Subgroups — C₂×C₇₁×#3320 #31882004

Order 18176.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3320	C₂	1	16	yes	maximal, direct product factor
4	C₂×#491×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#484×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#485×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#479×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#468×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#465×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#461×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#448×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#448×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#419×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#103×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₇₁	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₇₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
24	#553×C₇₁	—	2	4	no	—
25	#553×C₇₁	C₂²	1	8	yes	—
26	D₄×Q₈×C₇₁	—	2	4	no	—
27	D₄×Q₈×C₇₁	C₂²	1	8	yes	complemented
28	C₂×C₄⋊Q₈×C₇₁	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
30	C₂×#126×C₇₁	—	2	1	no	—
31	C₂×#125×C₇₁	C₂²	1	1	yes	characteristic
32	C₂×#123×C₇₁	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₇₁	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₇₁	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
37	C₂×#121×C₇₁	—	2	1	no	—
38	C₂×#121×C₇₁	C₂²	1	1	yes	characteristic
39	C₂×#121×C₇₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₇₁	—	2	1	no	—
42	C₂×C₄×D₄×C₇₁	—	2	1	no	—
43	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
45	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
47	#491×C₇₁	C₂²	1	8	yes	complemented
48	#485×C₇₁	C₂²	1	8	yes	complemented
49	#484×C₇₁	C₂²	1	8	yes	complemented
50	#479×C₇₁	C₂²	1	8	yes	complemented
51	#468×C₇₁	C₂²	1	8	yes	complemented
52	#465×C₇₁	C₂²	1	8	yes	complemented
53	#461×C₇₁	C₂²	1	8	yes	complemented
54	#448×C₇₁	C₂²	1	8	yes	complemented
55	#448×C₇₁	C₂²	1	8	yes	complemented
56	#440×C₇₁	C₂²	1	8	yes	complemented
57	#435×C₇₁	C₂²	1	8	yes	complemented
58	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
59	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
60	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
62	#419×C₇₁	C₂²	1	8	yes	complemented
63	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
64	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
65	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
66	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
68	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
69	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
70	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
71	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
72	C₂×#103×C₇₁	C₂²	1	8	yes	complemented
73	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
76	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₇₁	—	2	1	no	—
78	C₂²×Q₈×C₇₁	—	2	1	no	—
79	C₂²×Q₈×C₇₁	—	2	2	no	—
80	C₂²×Q₈×C₇₁	—	2	2	no	—
81	C₂²×Q₈×C₇₁	—	2	4	no	—
82	C₂²×Q₈×C₇₁	—	2	4	no	—
83	C₂²×Q₈×C₇₁	—	4	2	no	—
84	C₂²×Q₈×C₇₁	—	4	2	no	—
85	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
88	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
89	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₇₁	—	2	1	no	—
91	C₂²×D₄×C₇₁	—	2	1	no	—
92	C₂²×D₄×C₇₁	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇₁	—	2	1	no	—
95	C₂³×C₄×C₇₁	—	2	1	no	—
96	C₂³×C₄×C₇₁	—	2	1	no	—
97	C₂³×C₄×C₇₁	—	2	1	no	—
98	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
100	C₂×SD₁₆×C₇₁	—	2	4	no	—
101	C₂×SD₁₆×C₇₁	—	4	2	no	—
102	C₂×SD₁₆×C₇₁	—	4	2	no	—
103	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
106	C₂×M₁₆×C₇₁	—	4	2	no	—
107	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
108	C₂²×C₈×C₇₁	—	4	2	no	—
109	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₇₁	—	2	8	no	—
115	C₄⋊Q₈×C₇₁	—	2	2	no	—
116	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
117	#126×C₇₁	—	2	8	no	—
118	#125×C₇₁	—	2	2	no	—
119	#125×C₇₁	C₂³	1	4	yes	—
120	#123×C₇₁	—	2	8	no	—
121	C₂²⋊Q₈×C₇₁	—	2	2	no	—
122	C₂²⋊Q₈×C₇₁	—	2	2	no	—
123	C₂²⋊Q₈×C₇₁	—	2	8	no	—
124	C₂²⋊Q₈×C₇₁	—	2	8	no	—
125	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
126	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
127	#121×C₇₁	—	2	8	no	—
128	#121×C₇₁	—	2	2	no	—
129	#121×C₇₁	—	2	2	no	—
130	#121×C₇₁	C₂³	1	4	yes	—
131	#121×C₇₁	C₂³	1	4	yes	—
132	C₄×Q₈×C₇₁	—	2	2	no	—
133	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
134	C₄×D₄×C₇₁	—	2	8	no	—
135	C₄×D₄×C₇₁	—	2	8	no	—
136	C₄×D₄×C₇₁	—	2	2	no	—
137	C₄×D₄×C₇₁	D₄	1	4	yes	—
138	C₄×D₄×C₇₁	C₂³	1	4	yes	—
139	C₄×D₄×C₇₁	C₂³	1	4	yes	—
140	#117×C₇₁	—	2	2	no	—
141	#117×C₇₁	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
143	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
144	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
145	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
146	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
147	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
148	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
149	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
150	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
151	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₇₁	D₄	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₇₁	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₇₁	—	2	1	no	—
166	C₂×C₄²×C₇₁	—	2	1	no	—
167	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
168	#107×C₇₁	C₂³	1	4	yes	—
169	#107×C₇₁	C₂³	1	4	yes	—
170	#106×C₇₁	C₂³	1	4	yes	—
171	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
172	#103×C₇₁	C₂³	1	4	yes	—
173	#103×C₇₁	C₂³	1	4	yes	—
174	#103×C₇₁	C₂³	1	4	yes	—
175	#103×C₇₁	C₂³	1	4	yes	—
176	#103×C₇₁	C₂³	1	4	yes	—
177	#103×C₇₁	C₂³	1	4	yes	—
178	#103×C₇₁	C₂³	1	4	yes	—
179	#103×C₇₁	C₂³	1	4	yes	—
180	#103×C₇₁	C₂³	1	4	yes	—
181	#102×C₇₁	C₂³	1	4	yes	—
182	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
184	#97×C₇₁	C₂³	1	4	yes	—
185	C₂⁴×C₇₁	—	2	1	no	—
186	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₇₁	—	2	1	no	—
189	C₂×Q₈×C₇₁	—	2	4	no	—
190	C₂×Q₈×C₇₁	—	2	4	no	—
191	C₂×Q₈×C₇₁	—	2	1	no	—
192	C₂×Q₈×C₇₁	—	2	1	no	—
193	C₂×Q₈×C₇₁	—	2	2	no	—
194	C₂×Q₈×C₇₁	—	2	8	no	—
195	C₂×Q₈×C₇₁	—	2	8	no	—
196	C₂×Q₈×C₇₁	—	2	2	no	—
197	C₂×Q₈×C₇₁	—	2	2	no	—
198	C₂×Q₈×C₇₁	—	2	2	no	—
199	C₂×Q₈×C₇₁	—	2	2	no	—
200	C₂×Q₈×C₇₁	—	4	4	no	—
201	C₂×Q₈×C₇₁	—	4	4	no	—
202	C₂×Q₈×C₇₁	—	4	4	no	—
203	C₂×Q₈×C₇₁	—	4	4	no	—
204	C₂×Q₈×C₇₁	—	4	8	no	—
205	C₂×Q₈×C₇₁	—	4	8	no	—
206	C₂×Q₈×C₇₁	#41	1	4	yes	—
207	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₇₁	—	2	4	no	—
211	C₂×D₄×C₇₁	—	2	4	no	—
212	C₂×D₄×C₇₁	—	2	4	no	—
213	C₂×D₄×C₇₁	—	2	1	no	—
214	C₂×D₄×C₇₁	—	2	2	no	—
215	C₂×D₄×C₇₁	—	2	2	no	—
216	C₂×D₄×C₇₁	—	4	4	no	—
217	C₂×D₄×C₇₁	—	8	2	no	—
218	C₂×D₄×C₇₁	C₂×D₄	1	4	yes	—
219	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₇₁	—	2	1	no	—
221	C₂²×C₄×C₇₁	—	2	2	no	—
222	C₂²×C₄×C₇₁	—	2	2	no	—
223	C₂²×C₄×C₇₁	—	2	2	no	—
224	C₂²×C₄×C₇₁	—	2	2	no	—
225	C₂²×C₄×C₇₁	—	2	4	no	—
226	C₂²×C₄×C₇₁	—	2	4	no	—
227	C₂²×C₄×C₇₁	—	2	1	no	—
228	C₂²×C₄×C₇₁	—	2	1	no	—
229	C₂²×C₄×C₇₁	—	2	1	no	—
230	C₂²×C₄×C₇₁	—	2	1	no	—
231	C₂²×C₄×C₇₁	—	2	1	no	—
232	C₂²×C₄×C₇₁	—	2	1	no	—
233	C₂²×C₄×C₇₁	—	2	4	no	—
234	C₂²×C₄×C₇₁	—	2	4	no	—
235	C₂²×C₄×C₇₁	—	4	4	no	—
236	C₂²×C₄×C₇₁	—	4	4	no	—
237	C₂²×C₄×C₇₁	—	8	2	no	—
238	C₂²×C₄×C₇₁	—	8	2	no	—
239	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₇₁	—	2	8	no	—
249	SD₁₆×C₇₁	—	4	4	no	—
250	SD₁₆×C₇₁	—	4	4	no	—
251	M₁₆×C₇₁	—	4	4	no	—
252	C₂×C₈×C₇₁	—	2	2	no	—
253	C₂×C₈×C₇₁	—	2	2	no	—
254	C₂×C₈×C₇₁	—	2	2	no	—
255	C₂×C₈×C₇₁	—	2	2	no	—
256	C₂×C₈×C₇₁	—	4	4	no	—
257	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
258	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
259	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
260	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₇₁	—	2	1	no	—
262	C₄⋊C₄×C₇₁	—	2	1	no	—
263	C₄⋊C₄×C₇₁	—	2	4	no	—
264	C₄⋊C₄×C₇₁	—	2	4	no	—
265	C₄⋊C₄×C₇₁	—	2	4	no	—
266	C₄⋊C₄×C₇₁	—	2	4	no	—
267	C₄⋊C₄×C₇₁	—	2	4	no	—
268	C₄⋊C₄×C₇₁	—	2	4	no	—
269	C₄⋊C₄×C₇₁	—	2	4	no	—
270	C₄⋊C₄×C₇₁	—	2	4	no	—
271	C₄⋊C₄×C₇₁	—	2	1	no	—
272	C₄⋊C₄×C₇₁	—	2	1	no	—
273	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
274	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
278	C₂²⋊C₄×C₇₁	—	2	4	no	—
279	C₂²⋊C₄×C₇₁	—	2	4	no	—
280	C₂²⋊C₄×C₇₁	—	2	4	no	—
281	C₂²⋊C₄×C₇₁	—	2	4	no	—
282	C₂²⋊C₄×C₇₁	—	2	4	no	—
283	C₂²⋊C₄×C₇₁	—	2	4	no	—
284	C₂²⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
285	C₂²⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
286	C₄²×C₇₁	—	2	4	no	—
287	C₄²×C₇₁	—	2	4	no	—
288	C₄²×C₇₁	C₂×D₄	1	2	yes	—
289	C₄²×C₇₁	C₂⁴	1	2	yes	—
290	C₂³×C₇₁	—	2	2	no	—
291	C₂³×C₇₁	—	2	2	no	—
292	C₂³×C₇₁	—	2	2	no	—
293	C₂³×C₇₁	—	2	2	no	—
294	C₂³×C₇₁	—	2	2	no	—
295	C₂³×C₇₁	—	2	2	no	—
296	C₂³×C₇₁	—	4	2	no	—
297	C₂³×C₇₁	—	4	2	no	—
298	C₂³×C₇₁	—	4	2	no	—
299	C₂³×C₇₁	#137	1	4	yes	—
300	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
301	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
302	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₇₁	—	2	4	no	—
304	Q₈×C₇₁	—	2	2	no	—
305	Q₈×C₇₁	—	2	2	no	—
306	Q₈×C₇₁	—	2	2	no	—
307	Q₈×C₇₁	—	2	2	no	—
308	Q₈×C₇₁	—	2	2	no	—
309	Q₈×C₇₁	—	4	8	no	—
310	Q₈×C₇₁	—	4	8	no	—
311	Q₈×C₇₁	—	4	2	no	—
312	Q₈×C₇₁	—	4	2	no	—
313	Q₈×C₇₁	C₂×#41	1	4	yes	—
314	D₄×C₇₁	—	2	8	no	—
315	D₄×C₇₁	—	2	2	no	—
316	D₄×C₇₁	—	2	2	no	—
317	D₄×C₇₁	—	4	8	no	—
318	D₄×C₇₁	—	4	2	no	—
319	D₄×C₇₁	—	8	4	no	—
320	C₂×C₄×C₇₁	—	2	2	no	—
321	C₂×C₄×C₇₁	—	2	2	no	—
322	C₂×C₄×C₇₁	—	2	4	no	—
323	C₂×C₄×C₇₁	—	2	2	no	—
324	C₂×C₄×C₇₁	—	2	2	no	—
325	C₂×C₄×C₇₁	—	2	2	no	—
326	C₂×C₄×C₇₁	—	2	4	no	—
327	C₂×C₄×C₇₁	—	2	4	no	—
328	C₂×C₄×C₇₁	—	2	2	no	—
329	C₂×C₄×C₇₁	—	2	2	no	—
330	C₂×C₄×C₇₁	—	2	2	no	—
331	C₂×C₄×C₇₁	—	2	2	no	—
332	C₂×C₄×C₇₁	—	2	2	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	—	4	8	no	—
339	C₂×C₄×C₇₁	—	4	8	no	—
340	C₂×C₄×C₇₁	—	4	2	no	—
341	C₂×C₄×C₇₁	—	4	2	no	—
342	C₂×C₄×C₇₁	—	4	2	no	—
343	C₂×C₄×C₇₁	—	4	2	no	—
344	C₂×C₄×C₇₁	—	4	2	no	—
345	C₂×C₄×C₇₁	—	4	2	no	—
346	C₂×C₄×C₇₁	—	8	4	no	—
347	C₂×C₄×C₇₁	—	8	4	no	—
348	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
354	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
355	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
356	C₈×C₇₁	—	2	2	no	—
357	C₈×C₇₁	—	2	2	no	—
358	C₈×C₇₁	—	2	2	no	—
359	C₈×C₇₁	—	2	2	no	—
360	C₂²×C₇₁	—	2	2	no	—
361	C₂²×C₇₁	—	2	8	no	—
362	C₂²×C₇₁	—	2	2	no	—
363	C₂²×C₇₁	—	2	2	no	—
364	C₂²×C₇₁	—	2	2	no	—
365	C₂²×C₇₁	—	2	2	no	—
366	C₂²×C₇₁	—	4	4	no	—
367	C₂²×C₇₁	—	4	2	no	—
368	C₂²×C₇₁	—	4	2	no	—
369	C₂²×C₇₁	—	4	2	no	—
370	C₂²×C₇₁	—	8	4	no	—
371	C₂²×C₇₁	#546	1	2	yes	—
372	C₂²×C₇₁	C₂×#137	1	4	yes	—
373	C₂²×C₇₁	C₂×#137	1	2	yes	—
374	C₂²×C₇₁	#577	1	2	yes	—
375	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₇₁	—	2	2	no	—
377	C₄×C₇₁	—	2	2	no	—
378	C₄×C₇₁	—	2	4	no	—
379	C₄×C₇₁	—	2	2	no	—
380	C₄×C₇₁	—	2	2	no	—
381	C₄×C₇₁	—	4	2	no	—
382	C₄×C₇₁	—	4	2	no	—
383	C₄×C₇₁	—	4	2	no	—
384	C₄×C₇₁	—	4	2	no	—
385	C₄×C₇₁	—	4	2	no	—
386	C₄×C₇₁	—	4	2	no	—
387	C₄×C₇₁	#546	1	2	yes	—
388	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
389	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×#3320	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₇₁	—	2	4	no	—
392	C₂×C₇₁	—	4	2	no	—
393	C₂×C₇₁	—	8	2	no	—
394	C₂×C₇₁	#3320	1	4	yes	direct product factor
395	C₂×C₇₁	C₂×#546	1	1	yes	characteristic
396	C₂×C₇₁	C₂²×#137	1	1	yes	characteristic
397	C₂×C₇₁	C₂×#577	1	1	yes	characteristic
398	C₂×#553	C₂×C₇₁	1	1	yes	characteristic
399	C₂×D₄×Q₈	C₂×C₇₁	1	1	yes	characteristic, complemented
400	#3320	C₂×C₇₁	1	16	yes	direct product factor
401	C₂×#491	C₂×C₇₁	1	1	yes	characteristic, complemented
402	C₂×#484	C₂×C₇₁	1	1	yes	characteristic, complemented
403	C₂×#485	C₂×C₇₁	1	1	yes	characteristic, complemented
404	C₂×#479	C₂×C₇₁	1	1	yes	characteristic, complemented
405	C₂×#468	C₂×C₇₁	1	1	yes	characteristic, complemented
406	C₂×#465	C₂×C₇₁	1	1	yes	characteristic, complemented
407	C₂×#461	C₂×C₇₁	1	1	yes	characteristic, complemented
408	C₂×#448	C₂×C₇₁	1	1	yes	characteristic, complemented
409	C₂×#448	C₂×C₇₁	1	1	yes	characteristic, complemented
410	C₂×#440	C₂×C₇₁	1	1	yes	characteristic, complemented
411	C₂×#435	C₂×C₇₁	1	1	yes	characteristic, complemented
412	C₂×#419	C₂×C₇₁	1	1	yes	characteristic, complemented
413	C₂²×#103	C₂×C₇₁	1	1	yes	characteristic, complemented
414	C₇₁	C₂×#3320	1	1	yes	characteristic, direct product factor, Sylow
415	C₂³×Q₈	C₂²×C₇₁	1	1	yes	characteristic
416	C₂³×Q₈	C₂²×C₇₁	1	1	yes	characteristic
417	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
420	C₂²×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
421	C₂³×C₈	C₂²×C₇₁	1	1	yes	characteristic
422	#553	—	2	4	no	—
423	#553	C₂²×C₇₁	1	8	yes	—
424	D₄×Q₈	—	2	4	no	—
425	D₄×Q₈	C₂²×C₇₁	1	8	yes	complemented
426	C₂×C₄⋊Q₈	—	2	1	no	—
427	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
428	C₂×#126	—	2	1	no	—
429	C₂×#125	C₂²×C₇₁	1	1	yes	characteristic
430	C₂×#123	—	2	1	no	—
431	C₂×C₂²⋊Q₈	—	2	1	no	—
432	C₂×C₂²⋊Q₈	—	2	1	no	—
433	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
434	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
435	C₂×#121	—	2	1	no	—
436	C₂×#121	C₂²×C₇₁	1	1	yes	characteristic
437	C₂×#121	C₂²×C₇₁	1	1	yes	characteristic
438	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	—	2	1	no	—
441	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
443	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
445	#491	C₂²×C₇₁	1	8	yes	complemented
446	#485	C₂²×C₇₁	1	8	yes	complemented
447	#484	C₂²×C₇₁	1	8	yes	complemented
448	#479	C₂²×C₇₁	1	8	yes	complemented
449	#468	C₂²×C₇₁	1	8	yes	complemented
450	#465	C₂²×C₇₁	1	8	yes	complemented
451	#461	C₂²×C₇₁	1	8	yes	complemented
452	#448	C₂²×C₇₁	1	8	yes	complemented
453	#448	C₂²×C₇₁	1	8	yes	complemented
454	#440	C₂²×C₇₁	1	8	yes	complemented
455	#435	C₂²×C₇₁	1	8	yes	complemented
456	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
457	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
458	C₂×#106	C₂²×C₇₁	1	1	yes	characteristic
459	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
460	#419	C₂²×C₇₁	1	8	yes	complemented
461	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
462	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
463	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
464	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
465	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
466	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
467	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
468	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
469	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
470	C₂×#103	C₂²×C₇₁	1	8	yes	complemented
471	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
472	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
473	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
474	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
475	C₂²×Q₈	—	2	1	no	—
476	C₂²×Q₈	—	2	1	no	—
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	—	2	2	no	—
479	C₂²×Q₈	—	2	4	no	—
480	C₂²×Q₈	—	2	4	no	—
481	C₂²×Q₈	—	4	2	no	—
482	C₂²×Q₈	—	4	2	no	—
483	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₇₁	1	4	yes	—
486	C₂²×Q₈	C₂³×C₇₁	1	4	yes	—
487	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	D₄×C₇₁	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
498	C₂×SD₁₆	—	2	4	no	—
499	C₂×SD₁₆	—	4	2	no	—
500	C₂×SD₁₆	—	4	2	no	—
501	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
504	C₂×M₁₆	—	4	2	no	—
505	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
506	C₂²×C₈	—	4	2	no	—
507	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
512	C₄⋊Q₈	—	2	8	no	—
513	C₄⋊Q₈	—	2	2	no	—
514	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
515	#126	—	2	8	no	—
516	#125	—	2	2	no	—
517	#125	C₂³×C₇₁	1	4	yes	—
518	#123	—	2	8	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	8	no	—
522	C₂²⋊Q₈	—	2	8	no	—
523	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
524	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
525	#121	—	2	8	no	—
526	#121	—	2	2	no	—
527	#121	—	2	2	no	—
528	#121	C₂³×C₇₁	1	4	yes	—
529	#121	C₂³×C₇₁	1	4	yes	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	D₄×C₇₁	1	4	yes	—
536	C₄×D₄	C₂³×C₇₁	1	4	yes	—
537	C₄×D₄	C₂³×C₇₁	1	4	yes	—
538	#117	—	2	2	no	—
539	#117	C₂³×C₇₁	1	4	yes	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	D₄×C₇₁	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	D₄×C₇₁	1	1	yes	characteristic
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	—	2	1	no	—
565	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
566	#107	C₂³×C₇₁	1	4	yes	—
567	#107	C₂³×C₇₁	1	4	yes	—
568	#106	C₂³×C₇₁	1	4	yes	—
569	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
570	#103	C₂³×C₇₁	1	4	yes	—
571	#103	C₂³×C₇₁	1	4	yes	—
572	#103	C₂³×C₇₁	1	4	yes	—
573	#103	C₂³×C₇₁	1	4	yes	—
574	#103	C₂³×C₇₁	1	4	yes	—
575	#103	C₂³×C₇₁	1	4	yes	—
576	#103	C₂³×C₇₁	1	4	yes	—
577	#103	C₂³×C₇₁	1	4	yes	—
578	#103	C₂³×C₇₁	1	4	yes	—
579	#102	C₂³×C₇₁	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
582	#97	C₂³×C₇₁	1	4	yes	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
585	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	2	8	no	—
593	C₂×Q₈	—	2	8	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	4	4	no	—
599	C₂×Q₈	—	4	4	no	—
600	C₂×Q₈	—	4	4	no	—
601	C₂×Q₈	—	4	4	no	—
602	C₂×Q₈	—	4	8	no	—
603	C₂×Q₈	—	4	8	no	—
604	C₂×Q₈	#41×C₇₁	1	4	yes	—
605	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
606	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	8	2	no	—
616	C₂×D₄	C₂×D₄×C₇₁	1	4	yes	—
617	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	4	4	no	—
634	C₂²×C₄	—	4	4	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	—	8	2	no	—
637	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
642	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	4	4	no	—
648	SD₁₆	—	4	4	no	—
649	M₁₆	—	4	4	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	4	4	no	—
655	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
656	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
657	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
658	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
672	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
683	C₂²⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	C₂×D₄×C₇₁	1	2	yes	—
687	C₄²	C₂⁴×C₇₁	1	2	yes	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	#137×C₇₁	1	4	yes	—
698	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
699	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
700	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
701	Q₈	—	2	4	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	8	no	—
708	Q₈	—	4	8	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	C₂×#41×C₇₁	1	4	yes	—
712	D₄	—	2	8	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	2	no	—
717	D₄	—	8	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
748	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
749	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
750	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
751	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
752	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
753	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₈	—	2	2	no	—
758	C₂²	—	2	8	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	4	no	—
769	C₂²	#546×C₇₁	1	2	yes	—
770	C₂²	C₂×#137×C₇₁	1	4	yes	—
771	C₂²	C₂×#137×C₇₁	1	2	yes	—
772	C₂²	#577×C₇₁	1	2	yes	—
773	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	#546×C₇₁	1	2	yes	—
786	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
787	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	C₇₁×#3320	1	4	yes	direct product factor
792	C₂	C₂×#546×C₇₁	1	1	yes	characteristic
793	C₂	C₂²×#137×C₇₁	1	1	yes	characteristic
794	C₂	C₂×#577×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₂×#553×C₇₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂×C₄×D₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₇₁	C₂	semidirect
3. C₇₁×#3320	C₂	direct (N × H)
4. C₂×#491×C₇₁	C₂	semidirect
5. C₂×#484×C₇₁	C₂	semidirect
6. C₂×#485×C₇₁	C₂	semidirect
7. C₂×#479×C₇₁	C₂	semidirect
8. C₂×#468×C₇₁	C₂	semidirect
9. C₂×#465×C₇₁	C₂	semidirect
10. C₂×#461×C₇₁	C₂	semidirect
11. C₂×#448×C₇₁	C₂	semidirect
12. C₂×#448×C₇₁	C₂	semidirect
13. C₂×#440×C₇₁	C₂	semidirect
14. C₂×#435×C₇₁	C₂	semidirect
15. C₂×#419×C₇₁	C₂	semidirect
16. C₂²×#103×C₇₁	C₂	semidirect
27. D₄×Q₈×C₇₁	C₂²	semidirect
47. #491×C₇₁	C₂²	semidirect
48. #485×C₇₁	C₂²	semidirect
49. #484×C₇₁	C₂²	semidirect
50. #479×C₇₁	C₂²	semidirect
51. #468×C₇₁	C₂²	semidirect
52. #465×C₇₁	C₂²	semidirect
53. #461×C₇₁	C₂²	semidirect
54. #448×C₇₁	C₂²	semidirect
55. #448×C₇₁	C₂²	semidirect
56. #440×C₇₁	C₂²	semidirect
57. #435×C₇₁	C₂²	semidirect
62. #419×C₇₁	C₂²	semidirect
72. C₂×#103×C₇₁	C₂²	semidirect
390. C₂×#3320	C₇₁	direct (N × H)
394. C₂×C₇₁	#3320	direct (N × H)
399. C₂×D₄×Q₈	C₂×C₇₁	semidirect
400. #3320	C₂×C₇₁	direct (N × H)
401. C₂×#491	C₂×C₇₁	semidirect
402. C₂×#484	C₂×C₇₁	semidirect
403. C₂×#485	C₂×C₇₁	semidirect
404. C₂×#479	C₂×C₇₁	semidirect
405. C₂×#468	C₂×C₇₁	semidirect
406. C₂×#465	C₂×C₇₁	semidirect
407. C₂×#461	C₂×C₇₁	semidirect
408. C₂×#448	C₂×C₇₁	semidirect
409. C₂×#448	C₂×C₇₁	semidirect
410. C₂×#440	C₂×C₇₁	semidirect
411. C₂×#435	C₂×C₇₁	semidirect
412. C₂×#419	C₂×C₇₁	semidirect
413. C₂²×#103	C₂×C₇₁	semidirect
414. C₇₁	C₂×#3320	direct (N × H)
425. D₄×Q₈	C₂²×C₇₁	semidirect
445. #491	C₂²×C₇₁	semidirect
446. #485	C₂²×C₇₁	semidirect
447. #484	C₂²×C₇₁	semidirect
448. #479	C₂²×C₇₁	semidirect
449. #468	C₂²×C₇₁	semidirect
450. #465	C₂²×C₇₁	semidirect
451. #461	C₂²×C₇₁	semidirect
452. #448	C₂²×C₇₁	semidirect
453. #448	C₂²×C₇₁	semidirect
454. #440	C₂²×C₇₁	semidirect
455. #435	C₂²×C₇₁	semidirect
460. #419	C₂²×C₇₁	semidirect
470. C₂×#103	C₂²×C₇₁	semidirect
791. C₂	C₇₁×#3320	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#553×C₇₁	2
C₂×D₄×Q₈×C₇₁	2
C₇₁×#3320	2
C₂×#491×C₇₁	2
C₂×#484×C₇₁	2
C₂×#485×C₇₁	2
C₂×#479×C₇₁	2
C₂×#468×C₇₁	2
C₂×#465×C₇₁	2
C₂×#461×C₇₁	2
C₂×#448×C₇₁	2
C₂×#440×C₇₁	2
C₂×#435×C₇₁	2
C₂×#419×C₇₁	2
C₂²×#103×C₇₁	2
C₂×#3320	71

Subgroups — C2×C71×#3320 #31882004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×#3320 #31882004