Subgroups — #6568272

Order 512.

1539 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36196	C₂	1	1	yes	maximal, characteristic, complemented
2	#34320	C₂	1	1	yes	maximal, characteristic
3	#30174	C₂	1	1	yes	maximal, characteristic, complemented
4	#30167	C₂	1	1	yes	maximal, characteristic, complemented
5	#29870	C₂	1	1	yes	maximal, characteristic, complemented
6	#29261	C₂	1	1	yes	maximal, characteristic, complemented
7	#29114	C₂	1	1	yes	maximal, characteristic, complemented
8	#29110	C₂	1	1	yes	maximal, characteristic, complemented
9	#28721	C₂	1	1	yes	maximal, characteristic, complemented
10	#27590	C₂	1	1	yes	maximal, characteristic, complemented
11	#27588	C₂	1	1	yes	maximal, characteristic, complemented
12	#27548	C₂	1	1	yes	maximal, characteristic, complemented
13	#27546	C₂	1	1	yes	maximal, characteristic, complemented
14	#27541	C₂	1	1	yes	maximal, characteristic, complemented
15	#27539	C₂	1	1	yes	maximal, characteristic, complemented
16	#27124	C₂	1	1	yes	maximal, characteristic, complemented
17	#27122	C₂	1	1	yes	maximal, characteristic, complemented
18	#27117	C₂	1	1	yes	maximal, characteristic, complemented
19	#27115	C₂	1	1	yes	maximal, characteristic, complemented
20	#26307	C₂	1	1	yes	maximal, characteristic, complemented
21	#26305	C₂	1	1	yes	maximal, characteristic, complemented
22	#25890	C₂	1	1	yes	maximal, characteristic
23	#25890	C₂	1	1	yes	maximal, characteristic
24	#23778	C₂	1	1	yes	maximal, characteristic, complemented
25	#23765	C₂	1	1	yes	maximal, characteristic, complemented
26	#23764	C₂	1	1	yes	maximal, characteristic, complemented
27	#23225	C₂	1	1	yes	maximal, characteristic, complemented
28	#23224	C₂	1	1	yes	maximal, characteristic, complemented
29	#23071	C₂	1	1	yes	maximal, characteristic, complemented
30	#23071	C₂	1	1	yes	maximal, characteristic, complemented
31	#22839	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#546	C₂²	1	1	yes	characteristic
33	C₂×#488	C₂²	1	1	yes	characteristic
34	C₂×#488	C₂²	1	1	yes	characteristic
35	C₂×#478	C₂²	1	1	yes	characteristic
36	C₂×#478	C₂²	1	1	yes	characteristic
37	#2859	C₂²	1	1	yes	characteristic, complemented
38	#2851	C₂²	1	1	yes	characteristic
39	#2851	C₂²	1	1	yes	characteristic, complemented
40	#2573	—	2	1	no	—
41	#2573	—	2	1	no	—
42	#2562	C₂²	1	1	yes	characteristic
43	#2562	C₂²	1	1	yes	characteristic
44	#2533	—	2	1	no	—
45	#2533	—	2	1	no	—
46	#2497	C₂²	1	1	yes	characteristic
47	#2497	C₂²	1	1	yes	characteristic, complemented
48	#2496	C₂²	1	1	yes	characteristic
49	#2496	C₂²	1	1	yes	characteristic, complemented
50	#2466	—	2	1	no	—
51	#2466	—	2	1	no	—
52	#2374	—	2	1	no	—
53	#2373	—	2	1	no	—
54	#2373	—	2	1	no	—
55	#2370	C₂²	1	1	yes	characteristic, complemented
56	#2370	C₂²	1	1	yes	characteristic, complemented
57	#2367	C₂²	1	1	yes	characteristic
58	#2363	—	2	1	no	—
59	#2363	C₂²	1	1	yes	characteristic
60	#2360	C₂²	1	1	yes	characteristic
61	#2358	—	2	1	no	—
62	#2357	C₂²	1	1	yes	characteristic
63	#2352	C₂²	1	1	yes	characteristic
64	#2342	—	2	1	no	—
65	#2341	C₂²	1	1	yes	characteristic
66	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	#2335	—	2	1	no	—
68	#2333	—	2	1	no	—
69	#2321	—	2	1	no	—
70	C₄×#125	C₂²	1	1	yes	characteristic, complemented
71	C₄×#124	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
73	C₄×#121	C₂²	1	1	yes	characteristic
74	#2297	C₂²	1	1	yes	characteristic
75	#2293	C₂²	1	1	yes	characteristic
76	C₂×#390	C₂²	1	1	yes	characteristic
77	#2283	C₂²	1	1	yes	characteristic
78	#2283	C₂²	1	1	yes	characteristic, complemented
79	#2273	—	2	1	no	—
80	C₄²×D₄	C₂²	1	1	yes	characteristic
81	#2101	C₂²	1	1	yes	characteristic, complemented
82	#2097	C₂²	1	1	yes	characteristic, complemented
83	#2092	C₂²	1	1	yes	characteristic
84	#2092	C₂²	1	1	yes	characteristic
85	#2088	C₂²	1	1	yes	characteristic, complemented
86	#2087	C₂²	1	1	yes	characteristic, complemented
87	#2085	C₂²	1	1	yes	characteristic, complemented
88	#2085	C₂²	1	1	yes	characteristic, complemented
89	#2084	C₂²	1	1	yes	characteristic, complemented
90	#2083	C₂²	1	1	yes	characteristic, complemented
91	#2077	C₂²	1	1	yes	characteristic
92	#2077	C₂²	1	1	yes	characteristic
93	#2077	C₂²	1	1	yes	characteristic, complemented
94	#2077	C₂²	1	1	yes	characteristic, complemented
95	#2076	C₂²	1	1	yes	characteristic
96	#2076	C₂²	1	1	yes	characteristic
97	#2076	C₂²	1	1	yes	characteristic, complemented
98	#2075	C₂²	1	1	yes	characteristic, complemented
99	#2074	C₂²	1	1	yes	characteristic, complemented
100	#2074	C₂²	1	1	yes	characteristic, complemented
101	#2073	C₂²	1	1	yes	characteristic
102	#2073	C₂²	1	1	yes	characteristic
103	#2073	C₂²	1	1	yes	characteristic
104	#2073	C₂²	1	1	yes	characteristic
105	#2071	C₂²	1	1	yes	characteristic
106	#2071	C₂²	1	1	yes	characteristic
107	#2067	C₂²	1	1	yes	characteristic
108	#2065	C₂²	1	1	yes	characteristic
109	#2059	C₂²	1	1	yes	characteristic, complemented
110	#2036	C₂²	1	1	yes	characteristic
111	#2036	C₂²	1	1	yes	characteristic
112	#2035	C₂²	1	1	yes	characteristic
113	#2035	C₂²	1	1	yes	characteristic
114	#2034	C₂²	1	1	yes	characteristic
115	#2034	C₂²	1	1	yes	characteristic
116	#2033	C₂²	1	1	yes	characteristic
117	#2033	C₂²	1	1	yes	characteristic
118	#2026	C₂²	1	1	yes	characteristic, complemented
119	#2025	C₂²	1	1	yes	characteristic
120	#2025	C₂²	1	1	yes	characteristic
121	#1991	C₂²	1	1	yes	characteristic, complemented
122	#1991	C₂²	1	1	yes	characteristic, complemented
123	#1989	C₂²	1	1	yes	characteristic, complemented
124	#1989	C₂²	1	1	yes	characteristic, complemented
125	#1983	C₂²	1	1	yes	characteristic
126	#1983	C₂²	1	1	yes	characteristic
127	#1954	C₂²	1	1	yes	characteristic
128	#1954	C₂²	1	1	yes	characteristic
129	#1949	C₂²	1	1	yes	characteristic, complemented
130	#1949	C₂²	1	1	yes	characteristic, complemented
131	#1936	C₂²	1	1	yes	characteristic
132	#1936	C₂²	1	1	yes	characteristic
133	#1936	C₂²	1	1	yes	characteristic
134	#1936	C₂²	1	1	yes	characteristic
135	#1936	C₂²	1	1	yes	characteristic
136	#1936	C₂²	1	1	yes	characteristic
137	#1935	C₂²	1	1	yes	characteristic, complemented
138	#1935	C₂²	1	1	yes	characteristic, complemented
139	#1928	C₂²	1	1	yes	characteristic, complemented
140	#1927	C₂²	1	1	yes	characteristic, complemented
141	#1926	C₂²	1	1	yes	characteristic
142	#1926	C₂²	1	1	yes	characteristic
143	#1926	C₂²	1	1	yes	characteristic
144	#1925	C₂²	1	1	yes	characteristic
145	#1925	C₂²	1	1	yes	characteristic
146	#1925	C₂²	1	1	yes	characteristic
147	#1924	C₂²	1	1	yes	characteristic
148	#1924	C₂²	1	1	yes	characteristic
149	#1924	C₂²	1	1	yes	characteristic, complemented
150	#1924	C₂²	1	1	yes	characteristic, complemented
151	#1920	C₂²	1	1	yes	characteristic, complemented
152	#1920	C₂²	1	1	yes	characteristic, complemented
153	#1918	C₂²	1	1	yes	characteristic, complemented
154	#1918	C₂²	1	1	yes	characteristic, complemented
155	#1865	C₂²	1	1	yes	characteristic, complemented
156	#1865	C₂²	1	1	yes	characteristic, complemented
157	#1864	C₂²	1	1	yes	characteristic
158	#1864	C₂²	1	1	yes	characteristic
159	#1863	C₂²	1	1	yes	characteristic, complemented
160	#1863	C₂²	1	1	yes	characteristic, complemented
161	#1862	C₂²	1	1	yes	characteristic
162	#1862	C₂²	1	1	yes	characteristic
163	#1854	C₂²	1	1	yes	characteristic, complemented
164	#1854	C₂²	1	1	yes	characteristic, complemented
165	#1853	C₂²	1	1	yes	characteristic
166	#1852	C₂²	1	1	yes	characteristic
167	#1831	C₂²	1	1	yes	characteristic, complemented
168	#1825	C₂²	1	1	yes	characteristic, complemented
169	#1825	C₂²	1	1	yes	characteristic, complemented
170	#1823	C₂²	1	1	yes	characteristic
171	#1823	C₂²	1	1	yes	characteristic
172	#1817	C₂²	1	1	yes	characteristic
173	#1817	C₂²	1	1	yes	characteristic, complemented
174	#1803	C₂²	1	1	yes	characteristic, complemented
175	#1803	C₂²	1	1	yes	characteristic, complemented
176	#1802	C₂²	1	1	yes	characteristic
177	#1802	C₂²	1	1	yes	characteristic
178	#1788	C₂²	1	1	yes	characteristic
179	#1788	C₂²	1	1	yes	characteristic
180	#1788	C₂²	1	1	yes	characteristic
181	#1788	C₂²	1	1	yes	characteristic
182	#1786	C₂²	1	1	yes	characteristic
183	#1786	C₂²	1	1	yes	characteristic
184	#1786	C₂²	1	1	yes	characteristic
185	#1786	C₂²	1	1	yes	characteristic
186	#1776	C₂²	1	1	yes	characteristic, complemented
187	#1776	C₂²	1	1	yes	characteristic, complemented
188	#1776	C₂²	1	1	yes	characteristic, complemented
189	#1776	C₂²	1	1	yes	characteristic, complemented
190	C₄×#107	C₂²	1	1	yes	characteristic, complemented
191	C₄×#106	C₂²	1	1	yes	characteristic, complemented
192	#1770	C₂²	1	1	yes	characteristic, complemented
193	#1770	C₂²	1	1	yes	characteristic, complemented
194	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
195	#1763	C₂²	1	1	yes	characteristic, complemented
196	#1763	C₂²	1	1	yes	characteristic, complemented
197	#1762	C₂²	1	1	yes	characteristic
198	#1762	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	C₄×#102	C₂²	1	1	yes	characteristic
201	#1749	C₂²	1	1	yes	characteristic
202	#1749	C₂²	1	1	yes	characteristic, complemented
203	C₂²×#41	C₂³	1	1	yes	characteristic
204	C₂³×D₄	C₂³	1	1	yes	characteristic
205	#546	—	2	4	no	—
206	#546	—	2	4	no	—
207	C₂×#126	—	2	1	no	—
208	C₂×#126	—	2	1	no	—
209	C₂×#125	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#124	C₂³	1	1	yes	characteristic
213	C₂×#123	—	2	1	no	—
214	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×#121	—	2	1	no	—
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×#120	—	2	1	no	—
218	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	D₄	1	1	yes	characteristic
222	C₂×C₄×D₄	D₄	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₂×#117	—	2	1	no	—
228	C₂×#117	C₂³	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂²×C₂²⋊C₄	—	2	1	no	—
232	C₂²×C₂²⋊C₄	—	2	1	no	—
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	C₂²×C₄²	C₂³	1	1	yes	characteristic
235	C₂²×C₄²	C₂³	1	1	yes	characteristic
236	#488	—	2	4	no	—
237	#488	—	2	4	no	—
238	#478	—	2	4	no	—
239	#478	—	2	4	no	—
240	C₂×#107	C₂³	1	1	yes	characteristic
241	C₂×#107	C₂³	1	1	yes	characteristic
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#107	C₂³	1	1	yes	characteristic
244	C₂×#107	C₂³	1	1	yes	characteristic
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#106	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×#106	C₂³	1	1	yes	characteristic
249	C₂×#106	C₂³	1	1	yes	characteristic
250	C₂×#106	C₂³	1	1	yes	characteristic
251	C₂×#106	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₂×#103	C₂³	1	1	yes	characteristic
257	C₂×#103	C₂³	1	1	yes	characteristic
258	C₂×#103	C₂³	1	1	yes	characteristic
259	C₂×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#102	C₂³	1	1	yes	characteristic
265	C₂×#102	C₂³	1	1	yes	characteristic
266	C₂×#102	C₂³	1	1	yes	characteristic
267	C₂×#102	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	#400	—	2	1	no	—
295	#400	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#397	—	2	1	no	—
301	#397	—	2	1	no	—
302	#396	—	2	1	no	—
303	#396	—	2	1	no	—
304	#394	—	2	1	no	—
305	#394	—	2	1	no	—
306	#391	C₂³	1	1	yes	characteristic
307	#391	C₂³	1	1	yes	characteristic
308	#390	—	2	1	no	—
309	#390	—	2	1	no	—
310	#390	—	2	1	no	—
311	#390	—	2	1	no	—
312	#390	—	2	1	no	—
313	#390	C₂³	1	1	yes	characteristic
314	#390	C₂³	1	1	yes	characteristic
315	#390	C₂³	1	1	yes	characteristic
316	#390	C₂³	1	1	yes	characteristic
317	#390	C₂³	1	1	yes	characteristic
318	#390	C₂³	1	1	yes	characteristic
319	#389	—	2	1	no	—
320	#389	—	2	1	no	—
321	#389	—	2	1	no	—
322	#389	—	2	1	no	—
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	C₂³	1	1	yes	characteristic
327	#389	C₂³	1	1	yes	characteristic
328	#389	C₂³	1	1	yes	characteristic
329	#389	C₂³	1	1	yes	characteristic
330	#389	C₂³	1	1	yes	characteristic
331	#389	C₂³	1	1	yes	characteristic
332	#389	C₂³	1	1	yes	characteristic
333	#389	C₂³	1	1	yes	characteristic
334	#388	—	2	1	no	—
335	#388	—	2	1	no	—
336	#388	—	2	1	no	—
337	#388	—	2	1	no	—
338	#388	—	2	1	no	—
339	#388	—	2	1	no	—
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#388	—	2	1	no	—
349	#388	—	2	1	no	—
350	#388	—	2	1	no	—
351	#387	—	2	1	no	—
352	#387	—	2	1	no	—
353	#387	—	2	1	no	—
354	#387	—	2	1	no	—
355	#387	—	2	1	no	—
356	#387	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#386	—	2	1	no	—
369	#386	—	2	1	no	—
370	#386	—	2	1	no	—
371	#386	—	2	1	no	—
372	#386	—	2	1	no	—
373	#386	—	2	1	no	—
374	#386	—	2	1	no	—
375	#385	—	2	1	no	—
376	#385	—	2	1	no	—
377	#385	—	2	1	no	—
378	#385	—	2	1	no	—
379	#385	—	2	1	no	—
380	#385	—	2	1	no	—
381	#385	—	2	1	no	—
382	#384	C₂³	1	1	yes	characteristic
383	#384	C₂³	1	1	yes	characteristic
384	#383	—	2	1	no	—
385	#383	—	2	1	no	—
386	#382	C₂³	1	1	yes	characteristic
387	#382	C₂³	1	1	yes	characteristic
388	#382	C₂³	1	1	yes	characteristic
389	#382	C₂³	1	1	yes	characteristic
390	#381	—	2	1	no	—
391	#381	—	2	1	no	—
392	#381	—	2	1	no	—
393	#380	—	2	1	no	—
394	#380	C₂³	1	1	yes	characteristic
395	#380	C₂³	1	1	yes	characteristic
396	#380	C₂³	1	1	yes	characteristic
397	#380	C₂³	1	1	yes	characteristic
398	#380	C₂³	1	1	yes	characteristic
399	#380	C₂³	1	1	yes	characteristic
400	#380	C₂³	1	1	yes	characteristic
401	#380	C₂³	1	1	yes	characteristic
402	#380	C₂³	1	1	yes	characteristic
403	#380	C₂³	1	1	yes	characteristic
404	#379	—	2	1	no	—
405	C₄×C₄⋊C₄	—	2	1	no	—
406	C₄×C₄⋊C₄	—	2	1	no	—
407	C₄×C₄⋊C₄	—	2	1	no	—
408	C₄×C₄⋊C₄	—	2	1	no	—
409	C₄×C₄⋊C₄	—	2	1	no	—
410	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
411	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
422	C₄×C₂²⋊C₄	—	2	1	no	—
423	C₄×C₂²⋊C₄	—	2	1	no	—
424	C₄×C₂²⋊C₄	—	2	1	no	—
425	C₄×C₂²⋊C₄	—	2	1	no	—
426	C₄×C₂²⋊C₄	—	2	1	no	—
427	C₄×C₂²⋊C₄	—	2	1	no	—
428	C₄×C₂²⋊C₄	—	2	1	no	—
429	C₄×C₂²⋊C₄	—	2	1	no	—
430	C₄×C₂²⋊C₄	—	2	1	no	—
431	C₄×C₂²⋊C₄	—	2	1	no	—
432	C₄×C₂²⋊C₄	—	2	1	no	—
433	C₄×C₂²⋊C₄	—	2	1	no	—
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	—	2	1	no	—
437	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
439	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
443	#376	—	2	1	no	—
444	#376	—	2	1	no	—
445	C₄³	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#336	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	C₂⁵	—	2	1	no	—
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	4	1	no	—
488	C₂×#41	—	4	1	no	—
489	C₂×#41	—	4	1	no	—
490	C₂×#41	—	4	1	no	—
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
502	C₂²×D₄	C₂⁴	1	1	yes	characteristic
503	C₂²×D₄	C₂⁴	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂⁴	1	1	yes	characteristic
514	C₂³×C₄	C₂⁴	1	1	yes	characteristic
515	C₂²×C₈	C₂⁴	1	1	yes	characteristic
516	C₂²×C₈	C₂⁴	1	1	yes	characteristic
517	C₂²×C₈	C₂⁴	1	1	yes	characteristic
518	C₂²×C₈	C₂⁴	1	1	yes	characteristic
519	C₂²×C₈	C₂⁴	1	1	yes	characteristic
520	C₂²×C₈	C₂⁴	1	1	yes	characteristic
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	#126	—	4	4	no	—
524	#126	—	4	4	no	—
525	#125	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	—	2	2	no	—
528	#125	—	2	2	no	—
529	#125	—	4	1	no	—
530	#125	—	4	1	no	—
531	#124	—	2	2	no	—
532	#124	#41	1	4	yes	—
533	#123	—	2	8	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	#121	—	2	8	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#120	—	2	8	no	—
540	C₄×Q₈	—	4	1	no	—
541	C₄×Q₈	—	4	1	no	—
542	C₄×Q₈	—	4	1	no	—
543	C₄×Q₈	—	4	1	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	4	2	no	—
548	C₄×D₄	—	4	1	no	—
549	C₄×D₄	—	4	1	no	—
550	C₄×D₄	—	4	1	no	—
551	C₄×D₄	—	4	1	no	—
552	C₄×D₄	—	4	2	no	—
553	C₄×D₄	—	8	2	no	—
554	C₄×D₄	#41	1	4	yes	—
555	#117	—	4	1	no	—
556	#117	—	4	1	no	—
557	#117	—	8	2	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	4	1	no	—
581	C₂×C₄⋊C₄	—	4	1	no	—
582	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	—	2	8	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	4	4	no	—
630	C₂×C₂²⋊C₄	—	4	4	no	—
631	C₂×C₂²⋊C₄	—	8	2	no	—
632	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	4	1	no	—
651	C₂×C₄²	—	4	1	no	—
652	C₂×C₄²	—	4	1	no	—
653	C₂×C₄²	—	4	1	no	—
654	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	1	yes	characteristic
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	#107	—	2	2	no	—
668	#107	—	2	2	no	—
669	#107	—	4	1	no	—
670	#107	—	4	1	no	—
671	#107	—	4	1	no	—
672	#107	—	4	1	no	—
673	#106	—	2	2	no	—
674	#106	—	2	2	no	—
675	#106	—	4	1	no	—
676	#106	—	4	1	no	—
677	#106	—	4	1	no	—
678	#106	—	4	1	no	—
679	C₄⋊C₈	—	2	2	no	—
680	C₄⋊C₈	—	2	2	no	—
681	C₄⋊C₈	—	4	1	no	—
682	C₄⋊C₈	—	4	1	no	—
683	#103	—	2	2	no	—
684	#103	—	2	2	no	—
685	#103	—	2	2	no	—
686	#103	—	2	2	no	—
687	#103	—	4	1	no	—
688	#103	—	4	1	no	—
689	#103	—	4	1	no	—
690	#103	—	4	1	no	—
691	#102	—	2	2	no	—
692	#102	—	2	2	no	—
693	#102	—	2	2	no	—
694	#102	—	2	2	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	2	2	no	—
699	#102	—	4	1	no	—
700	#102	—	4	1	no	—
701	#102	—	4	1	no	—
702	#102	—	4	1	no	—
703	#102	—	4	1	no	—
704	#102	—	4	1	no	—
705	#102	—	4	1	no	—
706	#102	—	4	1	no	—
707	C₂²⋊C₈	—	4	1	no	—
708	C₂²⋊C₈	—	4	1	no	—
709	C₂²⋊C₈	—	4	1	no	—
710	C₂²⋊C₈	—	4	1	no	—
711	C₂²⋊C₈	—	4	1	no	—
712	C₂²⋊C₈	—	4	1	no	—
713	C₂²⋊C₈	—	4	1	no	—
714	C₂²⋊C₈	—	4	1	no	—
715	#97	—	4	1	no	—
716	#97	—	4	1	no	—
717	#97	—	4	1	no	—
718	#97	—	4	1	no	—
719	C₄×C₈	—	2	2	no	—
720	C₄×C₈	—	2	2	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	C₂⁴	—	2	4	no	—
767	C₂⁴	—	2	1	no	—
768	C₂⁴	—	2	1	no	—
769	C₂⁴	—	4	2	no	—
770	C₂⁴	—	4	2	no	—
771	C₂⁴	—	8	1	no	—
772	C₂⁴	—	8	1	no	—
773	C₂⁴	—	8	1	no	—
774	C₂⁴	—	8	1	no	—
775	C₂⁴	C₂²×D₄	1	1	yes	characteristic
776	C₂⁴	C₂²×D₄	1	1	yes	characteristic
777	#41	—	8	2	no	—
778	#41	—	8	2	no	—
779	#41	—	8	2	no	—
780	#41	—	8	2	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	C₂×#41	1	2	yes	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	4	1	no	—
803	C₂×D₄	—	8	1	no	—
804	C₂×D₄	—	8	1	no	—
805	C₂×D₄	—	8	2	no	—
806	C₂×D₄	—	8	2	no	—
807	C₂×D₄	—	8	2	no	—
808	C₂×D₄	—	8	2	no	—
809	C₂×D₄	—	8	1	no	—
810	C₂×D₄	—	8	1	no	—
811	C₂×D₄	—	8	1	no	—
812	C₂×D₄	—	8	1	no	—
813	C₂×D₄	C₂×#41	1	2	yes	—
814	C₂×D₄	C₂×#41	1	2	yes	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	8	1	no	—
859	C₂²×C₄	—	8	1	no	—
860	C₂²×C₄	—	8	1	no	—
861	C₂²×C₄	—	8	1	no	—
862	C₂²×C₄	—	8	1	no	—
863	C₂²×C₄	—	8	1	no	—
864	C₂²×C₄	—	8	1	no	—
865	C₂²×C₄	—	8	1	no	—
866	C₂²×C₄	—	8	1	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
869	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	C₂⁵	1	1	yes	characteristic
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	4	1	no	—
933	C₄⋊C₄	—	4	1	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	8	1	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	—	8	1	no	—
950	C₄⋊C₄	—	8	1	no	—
951	C₄⋊C₄	—	8	1	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	C₂×#41	1	2	yes	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	2	4	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	4	1	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	8	1	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	—	8	1	no	—
984	C₂²⋊C₄	—	8	1	no	—
985	C₂²⋊C₄	—	8	1	no	—
986	C₂²⋊C₄	—	8	1	no	—
987	C₂²⋊C₄	—	8	1	no	—
988	C₂²⋊C₄	—	8	1	no	—
989	C₂²⋊C₄	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	4	1	no	—
1002	C₄²	—	4	1	no	—
1003	C₄²	—	4	1	no	—
1004	C₄²	—	4	1	no	—
1005	C₄²	—	4	1	no	—
1006	C₄²	—	4	1	no	—
1007	C₄²	—	4	1	no	—
1008	C₄²	—	4	2	no	—
1009	C₄²	—	4	2	no	—
1010	C₄²	—	8	1	no	—
1011	C₄²	—	8	1	no	—
1012	C₄²	—	8	1	no	—
1013	C₄²	—	8	1	no	—
1014	C₄²	—	8	1	no	—
1015	C₄²	—	8	1	no	—
1016	C₄²	—	8	1	no	—
1017	C₄²	—	8	1	no	—
1018	C₄²	—	8	1	no	—
1019	C₄²	—	8	1	no	—
1020	C₄²	C₂×#41	1	2	yes	—
1021	C₄²	C₂×#41	1	2	yes	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	4	8	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	—	4	1	no	—
1045	C₂³	—	4	1	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	8	4	no	—
1051	C₂³	—	8	4	no	—
1052	C₂³	—	16	2	no	—
1053	C₂³	—	16	2	no	—
1054	C₂³	—	16	2	no	—
1055	C₂³	—	16	2	no	—
1056	C₂³	#575	1	2	yes	—
1057	C₂³	C₂³×D₄	1	1	yes	characteristic
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	4	1	no	—
1061	Q₈	—	4	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	8	4	no	—
1072	D₄	—	8	4	no	—
1073	D₄	—	8	4	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	8	4	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	4	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	2	no	—
1163	C₂×C₄	—	16	2	no	—
1164	C₂×C₄	—	16	2	no	—
1165	C₂×C₄	—	16	2	no	—
1166	C₂×C₄	#525	1	2	yes	—
1167	C₂×C₄	#525	1	2	yes	—
1168	C₂×C₄	#575	1	2	yes	—
1169	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1170	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1171	C₂×C₄	#585	1	1	yes	characteristic
1172	C₂×C₄	#585	1	1	yes	characteristic
1173	C₂×C₄	#585	1	1	yes	characteristic
1174	C₂×C₄	#585	1	1	yes	characteristic
1175	C₈	—	4	1	no	—
1176	C₈	—	4	1	no	—
1177	C₈	—	4	1	no	—
1178	C₈	—	4	1	no	—
1179	C₈	—	4	1	no	—
1180	C₈	—	4	1	no	—
1181	C₈	—	4	1	no	—
1182	C₈	—	4	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	—	8	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	8	1	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	16	8	no	—
1212	C₂²	C₂×#525	1	1	yes	characteristic
1213	C₂²	#3485	1	1	yes	characteristic
1214	C₂²	#3500	1	1	yes	characteristic
1215	C₂²	C₂×#575	1	1	yes	characteristic
1216	C₂²	C₂×#575	1	1	yes	characteristic
1217	C₂²	#3584	1	1	yes	characteristic
1218	C₂²	#3585	1	1	yes	characteristic
1219	C₄	—	2	2	no	—
1220	C₄	—	2	2	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	2	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	8	1	no	—
1234	C₄	—	8	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	#3510	1	1	yes	characteristic
1246	C₄	#3510	1	1	yes	characteristic
1247	C₄	#3521	1	1	yes	characteristic
1248	C₄	#3521	1	1	yes	characteristic
1249	C₂	—	4	2	no	—
1250	C₂	—	8	1	no	—
1251	C₂	—	8	2	no	—
1252	C₂	—	8	2	no	—
1253	C₂	#36033	1	1	yes	characteristic
1254	C₂	#60546	1	1	yes	characteristic
1255	C₂	#60601	1	1	yes	characteristic
1256	C₂	#61725	1	1	yes	characteristic
1257	C₂	#61732	1	1	yes	characteristic
1258	C₂	#62547	1	1	yes	characteristic
1259	C₂	#62578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#546	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄²×D₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #36196	C₂	semidirect
3. #30174	C₂	semidirect
4. #30167	C₂	semidirect
5. #29870	C₂	semidirect
6. #29261	C₂	semidirect
7. #29114	C₂	semidirect
8. #29110	C₂	semidirect
9. #28721	C₂	semidirect
10. #27590	C₂	semidirect
11. #27588	C₂	semidirect
12. #27548	C₂	semidirect
13. #27546	C₂	semidirect
14. #27541	C₂	semidirect
15. #27539	C₂	semidirect
16. #27124	C₂	semidirect
17. #27122	C₂	semidirect
18. #27117	C₂	semidirect
19. #27115	C₂	semidirect
20. #26307	C₂	semidirect
21. #26305	C₂	semidirect
24. #23778	C₂	semidirect
25. #23765	C₂	semidirect
26. #23764	C₂	semidirect
27. #23225	C₂	semidirect
28. #23224	C₂	semidirect
29. #23071	C₂	semidirect
30. #23071	C₂	semidirect
31. #22839	C₂	semidirect
37. #2859	C₂²	semidirect
39. #2851	C₂²	semidirect
47. #2497	C₂²	semidirect
49. #2496	C₂²	semidirect
55. #2370	C₂²	semidirect
56. #2370	C₂²	semidirect
70. C₄×#125	C₂²	semidirect
78. #2283	C₂²	semidirect
81. #2101	C₂²	semidirect
82. #2097	C₂²	semidirect
85. #2088	C₂²	semidirect
86. #2087	C₂²	semidirect
87. #2085	C₂²	semidirect
88. #2085	C₂²	semidirect
89. #2084	C₂²	semidirect
90. #2083	C₂²	semidirect
93. #2077	C₂²	semidirect
94. #2077	C₂²	semidirect
97. #2076	C₂²	semidirect
98. #2075	C₂²	semidirect
99. #2074	C₂²	semidirect
100. #2074	C₂²	semidirect
109. #2059	C₂²	semidirect
118. #2026	C₂²	semidirect
121. #1991	C₂²	semidirect
122. #1991	C₂²	semidirect
123. #1989	C₂²	semidirect
124. #1989	C₂²	semidirect
129. #1949	C₂²	semidirect
130. #1949	C₂²	semidirect
137. #1935	C₂²	semidirect
138. #1935	C₂²	semidirect
139. #1928	C₂²	semidirect
140. #1927	C₂²	semidirect
149. #1924	C₂²	semidirect
150. #1924	C₂²	semidirect
151. #1920	C₂²	semidirect
152. #1920	C₂²	semidirect
153. #1918	C₂²	semidirect
154. #1918	C₂²	semidirect
155. #1865	C₂²	semidirect
156. #1865	C₂²	semidirect
159. #1863	C₂²	semidirect
160. #1863	C₂²	semidirect
163. #1854	C₂²	semidirect
164. #1854	C₂²	semidirect
167. #1831	C₂²	semidirect
168. #1825	C₂²	semidirect
169. #1825	C₂²	semidirect
173. #1817	C₂²	semidirect
174. #1803	C₂²	semidirect
175. #1803	C₂²	semidirect
186. #1776	C₂²	semidirect
187. #1776	C₂²	semidirect
188. #1776	C₂²	semidirect
189. #1776	C₂²	semidirect
190. C₄×#107	C₂²	semidirect
191. C₄×#106	C₂²	semidirect
192. #1770	C₂²	semidirect
193. #1770	C₂²	semidirect
194. C₄×C₄⋊C₈	C₂²	semidirect
195. #1763	C₂²	semidirect
196. #1763	C₂²	semidirect
202. #1749	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36196	2
#34320	2
#30174	2
#30167	2
#29870	2
#29261	2
#29114	2
#29110	2
#28721	2
#27590	2
#27588	2
#27548	2
#27546	2
#27541	2
#27539	2
#27124	2
#27122	2
#27117	2
#27115	2
#26307	2
#26305	2
#25890	2
#23778	2
#23765	2
#23764	2
#23225	2
#23224	2
#23071	2
#22839	2