560	#536	—	2	1	no	—
561	#535	C₂²×C₇₁	1	2	yes	—
562	#533	C₂²×C₇₁	1	1	yes	characteristic
563	#532	C₂²×C₇₁	1	1	yes	characteristic
564	#532	C₂²×C₇₁	1	1	yes	characteristic
565	#529	C₂²×C₇₁	1	1	yes	characteristic
566	#525	—	2	2	no	—
567	#520	C₂²×C₇₁	1	2	yes	—
568	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
569	#497	C₂²×C₇₁	1	1	yes	characteristic, complemented
570	#496	C₂²×C₇₁	1	2	yes	—
571	#496	C₂²×C₇₁	1	2	yes	—
572	#496	C₂²×C₇₁	1	1	yes	characteristic, complemented
573	#496	C₂²×C₇₁	1	2	yes	complemented
574	#495	C₂²×C₇₁	1	2	yes	—
575	#493	C₂²×C₇₁	1	2	yes	—
576	#491	C₂²×C₇₁	1	1	yes	characteristic, complemented
577	#490	C₂²×C₇₁	1	2	yes	—
578	#490	C₂²×C₇₁	1	1	yes	characteristic, complemented
579	#489	C₂²×C₇₁	1	2	yes	—
580	#489	C₂²×C₇₁	1	2	yes	complemented
581	#488	C₂²×C₇₁	1	2	yes	—
582	#486	C₂²×C₇₁	1	2	yes	—
583	#483	C₂²×C₇₁	1	1	yes	characteristic
584	#481	C₂²×C₇₁	1	2	yes	—
585	#480	C₂²×C₇₁	1	1	yes	characteristic
586	#479	C₂²×C₇₁	1	2	yes	complemented
587	#478	C₂²×C₇₁	1	2	yes	—
588	#478	C₂²×C₇₁	1	2	yes	complemented
589	#476	C₂²×C₇₁	1	2	yes	—
590	#476	C₂²×C₇₁	1	2	yes	complemented
591	#475	C₂²×C₇₁	1	2	yes	complemented
592	#464	C₂²×C₇₁	1	2	yes	—
593	#464	C₂²×C₇₁	1	2	yes	complemented
594	#464	C₂²×C₇₁	1	2	yes	complemented
595	#463	C₂²×C₇₁	1	2	yes	—
596	#463	C₂²×C₇₁	1	2	yes	—
597	#463	C₂²×C₇₁	1	2	yes	—
598	#463	C₂²×C₇₁	1	2	yes	—
599	#463	C₂²×C₇₁	1	2	yes	complemented
600	#463	C₂²×C₇₁	1	2	yes	complemented
601	#461	C₂²×C₇₁	1	2	yes	complemented
602	#460	C₂²×C₇₁	1	2	yes	—
603	#460	C₂²×C₇₁	1	2	yes	complemented
604	#459	C₂²×C₇₁	1	2	yes	—
605	#459	C₂²×C₇₁	1	2	yes	—
606	#459	C₂²×C₇₁	1	2	yes	—
607	#459	C₂²×C₇₁	1	2	yes	—
608	#459	C₂²×C₇₁	1	2	yes	complemented
609	#459	C₂²×C₇₁	1	2	yes	complemented
610	#452	C₂²×C₇₁	1	2	yes	—
611	#450	C₂²×C₇₁	1	1	yes	characteristic
612	#449	C₂²×C₇₁	1	2	yes	—
613	#449	C₂²×C₇₁	1	2	yes	—
614	#449	C₂²×C₇₁	1	2	yes	—
615	#447	C₂²×C₇₁	1	2	yes	—
616	#447	C₂²×C₇₁	1	1	yes	characteristic
617	#446	C₂²×C₇₁	1	2	yes	complemented
618	#446	C₂²×C₇₁	1	2	yes	complemented
619	#446	C₂²×C₇₁	1	2	yes	complemented
620	#446	C₂²×C₇₁	1	2	yes	complemented
621	#442	C₂²×C₇₁	1	2	yes	—
622	#442	C₂²×C₇₁	1	2	yes	—
623	#442	C₂²×C₇₁	1	2	yes	—
624	#442	C₂²×C₇₁	1	2	yes	complemented
625	#442	C₂²×C₇₁	1	2	yes	complemented
626	#441	C₂²×C₇₁	1	2	yes	complemented
627	#440	C₂²×C₇₁	1	2	yes	—
628	#440	C₂²×C₇₁	1	2	yes	complemented
629	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
630	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
631	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
632	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
633	#433	C₂²×C₇₁	1	2	yes	—
634	#433	C₂²×C₇₁	1	2	yes	—
635	#432	C₂²×C₇₁	1	1	yes	characteristic
636	#432	C₂²×C₇₁	1	1	yes	characteristic
637	C₂×#41	—	2	2	no	—
638	C₂×#41	—	2	1	no	—
639	C₂×#41	—	2	1	no	—
640	C₂×#41	C₂³×C₇₁	1	2	yes	—
641	C₂²×Q₈	—	2	1	no	—
642	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
643	C₂³×C₄	—	2	1	no	—
644	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
645	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
646	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
647	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
649	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
650	C₂×D₈	C₂³×C₇₁	1	2	yes	—
651	C₂×D₈	C₂³×C₇₁	1	2	yes	—
652	C₂×D₈	C₂³×C₇₁	1	2	yes	—
653	C₂×D₈	C₂³×C₇₁	1	2	yes	—
654	C₂×D₈	C₂³×C₇₁	1	2	yes	—
655	C₂×D₈	C₂³×C₇₁	1	2	yes	—
656	C₄⋊Q₈	—	2	1	no	—
657	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
658	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
659	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
660	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
661	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
662	#127	C₂³×C₇₁	1	1	yes	characteristic
663	#127	C₂³×C₇₁	1	1	yes	characteristic
664	#127	C₂³×C₇₁	1	2	yes	—
665	#127	C₂³×C₇₁	1	2	yes	—
666	#127	C₂³×C₇₁	1	2	yes	—
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	—	2	2	no	—
670	#126	—	2	1	no	—
671	#125	—	2	2	no	—
672	#125	D₄×C₇₁	1	2	yes	—
673	#125	C₂³×C₇₁	1	1	yes	characteristic
674	#125	C₂³×C₇₁	1	2	yes	—
675	#124	—	2	1	no	—
676	#124	—	2	2	no	—
677	#124	—	2	2	no	—
678	#124	—	2	2	no	—
679	#124	—	2	2	no	—
680	#124	—	2	1	no	—
681	#124	C₂³×C₇₁	1	1	yes	characteristic
682	#124	C₂³×C₇₁	1	2	yes	—
683	#124	C₂³×C₇₁	1	2	yes	—
684	#124	C₂³×C₇₁	1	2	yes	—
685	#124	C₂³×C₇₁	1	2	yes	—
686	#123	—	2	1	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	1	no	—
704	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
705	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
706	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
707	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
708	#121	—	2	1	no	—
709	#121	—	2	1	no	—
710	#121	—	2	1	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	1	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	C₂³×C₇₁	1	1	yes	characteristic
721	#121	C₂³×C₇₁	1	2	yes	—
722	#120	—	2	2	no	—
723	#120	—	2	2	no	—
724	C₄×Q₈	—	2	1	no	—
725	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
726	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
727	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
728	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
729	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
730	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
731	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	1	no	—
740	C₄×D₄	—	2	1	no	—
741	C₄×D₄	—	2	1	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	C₂³×C₇₁	1	2	yes	—
745	C₄×D₄	C₂³×C₇₁	1	2	yes	—
746	C₄×D₄	C₂³×C₇₁	1	2	yes	—
747	C₄×D₄	C₂³×C₇₁	1	2	yes	—
748	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
749	C₄×D₄	C₂³×C₇₁	1	2	yes	—
750	C₄×D₄	C₂³×C₇₁	1	2	yes	—
751	C₄×D₄	C₂³×C₇₁	1	2	yes	—
752	C₄×D₄	C₂³×C₇₁	1	2	yes	—
753	#117	—	2	2	no	—
754	#117	—	2	2	no	—
755	#117	—	2	1	no	—
756	#117	C₂³×C₇₁	1	2	yes	—
757	C₂×C₄⋊C₄	—	2	2	no	—
758	C₂×C₄⋊C₄	—	2	2	no	—
759	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	—	2	1	no	—
761	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
762	#107	C₂³×C₇₁	1	2	yes	—
763	#106	C₂³×C₇₁	1	2	yes	—
764	#106	C₂³×C₇₁	1	2	yes	—
765	#106	C₂³×C₇₁	1	2	yes	—
766	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
767	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
768	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
769	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
770	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
771	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
772	#103	C₂³×C₇₁	1	2	yes	—
773	#103	C₂³×C₇₁	1	2	yes	—
774	#103	C₂³×C₇₁	1	2	yes	—
775	#103	C₂³×C₇₁	1	2	yes	—
776	#103	C₂³×C₇₁	1	2	yes	—
777	#102	C₂³×C₇₁	1	2	yes	—
778	#102	C₂³×C₇₁	1	2	yes	—
779	#102	C₂³×C₇₁	1	2	yes	—
780	#102	C₂³×C₇₁	1	2	yes	—
781	#102	C₂³×C₇₁	1	2	yes	—
782	#102	C₂³×C₇₁	1	2	yes	—
783	#102	C₂³×C₇₁	1	2	yes	—
784	#102	C₂³×C₇₁	1	2	yes	—
785	#102	C₂³×C₇₁	1	2	yes	—
786	#102	C₂³×C₇₁	1	2	yes	—
787	#102	C₂³×C₇₁	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
789	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
791	#97	C₂³×C₇₁	1	2	yes	—
792	#97	C₂³×C₇₁	1	1	yes	characteristic
793	#97	C₂³×C₇₁	1	1	yes	characteristic
794	#97	C₂³×C₇₁	1	2	yes	—
795	#97	C₂³×C₇₁	1	2	yes	—
796	C₄×C₈	C₂³×C₇₁	1	2	yes	—
797	C₄×C₈	C₂³×C₇₁	1	2	yes	—
798	C₂⁴	—	2	1	no	—
799	#41	—	4	2	no	—
800	#41	—	4	2	no	—
801	#41	—	8	2	no	—
802	#41	—	8	4	no	—
803	#41	—	8	2	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	8	2	no	—
807	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
808	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
809	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
810	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
811	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
828	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
829	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
830	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	8	2	no	—
843	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
844	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
846	Q₁₆	—	4	2	no	—
847	SD₁₆	—	4	2	no	—
848	SD₁₆	—	4	2	no	—
849	SD₁₆	—	4	2	no	—
850	SD₁₆	—	4	2	no	—
851	SD₁₆	—	4	2	no	—
852	D₈	—	4	2	no	—
853	D₈	—	4	2	no	—
854	D₈	—	4	2	no	—
855	D₈	—	4	2	no	—
856	D₈	—	4	2	no	—
857	D₈	—	4	2	no	—
858	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
859	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
860	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
861	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
878	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
881	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
882	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
883	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
884	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
887	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
888	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	1	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	1	no	—
916	C₄²	—	2	2	no	—
917	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
918	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
919	C₄²	C₂⁴×C₇₁	1	2	yes	—
920	C₄²	C₂⁴×C₇₁	1	2	yes	—
921	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
922	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	8	1	no	—
929	C₂³	—	8	1	no	—
930	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	4	1	no	—
935	Q₈	—	4	2	no	—
936	Q₈	—	4	1	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	8	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	2	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	4	no	—
950	D₄	—	8	2	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	1	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	D₄	—	8	2	no	—
959	D₄	—	8	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	2	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	1	no	—
980	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
983	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
984	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
989	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
990	C₈	—	2	2	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	8	4	no	—
1010	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	#585×C₇₁	1	2	yes	—
1027	C₂	—	4	1	no	—
1028	C₂	—	8	2	no	—
1029	C₂	—	8	1	no	—
1030	C₂	—	8	2	no	—
1031	C₂	—	8	2	no	—
1032	C₂	C₇₁×#3487	1	1	yes	characteristic
1033	C₂	C₇₁×#3585	1	1	yes	characteristic
1034	C₂	C₇₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ #533×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3554	C₂	semidirect
2. C₇₁×#3506	C₂	semidirect
3. C₇₁×#3403	C₂	semidirect
4. C₇₁×#3401	C₂	semidirect
5. C₇₁×#3399	C₂	semidirect
6. C₇₁×#3399	C₂	semidirect
7. C₇₁×#3376	C₂	semidirect
8. C₇₁×#3373	C₂	semidirect
9. C₇₁×#3371	C₂	semidirect
10. C₇₁×#3366	C₂	semidirect
11. C₇₁×#3224	C₂	semidirect
12. C₇₁×#3220	C₂	semidirect
13. C₇₁×#3219	C₂	semidirect
14. C₇₁×#3214	C₂	semidirect
15. C₇₁×#3125	C₂	semidirect
16. C₇₁×#3119	C₂	semidirect
17. C₇₁×#3114	C₂	semidirect
18. C₇₁×#3109	C₂	semidirect
19. C₇₁×#2987	C₂	semidirect
23. #559×C₇₁	C₂²	semidirect
24. #559×C₇₁	C₂²	semidirect
25. #557×C₇₁	C₂²	semidirect
28. #554×C₇₁	C₂²	semidirect
31. #550×C₇₁	C₂²	semidirect
32. D₄×Q₈×C₇₁	C₂²	semidirect
51. #497×C₇₁	C₂²	semidirect
54. #496×C₇₁	C₂²	semidirect
55. #496×C₇₁	C₂²	semidirect
58. #491×C₇₁	C₂²	semidirect
60. #490×C₇₁	C₂²	semidirect
62. #489×C₇₁	C₂²	semidirect
68. #479×C₇₁	C₂²	semidirect
70. #478×C₇₁	C₂²	semidirect
72. #476×C₇₁	C₂²	semidirect
73. #475×C₇₁	C₂²	semidirect
75. #464×C₇₁	C₂²	semidirect
76. #464×C₇₁	C₂²	semidirect
81. #463×C₇₁	C₂²	semidirect
82. #463×C₇₁	C₂²	semidirect
83. #461×C₇₁	C₂²	semidirect
85. #460×C₇₁	C₂²	semidirect
90. #459×C₇₁	C₂²	semidirect
91. #459×C₇₁	C₂²	semidirect
99. #446×C₇₁	C₂²	semidirect
100. #446×C₇₁	C₂²	semidirect
101. #446×C₇₁	C₂²	semidirect
102. #446×C₇₁	C₂²	semidirect
106. #442×C₇₁	C₂²	semidirect
107. #442×C₇₁	C₂²	semidirect
108. #441×C₇₁	C₂²	semidirect
110. #440×C₇₁	C₂²	semidirect
111. C₄×SD₁₆×C₇₁	C₂²	semidirect
112. C₄×SD₁₆×C₇₁	C₂²	semidirect
113. C₄×SD₁₆×C₇₁	C₂²	semidirect
114. C₄×D₈×C₇₁	C₂²	semidirect
509. #61938	C₇₁	direct (N × H)
518. #3554	C₂×C₇₁	semidirect
519. #3506	C₂×C₇₁	semidirect
520. #3403	C₂×C₇₁	semidirect
521. #3401	C₂×C₇₁	semidirect
522. #3399	C₂×C₇₁	semidirect
523. #3399	C₂×C₇₁	semidirect
524. #3376	C₂×C₇₁	semidirect
525. #3373	C₂×C₇₁	semidirect
526. #3371	C₂×C₇₁	semidirect
527. #3366	C₂×C₇₁	semidirect
528. #3224	C₂×C₇₁	semidirect
529. #3220	C₂×C₇₁	semidirect
530. #3219	C₂×C₇₁	semidirect
531. #3214	C₂×C₇₁	semidirect
532. #3125	C₂×C₇₁	semidirect
533. #3119	C₂×C₇₁	semidirect
534. #3114	C₂×C₇₁	semidirect
535. #3109	C₂×C₇₁	semidirect
536. #2987	C₂×C₇₁	semidirect
537. C₇₁	#61938	direct (N × H)
541. #559	C₂²×C₇₁	semidirect
542. #559	C₂²×C₇₁	semidirect
543. #557	C₂²×C₇₁	semidirect
546. #554	C₂²×C₇₁	semidirect
549. #550	C₂²×C₇₁	semidirect
550. D₄×Q₈	C₂²×C₇₁	semidirect
569. #497	C₂²×C₇₁	semidirect
572. #496	C₂²×C₇₁	semidirect
573. #496	C₂²×C₇₁	semidirect
576. #491	C₂²×C₇₁	semidirect
578. #490	C₂²×C₇₁	semidirect
580. #489	C₂²×C₇₁	semidirect
586. #479	C₂²×C₇₁	semidirect
588. #478	C₂²×C₇₁	semidirect
590. #476	C₂²×C₇₁	semidirect
591. #475	C₂²×C₇₁	semidirect
593. #464	C₂²×C₇₁	semidirect
594. #464	C₂²×C₇₁	semidirect
599. #463	C₂²×C₇₁	semidirect
600. #463	C₂²×C₇₁	semidirect
601. #461	C₂²×C₇₁	semidirect
603. #460	C₂²×C₇₁	semidirect
608. #459	C₂²×C₇₁	semidirect
609. #459	C₂²×C₇₁	semidirect
617. #446	C₂²×C₇₁	semidirect
618. #446	C₂²×C₇₁	semidirect
619. #446	C₂²×C₇₁	semidirect
620. #446	C₂²×C₇₁	semidirect
624. #442	C₂²×C₇₁	semidirect
625. #442	C₂²×C₇₁	semidirect
626. #441	C₂²×C₇₁	semidirect
628. #440	C₂²×C₇₁	semidirect
629. C₄×SD₁₆	C₂²×C₇₁	semidirect
630. C₄×SD₁₆	C₂²×C₇₁	semidirect
631. C₄×SD₁₆	C₂²×C₇₁	semidirect
632. C₄×D₈	C₂²×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3554	2
C₇₁×#3506	2
C₇₁×#3403	2
C₇₁×#3401	2
C₇₁×#3399	2
C₇₁×#3376	2
C₇₁×#3373	2
C₇₁×#3371	2
C₇₁×#3366	2
C₇₁×#3224	2
C₇₁×#3220	2
C₇₁×#3219	2
C₇₁×#3214	2
C₇₁×#3125	2
C₇₁×#3119	2
C₇₁×#3114	2
C₇₁×#3109	2
C₇₁×#2987	2
#61938	71

Subgroups — C71×#61938 #31882810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61938 #31882810