Subgroups — #6565252

Order 512.

1498 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36208	C₂	1	1	yes	maximal, characteristic, complemented
2	#36203	C₂	1	1	yes	maximal, characteristic, complemented
3	#30364	C₂	1	1	yes	maximal, characteristic, complemented
4	#30362	C₂	1	1	yes	maximal, characteristic, complemented
5	#29730	C₂	1	1	yes	maximal, characteristic
6	#29461	C₂	1	1	yes	maximal, characteristic, complemented
7	#29460	C₂	1	1	yes	maximal, characteristic, complemented
8	#29000	C₂	1	1	yes	maximal, characteristic, complemented
9	#28999	C₂	1	1	yes	maximal, characteristic, complemented
10	#28866	C₂	1	1	yes	maximal, characteristic, complemented
11	#28865	C₂	1	1	yes	maximal, characteristic, complemented
12	#28773	C₂	1	1	yes	maximal, characteristic, complemented
13	#28091	C₂	1	1	yes	maximal, characteristic, complemented
14	#28086	C₂	1	1	yes	maximal, characteristic, complemented
15	#27928	C₂	1	1	yes	maximal, characteristic, complemented
16	#27879	C₂	1	1	yes	maximal, characteristic, complemented
17	#27877	C₂	1	1	yes	maximal, characteristic, complemented
18	#27854	C₂	1	1	yes	maximal, characteristic, complemented
19	#27851	C₂	1	1	yes	maximal, characteristic, complemented
20	#27702	C₂	1	1	yes	maximal, characteristic, complemented
21	#27696	C₂	1	1	yes	maximal, characteristic, complemented
22	#24560	C₂	1	1	yes	maximal, characteristic, complemented
23	#24560	C₂	1	1	yes	maximal, characteristic, complemented
24	#23764	C₂	1	1	yes	maximal, characteristic, complemented
25	#23760	C₂	1	1	yes	maximal, characteristic, complemented
26	#23638	C₂	1	1	yes	maximal, characteristic, complemented
27	#23137	C₂	1	1	yes	maximal, characteristic, complemented
28	#22935	C₂	1	1	yes	maximal, characteristic, complemented
29	#22933	C₂	1	1	yes	maximal, characteristic, complemented
30	#22616	C₂	1	1	yes	maximal, characteristic, complemented
31	#20525	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#482	C₂²	1	1	yes	characteristic
33	C₂×#482	C₂²	1	1	yes	characteristic
34	C₂×#466	C₂²	1	1	yes	characteristic
35	C₂×#427	C₂²	1	1	yes	characteristic
36	C₂×#407	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	#2857	C₂²	1	1	yes	characteristic
39	#2854	C₂²	1	1	yes	characteristic
40	#2854	C₂²	1	1	yes	characteristic
41	#2851	C₂²	1	1	yes	characteristic
42	#2847	C₂²	1	1	yes	characteristic
43	#2847	C₂²	1	1	yes	characteristic
44	#2576	—	2	1	no	—
45	#2572	—	2	1	no	—
46	#2534	—	2	1	no	—
47	#2526	—	2	1	no	—
48	#2518	—	2	1	no	—
49	#2518	—	2	1	no	—
50	#2516	—	2	1	no	—
51	#2510	—	2	1	no	—
52	#2500	C₂²	1	1	yes	characteristic
53	#2500	C₂²	1	1	yes	characteristic
54	#2497	C₂²	1	1	yes	characteristic
55	#2497	C₂²	1	1	yes	characteristic
56	#2495	C₂²	1	1	yes	characteristic
57	#2494	C₂²	1	1	yes	characteristic
58	#2491	C₂²	1	1	yes	characteristic
59	#2490	C₂²	1	1	yes	characteristic
60	#2488	—	2	1	no	—
61	#2472	—	2	1	no	—
62	#2441	C₂²	1	1	yes	characteristic
63	#2439	C₂²	1	1	yes	characteristic
64	#2422	C₂²	1	1	yes	characteristic
65	#2420	C₂²	1	1	yes	characteristic
66	#2418	—	2	1	no	—
67	#2411	—	2	1	no	—
68	#2374	—	2	1	no	—
69	#2372	—	2	1	no	—
70	#2363	C₂²	1	1	yes	characteristic
71	#2363	C₂²	1	1	yes	characteristic
72	#2359	—	2	1	no	—
73	#2353	—	2	1	no	—
74	#2347	C₂²	1	1	yes	characteristic
75	#2346	C₂²	1	1	yes	characteristic
76	C₄×#121	C₂²	1	1	yes	characteristic
77	C₄×#121	C₂²	1	1	yes	characteristic
78	#2285	C₂²	1	1	yes	characteristic
79	#2283	C₂²	1	1	yes	characteristic
80	#2280	C₂²	1	1	yes	characteristic
81	#2280	C₂²	1	1	yes	characteristic
82	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
83	#2101	C₂²	1	1	yes	characteristic, complemented
84	#2101	C₂²	1	1	yes	characteristic, complemented
85	#2100	C₂²	1	1	yes	characteristic, complemented
86	#2100	C₂²	1	1	yes	characteristic, complemented
87	#2094	C₂²	1	1	yes	characteristic, complemented
88	#2094	C₂²	1	1	yes	characteristic, complemented
89	#2092	C₂²	1	1	yes	characteristic, complemented
90	#2092	C₂²	1	1	yes	characteristic, complemented
91	#2085	C₂²	1	1	yes	characteristic, complemented
92	#2083	C₂²	1	1	yes	characteristic, complemented
93	#2077	C₂²	1	1	yes	characteristic
94	#2077	C₂²	1	1	yes	characteristic
95	#2077	C₂²	1	1	yes	characteristic
96	#2077	C₂²	1	1	yes	characteristic
97	#2077	C₂²	1	1	yes	characteristic
98	#2077	C₂²	1	1	yes	characteristic
99	#2076	C₂²	1	1	yes	characteristic
100	#2076	C₂²	1	1	yes	characteristic
101	#2075	C₂²	1	1	yes	characteristic
102	#2075	C₂²	1	1	yes	characteristic
103	#2075	C₂²	1	1	yes	characteristic
104	#2075	C₂²	1	1	yes	characteristic
105	#2075	C₂²	1	1	yes	characteristic
106	#2075	C₂²	1	1	yes	characteristic
107	#2073	C₂²	1	1	yes	characteristic, complemented
108	#2071	C₂²	1	1	yes	characteristic, complemented
109	#2059	C₂²	1	1	yes	characteristic, complemented
110	#2057	C₂²	1	1	yes	characteristic, complemented
111	#2034	C₂²	1	1	yes	characteristic
112	#2034	C₂²	1	1	yes	characteristic
113	#2033	C₂²	1	1	yes	characteristic
114	#2033	C₂²	1	1	yes	characteristic
115	#2033	C₂²	1	1	yes	characteristic
116	#2033	C₂²	1	1	yes	characteristic
117	#2033	C₂²	1	1	yes	characteristic
118	#2033	C₂²	1	1	yes	characteristic
119	#2025	C₂²	1	1	yes	characteristic, complemented
120	#2023	C₂²	1	1	yes	characteristic, complemented
121	#1999	C₂²	1	1	yes	characteristic
122	#1999	C₂²	1	1	yes	characteristic
123	#1991	C₂²	1	1	yes	characteristic, complemented
124	#1991	C₂²	1	1	yes	characteristic, complemented
125	#1990	C₂²	1	1	yes	characteristic, complemented
126	#1990	C₂²	1	1	yes	characteristic, complemented
127	#1970	C₂²	1	1	yes	characteristic, complemented
128	#1970	C₂²	1	1	yes	characteristic, complemented
129	#1944	C₂²	1	1	yes	characteristic, complemented
130	#1944	C₂²	1	1	yes	characteristic, complemented
131	#1944	C₂²	1	1	yes	characteristic, complemented
132	#1943	C₂²	1	1	yes	characteristic, complemented
133	#1942	C₂²	1	1	yes	characteristic, complemented
134	#1941	C₂²	1	1	yes	characteristic, complemented
135	#1936	C₂²	1	1	yes	characteristic, complemented
136	#1936	C₂²	1	1	yes	characteristic, complemented
137	#1936	C₂²	1	1	yes	characteristic, complemented
138	#1936	C₂²	1	1	yes	characteristic, complemented
139	#1934	C₂²	1	1	yes	characteristic, complemented
140	#1934	C₂²	1	1	yes	characteristic, complemented
141	#1934	C₂²	1	1	yes	characteristic, complemented
142	#1934	C₂²	1	1	yes	characteristic, complemented
143	#1926	C₂²	1	1	yes	characteristic, complemented
144	#1925	C₂²	1	1	yes	characteristic, complemented
145	#1921	C₂²	1	1	yes	characteristic, complemented
146	#1921	C₂²	1	1	yes	characteristic, complemented
147	#1920	C₂²	1	1	yes	characteristic, complemented
148	#1919	C₂²	1	1	yes	characteristic, complemented
149	#1918	C₂²	1	1	yes	characteristic, complemented
150	#1918	C₂²	1	1	yes	characteristic, complemented
151	#1918	C₂²	1	1	yes	characteristic, complemented
152	#1918	C₂²	1	1	yes	characteristic, complemented
153	#1918	C₂²	1	1	yes	characteristic, complemented
154	#1918	C₂²	1	1	yes	characteristic, complemented
155	#1895	C₂²	1	1	yes	characteristic
156	#1895	C₂²	1	1	yes	characteristic
157	#1895	C₂²	1	1	yes	characteristic
158	#1895	C₂²	1	1	yes	characteristic
159	#1893	C₂²	1	1	yes	characteristic
160	#1893	C₂²	1	1	yes	characteristic
161	#1879	C₂²	1	1	yes	characteristic, complemented
162	#1879	C₂²	1	1	yes	characteristic, complemented
163	#1875	C₂²	1	1	yes	characteristic
164	#1875	C₂²	1	1	yes	characteristic
165	#1864	C₂²	1	1	yes	characteristic, complemented
166	#1862	C₂²	1	1	yes	characteristic, complemented
167	#1854	C₂²	1	1	yes	characteristic
168	#1854	C₂²	1	1	yes	characteristic
169	#1846	C₂²	1	1	yes	characteristic, complemented
170	#1845	C₂²	1	1	yes	characteristic, complemented
171	#1835	C₂²	1	1	yes	characteristic, complemented
172	#1834	C₂²	1	1	yes	characteristic, complemented
173	#1825	C₂²	1	1	yes	characteristic
174	#1825	C₂²	1	1	yes	characteristic
175	#1809	C₂²	1	1	yes	characteristic
176	#1809	C₂²	1	1	yes	characteristic
177	#1809	C₂²	1	1	yes	characteristic
178	#1809	C₂²	1	1	yes	characteristic
179	#1808	C₂²	1	1	yes	characteristic
180	#1776	C₂²	1	1	yes	characteristic, complemented
181	#1776	C₂²	1	1	yes	characteristic, complemented
182	#1776	C₂²	1	1	yes	characteristic, complemented
183	#1776	C₂²	1	1	yes	characteristic, complemented
184	#1762	C₂²	1	1	yes	characteristic, complemented
185	#1762	C₂²	1	1	yes	characteristic, complemented
186	#1762	C₂²	1	1	yes	characteristic, complemented
187	#1762	C₂²	1	1	yes	characteristic, complemented
188	#1753	C₂²	1	1	yes	characteristic
189	#1753	C₂²	1	1	yes	characteristic
190	#1753	C₂²	1	1	yes	characteristic
191	#1753	C₂²	1	1	yes	characteristic
192	#1752	C₂²	1	1	yes	characteristic
193	#1752	C₂²	1	1	yes	characteristic
194	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
195	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
196	#1749	C₂²	1	1	yes	characteristic
197	#1749	C₂²	1	1	yes	characteristic
198	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
199	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
200	#1735	C₂²	1	1	yes	characteristic
201	#1735	C₂²	1	1	yes	characteristic
202	#1735	C₂²	1	1	yes	characteristic
203	C₂⁴×C₄	C₂³	1	1	yes	characteristic
204	C₂²×D₈	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂²×M₁₆	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×#123	—	2	1	no	—
213	C₂×#123	—	2	1	no	—
214	C₂×#123	—	2	1	no	—
215	C₂×C₂²⋊Q₈	—	2	1	no	—
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×#121	C₂³	1	1	yes	characteristic
218	C₂×#121	C₂³	1	1	yes	characteristic
219	C₂×#121	C₂³	1	1	yes	characteristic
220	C₂×#121	C₂³	1	1	yes	characteristic
221	C₂×#121	C₂³	1	1	yes	characteristic
222	C₂×#120	—	2	1	no	—
223	C₂×#120	—	2	1	no	—
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	—	2	1	no	—
226	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×#117	—	2	1	no	—
229	C₂×#117	C₂³	1	1	yes	characteristic
230	C₂×#117	C₂³	1	1	yes	characteristic
231	C₂×#117	C₂³	1	1	yes	characteristic
232	C₂×#117	C₂³	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	D₄	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	D₄	1	1	yes	characteristic
235	C₂²×C₄²	C₂³	1	1	yes	characteristic
236	C₂²×C₄²	C₂³	1	1	yes	characteristic
237	#482	—	2	4	no	—
238	#482	—	2	4	no	—
239	#466	—	2	4	no	—
240	#427	—	2	4	no	—
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×#107	C₂³	1	1	yes	characteristic
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#106	C₂³	1	1	yes	characteristic
251	C₂×#106	C₂³	1	1	yes	characteristic
252	C₂×#106	C₂³	1	1	yes	characteristic
253	C₂×#106	C₂³	1	1	yes	characteristic
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#102	C₂³	1	1	yes	characteristic
257	C₂×#102	C₂³	1	1	yes	characteristic
258	C₂×#102	C₂³	1	1	yes	characteristic
259	C₂×#102	C₂³	1	1	yes	characteristic
260	C₂×#102	C₂³	1	1	yes	characteristic
261	C₂×#102	C₂³	1	1	yes	characteristic
262	C₂×#102	C₂³	1	1	yes	characteristic
263	C₂×#102	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	#407	—	2	4	no	—
271	C₂×C₂²⋊C₈	—	2	4	no	—
272	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×#97	C₂³	1	1	yes	characteristic
281	C₂×#97	C₂³	1	1	yes	characteristic
282	C₂×#97	C₂³	1	1	yes	characteristic
283	C₂×#97	C₂³	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	#401	—	2	1	no	—
289	#400	—	2	1	no	—
290	#400	—	2	1	no	—
291	#400	—	2	1	no	—
292	#399	—	2	1	no	—
293	#397	—	2	1	no	—
294	#397	—	2	1	no	—
295	#397	—	2	1	no	—
296	#397	—	2	1	no	—
297	#397	—	2	1	no	—
298	#396	—	2	1	no	—
299	#396	—	2	1	no	—
300	#396	—	2	1	no	—
301	#396	—	2	1	no	—
302	#394	—	2	1	no	—
303	#394	—	2	1	no	—
304	#394	—	2	1	no	—
305	#394	—	2	1	no	—
306	#394	—	2	1	no	—
307	#394	—	2	1	no	—
308	#394	—	2	1	no	—
309	#394	—	2	1	no	—
310	#393	—	2	1	no	—
311	#393	—	2	1	no	—
312	#391	—	2	1	no	—
313	#391	—	2	1	no	—
314	#390	—	2	1	no	—
315	#390	—	2	1	no	—
316	#390	—	2	1	no	—
317	#390	C₂³	1	1	yes	characteristic
318	#390	C₂³	1	1	yes	characteristic
319	#390	C₂³	1	1	yes	characteristic
320	#390	C₂³	1	1	yes	characteristic
321	#390	C₂³	1	1	yes	characteristic
322	#390	C₂³	1	1	yes	characteristic
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	C₂³	1	1	yes	characteristic
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	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#388	—	2	1	no	—
356	#388	—	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	#386	—	2	1	no	—
365	#386	—	2	1	no	—
366	#386	—	2	1	no	—
367	#386	—	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	#386	—	2	1	no	—
376	#386	—	2	1	no	—
377	#385	—	2	1	no	—
378	#385	—	2	1	no	—
379	#385	—	2	1	no	—
380	#384	C₂³	1	1	yes	characteristic
381	#384	C₂³	1	1	yes	characteristic
382	#384	C₂³	1	1	yes	characteristic
383	#383	—	2	1	no	—
384	#383	—	2	1	no	—
385	#383	—	2	1	no	—
386	#382	—	2	1	no	—
387	#382	—	2	1	no	—
388	#382	C₂³	1	1	yes	characteristic
389	#382	C₂³	1	1	yes	characteristic
390	#382	C₂³	1	1	yes	characteristic
391	#381	—	2	1	no	—
392	#381	—	2	1	no	—
393	#381	—	2	1	no	—
394	#381	—	2	1	no	—
395	#380	—	2	1	no	—
396	#380	—	2	1	no	—
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	#380	C₂³	1	1	yes	characteristic
405	#380	C₂³	1	1	yes	characteristic
406	#380	C₂³	1	1	yes	characteristic
407	#380	C₂³	1	1	yes	characteristic
408	#380	C₂³	1	1	yes	characteristic
409	#380	C₂³	1	1	yes	characteristic
410	#380	C₂³	1	1	yes	characteristic
411	#379	—	2	1	no	—
412	#379	—	2	1	no	—
413	C₄×C₄⋊C₄	—	2	1	no	—
414	C₄×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
438	#376	—	2	1	no	—
439	#376	—	2	1	no	—
440	C₂×#95	D₄	1	1	yes	characteristic
441	C₂×#95	D₄	1	1	yes	characteristic
442	#340	C₂³	1	1	yes	characteristic
443	#340	C₂³	1	1	yes	characteristic
444	#340	C₂³	1	1	yes	characteristic
445	#340	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	#340	C₂³	1	1	yes	characteristic
475	#340	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	C₂×D₄	1	1	yes	characteristic
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	C₂⁴	1	1	yes	characteristic
493	C₂²×D₄	C₂⁴	1	1	yes	characteristic
494	C₂³×C₄	—	2	2	no	—
495	C₂³×C₄	—	2	2	no	—
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	4	1	no	—
499	C₂³×C₄	—	4	1	no	—
500	C₂³×C₄	—	4	1	no	—
501	C₂³×C₄	—	4	1	no	—
502	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
503	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
506	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂⁴	1	1	yes	characteristic
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂³×C₄	C₂⁴	1	1	yes	characteristic
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	4	1	no	—
514	C₂×D₈	—	4	1	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂×M₁₆	—	4	1	no	—
520	C₂×M₁₆	—	4	1	no	—
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	—	4	1	no	—
524	C₂²×C₈	—	4	1	no	—
525	C₂²×C₈	—	4	1	no	—
526	C₂²×C₈	#41	1	4	yes	—
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₄⋊Q₈	—	4	1	no	—
536	C₄⋊Q₈	—	4	1	no	—
537	#125	—	4	1	no	—
538	#125	—	4	1	no	—
539	#124	—	4	4	no	—
540	#123	—	4	4	no	—
541	#123	—	4	4	no	—
542	#123	—	8	2	no	—
543	C₂²⋊Q₈	—	8	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	4	1	no	—
549	#121	—	4	1	no	—
550	#121	—	4	1	no	—
551	#121	—	4	1	no	—
552	#121	—	4	1	no	—
553	#121	—	4	1	no	—
554	#121	—	4	1	no	—
555	#121	—	4	1	no	—
556	#120	—	8	2	no	—
557	#120	—	8	2	no	—
558	C₄×D₄	—	4	1	no	—
559	C₄×D₄	—	4	1	no	—
560	C₄×D₄	—	4	1	no	—
561	C₄×D₄	—	4	1	no	—
562	C₄×D₄	—	4	4	no	—
563	C₄×D₄	—	8	2	no	—
564	#117	—	2	2	no	—
565	#117	—	2	2	no	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	—	4	1	no	—
569	#117	—	4	1	no	—
570	#117	—	4	1	no	—
571	#117	—	4	1	no	—
572	#117	—	8	2	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	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	4	2	no	—
645	C₂×C₂²⋊C₄	—	4	2	no	—
646	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	4	1	no	—
665	C₂×C₄²	—	4	1	no	—
666	C₂×C₄²	—	4	1	no	—
667	C₂×C₄²	—	4	1	no	—
668	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂⁴	1	1	yes	characteristic
673	C₂×C₄²	C₂⁴	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	#107	—	2	2	no	—
677	#107	—	2	2	no	—
678	#107	—	2	2	no	—
679	#107	—	2	2	no	—
680	#107	—	2	2	no	—
681	#107	—	4	1	no	—
682	#107	—	4	1	no	—
683	#107	—	4	1	no	—
684	#107	—	4	1	no	—
685	#106	—	2	2	no	—
686	#106	—	2	2	no	—
687	#106	—	2	2	no	—
688	#106	—	2	2	no	—
689	#106	—	4	1	no	—
690	#106	—	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	—	4	1	no	—
698	#102	—	4	1	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	C₂²⋊C₈	—	2	2	no	—
706	C₂²⋊C₈	—	2	2	no	—
707	C₂²⋊C₈	—	2	2	no	—
708	C₂²⋊C₈	—	2	2	no	—
709	C₂²⋊C₈	—	2	2	no	—
710	C₂²⋊C₈	—	2	2	no	—
711	C₂²⋊C₈	—	2	2	no	—
712	C₂²⋊C₈	#41	1	4	yes	—
713	#97	—	4	1	no	—
714	#97	—	4	1	no	—
715	#97	—	4	1	no	—
716	#97	—	4	1	no	—
717	C₄×C₈	—	4	1	no	—
718	C₄×C₈	—	4	1	no	—
719	C₄×C₈	—	4	1	no	—
720	C₄×C₈	—	4	1	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	C₂×D₄	1	1	yes	characteristic
758	#95	C₂×D₄	1	1	yes	characteristic
759	#95	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	—	2	2	no	—
766	C₂⁴	—	2	2	no	—
767	C₂⁴	—	2	1	no	—
768	C₂⁴	—	2	1	no	—
769	C₂⁴	—	4	1	no	—
770	C₂⁴	—	4	1	no	—
771	C₂⁴	—	4	1	no	—
772	C₂⁴	—	4	1	no	—
773	C₂⁴	—	4	1	no	—
774	C₂⁴	C₂²×D₄	1	1	yes	characteristic
775	C₂⁴	C₂²×D₄	1	1	yes	characteristic
776	C₂⁴	C₂²×D₄	1	1	yes	characteristic
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	—	8	1	no	—
779	C₂×Q₈	—	8	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	8	1	no	—
803	C₂×D₄	—	8	1	no	—
804	C₂×D₄	—	8	1	no	—
805	C₂×D₄	—	8	1	no	—
806	C₂×D₄	—	8	1	no	—
807	C₂×D₄	—	8	1	no	—
808	C₂×D₄	—	8	1	no	—
809	C₂×D₄	—	8	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	1	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	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	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	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	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	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	1	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	8	2	no	—
864	C₂²×C₄	—	8	2	no	—
865	C₂²×C₄	—	8	2	no	—
866	C₂²×C₄	—	8	2	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	—	8	1	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂×#41	1	2	yes	—
883	C₂²×C₄	C₂×#41	1	2	yes	—
884	C₂²×C₄	C₂⁵	1	1	yes	characteristic
885	D₈	—	8	2	no	—
886	M₁₆	—	8	2	no	—
887	M₁₆	—	8	2	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	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	4	4	no	—
909	C₂×C₈	—	8	2	no	—
910	C₂×C₈	C₂×#41	1	2	yes	—
911	C₂×C₈	C₂×#41	1	2	yes	—
912	C₂×C₈	C₂×#41	1	2	yes	—
913	C₂×C₈	C₂×#41	1	2	yes	—
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	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	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	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	no	—
958	C₄⋊C₄	—	8	1	no	—
959	C₄⋊C₄	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	4	1	no	—
966	C₂²⋊C₄	—	4	1	no	—
967	C₂²⋊C₄	—	4	1	no	—
968	C₂²⋊C₄	—	4	1	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	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	1	no	—
1006	C₂²⋊C₄	—	8	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	4	1	no	—
1016	C₄²	—	4	1	no	—
1017	C₄²	—	4	1	no	—
1018	C₄²	—	4	1	no	—
1019	C₄²	—	4	2	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	—	4	2	no	—
1022	C₄²	—	4	2	no	—
1023	C₄²	—	8	1	no	—
1024	C₄²	—	8	1	no	—
1025	C₄²	—	8	1	no	—
1026	C₄²	—	8	1	no	—
1027	C₄²	—	8	1	no	—
1028	C₄²	—	8	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	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	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	4	4	no	—
1049	C₂³	—	4	4	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	1	no	—
1055	C₂³	—	4	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	4	1	no	—
1060	C₂³	—	4	1	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	1	no	—
1063	C₂³	—	4	1	no	—
1064	C₂³	—	8	2	no	—
1065	C₂³	—	8	2	no	—
1066	C₂³	—	8	2	no	—
1067	C₂³	—	8	2	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	#532	1	2	yes	—
1070	C₂³	#576	1	2	yes	—
1071	C₂³	C₂³×D₄	1	1	yes	characteristic
1072	Q₈	—	16	2	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	1	no	—
1078	D₄	—	4	1	no	—
1079	D₄	—	4	1	no	—
1080	D₄	—	4	1	no	—
1081	D₄	—	8	4	no	—
1082	D₄	—	8	4	no	—
1083	D₄	—	16	2	no	—
1084	D₄	—	16	2	no	—
1085	D₄	—	16	2	no	—
1086	D₄	—	16	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	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	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	4	4	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	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	2	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	16	2	no	—
1179	C₂×C₄	—	16	2	no	—
1180	C₂×C₄	#532	1	2	yes	—
1181	C₂×C₄	#575	1	2	yes	—
1182	C₂×C₄	#575	1	2	yes	—
1183	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1184	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1185	C₂×C₄	#585	1	1	yes	characteristic
1186	C₂×C₄	#585	1	1	yes	characteristic
1187	C₂×C₄	#585	1	1	yes	characteristic
1188	C₂×C₄	#585	1	1	yes	characteristic
1189	C₈	—	2	2	no	—
1190	C₈	—	2	2	no	—
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	4	1	no	—
1194	C₈	—	4	1	no	—
1195	C₈	—	4	1	no	—
1196	C₈	—	4	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	8	8	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	8	1	no	—
1222	C₂²	—	8	1	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	—	8	1	no	—
1229	C₂²	—	8	1	no	—
1230	C₂²	—	8	1	no	—
1231	C₂²	—	8	1	no	—
1232	C₂²	—	8	1	no	—
1233	C₂²	C₂×#532	1	1	yes	characteristic
1234	C₂²	#3485	1	1	yes	characteristic
1235	C₂²	#3485	1	1	yes	characteristic
1236	C₂²	C₂×#575	1	1	yes	characteristic
1237	C₂²	C₂×#575	1	1	yes	characteristic
1238	C₂²	C₂×#576	1	1	yes	characteristic
1239	C₂²	#3584	1	1	yes	characteristic
1240	C₄	—	2	2	no	—
1241	C₄	—	2	2	no	—
1242	C₄	—	2	2	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	8	1	no	—
1252	C₄	—	8	1	no	—
1253	C₄	—	8	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	#3491	1	1	yes	characteristic
1266	C₄	#3510	1	1	yes	characteristic
1267	C₄	#3521	1	1	yes	characteristic
1268	C₄	#3521	1	1	yes	characteristic
1269	C₂	—	4	2	no	—
1270	C₂	—	4	2	no	—
1271	C₂	—	8	1	no	—
1272	C₂	—	16	1	no	—
1273	C₂	—	16	1	no	—
1274	C₂	#36012	1	1	yes	characteristic
1275	C₂	#60693	1	1	yes	characteristic
1276	C₂	#60707	1	1	yes	characteristic
1277	C₂	#61727	1	1	yes	characteristic
1278	C₂	#61734	1	1	yes	characteristic
1279	C₂	#61740	1	1	yes	characteristic
1280	C₂	#61741	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#29730	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×C₂²⋊C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #36208	C₂	semidirect
2. #36203	C₂	semidirect
3. #30364	C₂	semidirect
4. #30362	C₂	semidirect
6. #29461	C₂	semidirect
7. #29460	C₂	semidirect
8. #29000	C₂	semidirect
9. #28999	C₂	semidirect
10. #28866	C₂	semidirect
11. #28865	C₂	semidirect
12. #28773	C₂	semidirect
13. #28091	C₂	semidirect
14. #28086	C₂	semidirect
15. #27928	C₂	semidirect
16. #27879	C₂	semidirect
17. #27877	C₂	semidirect
18. #27854	C₂	semidirect
19. #27851	C₂	semidirect
20. #27702	C₂	semidirect
21. #27696	C₂	semidirect
22. #24560	C₂	semidirect
23. #24560	C₂	semidirect
24. #23764	C₂	semidirect
25. #23760	C₂	semidirect
26. #23638	C₂	semidirect
27. #23137	C₂	semidirect
28. #22935	C₂	semidirect
29. #22933	C₂	semidirect
30. #22616	C₂	semidirect
31. #20525	C₂	semidirect
83. #2101	C₂²	semidirect
84. #2101	C₂²	semidirect
85. #2100	C₂²	semidirect
86. #2100	C₂²	semidirect
87. #2094	C₂²	semidirect
88. #2094	C₂²	semidirect
89. #2092	C₂²	semidirect
90. #2092	C₂²	semidirect
91. #2085	C₂²	semidirect
92. #2083	C₂²	semidirect
107. #2073	C₂²	semidirect
108. #2071	C₂²	semidirect
109. #2059	C₂²	semidirect
110. #2057	C₂²	semidirect
119. #2025	C₂²	semidirect
120. #2023	C₂²	semidirect
123. #1991	C₂²	semidirect
124. #1991	C₂²	semidirect
125. #1990	C₂²	semidirect
126. #1990	C₂²	semidirect
127. #1970	C₂²	semidirect
128. #1970	C₂²	semidirect
129. #1944	C₂²	semidirect
130. #1944	C₂²	semidirect
131. #1944	C₂²	semidirect
132. #1943	C₂²	semidirect
133. #1942	C₂²	semidirect
134. #1941	C₂²	semidirect
135. #1936	C₂²	semidirect
136. #1936	C₂²	semidirect
137. #1936	C₂²	semidirect
138. #1936	C₂²	semidirect
139. #1934	C₂²	semidirect
140. #1934	C₂²	semidirect
141. #1934	C₂²	semidirect
142. #1934	C₂²	semidirect
143. #1926	C₂²	semidirect
144. #1925	C₂²	semidirect
145. #1921	C₂²	semidirect
146. #1921	C₂²	semidirect
147. #1920	C₂²	semidirect
148. #1919	C₂²	semidirect
149. #1918	C₂²	semidirect
150. #1918	C₂²	semidirect
151. #1918	C₂²	semidirect
152. #1918	C₂²	semidirect
153. #1918	C₂²	semidirect
154. #1918	C₂²	semidirect
161. #1879	C₂²	semidirect
162. #1879	C₂²	semidirect
165. #1864	C₂²	semidirect
166. #1862	C₂²	semidirect
169. #1846	C₂²	semidirect
170. #1845	C₂²	semidirect
171. #1835	C₂²	semidirect
172. #1834	C₂²	semidirect
180. #1776	C₂²	semidirect
181. #1776	C₂²	semidirect
182. #1776	C₂²	semidirect
183. #1776	C₂²	semidirect
184. #1762	C₂²	semidirect
185. #1762	C₂²	semidirect
186. #1762	C₂²	semidirect
187. #1762	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36208	2
#36203	2
#30364	2
#30362	2
#29730	2
#29461	2
#29460	2
#29000	2
#28999	2
#28866	2
#28865	2
#28773	2
#28091	2
#28086	2
#27928	2
#27879	2
#27877	2
#27854	2
#27851	2
#27702	2
#27696	2
#24560	2
#23764	2
#23760	2
#23638	2
#23137	2
#22935	2
#22933	2
#22616	2
#20525	2