Subgroups — #6375228

Order 512.

1573 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34026	C₂	1	1	yes	maximal, characteristic
2	#22027	C₂	1	2	yes	maximal, complemented
3	#22026	C₂	1	2	yes	maximal, complemented
4	#22017	C₂	1	2	yes	maximal, complemented
5	#22016	C₂	1	2	yes	maximal, complemented
6	#22007	C₂	1	2	yes	maximal, complemented
7	#22006	C₂	1	2	yes	maximal, complemented
8	#22005	C₂	1	2	yes	maximal, complemented
9	#22004	C₂	1	2	yes	maximal, complemented
10	#21431	C₂	1	1	yes	maximal, characteristic, complemented
11	#21431	C₂	1	1	yes	maximal, characteristic, complemented
12	#21430	C₂	1	1	yes	maximal, characteristic, complemented
13	#21430	C₂	1	1	yes	maximal, characteristic, complemented
14	#21374	C₂	1	1	yes	maximal, characteristic
15	#21373	C₂	1	1	yes	maximal, characteristic
16	#21350	C₂	1	1	yes	maximal, characteristic, complemented
17	#21349	C₂	1	1	yes	maximal, characteristic, complemented
18	#20782	C₂	1	1	yes	maximal, characteristic, complemented
19	#20782	C₂	1	1	yes	maximal, characteristic, complemented
20	#20777	C₂	1	1	yes	maximal, characteristic, complemented
21	#20777	C₂	1	1	yes	maximal, characteristic, complemented
22	#20462	C₂	1	1	yes	maximal, characteristic, complemented
23	#20366	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄×#41	C₂²	1	1	yes	characteristic
25	C₂×#431	C₂²	1	1	yes	characteristic
26	C₂×#431	C₂²	1	1	yes	characteristic
27	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
29	#2298	C₄	1	1	yes	characteristic
30	#2298	C₄	1	1	yes	characteristic
31	#2298	C₄	1	1	yes	characteristic
32	#2298	C₄	1	1	yes	characteristic
33	#2297	C₄	1	1	yes	characteristic
34	#2297	C₄	1	1	yes	characteristic
35	#2296	C₄	1	1	yes	characteristic
36	#2296	C₄	1	1	yes	characteristic
37	#2295	C₄	1	1	yes	characteristic
38	#2295	C₄	1	1	yes	characteristic
39	#2295	C₂²	1	1	yes	characteristic
40	#2295	C₂²	1	1	yes	characteristic
41	#2293	C₄	1	1	yes	characteristic
42	#2293	C₄	1	1	yes	characteristic
43	#2293	C₂²	1	1	yes	characteristic
44	#2293	C₂²	1	1	yes	characteristic
45	#2290	C₄	1	1	yes	characteristic
46	#2290	C₄	1	1	yes	characteristic
47	#2290	C₄	1	1	yes	characteristic
48	#2290	C₄	1	1	yes	characteristic
49	#2290	C₂²	1	1	yes	characteristic
50	#2290	C₂²	1	1	yes	characteristic
51	#2290	C₂²	1	1	yes	characteristic
52	#2290	C₂²	1	1	yes	characteristic
53	C₄×#117	C₂²	1	1	yes	characteristic
54	C₄×#117	C₂²	1	1	yes	characteristic
55	C₄×#117	C₂²	1	1	yes	characteristic
56	C₄×#117	C₂²	1	1	yes	characteristic
57	C₄×#117	C₂²	1	1	yes	characteristic
58	C₂×C₄³	C₂²	1	1	yes	characteristic
59	#1985	C₂²	1	2	yes	—
60	#1984	C₂²	1	2	yes	—
61	#1955	C₂²	1	2	yes	—
62	#1954	C₂²	1	2	yes	—
63	#1940	C₂²	1	2	yes	—
64	#1940	C₂²	1	2	yes	—
65	#1939	C₂²	1	2	yes	—
66	#1939	C₂²	1	2	yes	—
67	#1924	C₂²	1	2	yes	—
68	#1924	C₂²	1	2	yes	—
69	#1924	C₂²	1	2	yes	—
70	#1924	C₂²	1	2	yes	—
71	#1923	C₂²	1	2	yes	—
72	#1923	C₂²	1	2	yes	—
73	#1923	C₂²	1	2	yes	—
74	#1923	C₂²	1	2	yes	—
75	#1917	C₂²	1	2	yes	—
76	#1917	C₂²	1	2	yes	—
77	#1917	C₂²	1	2	yes	—
78	#1917	C₂²	1	2	yes	—
79	#1916	C₂²	1	2	yes	—
80	#1916	C₂²	1	2	yes	—
81	#1916	C₂²	1	2	yes	—
82	#1916	C₂²	1	2	yes	—
83	#1870	C₂²	1	2	yes	—
84	#1870	C₂²	1	2	yes	—
85	#1869	C₂²	1	2	yes	—
86	#1869	C₂²	1	2	yes	—
87	#1851	C₂²	1	2	yes	—
88	#1851	C₂²	1	2	yes	—
89	#1850	C₂²	1	2	yes	—
90	#1850	C₂²	1	2	yes	—
91	#1840	C₂²	1	2	yes	—
92	#1840	C₂²	1	2	yes	—
93	#1839	C₂²	1	2	yes	—
94	#1839	C₂²	1	2	yes	—
95	#1832	C₂²	1	2	yes	—
96	#1832	C₂²	1	2	yes	—
97	#1831	C₂²	1	2	yes	—
98	#1831	C₂²	1	2	yes	—
99	#1818	C₂²	1	2	yes	—
100	#1818	C₂²	1	2	yes	—
101	#1817	C₂²	1	2	yes	—
102	#1817	C₂²	1	2	yes	—
103	#1798	C₂²	1	2	yes	—
104	#1798	C₂²	1	2	yes	—
105	#1797	C₂²	1	2	yes	—
106	#1797	C₂²	1	2	yes	—
107	#1768	C₂²	1	2	yes	—
108	#1768	C₂²	1	2	yes	—
109	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
117	#1750	C₂²	1	2	yes	—
118	#1750	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
124	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
125	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
126	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
127	#1746	C₂²	1	2	yes	—
128	#1746	C₂²	1	2	yes	—
129	#1744	C₂²	1	1	yes	characteristic
130	#1744	C₂²	1	1	yes	characteristic
131	#1744	C₂²	1	1	yes	characteristic
132	#1744	C₂²	1	1	yes	characteristic
133	#1744	C₂²	1	1	yes	characteristic
134	#1744	C₂²	1	1	yes	characteristic
135	#1729	C₂²	1	2	yes	—
136	#1729	C₂²	1	2	yes	—
137	C₄×#97	C₂²	1	1	yes	characteristic
138	C₄²×C₈	C₂²	1	1	yes	characteristic
139	C₂²×#41	C₂×C₄	1	1	yes	characteristic
140	C₂²×M₁₆	C₂³	1	2	yes	—
141	C₂³×C₈	C₂³	1	2	yes	—
142	C₄×#41	—	2	4	no	—
143	C₄×#41	—	2	4	no	—
144	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
145	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
147	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
148	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
149	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
152	C₂×#117	C₂×C₄	1	1	yes	characteristic
153	C₂×#117	C₂×C₄	1	1	yes	characteristic
154	C₂×#117	C₂×C₄	1	1	yes	characteristic
155	C₂×#117	C₂×C₄	1	1	yes	characteristic
156	C₂×#117	C₂×C₄	1	1	yes	characteristic
157	C₂×#117	C₂×C₄	1	1	yes	characteristic
158	C₂×#117	C₂×C₄	1	1	yes	characteristic
159	C₂×#117	C₂×C₄	1	1	yes	characteristic
160	C₂×#117	C₂×C₄	1	1	yes	characteristic
161	C₂×#117	C₂³	1	1	yes	characteristic
162	C₂×#117	C₂³	1	1	yes	characteristic
163	C₂×#117	C₂³	1	1	yes	characteristic
164	C₂×#117	C₂³	1	1	yes	characteristic
165	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
166	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
167	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
168	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
169	C₂²×C₄²	C₂³	1	1	yes	characteristic
170	C₂²×C₄²	C₂³	1	1	yes	characteristic
171	C₂²×C₄²	C₂³	1	1	yes	characteristic
172	C₂²×C₄²	C₂³	1	1	yes	characteristic
173	C₂²×C₄²	C₂³	1	1	yes	characteristic
174	#431	—	2	4	no	—
175	#431	—	2	4	no	—
176	C₂×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂×C₄⋊C₈	C₂³	1	2	yes	—
179	C₂×C₄⋊C₈	C₂³	1	2	yes	—
180	C₂×C₄⋊C₈	C₂³	1	2	yes	—
181	C₂×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂×C₄⋊C₈	C₂³	1	2	yes	—
184	C₂×C₄⋊C₈	C₂³	1	2	yes	—
185	C₂×C₄⋊C₈	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₄×M₁₆	—	2	4	no	—
197	C₂×#97	C₂³	1	2	yes	—
198	C₂×#97	C₂³	1	2	yes	—
199	C₂×#97	C₂³	1	2	yes	—
200	C₂×C₄×C₈	—	2	4	no	—
201	C₂×C₄×C₈	C₂³	1	2	yes	—
202	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂³	1	2	yes	—
211	C₂×C₄×C₈	C₂³	1	2	yes	—
212	#391	C₂×C₄	1	1	yes	characteristic
213	#391	C₂×C₄	1	1	yes	characteristic
214	#391	C₂×C₄	1	1	yes	characteristic
215	#391	C₂×C₄	1	1	yes	characteristic
216	#390	C₂×C₄	1	1	yes	characteristic
217	#390	C₂×C₄	1	1	yes	characteristic
218	#390	C₂×C₄	1	1	yes	characteristic
219	#390	C₂×C₄	1	1	yes	characteristic
220	#389	C₂×C₄	1	1	yes	characteristic
221	#389	C₂×C₄	1	1	yes	characteristic
222	#389	C₂×C₄	1	1	yes	characteristic
223	#389	C₂×C₄	1	1	yes	characteristic
224	#389	C₂×C₄	1	1	yes	characteristic
225	#389	C₂×C₄	1	1	yes	characteristic
226	#389	C₂×C₄	1	1	yes	characteristic
227	#389	C₂×C₄	1	1	yes	characteristic
228	#388	C₂×C₄	1	1	yes	characteristic
229	#388	C₂×C₄	1	1	yes	characteristic
230	#388	C₂×C₄	1	1	yes	characteristic
231	#388	C₂×C₄	1	1	yes	characteristic
232	#388	C₂×C₄	1	1	yes	characteristic
233	#388	C₂×C₄	1	1	yes	characteristic
234	#388	C₂×C₄	1	1	yes	characteristic
235	#388	C₂×C₄	1	1	yes	characteristic
236	#388	C₂×C₄	1	1	yes	characteristic
237	#388	C₂×C₄	1	1	yes	characteristic
238	#388	C₂×C₄	1	1	yes	characteristic
239	#388	C₂×C₄	1	1	yes	characteristic
240	#388	C₂×C₄	1	1	yes	characteristic
241	#388	C₂×C₄	1	1	yes	characteristic
242	#388	C₂×C₄	1	1	yes	characteristic
243	#388	C₂×C₄	1	1	yes	characteristic
244	#387	C₂×C₄	1	1	yes	characteristic
245	#387	C₂×C₄	1	1	yes	characteristic
246	#387	C₂×C₄	1	1	yes	characteristic
247	#387	C₂×C₄	1	1	yes	characteristic
248	#387	C₂×C₄	1	1	yes	characteristic
249	#387	C₂×C₄	1	1	yes	characteristic
250	#387	C₂×C₄	1	1	yes	characteristic
251	#387	C₂×C₄	1	1	yes	characteristic
252	#387	C₂×C₄	1	1	yes	characteristic
253	#387	C₂×C₄	1	1	yes	characteristic
254	#387	C₂×C₄	1	1	yes	characteristic
255	#387	C₂×C₄	1	1	yes	characteristic
256	#387	C₂×C₄	1	1	yes	characteristic
257	#387	C₂×C₄	1	1	yes	characteristic
258	#387	C₂×C₄	1	1	yes	characteristic
259	#387	C₂×C₄	1	1	yes	characteristic
260	#386	C₂×C₄	1	1	yes	characteristic
261	#386	C₂×C₄	1	1	yes	characteristic
262	#386	C₂×C₄	1	1	yes	characteristic
263	#386	C₂×C₄	1	1	yes	characteristic
264	#386	C₂×C₄	1	1	yes	characteristic
265	#386	C₂×C₄	1	1	yes	characteristic
266	#386	C₂×C₄	1	1	yes	characteristic
267	#386	C₂×C₄	1	1	yes	characteristic
268	#385	C₂×C₄	1	1	yes	characteristic
269	#385	C₂×C₄	1	1	yes	characteristic
270	#385	C₂×C₄	1	1	yes	characteristic
271	#385	C₂×C₄	1	1	yes	characteristic
272	#385	C₂×C₄	1	1	yes	characteristic
273	#385	C₂×C₄	1	1	yes	characteristic
274	#385	C₂×C₄	1	1	yes	characteristic
275	#385	C₂×C₄	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
279	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
282	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
286	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
297	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
298	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
299	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
304	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
305	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
306	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
307	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
308	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
309	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	#376	C₂×C₄	1	1	yes	characteristic
317	#376	C₂×C₄	1	1	yes	characteristic
318	#376	C₂×C₄	1	1	yes	characteristic
319	#376	C₂×C₄	1	1	yes	characteristic
320	#376	C₂×C₄	1	1	yes	characteristic
321	#376	C₂×C₄	1	1	yes	characteristic
322	#376	C₂³	1	1	yes	characteristic
323	#376	C₂³	1	1	yes	characteristic
324	#376	C₂³	1	1	yes	characteristic
325	#376	C₂³	1	1	yes	characteristic
326	C₄³	C₂×C₄	1	1	yes	characteristic
327	C₄³	C₂×C₄	1	1	yes	characteristic
328	C₄³	C₂×C₄	1	1	yes	characteristic
329	C₄³	C₂×C₄	1	1	yes	characteristic
330	C₄³	C₂³	1	1	yes	characteristic
331	C₄³	C₂³	1	1	yes	characteristic
332	C₄³	C₂³	1	1	yes	characteristic
333	C₄³	C₂³	1	1	yes	characteristic
334	C₄³	C₂³	1	1	yes	characteristic
335	C₄³	C₂³	1	1	yes	characteristic
336	#336	C₂³	1	2	yes	—
337	#336	C₂³	1	2	yes	—
338	#336	C₂³	1	2	yes	—
339	#336	C₂³	1	2	yes	—
340	#336	C₂³	1	2	yes	—
341	#336	C₂³	1	2	yes	—
342	#336	C₂³	1	2	yes	—
343	#336	C₂³	1	2	yes	—
344	#336	C₂³	1	2	yes	—
345	#336	C₂³	1	2	yes	—
346	#336	C₂³	1	2	yes	—
347	#336	C₂³	1	2	yes	—
348	#336	C₂³	1	2	yes	—
349	#336	C₂³	1	2	yes	—
350	#336	C₂³	1	2	yes	—
351	#336	C₂³	1	2	yes	—
352	#336	C₂³	1	2	yes	—
353	#336	C₂³	1	2	yes	—
354	#336	C₂³	1	2	yes	—
355	#336	C₂³	1	2	yes	—
356	#336	C₂³	1	2	yes	—
357	#336	C₂³	1	2	yes	—
358	#336	C₂³	1	2	yes	—
359	#336	C₂³	1	2	yes	—
360	#336	C₂³	1	2	yes	—
361	#336	C₂³	1	2	yes	—
362	#336	C₂³	1	2	yes	—
363	#336	C₂³	1	2	yes	—
364	C₂×#41	—	2	4	no	—
365	C₂×#41	—	2	4	no	—
366	C₂×#41	—	4	2	no	—
367	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
368	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
369	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
370	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
371	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
372	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
373	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
374	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
375	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
376	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
377	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
378	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
379	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
380	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
381	C₂³×C₄	C₂⁴	1	1	yes	characteristic
382	C₂³×C₄	C₂⁴	1	1	yes	characteristic
383	C₂³×C₄	C₂⁴	1	1	yes	characteristic
384	C₂×M₁₆	—	2	4	no	—
385	C₂×M₁₆	—	4	2	no	—
386	C₂×M₁₆	—	4	2	no	—
387	C₂²×C₈	—	2	4	no	—
388	C₂²×C₈	—	4	2	no	—
389	C₂²×C₈	—	4	2	no	—
390	C₂²×C₈	C₂⁴	1	2	yes	—
391	C₂²×C₈	C₂⁴	1	2	yes	—
392	C₂²×C₈	C₂⁴	1	2	yes	—
393	C₂²×C₈	C₂⁴	1	2	yes	—
394	C₂²×C₈	C₂⁴	1	2	yes	—
395	C₂²×C₈	C₂⁴	1	2	yes	—
396	C₂²×C₈	C₂⁴	1	2	yes	—
397	C₂²×C₈	C₂⁴	1	2	yes	—
398	C₄×Q₈	—	2	4	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	#117	—	2	4	no	—
411	#117	—	2	4	no	—
412	#117	—	2	4	no	—
413	#117	—	2	4	no	—
414	#117	—	2	4	no	—
415	#117	—	2	4	no	—
416	#117	—	4	2	no	—
417	#117	—	4	2	no	—
418	#117	—	4	2	no	—
419	#117	—	4	2	no	—
420	#117	—	4	2	no	—
421	#117	—	4	2	no	—
422	#117	—	4	2	no	—
423	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
475	C₂×C₄²	—	2	4	no	—
476	C₂×C₄²	—	2	4	no	—
477	C₂×C₄²	—	2	2	no	—
478	C₂×C₄²	—	2	2	no	—
479	C₂×C₄²	—	2	2	no	—
480	C₂×C₄²	—	2	2	no	—
481	C₂×C₄²	—	4	2	no	—
482	C₂×C₄²	—	4	2	no	—
483	C₂×C₄²	—	4	2	no	—
484	C₂×C₄²	—	4	2	no	—
485	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
486	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
487	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
488	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
489	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
490	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
491	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
492	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
493	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
494	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
495	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
496	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
497	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
498	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
499	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
500	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
501	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
502	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
503	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
504	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
505	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
506	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
507	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
508	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
509	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
510	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
511	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
512	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
513	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
514	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
515	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
516	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
517	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
518	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
519	C₂×C₄²	#41	1	4	yes	—
520	C₂×C₄²	#41	1	4	yes	—
521	C₂×C₄²	C₂⁴	1	1	yes	characteristic
522	C₂×C₄²	C₂⁴	1	1	yes	characteristic
523	C₂×C₄²	C₂⁴	1	1	yes	characteristic
524	C₂×C₄²	C₂⁴	1	1	yes	characteristic
525	C₂×C₄²	C₂⁴	1	1	yes	characteristic
526	C₂×C₄²	C₂⁴	1	1	yes	characteristic
527	C₂×C₄²	C₂⁴	1	1	yes	characteristic
528	C₂×C₄²	C₂⁴	1	1	yes	characteristic
529	C₂×C₄²	C₂⁴	1	1	yes	characteristic
530	C₂×C₄²	C₂⁴	1	1	yes	characteristic
531	C₂×C₄²	C₂⁴	1	1	yes	characteristic
532	C₂×C₄²	C₂⁴	1	1	yes	characteristic
533	C₄⋊C₈	—	2	4	no	—
534	C₄⋊C₈	—	2	4	no	—
535	C₄⋊C₈	—	4	2	no	—
536	C₄⋊C₈	—	4	2	no	—
537	C₄⋊C₈	—	4	2	no	—
538	C₄⋊C₈	—	4	2	no	—
539	C₄⋊C₈	—	4	2	no	—
540	C₄⋊C₈	—	4	2	no	—
541	C₄⋊C₈	—	4	2	no	—
542	C₄⋊C₈	—	4	2	no	—
543	C₂²⋊C₈	—	2	4	no	—
544	C₂²⋊C₈	—	2	4	no	—
545	C₂²⋊C₈	—	4	2	no	—
546	C₂²⋊C₈	—	4	2	no	—
547	C₂²⋊C₈	—	4	2	no	—
548	C₂²⋊C₈	—	4	2	no	—
549	C₂²⋊C₈	—	4	2	no	—
550	C₂²⋊C₈	—	4	2	no	—
551	C₂²⋊C₈	—	4	2	no	—
552	C₂²⋊C₈	—	4	2	no	—
553	#97	—	2	4	no	—
554	#97	—	4	2	no	—
555	#97	—	4	2	no	—
556	C₄×C₈	—	2	2	no	—
557	C₄×C₈	—	2	2	no	—
558	C₄×C₈	—	2	4	no	—
559	C₄×C₈	—	2	2	no	—
560	C₄×C₈	—	2	2	no	—
561	C₄×C₈	—	2	2	no	—
562	C₄×C₈	—	2	2	no	—
563	C₄×C₈	—	2	2	no	—
564	C₄×C₈	—	2	2	no	—
565	C₄×C₈	—	4	2	no	—
566	C₄×C₈	—	4	2	no	—
567	#95	C₂²×C₄	1	1	yes	characteristic
568	#95	C₂²×C₄	1	1	yes	characteristic
569	#95	C₂²×C₄	1	1	yes	characteristic
570	#95	C₂²×C₄	1	1	yes	characteristic
571	#95	C₂²×C₄	1	1	yes	characteristic
572	#95	C₂²×C₄	1	1	yes	characteristic
573	#95	C₂²×C₄	1	1	yes	characteristic
574	#95	C₂²×C₄	1	1	yes	characteristic
575	#95	C₂²×C₄	1	1	yes	characteristic
576	#95	C₂²×C₄	1	1	yes	characteristic
577	#95	C₂²×C₄	1	1	yes	characteristic
578	#95	C₂²×C₄	1	1	yes	characteristic
579	#95	C₂²×C₄	1	1	yes	characteristic
580	#95	C₂²×C₄	1	1	yes	characteristic
581	#95	C₂²×C₄	1	1	yes	characteristic
582	#95	C₂²×C₄	1	1	yes	characteristic
583	#95	C₂²×C₄	1	1	yes	characteristic
584	#95	C₂²×C₄	1	1	yes	characteristic
585	#95	C₂²×C₄	1	1	yes	characteristic
586	#95	C₂²×C₄	1	1	yes	characteristic
587	#95	C₂²×C₄	1	1	yes	characteristic
588	#95	C₂²×C₄	1	1	yes	characteristic
589	#95	C₂²×C₄	1	1	yes	characteristic
590	#95	C₂²×C₄	1	1	yes	characteristic
591	#95	C₂²×C₄	1	1	yes	characteristic
592	#95	C₂²×C₄	1	1	yes	characteristic
593	#95	C₂²×C₄	1	1	yes	characteristic
594	#95	C₂²×C₄	1	1	yes	characteristic
595	#95	C₂²×C₄	1	1	yes	characteristic
596	#95	C₂²×C₄	1	1	yes	characteristic
597	#95	C₂²×C₄	1	1	yes	characteristic
598	#95	C₂²×C₄	1	1	yes	characteristic
599	#95	C₂²×C₄	1	1	yes	characteristic
600	#95	C₂²×C₄	1	1	yes	characteristic
601	#95	C₂²×C₄	1	1	yes	characteristic
602	#95	C₂²×C₄	1	1	yes	characteristic
603	#95	C₂²×C₄	1	1	yes	characteristic
604	#95	C₂²×C₄	1	1	yes	characteristic
605	#95	C₂²×C₄	1	1	yes	characteristic
606	#95	C₂²×C₄	1	1	yes	characteristic
607	C₂⁴	C₂³×C₄	1	1	yes	characteristic
608	C₂⁴	C₂³×C₄	1	1	yes	characteristic
609	C₂⁴	C₂³×C₄	1	1	yes	characteristic
610	#41	—	4	16	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	4	1	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	4	1	no	—
621	C₂×D₄	—	4	1	no	—
622	C₂×D₄	—	4	1	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	4	1	no	—
653	C₂²×C₄	—	4	1	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	1	no	—
656	C₂²×C₄	—	4	1	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	#117	1	4	yes	—
661	C₂²×C₄	#117	1	4	yes	—
662	C₂²×C₄	#131	1	4	yes	—
663	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
664	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
665	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
666	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
667	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
668	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
669	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
670	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
671	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
672	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
673	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
674	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
675	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
676	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
677	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
678	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
679	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
680	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
681	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
682	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
683	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
684	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
685	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
686	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
687	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
688	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
689	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
690	C₂²×C₄	C₂×#41	1	2	yes	—
691	C₂²×C₄	C₂×#41	1	2	yes	—
692	C₂²×C₄	C₂⁵	1	1	yes	characteristic
693	M₁₆	—	4	8	no	—
694	C₂×C₈	—	2	2	no	—
695	C₂×C₈	—	2	2	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	—	2	2	no	—
698	C₂×C₈	—	2	2	no	—
699	C₂×C₈	—	2	2	no	—
700	C₂×C₈	—	2	2	no	—
701	C₂×C₈	—	2	2	no	—
702	C₂×C₈	—	2	2	no	—
703	C₂×C₈	—	2	2	no	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	—	2	2	no	—
706	C₂×C₈	—	2	2	no	—
707	C₂×C₈	—	2	2	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	2	2	no	—
710	C₂×C₈	—	2	2	no	—
711	C₂×C₈	—	2	2	no	—
712	C₂×C₈	—	2	2	no	—
713	C₂×C₈	—	2	2	no	—
714	C₂×C₈	—	2	2	no	—
715	C₂×C₈	—	2	2	no	—
716	C₂×C₈	—	2	2	no	—
717	C₂×C₈	—	2	2	no	—
718	C₂×C₈	—	4	8	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	1	no	—
743	C₄⋊C₄	—	4	1	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	—	4	1	no	—
759	C₂²⋊C₄	—	4	1	no	—
760	C₂²⋊C₄	—	4	1	no	—
761	C₂²⋊C₄	—	4	1	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	1	no	—
766	C₂²⋊C₄	—	4	1	no	—
767	C₂²⋊C₄	—	4	1	no	—
768	C₂²⋊C₄	—	4	1	no	—
769	C₂²⋊C₄	—	4	1	no	—
770	C₂²⋊C₄	—	4	1	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	2	1	no	—
796	C₄²	—	2	1	no	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	4	1	no	—
807	C₄²	—	4	1	no	—
808	C₄²	—	4	1	no	—
809	C₄²	—	4	1	no	—
810	C₄²	—	4	1	no	—
811	C₄²	—	4	1	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	1	no	—
814	C₄²	#117	1	4	yes	—
815	C₄²	#117	1	4	yes	—
816	C₄²	#131	1	4	yes	—
817	C₄²	C₂×#41	1	2	yes	—
818	C₄²	C₂×#41	1	2	yes	—
819	C₄²	C₂×#41	1	2	yes	—
820	C₄²	C₂×#41	1	2	yes	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	C₂×#117	1	2	yes	—
841	C₂³	C₂×#131	1	2	yes	—
842	C₂³	C₂⁴×C₄	1	1	yes	characteristic
843	Q₈	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	8	no	—
860	C₂×C₄	—	2	8	no	—
861	C₂×C₄	—	2	8	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	2	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	C₂×#117	1	2	yes	—
933	C₂×C₄	C₂×#117	1	2	yes	—
934	C₂×C₄	C₂×#117	1	2	yes	—
935	C₂×C₄	C₂×#117	1	2	yes	—
936	C₂×C₄	C₂×#117	1	2	yes	—
937	C₂×C₄	C₂×#131	1	2	yes	—
938	C₂×C₄	C₂×#131	1	2	yes	—
939	C₂×C₄	C₂×#131	1	2	yes	—
940	C₂×C₄	C₂×#131	1	2	yes	—
941	C₂×C₄	C₂×#131	1	2	yes	—
942	C₂×C₄	#568	1	2	yes	—
943	C₂×C₄	#568	1	2	yes	—
944	C₂×C₄	C₂²×#41	1	1	yes	characteristic
945	C₂×C₄	C₂²×#41	1	1	yes	characteristic
946	C₂×C₄	#585	1	2	yes	—
947	C₂×C₄	#585	1	2	yes	—
948	C₈	—	4	2	no	—
949	C₈	—	4	2	no	—
950	C₈	—	4	2	no	—
951	C₈	—	4	2	no	—
952	C₈	—	4	2	no	—
953	C₈	—	4	2	no	—
954	C₈	—	4	2	no	—
955	C₈	—	4	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	C₂²×#117	1	1	yes	characteristic
978	C₂²	#3428	1	1	yes	characteristic
979	C₂²	#3428	1	1	yes	characteristic
980	C₂²	C₂²×#131	1	1	yes	characteristic
981	C₂²	C₂²×#131	1	1	yes	characteristic
982	C₂²	C₂×#568	1	1	yes	characteristic
983	C₂²	C₂×#568	1	1	yes	characteristic
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	1	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	1	no	—
1009	C₄	#2924	1	4	yes	—
1010	C₄	#2925	1	4	yes	—
1011	C₄	#3455	1	2	yes	—
1012	C₄	#3455	1	2	yes	—
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	8	1	no	—
1016	C₂	#34056	1	1	yes	characteristic
1017	C₂	C₂×#2924	1	1	yes	characteristic
1018	C₂	C₂×#2925	1	1	yes	characteristic
1019	C₂	#60279	1	1	yes	characteristic
1020	C₂	#60279	1	1	yes	characteristic
1021	C₂	#60280	1	1	yes	characteristic
1022	C₂	#60281	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂⁴
commutator, socle	C₂³	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×#41	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #22027	C₂	semidirect
3. #22026	C₂	semidirect
4. #22017	C₂	semidirect
5. #22016	C₂	semidirect
6. #22007	C₂	semidirect
7. #22006	C₂	semidirect
8. #22005	C₂	semidirect
9. #22004	C₂	semidirect
10. #21431	C₂	semidirect
11. #21431	C₂	semidirect
12. #21430	C₂	semidirect
13. #21430	C₂	semidirect
16. #21350	C₂	semidirect
17. #21349	C₂	semidirect
18. #20782	C₂	semidirect
19. #20782	C₂	semidirect
20. #20777	C₂	semidirect
21. #20777	C₂	semidirect
22. #20462	C₂	semidirect
23. #20366	C₂	semidirect

Maximal subgroups

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

subgroup	index
#34026	2
#22027	2
#22026	2
#22017	2
#22016	2
#22007	2
#22006	2
#22005	2
#22004	2
#21431	2
#21430	2
#21374	2
#21373	2
#21350	2
#21349	2
#20782	2
#20777	2
#20462	2
#20366	2