Subgroups — C₇₁×#60960 #31881832

Order 18176.

1814 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#3248	C₂	1	4	yes	maximal, complemented
4	C₇₁×#3239	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3236	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3218	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3215	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3189	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3187	C₂	1	2	yes	maximal
10	C₇₁×#3181	C₂	1	4	yes	maximal, complemented
11	C₇₁×#3117	C₂	1	4	yes	maximal, complemented
12	C₇₁×#3113	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3110	C₂	1	2	yes	maximal, complemented
14	C₂×#432×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#533×C₇₁	—	2	1	no	—
16	#533×C₇₁	—	2	1	no	—
17	#533×C₇₁	—	2	1	no	—
18	#533×C₇₁	—	2	1	no	—
19	#533×C₇₁	C₂²	1	2	yes	—
20	#533×C₇₁	C₂²	1	2	yes	—
21	#533×C₇₁	C₂²	1	2	yes	complemented
22	#533×C₇₁	C₂²	1	2	yes	complemented
23	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
25	#529×C₇₁	—	2	1	no	—
26	#529×C₇₁	—	2	1	no	—
27	#529×C₇₁	—	2	1	no	—
28	#529×C₇₁	—	2	1	no	—
29	#529×C₇₁	C₂²	1	2	yes	—
30	#529×C₇₁	C₂²	1	2	yes	—
31	#529×C₇₁	C₂²	1	2	yes	—
32	#529×C₇₁	C₂²	1	2	yes	—
33	C₂×#126×C₇₁	—	2	1	no	—
34	C₂×#125×C₇₁	—	2	1	no	—
35	C₂×#125×C₇₁	C₂²	1	1	yes	characteristic
36	C₂×#124×C₇₁	C₂²	1	1	yes	characteristic
37	C₂×#123×C₇₁	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₇₁	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
41	C₂×#121×C₇₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₇₁	—	2	1	no	—
43	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₇₁	—	2	1	no	—
46	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
47	C₂×#117×C₇₁	—	2	1	no	—
48	C₂×#117×C₇₁	—	2	1	no	—
49	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
50	#501×C₇₁	C₂²	1	4	yes	complemented
51	#497×C₇₁	C₂²	1	4	yes	complemented
52	#491×C₇₁	C₂²	1	4	yes	complemented
53	#489×C₇₁	C₂²	1	4	yes	complemented
54	#484×C₇₁	C₂²	1	4	yes	—
55	#484×C₇₁	C₂²	1	4	yes	complemented
56	#483×C₇₁	C₂²	1	4	yes	—
57	#481×C₇₁	C₂²	1	4	yes	—
58	#479×C₇₁	C₂²	1	8	yes	complemented
59	#475×C₇₁	C₂²	1	4	yes	complemented
60	#474×C₇₁	C₂²	1	4	yes	complemented
61	#467×C₇₁	C₂²	1	8	yes	complemented
62	#465×C₇₁	C₂²	1	8	yes	—
63	#464×C₇₁	C₂²	1	8	yes	complemented
64	#462×C₇₁	C₂²	1	4	yes	complemented
65	#461×C₇₁	C₂²	1	4	yes	complemented
66	#451×C₇₁	C₂²	1	4	yes	—
67	#451×C₇₁	C₂²	1	4	yes	complemented
68	#450×C₇₁	C₂²	1	4	yes	—
69	#448×C₇₁	C₂²	1	4	yes	—
70	#441×C₇₁	C₂²	1	8	yes	complemented
71	#440×C₇₁	C₂²	1	8	yes	complemented
72	#432×C₇₁	C₂²	1	2	yes	—
73	#432×C₇₁	C₂²	1	2	yes	—
74	#432×C₇₁	C₂²	1	2	yes	complemented
75	#432×C₇₁	C₂²	1	2	yes	complemented
76	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	complemented
77	C₂×C₂²⋊C₈×C₇₁	C₂²	1	2	yes	—
78	C₂×#97×C₇₁	C₂²	1	2	yes	complemented
79	C₂²×Q₈×C₇₁	—	2	1	no	—
80	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
81	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₇₁	—	2	1	no	—
83	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇₁	—	2	1	no	—
85	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
88	C₂×Q₁₆×C₇₁	C₂³	1	8	yes	—
89	C₂×SD₁₆×C₇₁	C₂³	1	8	yes	—
90	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
91	C₄⋊Q₈×C₇₁	—	2	1	no	—
92	C₄⋊Q₈×C₇₁	—	2	1	no	—
93	C₄⋊Q₈×C₇₁	—	2	1	no	—
94	C₄⋊Q₈×C₇₁	—	2	1	no	—
95	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
99	#126×C₇₁	—	2	2	no	—
100	#126×C₇₁	—	2	2	no	—
101	#126×C₇₁	—	2	2	no	—
102	#126×C₇₁	—	2	2	no	—
103	#125×C₇₁	—	2	2	no	—
104	#125×C₇₁	—	2	2	no	—
105	#125×C₇₁	—	2	2	no	—
106	#125×C₇₁	—	2	2	no	—
107	#125×C₇₁	—	2	1	no	—
108	#125×C₇₁	—	2	1	no	—
109	#125×C₇₁	C₂³	1	2	yes	—
110	#125×C₇₁	C₂³	1	2	yes	—
111	#124×C₇₁	—	2	1	no	—
112	#124×C₇₁	—	2	1	no	—
113	#124×C₇₁	C₂³	1	2	yes	—
114	#124×C₇₁	C₂³	1	2	yes	—
115	#123×C₇₁	—	2	2	no	—
116	#123×C₇₁	—	2	2	no	—
117	#123×C₇₁	—	2	2	no	—
118	#123×C₇₁	—	2	2	no	—
119	C₂²⋊Q₈×C₇₁	—	2	2	no	—
120	C₂²⋊Q₈×C₇₁	—	2	2	no	—
121	C₂²⋊Q₈×C₇₁	—	2	2	no	—
122	C₂²⋊Q₈×C₇₁	—	2	2	no	—
123	C₂²⋊Q₈×C₇₁	—	2	1	no	—
124	C₂²⋊Q₈×C₇₁	—	2	1	no	—
125	C₂²⋊Q₈×C₇₁	—	2	2	no	—
126	C₂²⋊Q₈×C₇₁	—	2	2	no	—
127	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
128	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
129	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
130	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
131	#121×C₇₁	—	2	1	no	—
132	#121×C₇₁	—	2	1	no	—
133	#121×C₇₁	C₂³	1	2	yes	—
134	#121×C₇₁	C₂³	1	2	yes	—
135	C₄×Q₈×C₇₁	—	2	2	no	—
136	C₄×Q₈×C₇₁	—	2	2	no	—
137	C₄×Q₈×C₇₁	—	2	2	no	—
138	C₄×Q₈×C₇₁	—	2	2	no	—
139	C₄×Q₈×C₇₁	—	2	1	no	—
140	C₄×Q₈×C₇₁	—	2	1	no	—
141	C₄×Q₈×C₇₁	—	2	2	no	—
142	C₄×Q₈×C₇₁	—	2	2	no	—
143	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
144	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
145	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
146	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
147	C₄×D₄×C₇₁	—	2	2	no	—
148	C₄×D₄×C₇₁	—	2	2	no	—
149	C₄×D₄×C₇₁	—	2	2	no	—
150	C₄×D₄×C₇₁	—	2	2	no	—
151	C₄×D₄×C₇₁	—	2	1	no	—
152	C₄×D₄×C₇₁	—	2	1	no	—
153	C₄×D₄×C₇₁	C₂³	1	2	yes	—
154	C₄×D₄×C₇₁	C₂³	1	2	yes	—
155	#117×C₇₁	—	2	2	no	—
156	#117×C₇₁	—	2	2	no	—
157	#117×C₇₁	—	2	2	no	—
158	#117×C₇₁	—	2	2	no	—
159	#117×C₇₁	—	2	2	no	—
160	#117×C₇₁	—	2	2	no	—
161	#117×C₇₁	—	2	2	no	—
162	#117×C₇₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
164	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
165	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
166	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
167	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
172	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
176	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
181	C₂×C₄²×C₇₁	—	2	1	no	—
182	C₂×C₄²×C₇₁	—	2	2	no	—
183	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
195	#107×C₇₁	C₂³	1	8	yes	—
196	#106×C₇₁	C₂³	1	8	yes	—
197	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
198	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
199	#103×C₇₁	C₂³	1	8	yes	—
200	#103×C₇₁	C₂³	1	8	yes	—
201	#103×C₇₁	C₂³	1	8	yes	—
202	#102×C₇₁	C₂³	1	8	yes	—
203	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
204	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
205	#97×C₇₁	C₂³	1	4	yes	—
206	#97×C₇₁	C₂³	1	4	yes	—
207	C₂⁴×C₇₁	—	2	1	no	—
208	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₇₁	—	2	1	no	—
210	C₂×Q₈×C₇₁	—	2	2	no	—
211	C₂×Q₈×C₇₁	—	2	2	no	—
212	C₂×Q₈×C₇₁	—	2	2	no	—
213	C₂×Q₈×C₇₁	—	4	2	no	—
214	C₂×Q₈×C₇₁	—	4	4	no	—
215	C₂×Q₈×C₇₁	—	4	4	no	—
216	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
218	C₂×D₄×C₇₁	—	2	2	no	—
219	C₂×D₄×C₇₁	—	2	2	no	—
220	C₂×D₄×C₇₁	—	2	1	no	—
221	C₂×D₄×C₇₁	—	4	2	no	—
222	C₂×D₄×C₇₁	—	4	4	no	—
223	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₇₁	—	2	4	no	—
225	C₂²×C₄×C₇₁	—	2	1	no	—
226	C₂²×C₄×C₇₁	—	2	2	no	—
227	C₂²×C₄×C₇₁	—	2	1	no	—
228	C₂²×C₄×C₇₁	—	2	2	no	—
229	C₂²×C₄×C₇₁	—	2	1	no	—
230	C₂²×C₄×C₇₁	—	2	2	no	—
231	C₂²×C₄×C₇₁	—	2	2	no	—
232	C₂²×C₄×C₇₁	—	4	2	no	—
233	C₂²×C₄×C₇₁	—	4	2	no	—
234	C₂²×C₄×C₇₁	—	4	4	no	—
235	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
253	Q₁₆×C₇₁	—	4	8	no	—
254	SD₁₆×C₇₁	—	4	8	no	—
255	C₂×C₈×C₇₁	—	4	4	no	—
256	C₂×C₈×C₇₁	C₂⁴	1	8	yes	—
257	C₄⋊C₄×C₇₁	—	2	2	no	—
258	C₄⋊C₄×C₇₁	—	2	2	no	—
259	C₄⋊C₄×C₇₁	—	2	2	no	—
260	C₄⋊C₄×C₇₁	—	2	2	no	—
261	C₄⋊C₄×C₇₁	—	2	2	no	—
262	C₄⋊C₄×C₇₁	—	2	2	no	—
263	C₄⋊C₄×C₇₁	—	2	2	no	—
264	C₄⋊C₄×C₇₁	—	2	2	no	—
265	C₄⋊C₄×C₇₁	—	2	2	no	—
266	C₄⋊C₄×C₇₁	—	2	2	no	—
267	C₄⋊C₄×C₇₁	—	2	2	no	—
268	C₄⋊C₄×C₇₁	—	2	2	no	—
269	C₄⋊C₄×C₇₁	—	2	4	no	—
270	C₄⋊C₄×C₇₁	—	2	4	no	—
271	C₄⋊C₄×C₇₁	—	2	4	no	—
272	C₄⋊C₄×C₇₁	—	2	4	no	—
273	C₄⋊C₄×C₇₁	—	2	2	no	—
274	C₄⋊C₄×C₇₁	—	2	2	no	—
275	C₄⋊C₄×C₇₁	—	2	1	no	—
276	C₄⋊C₄×C₇₁	—	2	1	no	—
277	C₄⋊C₄×C₇₁	—	2	2	no	—
278	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₇₁	—	2	4	no	—
282	C₂²⋊C₄×C₇₁	—	2	4	no	—
283	C₂²⋊C₄×C₇₁	—	2	2	no	—
284	C₂²⋊C₄×C₇₁	—	2	2	no	—
285	C₂²⋊C₄×C₇₁	—	2	2	no	—
286	C₂²⋊C₄×C₇₁	—	2	2	no	—
287	C₂²⋊C₄×C₇₁	—	2	2	no	—
288	C₂²⋊C₄×C₇₁	—	2	2	no	—
289	C₂²⋊C₄×C₇₁	—	2	2	no	—
290	C₂²⋊C₄×C₇₁	—	2	2	no	—
291	C₂²⋊C₄×C₇₁	—	2	2	no	—
292	C₂²⋊C₄×C₇₁	—	2	2	no	—
293	C₄²×C₇₁	—	2	2	no	—
294	C₄²×C₇₁	—	2	2	no	—
295	C₄²×C₇₁	—	2	4	no	—
296	C₄²×C₇₁	—	2	4	no	—
297	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
311	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
312	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
313	C₂³×C₇₁	—	2	2	no	—
314	C₂³×C₇₁	—	4	1	no	—
315	C₂³×C₇₁	—	4	1	no	—
316	C₂³×C₇₁	—	4	2	no	—
317	C₂³×C₇₁	—	4	2	no	—
318	C₂³×C₇₁	—	4	2	no	—
319	C₂³×C₇₁	#137	1	4	yes	—
320	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
322	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₇₁	—	2	8	no	—
324	Q₈×C₇₁	—	2	4	no	—
325	Q₈×C₇₁	—	4	2	no	—
326	Q₈×C₇₁	—	4	4	no	—
327	Q₈×C₇₁	—	4	4	no	—
328	Q₈×C₇₁	—	4	4	no	—
329	D₄×C₇₁	—	2	4	no	—
330	D₄×C₇₁	—	4	2	no	—
331	D₄×C₇₁	—	4	4	no	—
332	D₄×C₇₁	—	4	4	no	—
333	C₂×C₄×C₇₁	—	2	2	no	—
334	C₂×C₄×C₇₁	—	2	2	no	—
335	C₂×C₄×C₇₁	—	2	2	no	—
336	C₂×C₄×C₇₁	—	2	2	no	—
337	C₂×C₄×C₇₁	—	2	2	no	—
338	C₂×C₄×C₇₁	—	2	2	no	—
339	C₂×C₄×C₇₁	—	2	2	no	—
340	C₂×C₄×C₇₁	—	2	2	no	—
341	C₂×C₄×C₇₁	—	2	2	no	—
342	C₂×C₄×C₇₁	—	2	2	no	—
343	C₂×C₄×C₇₁	—	2	2	no	—
344	C₂×C₄×C₇₁	—	2	2	no	—
345	C₂×C₄×C₇₁	—	2	2	no	—
346	C₂×C₄×C₇₁	—	2	4	no	—
347	C₂×C₄×C₇₁	—	2	2	no	—
348	C₂×C₄×C₇₁	—	2	4	no	—
349	C₂×C₄×C₇₁	—	2	2	no	—
350	C₂×C₄×C₇₁	—	4	1	no	—
351	C₂×C₄×C₇₁	—	4	1	no	—
352	C₂×C₄×C₇₁	—	4	1	no	—
353	C₂×C₄×C₇₁	—	4	1	no	—
354	C₂×C₄×C₇₁	—	4	1	no	—
355	C₂×C₄×C₇₁	—	4	1	no	—
356	C₂×C₄×C₇₁	—	4	4	no	—
357	C₂×C₄×C₇₁	—	4	2	no	—
358	C₂×C₄×C₇₁	—	4	4	no	—
359	C₂×C₄×C₇₁	—	4	2	no	—
360	C₂×C₄×C₇₁	—	4	4	no	—
361	C₂×C₄×C₇₁	—	4	2	no	—
362	C₂×C₄×C₇₁	—	4	4	no	—
363	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
375	C₈×C₇₁	—	2	8	no	—
376	C₂²×C₇₁	—	2	1	no	—
377	C₂²×C₇₁	—	2	1	no	—
378	C₂²×C₇₁	—	2	1	no	—
379	C₂²×C₇₁	—	2	1	no	—
380	C₂²×C₇₁	—	2	1	no	—
381	C₂²×C₇₁	—	2	1	no	—
382	C₂²×C₇₁	—	4	4	no	—
383	C₂²×C₇₁	—	4	2	no	—
384	C₂²×C₇₁	—	4	2	no	—
385	C₂²×C₇₁	—	4	2	no	—
386	C₂²×C₇₁	—	8	4	no	—
387	C₂²×C₇₁	C₂×#137	1	2	yes	—
388	C₂²×C₇₁	C₂×#137	1	2	yes	—
389	C₂²×C₇₁	C₂×#137	1	2	yes	—
390	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₇₁	—	2	1	no	—
392	C₄×C₇₁	—	2	1	no	—
393	C₄×C₇₁	—	2	1	no	—
394	C₄×C₇₁	—	2	1	no	—
395	C₄×C₇₁	—	2	1	no	—
396	C₄×C₇₁	—	2	1	no	—
397	C₄×C₇₁	—	2	1	no	—
398	C₄×C₇₁	—	2	1	no	—
399	C₄×C₇₁	—	2	1	no	—
400	C₄×C₇₁	—	2	1	no	—
401	C₄×C₇₁	—	4	2	no	—
402	C₄×C₇₁	—	4	4	no	—
403	C₄×C₇₁	—	4	2	no	—
404	C₄×C₇₁	—	4	2	no	—
405	C₄×C₇₁	—	4	4	no	—
406	C₄×C₇₁	#575	1	2	yes	—
407	C₄×C₇₁	#585	1	2	yes	—
408	#60960	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₂×C₇₁	—	2	2	no	—
410	C₂×C₇₁	—	2	2	no	—
411	C₂×C₇₁	—	2	2	no	—
412	C₂×C₇₁	—	8	2	no	—
413	C₂×C₇₁	#3449	1	1	yes	characteristic
414	C₂×C₇₁	C₂²×#137	1	1	yes	characteristic
415	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
416	C₂×#533	C₂×C₇₁	1	1	yes	characteristic, complemented
417	C₂×#529	C₂×C₇₁	1	1	yes	characteristic
418	#3248	C₂×C₇₁	1	4	yes	complemented
419	#3239	C₂×C₇₁	1	2	yes	complemented
420	#3236	C₂×C₇₁	1	2	yes	complemented
421	#3218	C₂×C₇₁	1	2	yes	complemented
422	#3215	C₂×C₇₁	1	2	yes	complemented
423	#3189	C₂×C₇₁	1	2	yes	complemented
424	#3187	C₂×C₇₁	1	2	yes	—
425	#3181	C₂×C₇₁	1	4	yes	complemented
426	#3117	C₂×C₇₁	1	4	yes	complemented
427	#3113	C₂×C₇₁	1	2	yes	complemented
428	#3110	C₂×C₇₁	1	2	yes	complemented
429	C₂×#432	C₂×C₇₁	1	1	yes	characteristic, complemented
430	C₇₁	#60960	1	1	yes	characteristic, direct product factor, Sylow
431	#533	—	2	1	no	—
432	#533	—	2	1	no	—
433	#533	—	2	1	no	—
434	#533	—	2	1	no	—
435	#533	C₂²×C₇₁	1	2	yes	—
436	#533	C₂²×C₇₁	1	2	yes	—
437	#533	C₂²×C₇₁	1	2	yes	complemented
438	#533	C₂²×C₇₁	1	2	yes	complemented
439	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
440	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
441	#529	—	2	1	no	—
442	#529	—	2	1	no	—
443	#529	—	2	1	no	—
444	#529	—	2	1	no	—
445	#529	C₂²×C₇₁	1	2	yes	—
446	#529	C₂²×C₇₁	1	2	yes	—
447	#529	C₂²×C₇₁	1	2	yes	—
448	#529	C₂²×C₇₁	1	2	yes	—
449	C₂×#126	—	2	1	no	—
450	C₂×#125	—	2	1	no	—
451	C₂×#125	C₂²×C₇₁	1	1	yes	characteristic
452	C₂×#124	C₂²×C₇₁	1	1	yes	characteristic
453	C₂×#123	—	2	1	no	—
454	C₂×C₂²⋊Q₈	—	2	1	no	—
455	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
457	C₂×#121	C₂²×C₇₁	1	1	yes	characteristic
458	C₂×C₄×Q₈	—	2	1	no	—
459	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
460	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	complemented
461	C₂×C₄×D₄	—	2	1	no	—
462	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
463	C₂×#117	—	2	1	no	—
464	C₂×#117	—	2	1	no	—
465	C₂²×C₄²	C₂²×C₇₁	1	1	yes	characteristic
466	#501	C₂²×C₇₁	1	4	yes	complemented
467	#497	C₂²×C₇₁	1	4	yes	complemented
468	#491	C₂²×C₇₁	1	4	yes	complemented
469	#489	C₂²×C₇₁	1	4	yes	complemented
470	#484	C₂²×C₇₁	1	4	yes	—
471	#484	C₂²×C₇₁	1	4	yes	complemented
472	#483	C₂²×C₇₁	1	4	yes	—
473	#481	C₂²×C₇₁	1	4	yes	—
474	#479	C₂²×C₇₁	1	8	yes	complemented
475	#475	C₂²×C₇₁	1	4	yes	complemented
476	#474	C₂²×C₇₁	1	4	yes	complemented
477	#467	C₂²×C₇₁	1	8	yes	complemented
478	#465	C₂²×C₇₁	1	8	yes	—
479	#464	C₂²×C₇₁	1	8	yes	complemented
480	#462	C₂²×C₇₁	1	4	yes	complemented
481	#461	C₂²×C₇₁	1	4	yes	complemented
482	#451	C₂²×C₇₁	1	4	yes	—
483	#451	C₂²×C₇₁	1	4	yes	complemented
484	#450	C₂²×C₇₁	1	4	yes	—
485	#448	C₂²×C₇₁	1	4	yes	—
486	#441	C₂²×C₇₁	1	8	yes	complemented
487	#440	C₂²×C₇₁	1	8	yes	complemented
488	#432	C₂²×C₇₁	1	2	yes	—
489	#432	C₂²×C₇₁	1	2	yes	—
490	#432	C₂²×C₇₁	1	2	yes	complemented
491	#432	C₂²×C₇₁	1	2	yes	complemented
492	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
493	C₂×C₂²⋊C₈	C₂²×C₇₁	1	2	yes	—
494	C₂×#97	C₂²×C₇₁	1	2	yes	complemented
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
502	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
504	C₂×Q₁₆	C₂³×C₇₁	1	8	yes	—
505	C₂×SD₁₆	C₂³×C₇₁	1	8	yes	—
506	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#126	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	2	no	—
521	#125	—	2	2	no	—
522	#125	—	2	2	no	—
523	#125	—	2	1	no	—
524	#125	—	2	1	no	—
525	#125	C₂³×C₇₁	1	2	yes	—
526	#125	C₂³×C₇₁	1	2	yes	—
527	#124	—	2	1	no	—
528	#124	—	2	1	no	—
529	#124	C₂³×C₇₁	1	2	yes	—
530	#124	C₂³×C₇₁	1	2	yes	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
545	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
546	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
547	#121	—	2	1	no	—
548	#121	—	2	1	no	—
549	#121	C₂³×C₇₁	1	2	yes	—
550	#121	C₂³×C₇₁	1	2	yes	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
560	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
561	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
562	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	C₂³×C₇₁	1	2	yes	—
570	C₄×D₄	C₂³×C₇₁	1	2	yes	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	#117	—	2	2	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	2	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	2	no	—
588	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
591	C₂×C₂²⋊C₄	—	2	2	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₄²	—	2	1	no	—
598	C₂×C₄²	—	2	2	no	—
599	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
600	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
601	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
602	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
603	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
604	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
611	#107	C₂³×C₇₁	1	8	yes	—
612	#106	C₂³×C₇₁	1	8	yes	—
613	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
614	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
615	#103	C₂³×C₇₁	1	8	yes	—
616	#103	C₂³×C₇₁	1	8	yes	—
617	#103	C₂³×C₇₁	1	8	yes	—
618	#102	C₂³×C₇₁	1	8	yes	—
619	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
620	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
621	#97	C₂³×C₇₁	1	4	yes	—
622	#97	C₂³×C₇₁	1	4	yes	—
623	C₂⁴	—	2	1	no	—
624	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	—	4	4	no	—
632	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	4	no	—
651	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
669	Q₁₆	—	4	8	no	—
670	SD₁₆	—	4	8	no	—
671	C₂×C₈	—	4	4	no	—
672	C₂×C₈	C₂⁴×C₇₁	1	8	yes	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
695	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	2	4	no	—
713	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
719	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
720	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
721	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
722	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
723	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
724	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
725	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
726	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
727	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
728	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
729	C₂³	—	2	2	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	#137×C₇₁	1	4	yes	—
736	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
737	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
738	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
739	Q₈	—	2	8	no	—
740	Q₈	—	2	4	no	—
741	Q₈	—	4	4	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	4	no	—
745	D₄	—	2	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
790	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
791	C₈	—	2	8	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	8	4	no	—
803	C₂²	C₂×#137×C₇₁	1	2	yes	—
804	C₂²	C₂×#137×C₇₁	1	2	yes	—
805	C₂²	C₂×#137×C₇₁	1	2	yes	—
806	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	4	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	4	no	—
822	C₄	#575×C₇₁	1	2	yes	—
823	C₄	#585×C₇₁	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	2	no	—
826	C₂	—	2	2	no	—
827	C₂	—	8	2	no	—
828	C₂	C₇₁×#3449	1	1	yes	characteristic
829	C₂	C₂²×#137×C₇₁	1	1	yes	characteristic
830	C₂	C₂×#575×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₂×#121×C₇₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂²×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₇₁	C₂	semidirect
3. C₇₁×#3248	C₂	semidirect
4. C₇₁×#3239	C₂	semidirect
5. C₇₁×#3236	C₂	semidirect
6. C₇₁×#3218	C₂	semidirect
7. C₇₁×#3215	C₂	semidirect
8. C₇₁×#3189	C₂	semidirect
10. C₇₁×#3181	C₂	semidirect
11. C₇₁×#3117	C₂	semidirect
12. C₇₁×#3113	C₂	semidirect
13. C₇₁×#3110	C₂	semidirect
14. C₂×#432×C₇₁	C₂	semidirect
21. #533×C₇₁	C₂²	semidirect
22. #533×C₇₁	C₂²	semidirect
23. C₂×C₄⋊Q₈×C₇₁	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₇₁	C₂²	semidirect
44. C₂×C₄×Q₈×C₇₁	C₂²	semidirect
50. #501×C₇₁	C₂²	semidirect
51. #497×C₇₁	C₂²	semidirect
52. #491×C₇₁	C₂²	semidirect
53. #489×C₇₁	C₂²	semidirect
55. #484×C₇₁	C₂²	semidirect
58. #479×C₇₁	C₂²	semidirect
59. #475×C₇₁	C₂²	semidirect
60. #474×C₇₁	C₂²	semidirect
61. #467×C₇₁	C₂²	semidirect
63. #464×C₇₁	C₂²	semidirect
64. #462×C₇₁	C₂²	semidirect
65. #461×C₇₁	C₂²	semidirect
67. #451×C₇₁	C₂²	semidirect
70. #441×C₇₁	C₂²	semidirect
71. #440×C₇₁	C₂²	semidirect
74. #432×C₇₁	C₂²	semidirect
75. #432×C₇₁	C₂²	semidirect
76. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
78. C₂×#97×C₇₁	C₂²	semidirect
408. #60960	C₇₁	direct (N × H)
416. C₂×#533	C₂×C₇₁	semidirect
418. #3248	C₂×C₇₁	semidirect
419. #3239	C₂×C₇₁	semidirect
420. #3236	C₂×C₇₁	semidirect
421. #3218	C₂×C₇₁	semidirect
422. #3215	C₂×C₇₁	semidirect
423. #3189	C₂×C₇₁	semidirect
425. #3181	C₂×C₇₁	semidirect
426. #3117	C₂×C₇₁	semidirect
427. #3113	C₂×C₇₁	semidirect
428. #3110	C₂×C₇₁	semidirect
429. C₂×#432	C₂×C₇₁	semidirect
430. C₇₁	#60960	direct (N × H)
437. #533	C₂²×C₇₁	semidirect
438. #533	C₂²×C₇₁	semidirect
439. C₂×C₄⋊Q₈	C₂²×C₇₁	semidirect
440. C₂×C₄⋊Q₈	C₂²×C₇₁	semidirect
460. C₂×C₄×Q₈	C₂²×C₇₁	semidirect
466. #501	C₂²×C₇₁	semidirect
467. #497	C₂²×C₇₁	semidirect
468. #491	C₂²×C₇₁	semidirect
469. #489	C₂²×C₇₁	semidirect
471. #484	C₂²×C₇₁	semidirect
474. #479	C₂²×C₇₁	semidirect
475. #475	C₂²×C₇₁	semidirect
476. #474	C₂²×C₇₁	semidirect
477. #467	C₂²×C₇₁	semidirect
479. #464	C₂²×C₇₁	semidirect
480. #462	C₂²×C₇₁	semidirect
481. #461	C₂²×C₇₁	semidirect
483. #451	C₂²×C₇₁	semidirect
486. #441	C₂²×C₇₁	semidirect
487. #440	C₂²×C₇₁	semidirect
490. #432	C₂²×C₇₁	semidirect
491. #432	C₂²×C₇₁	semidirect
492. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
494. C₂×#97	C₂²×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₇₁	2
C₂×#529×C₇₁	2
C₇₁×#3248	2
C₇₁×#3239	2
C₇₁×#3236	2
C₇₁×#3218	2
C₇₁×#3215	2
C₇₁×#3189	2
C₇₁×#3187	2
C₇₁×#3181	2
C₇₁×#3117	2
C₇₁×#3113	2
C₇₁×#3110	2
C₂×#432×C₇₁	2
#60960	71

Subgroups — C71×#60960 #31881832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#60960 #31881832