Subgroups — C₂×C₇₁×#3269 #31881899

Order 18176.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#548×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#547×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3269	C₂	1	16	yes	maximal, direct product factor
6	C₂×#497×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#468×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#467×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#462×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#463×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#452×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#452×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#449×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#451×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#440×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#435×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₇₁	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₇₁	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₇₁	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×#137×C₇₁	—	2	8	no	—
22	C₂×#137×C₇₁	C₂²	1	8	yes	complemented
23	C₂×#135×C₇₁	—	2	8	no	—
24	C₂×#135×C₇₁	C₂²	1	8	yes	complemented
25	C₂²×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
33	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
36	#548×C₇₁	—	2	4	no	—
37	#548×C₇₁	C₂²	1	8	yes	complemented
38	#547×C₇₁	—	2	4	no	—
39	#547×C₇₁	C₂²	1	8	yes	complemented
40	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
41	C₂×#124×C₇₁	—	2	1	no	—
42	C₂×#124×C₇₁	C₂²	1	1	yes	characteristic
43	C₂×#123×C₇₁	—	2	1	no	—
44	C₂×#123×C₇₁	—	2	1	no	—
45	C₂×C₂²⋊Q₈×C₇₁	—	2	1	no	—
46	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
49	C₂×#121×C₇₁	—	2	1	no	—
50	C₂×#121×C₇₁	—	2	1	no	—
51	C₂×#121×C₇₁	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₇₁	—	2	1	no	—
54	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄×C₇₁	—	2	1	no	—
57	#497×C₇₁	C₂²	1	8	yes	complemented
58	#468×C₇₁	C₂²	1	8	yes	complemented
59	#467×C₇₁	C₂²	1	8	yes	complemented
60	#463×C₇₁	C₂²	1	8	yes	complemented
61	#462×C₇₁	C₂²	1	8	yes	complemented
62	#452×C₇₁	C₂²	1	8	yes	complemented
63	#452×C₇₁	C₂²	1	8	yes	complemented
64	#451×C₇₁	C₂²	1	8	yes	complemented
65	#449×C₇₁	C₂²	1	8	yes	complemented
66	#440×C₇₁	C₂²	1	8	yes	complemented
67	#435×C₇₁	C₂²	1	8	yes	complemented
68	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
69	C₂×C₄⋊C₈×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	1	yes	characteristic
73	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
74	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
75	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
78	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
79	C₂×#41×C₇₁	—	2	2	no	—
80	C₂×#41×C₇₁	—	2	2	no	—
81	C₂×#41×C₇₁	—	2	2	no	—
82	C₂×#41×C₇₁	—	2	4	no	—
83	C₂×#41×C₇₁	—	2	4	no	—
84	C₂×#41×C₇₁	—	2	4	no	—
85	C₂×#41×C₇₁	—	4	2	no	—
86	C₂×#41×C₇₁	—	4	2	no	—
87	C₂×#41×C₇₁	—	4	2	no	—
88	C₂×#41×C₇₁	C₂³	1	4	yes	—
89	C₂×#41×C₇₁	C₂³	1	4	yes	—
90	C₂×#41×C₇₁	C₂³	1	4	yes	—
91	C₂²×Q₈×C₇₁	—	2	1	no	—
92	C₂²×Q₈×C₇₁	—	2	2	no	—
93	C₂²×Q₈×C₇₁	—	2	4	no	—
94	C₂²×Q₈×C₇₁	—	4	2	no	—
95	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₇₁	—	2	1	no	—
101	C₂²×D₄×C₇₁	—	2	1	no	—
102	C₂²×D₄×C₇₁	—	2	1	no	—
103	C₂²×D₄×C₇₁	—	2	1	no	—
104	C₂²×D₄×C₇₁	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇₁	—	2	1	no	—
108	C₂³×C₄×C₇₁	—	2	1	no	—
109	C₂³×C₄×C₇₁	—	2	1	no	—
110	C₂³×C₄×C₇₁	—	2	1	no	—
111	C₂³×C₄×C₇₁	—	2	1	no	—
112	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
114	#137×C₇₁	—	2	32	no	—
115	#135×C₇₁	—	2	32	no	—
116	C₂×Q₁₆×C₇₁	—	2	4	no	—
117	C₂×Q₁₆×C₇₁	—	2	4	no	—
118	C₂×Q₁₆×C₇₁	—	2	4	no	—
119	C₂×Q₁₆×C₇₁	—	4	2	no	—
120	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
121	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
122	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
123	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₇₁	—	2	4	no	—
125	C₂×SD₁₆×C₇₁	—	2	4	no	—
126	C₂×SD₁₆×C₇₁	—	4	2	no	—
127	C₂×SD₁₆×C₇₁	D₄	1	8	yes	complemented
128	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
132	C₂×D₈×C₇₁	—	2	4	no	—
133	C₂×D₈×C₇₁	C₂³	1	4	yes	—
134	C₂×M₁₆×C₇₁	—	2	4	no	—
135	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
136	C₂²×C₈×C₇₁	—	2	4	no	—
137	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
141	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₇₁	—	2	2	no	—
143	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
144	#124×C₇₁	—	2	8	no	—
145	#124×C₇₁	—	2	2	no	—
146	#124×C₇₁	C₂³	1	4	yes	—
147	#123×C₇₁	—	2	8	no	—
148	#123×C₇₁	—	2	8	no	—
149	C₂²⋊Q₈×C₇₁	—	2	2	no	—
150	C₂²⋊Q₈×C₇₁	—	2	2	no	—
151	C₂²⋊Q₈×C₇₁	—	2	2	no	—
152	C₂²⋊Q₈×C₇₁	—	2	8	no	—
153	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
154	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
155	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
156	#121×C₇₁	—	2	8	no	—
157	#121×C₇₁	—	2	8	no	—
158	#121×C₇₁	—	2	2	no	—
159	#121×C₇₁	C₂³	1	4	yes	—
160	C₄×Q₈×C₇₁	—	2	2	no	—
161	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
162	C₄×D₄×C₇₁	—	2	8	no	—
163	C₄×D₄×C₇₁	—	2	2	no	—
164	C₄×D₄×C₇₁	D₄	1	4	yes	—
165	C₄×D₄×C₇₁	C₂³	1	4	yes	—
166	C₄×D₄×C₇₁	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₇₁	—	2	8	no	—
174	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₇₁	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₇₁	D₄	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₇₁	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₇₁	—	2	1	no	—
187	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
188	#107×C₇₁	C₂³	1	4	yes	—
189	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
190	#103×C₇₁	C₂³	1	4	yes	—
191	#103×C₇₁	C₂³	1	4	yes	—
192	#103×C₇₁	C₂³	1	4	yes	—
193	#103×C₇₁	C₂³	1	4	yes	—
194	#102×C₇₁	C₂³	1	4	yes	—
195	#102×C₇₁	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
198	#97×C₇₁	C₂³	1	4	yes	—
199	C₂⁴×C₇₁	—	2	1	no	—
200	C₂⁴×C₇₁	—	2	1	no	—
201	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
202	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
203	#41×C₇₁	—	2	8	no	—
204	#41×C₇₁	—	2	8	no	—
205	#41×C₇₁	—	2	8	no	—
206	#41×C₇₁	—	4	4	no	—
207	#41×C₇₁	—	4	4	no	—
208	#41×C₇₁	—	4	4	no	—
209	#41×C₇₁	—	4	8	no	—
210	#41×C₇₁	—	4	8	no	—
211	#41×C₇₁	—	4	8	no	—
212	C₂×Q₈×C₇₁	—	2	1	no	—
213	C₂×Q₈×C₇₁	—	2	4	no	—
214	C₂×Q₈×C₇₁	—	2	1	no	—
215	C₂×Q₈×C₇₁	—	2	1	no	—
216	C₂×Q₈×C₇₁	—	2	1	no	—
217	C₂×Q₈×C₇₁	—	2	2	no	—
218	C₂×Q₈×C₇₁	—	2	8	no	—
219	C₂×Q₈×C₇₁	—	2	2	no	—
220	C₂×Q₈×C₇₁	—	2	2	no	—
221	C₂×Q₈×C₇₁	—	2	2	no	—
222	C₂×Q₈×C₇₁	—	2	2	no	—
223	C₂×Q₈×C₇₁	—	2	2	no	—
224	C₂×Q₈×C₇₁	—	2	2	no	—
225	C₂×Q₈×C₇₁	—	4	4	no	—
226	C₂×Q₈×C₇₁	—	4	4	no	—
227	C₂×Q₈×C₇₁	—	4	8	no	—
228	C₂×Q₈×C₇₁	C₂×D₄	1	4	yes	—
229	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
233	C₂×D₄×C₇₁	—	2	4	no	—
234	C₂×D₄×C₇₁	—	2	4	no	—
235	C₂×D₄×C₇₁	—	2	4	no	—
236	C₂×D₄×C₇₁	—	2	4	no	—
237	C₂×D₄×C₇₁	—	2	1	no	—
238	C₂×D₄×C₇₁	—	2	2	no	—
239	C₂×D₄×C₇₁	—	2	1	no	—
240	C₂×D₄×C₇₁	—	2	2	no	—
241	C₂×D₄×C₇₁	—	2	2	no	—
242	C₂×D₄×C₇₁	—	4	2	no	—
243	C₂×D₄×C₇₁	—	4	4	no	—
244	C₂×D₄×C₇₁	—	4	4	no	—
245	C₂×D₄×C₇₁	—	4	4	no	—
246	C₂×D₄×C₇₁	—	4	4	no	—
247	C₂×D₄×C₇₁	C₂×D₄	1	4	yes	—
248	C₂×D₄×C₇₁	C₂×D₄	1	4	yes	—
249	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
250	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇₁	—	2	1	no	—
252	C₂²×C₄×C₇₁	—	2	2	no	—
253	C₂²×C₄×C₇₁	—	2	2	no	—
254	C₂²×C₄×C₇₁	—	2	2	no	—
255	C₂²×C₄×C₇₁	—	2	2	no	—
256	C₂²×C₄×C₇₁	—	2	4	no	—
257	C₂²×C₄×C₇₁	—	2	1	no	—
258	C₂²×C₄×C₇₁	—	2	1	no	—
259	C₂²×C₄×C₇₁	—	2	1	no	—
260	C₂²×C₄×C₇₁	—	2	1	no	—
261	C₂²×C₄×C₇₁	—	2	1	no	—
262	C₂²×C₄×C₇₁	—	2	4	no	—
263	C₂²×C₄×C₇₁	—	2	4	no	—
264	C₂²×C₄×C₇₁	—	2	4	no	—
265	C₂²×C₄×C₇₁	—	2	4	no	—
266	C₂²×C₄×C₇₁	—	4	4	no	—
267	C₂²×C₄×C₇₁	—	4	4	no	—
268	C₂²×C₄×C₇₁	—	4	4	no	—
269	C₂²×C₄×C₇₁	—	4	4	no	—
270	C₂²×C₄×C₇₁	—	4	4	no	—
271	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
280	Q₁₆×C₇₁	—	2	8	no	—
281	Q₁₆×C₇₁	—	2	8	no	—
282	Q₁₆×C₇₁	—	2	8	no	—
283	Q₁₆×C₇₁	—	4	4	no	—
284	SD₁₆×C₇₁	—	2	8	no	—
285	SD₁₆×C₇₁	—	2	8	no	—
286	SD₁₆×C₇₁	—	4	4	no	—
287	SD₁₆×C₇₁	C₂×D₄	1	16	yes	complemented
288	D₈×C₇₁	—	2	8	no	—
289	M₁₆×C₇₁	—	2	8	no	—
290	C₂×C₈×C₇₁	—	2	2	no	—
291	C₂×C₈×C₇₁	—	2	2	no	—
292	C₂×C₈×C₇₁	—	2	2	no	—
293	C₂×C₈×C₇₁	—	2	8	no	—
294	C₂×C₈×C₇₁	C₂×D₄	1	4	yes	—
295	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
296	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
297	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
298	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₇₁	—	2	4	no	—
300	C₄⋊C₄×C₇₁	—	2	4	no	—
301	C₄⋊C₄×C₇₁	—	2	4	no	—
302	C₄⋊C₄×C₇₁	—	2	4	no	—
303	C₄⋊C₄×C₇₁	—	2	4	no	—
304	C₄⋊C₄×C₇₁	—	2	4	no	—
305	C₄⋊C₄×C₇₁	—	2	1	no	—
306	C₄⋊C₄×C₇₁	—	2	1	no	—
307	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
308	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
310	C₂²⋊C₄×C₇₁	—	2	4	no	—
311	C₂²⋊C₄×C₇₁	—	2	4	no	—
312	C₂²⋊C₄×C₇₁	—	2	4	no	—
313	C₂²⋊C₄×C₇₁	—	2	4	no	—
314	C₂²⋊C₄×C₇₁	—	2	4	no	—
315	C₂²⋊C₄×C₇₁	—	2	4	no	—
316	C₂²⋊C₄×C₇₁	—	2	4	no	—
317	C₂²⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
318	C₂²⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
319	C₄²×C₇₁	—	2	4	no	—
320	C₄²×C₇₁	C₂×D₄	1	2	yes	—
321	C₄²×C₇₁	C₂⁴	1	2	yes	—
322	C₂³×C₇₁	—	2	2	no	—
323	C₂³×C₇₁	—	2	2	no	—
324	C₂³×C₇₁	—	2	4	no	—
325	C₂³×C₇₁	—	2	2	no	—
326	C₂³×C₇₁	—	2	2	no	—
327	C₂³×C₇₁	—	2	2	no	—
328	C₂³×C₇₁	—	2	2	no	—
329	C₂³×C₇₁	—	2	2	no	—
330	C₂³×C₇₁	—	2	2	no	—
331	C₂³×C₇₁	—	4	2	no	—
332	C₂³×C₇₁	—	4	2	no	—
333	C₂³×C₇₁	—	4	2	no	—
334	C₂³×C₇₁	—	4	2	no	—
335	C₂³×C₇₁	—	4	2	no	—
336	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
337	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
338	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₇₁	—	2	4	no	—
340	Q₈×C₇₁	—	2	2	no	—
341	Q₈×C₇₁	—	2	2	no	—
342	Q₈×C₇₁	—	2	2	no	—
343	Q₈×C₇₁	—	2	2	no	—
344	Q₈×C₇₁	—	2	2	no	—
345	Q₈×C₇₁	—	2	2	no	—
346	Q₈×C₇₁	—	2	2	no	—
347	Q₈×C₇₁	—	4	8	no	—
348	Q₈×C₇₁	—	4	2	no	—
349	Q₈×C₇₁	—	4	2	no	—
350	Q₈×C₇₁	—	4	2	no	—
351	Q₈×C₇₁	C₂²×D₄	1	4	yes	—
352	D₄×C₇₁	—	2	4	no	—
353	D₄×C₇₁	—	2	2	no	—
354	D₄×C₇₁	—	2	2	no	—
355	D₄×C₇₁	—	2	2	no	—
356	D₄×C₇₁	—	4	4	no	—
357	D₄×C₇₁	—	4	8	no	—
358	D₄×C₇₁	—	4	8	no	—
359	D₄×C₇₁	—	4	8	no	—
360	D₄×C₇₁	—	4	8	no	—
361	D₄×C₇₁	—	4	2	no	—
362	D₄×C₇₁	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₇₁	—	2	2	no	—
364	C₂×C₄×C₇₁	—	2	2	no	—
365	C₂×C₄×C₇₁	—	2	4	no	—
366	C₂×C₄×C₇₁	—	2	2	no	—
367	C₂×C₄×C₇₁	—	2	2	no	—
368	C₂×C₄×C₇₁	—	2	2	no	—
369	C₂×C₄×C₇₁	—	2	4	no	—
370	C₂×C₄×C₇₁	—	2	4	no	—
371	C₂×C₄×C₇₁	—	2	2	no	—
372	C₂×C₄×C₇₁	—	2	2	no	—
373	C₂×C₄×C₇₁	—	2	2	no	—
374	C₂×C₄×C₇₁	—	2	2	no	—
375	C₂×C₄×C₇₁	—	2	2	no	—
376	C₂×C₄×C₇₁	—	2	2	no	—
377	C₂×C₄×C₇₁	—	2	2	no	—
378	C₂×C₄×C₇₁	—	2	2	no	—
379	C₂×C₄×C₇₁	—	2	2	no	—
380	C₂×C₄×C₇₁	—	4	8	no	—
381	C₂×C₄×C₇₁	—	4	8	no	—
382	C₂×C₄×C₇₁	—	4	8	no	—
383	C₂×C₄×C₇₁	—	4	8	no	—
384	C₂×C₄×C₇₁	—	4	8	no	—
385	C₂×C₄×C₇₁	—	4	2	no	—
386	C₂×C₄×C₇₁	—	4	2	no	—
387	C₂×C₄×C₇₁	—	4	2	no	—
388	C₂×C₄×C₇₁	—	4	2	no	—
389	C₂×C₄×C₇₁	—	4	2	no	—
390	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
398	C₈×C₇₁	—	2	2	no	—
399	C₈×C₇₁	—	2	2	no	—
400	C₈×C₇₁	—	2	2	no	—
401	C₈×C₇₁	C₂²×D₄	1	4	yes	—
402	C₂²×C₇₁	—	2	2	no	—
403	C₂²×C₇₁	—	2	2	no	—
404	C₂²×C₇₁	—	2	4	no	—
405	C₂²×C₇₁	—	2	2	no	—
406	C₂²×C₇₁	—	2	2	no	—
407	C₂²×C₇₁	—	2	2	no	—
408	C₂²×C₇₁	—	2	2	no	—
409	C₂²×C₇₁	—	4	4	no	—
410	C₂²×C₇₁	—	4	4	no	—
411	C₂²×C₇₁	—	4	8	no	—
412	C₂²×C₇₁	—	4	2	no	—
413	C₂²×C₇₁	—	4	2	no	—
414	C₂²×C₇₁	—	4	2	no	—
415	C₂²×C₇₁	—	4	2	no	—
416	C₂²×C₇₁	—	4	2	no	—
417	C₂²×C₇₁	—	8	4	no	—
418	C₂²×C₇₁	D₄²	1	2	yes	—
419	C₂²×C₇₁	#575	1	2	yes	—
420	C₂²×C₇₁	#578	1	2	yes	—
421	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₇₁	—	2	2	no	—
423	C₄×C₇₁	—	2	2	no	—
424	C₄×C₇₁	—	2	4	no	—
425	C₄×C₇₁	—	2	2	no	—
426	C₄×C₇₁	—	2	2	no	—
427	C₄×C₇₁	—	4	2	no	—
428	C₄×C₇₁	—	4	2	no	—
429	C₄×C₇₁	—	4	2	no	—
430	C₄×C₇₁	—	4	2	no	—
431	C₄×C₇₁	—	4	2	no	—
432	C₄×C₇₁	D₄²	1	2	yes	—
433	C₄×C₇₁	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×#3269	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₂×C₇₁	—	4	2	no	—
437	C₂×C₇₁	—	4	2	no	—
438	C₂×C₇₁	—	4	4	no	—
439	C₂×C₇₁	—	8	2	no	—
440	C₂×C₇₁	#3269	1	4	yes	direct product factor
441	C₂×C₇₁	C₂×D₄²	1	1	yes	characteristic
442	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
443	C₂×C₇₁	C₂×#578	1	1	yes	characteristic
444	C₂²×#137	C₂×C₇₁	1	1	yes	characteristic, complemented
445	C₂²×#135	C₂×C₇₁	1	1	yes	characteristic, complemented
446	C₂×#548	C₂×C₇₁	1	1	yes	characteristic, complemented
447	C₂×#547	C₂×C₇₁	1	1	yes	characteristic, complemented
448	#3269	C₂×C₇₁	1	16	yes	direct product factor
449	C₂×#497	C₂×C₇₁	1	1	yes	characteristic, complemented
450	C₂×#468	C₂×C₇₁	1	1	yes	characteristic, complemented
451	C₂×#467	C₂×C₇₁	1	1	yes	characteristic, complemented
452	C₂×#462	C₂×C₇₁	1	1	yes	characteristic, complemented
453	C₂×#463	C₂×C₇₁	1	1	yes	characteristic, complemented
454	C₂×#452	C₂×C₇₁	1	1	yes	characteristic, complemented
455	C₂×#452	C₂×C₇₁	1	1	yes	characteristic, complemented
456	C₂×#449	C₂×C₇₁	1	1	yes	characteristic, complemented
457	C₂×#451	C₂×C₇₁	1	1	yes	characteristic, complemented
458	C₂×#440	C₂×C₇₁	1	1	yes	characteristic, complemented
459	C₂×#435	C₂×C₇₁	1	1	yes	characteristic, complemented
460	C₇₁	C₂×#3269	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²×#41	C₂²×C₇₁	1	1	yes	characteristic
462	C₂²×#41	C₂²×C₇₁	1	1	yes	characteristic
463	C₂²×#41	C₂²×C₇₁	1	1	yes	characteristic
464	C₂³×Q₈	C₂²×C₇₁	1	1	yes	characteristic
465	C₂×#137	—	2	8	no	—
466	C₂×#137	C₂²×C₇₁	1	8	yes	complemented
467	C₂×#135	—	2	8	no	—
468	C₂×#135	C₂²×C₇₁	1	8	yes	complemented
469	C₂²×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
470	C₂²×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
471	C₂²×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
472	C₂²×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
473	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
474	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
475	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
476	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
477	C₂²×D₈	C₂²×C₇₁	1	1	yes	characteristic
478	C₂²×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
479	C₂³×C₈	C₂²×C₇₁	1	1	yes	characteristic
480	#548	—	2	4	no	—
481	#548	C₂²×C₇₁	1	8	yes	complemented
482	#547	—	2	4	no	—
483	#547	C₂²×C₇₁	1	8	yes	complemented
484	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
485	C₂×#124	—	2	1	no	—
486	C₂×#124	C₂²×C₇₁	1	1	yes	characteristic
487	C₂×#123	—	2	1	no	—
488	C₂×#123	—	2	1	no	—
489	C₂×C₂²⋊Q₈	—	2	1	no	—
490	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
491	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
492	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
493	C₂×#121	—	2	1	no	—
494	C₂×#121	—	2	1	no	—
495	C₂×#121	C₂²×C₇₁	1	1	yes	characteristic
496	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
497	C₂×C₄×D₄	—	2	1	no	—
498	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
500	C₂²×C₄⋊C₄	—	2	1	no	—
501	#497	C₂²×C₇₁	1	8	yes	complemented
502	#468	C₂²×C₇₁	1	8	yes	complemented
503	#467	C₂²×C₇₁	1	8	yes	complemented
504	#463	C₂²×C₇₁	1	8	yes	complemented
505	#462	C₂²×C₇₁	1	8	yes	complemented
506	#452	C₂²×C₇₁	1	8	yes	complemented
507	#452	C₂²×C₇₁	1	8	yes	complemented
508	#451	C₂²×C₇₁	1	8	yes	complemented
509	#449	C₂²×C₇₁	1	8	yes	complemented
510	#440	C₂²×C₇₁	1	8	yes	complemented
511	#435	C₂²×C₇₁	1	8	yes	complemented
512	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
513	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
514	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
515	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
516	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
517	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
518	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
519	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
520	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
521	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
522	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
523	C₂×#41	—	2	2	no	—
524	C₂×#41	—	2	2	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	—	2	4	no	—
527	C₂×#41	—	2	4	no	—
528	C₂×#41	—	2	4	no	—
529	C₂×#41	—	4	2	no	—
530	C₂×#41	—	4	2	no	—
531	C₂×#41	—	4	2	no	—
532	C₂×#41	C₂³×C₇₁	1	4	yes	—
533	C₂×#41	C₂³×C₇₁	1	4	yes	—
534	C₂×#41	C₂³×C₇₁	1	4	yes	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	2	no	—
537	C₂²×Q₈	—	2	4	no	—
538	C₂²×Q₈	—	4	2	no	—
539	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
540	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₇₁	1	4	yes	—
543	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	D₄×C₇₁	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
551	C₂³×C₄	—	2	1	no	—
552	C₂³×C₄	—	2	1	no	—
553	C₂³×C₄	—	2	1	no	—
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	—	2	1	no	—
556	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
558	#137	—	2	32	no	—
559	#135	—	2	32	no	—
560	C₂×Q₁₆	—	2	4	no	—
561	C₂×Q₁₆	—	2	4	no	—
562	C₂×Q₁₆	—	2	4	no	—
563	C₂×Q₁₆	—	4	2	no	—
564	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
565	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
566	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
567	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
568	C₂×SD₁₆	—	2	4	no	—
569	C₂×SD₁₆	—	2	4	no	—
570	C₂×SD₁₆	—	4	2	no	—
571	C₂×SD₁₆	D₄×C₇₁	1	8	yes	complemented
572	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
575	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
576	C₂×D₈	—	2	4	no	—
577	C₂×D₈	C₂³×C₇₁	1	4	yes	—
578	C₂×M₁₆	—	2	4	no	—
579	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
580	C₂²×C₈	—	2	4	no	—
581	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
583	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
584	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
586	C₄⋊Q₈	—	2	2	no	—
587	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
588	#124	—	2	8	no	—
589	#124	—	2	2	no	—
590	#124	C₂³×C₇₁	1	4	yes	—
591	#123	—	2	8	no	—
592	#123	—	2	8	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	8	no	—
597	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
598	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
599	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
600	#121	—	2	8	no	—
601	#121	—	2	8	no	—
602	#121	—	2	2	no	—
603	#121	C₂³×C₇₁	1	4	yes	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
606	C₄×D₄	—	2	8	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	D₄×C₇₁	1	4	yes	—
609	C₄×D₄	C₂³×C₇₁	1	4	yes	—
610	C₄×D₄	C₂³×C₇₁	1	4	yes	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	8	no	—
618	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	D₄×C₇₁	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	D₄×C₇₁	1	1	yes	characteristic
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
632	#107	C₂³×C₇₁	1	4	yes	—
633	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
634	#103	C₂³×C₇₁	1	4	yes	—
635	#103	C₂³×C₇₁	1	4	yes	—
636	#103	C₂³×C₇₁	1	4	yes	—
637	#103	C₂³×C₇₁	1	4	yes	—
638	#102	C₂³×C₇₁	1	4	yes	—
639	#102	C₂³×C₇₁	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
641	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
642	#97	C₂³×C₇₁	1	4	yes	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	—	2	1	no	—
645	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
646	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
647	#41	—	2	8	no	—
648	#41	—	2	8	no	—
649	#41	—	2	8	no	—
650	#41	—	4	4	no	—
651	#41	—	4	4	no	—
652	#41	—	4	4	no	—
653	#41	—	4	8	no	—
654	#41	—	4	8	no	—
655	#41	—	4	8	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	8	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	4	4	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	—	4	8	no	—
672	C₂×Q₈	C₂×D₄×C₇₁	1	4	yes	—
673	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	C₂×D₄×C₇₁	1	4	yes	—
692	C₂×D₄	C₂×D₄×C₇₁	1	4	yes	—
693	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
694	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	—	4	4	no	—
712	C₂²×C₄	—	4	4	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	—	4	4	no	—
715	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
720	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
724	Q₁₆	—	2	8	no	—
725	Q₁₆	—	2	8	no	—
726	Q₁₆	—	2	8	no	—
727	Q₁₆	—	4	4	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	2	8	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	C₂×D₄×C₇₁	1	16	yes	complemented
732	D₈	—	2	8	no	—
733	M₁₆	—	2	8	no	—
734	C₂×C₈	—	2	2	no	—
735	C₂×C₈	—	2	2	no	—
736	C₂×C₈	—	2	2	no	—
737	C₂×C₈	—	2	8	no	—
738	C₂×C₈	C₂×D₄×C₇₁	1	4	yes	—
739	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
740	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
741	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
742	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
762	C₂²⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
763	C₄²	—	2	4	no	—
764	C₄²	C₂×D₄×C₇₁	1	2	yes	—
765	C₄²	C₂⁴×C₇₁	1	2	yes	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
781	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
782	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
783	Q₈	—	2	4	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	2	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	4	8	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	4	2	no	—
795	Q₈	C₂²×D₄×C₇₁	1	4	yes	—
796	D₄	—	2	4	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	8	no	—
805	D₄	—	4	2	no	—
806	D₄	C₂²×D₄×C₇₁	1	4	yes	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	4	8	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
840	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
841	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₈	—	2	2	no	—
845	C₈	C₂²×D₄×C₇₁	1	4	yes	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	4	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	8	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	8	4	no	—
862	C₂²	D₄²×C₇₁	1	2	yes	—
863	C₂²	#575×C₇₁	1	2	yes	—
864	C₂²	#578×C₇₁	1	2	yes	—
865	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	4	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	D₄²×C₇₁	1	2	yes	—
877	C₄	C₂³×D₄×C₇₁	1	1	yes	characteristic
878	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
879	C₂	—	4	2	no	—
880	C₂	—	4	2	no	—
881	C₂	—	4	4	no	—
882	C₂	—	8	2	no	—
883	C₂	C₇₁×#3269	1	4	yes	direct product factor
884	C₂	C₂×D₄²×C₇₁	1	1	yes	characteristic
885	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
886	C₂	C₂×#578×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
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
1. C₂²×#137×C₇₁	C₂	semidirect
2. C₂²×#135×C₇₁	C₂	semidirect
3. C₂×#548×C₇₁	C₂	semidirect
4. C₂×#547×C₇₁	C₂	semidirect
5. C₇₁×#3269	C₂	direct (N × H)
6. C₂×#497×C₇₁	C₂	semidirect
7. C₂×#468×C₇₁	C₂	semidirect
8. C₂×#467×C₇₁	C₂	semidirect
9. C₂×#462×C₇₁	C₂	semidirect
10. C₂×#463×C₇₁	C₂	semidirect
11. C₂×#452×C₇₁	C₂	semidirect
12. C₂×#452×C₇₁	C₂	semidirect
13. C₂×#449×C₇₁	C₂	semidirect
14. C₂×#451×C₇₁	C₂	semidirect
15. C₂×#440×C₇₁	C₂	semidirect
16. C₂×#435×C₇₁	C₂	semidirect
22. C₂×#137×C₇₁	C₂²	semidirect
24. C₂×#135×C₇₁	C₂²	semidirect
37. #548×C₇₁	C₂²	semidirect
39. #547×C₇₁	C₂²	semidirect
57. #497×C₇₁	C₂²	semidirect
58. #468×C₇₁	C₂²	semidirect
59. #467×C₇₁	C₂²	semidirect
60. #463×C₇₁	C₂²	semidirect
61. #462×C₇₁	C₂²	semidirect
62. #452×C₇₁	C₂²	semidirect
63. #452×C₇₁	C₂²	semidirect
64. #451×C₇₁	C₂²	semidirect
65. #449×C₇₁	C₂²	semidirect
66. #440×C₇₁	C₂²	semidirect
67. #435×C₇₁	C₂²	semidirect
127. C₂×SD₁₆×C₇₁	D₄	semidirect
287. SD₁₆×C₇₁	C₂×D₄	semidirect
435. C₂×#3269	C₇₁	direct (N × H)
440. C₂×C₇₁	#3269	direct (N × H)
444. C₂²×#137	C₂×C₇₁	semidirect
445. C₂²×#135	C₂×C₇₁	semidirect
446. C₂×#548	C₂×C₇₁	semidirect
447. C₂×#547	C₂×C₇₁	semidirect
448. #3269	C₂×C₇₁	direct (N × H)
449. C₂×#497	C₂×C₇₁	semidirect
450. C₂×#468	C₂×C₇₁	semidirect
451. C₂×#467	C₂×C₇₁	semidirect
452. C₂×#462	C₂×C₇₁	semidirect
453. C₂×#463	C₂×C₇₁	semidirect
454. C₂×#452	C₂×C₇₁	semidirect
455. C₂×#452	C₂×C₇₁	semidirect
456. C₂×#449	C₂×C₇₁	semidirect
457. C₂×#451	C₂×C₇₁	semidirect
458. C₂×#440	C₂×C₇₁	semidirect
459. C₂×#435	C₂×C₇₁	semidirect
460. C₇₁	C₂×#3269	direct (N × H)
466. C₂×#137	C₂²×C₇₁	semidirect
468. C₂×#135	C₂²×C₇₁	semidirect
481. #548	C₂²×C₇₁	semidirect
483. #547	C₂²×C₇₁	semidirect
501. #497	C₂²×C₇₁	semidirect
502. #468	C₂²×C₇₁	semidirect
503. #467	C₂²×C₇₁	semidirect
504. #463	C₂²×C₇₁	semidirect
505. #462	C₂²×C₇₁	semidirect
506. #452	C₂²×C₇₁	semidirect
507. #452	C₂²×C₇₁	semidirect
508. #451	C₂²×C₇₁	semidirect
509. #449	C₂²×C₇₁	semidirect
510. #440	C₂²×C₇₁	semidirect
511. #435	C₂²×C₇₁	semidirect
571. C₂×SD₁₆	D₄×C₇₁	semidirect
731. SD₁₆	C₂×D₄×C₇₁	semidirect
883. C₂	C₇₁×#3269	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₇₁	2
C₂²×#135×C₇₁	2
C₂×#548×C₇₁	2
C₂×#547×C₇₁	2
C₇₁×#3269	2
C₂×#497×C₇₁	2
C₂×#468×C₇₁	2
C₂×#467×C₇₁	2
C₂×#462×C₇₁	2
C₂×#463×C₇₁	2
C₂×#452×C₇₁	2
C₂×#449×C₇₁	2
C₂×#451×C₇₁	2
C₂×#440×C₇₁	2
C₂×#435×C₇₁	2
C₂×#3269	71

Subgroups — C2×C71×#3269 #31881899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×#3269 #31881899