Subgroups — #6464409

Order 512.

1660 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34281	C₂	1	1	yes	maximal, characteristic, complemented
2	#34086	C₂	1	1	yes	maximal, characteristic
3	#29424	C₂	1	1	yes	maximal, characteristic, complemented
4	#29423	C₂	1	1	yes	maximal, characteristic, complemented
5	#29420	C₂	1	1	yes	maximal, characteristic, complemented
6	#29419	C₂	1	1	yes	maximal, characteristic, complemented
7	#29397	C₂	1	1	yes	maximal, characteristic, complemented
8	#29396	C₂	1	1	yes	maximal, characteristic, complemented
9	#29369	C₂	1	1	yes	maximal, characteristic, complemented
10	#29368	C₂	1	1	yes	maximal, characteristic, complemented
11	#29282	C₂	1	1	yes	maximal, characteristic, complemented
12	#29265	C₂	1	1	yes	maximal, characteristic, complemented
13	#28213	C₂	1	1	yes	maximal, characteristic, complemented
14	#28169	C₂	1	1	yes	maximal, characteristic, complemented
15	#27635	C₂	1	1	yes	maximal, characteristic, complemented
16	#27634	C₂	1	1	yes	maximal, characteristic, complemented
17	#24156	C₂	1	1	yes	maximal, characteristic
18	#24154	C₂	1	1	yes	maximal, characteristic
19	#23770	C₂	1	1	yes	maximal, characteristic, complemented
20	#23766	C₂	1	1	yes	maximal, characteristic, complemented
21	#23584	C₂	1	1	yes	maximal, characteristic, complemented
22	#23584	C₂	1	1	yes	maximal, characteristic, complemented
23	#21626	C₂	1	1	yes	maximal, characteristic, complemented
24	#21625	C₂	1	1	yes	maximal, characteristic, complemented
25	#21515	C₂	1	1	yes	maximal, characteristic, complemented
26	#21515	C₂	1	1	yes	maximal, characteristic, complemented
27	#21121	C₂	1	1	yes	maximal, characteristic, complemented
28	#21121	C₂	1	1	yes	maximal, characteristic, complemented
29	#21117	C₂	1	1	yes	maximal, characteristic, complemented
30	#21114	C₂	1	1	yes	maximal, characteristic, complemented
31	#20785	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#541	C₂²	1	1	yes	characteristic
33	C₂×#532	C₂²	1	1	yes	characteristic
34	C₂×#477	C₂²	1	1	yes	characteristic
35	C₂×#475	C₂²	1	1	yes	characteristic
36	C₂×#460	C₂²	1	1	yes	characteristic
37	C₂×#460	C₂²	1	1	yes	characteristic
38	C₂×#440	C₂²	1	1	yes	characteristic
39	C₂×#440	C₂²	1	1	yes	characteristic
40	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
42	#2373	—	2	1	no	—
43	#2373	—	2	1	no	—
44	#2373	—	2	1	no	—
45	#2373	—	2	1	no	—
46	#2371	—	2	1	no	—
47	#2371	—	2	1	no	—
48	#2370	—	2	1	no	—
49	#2370	—	2	1	no	—
50	#2337	—	2	1	no	—
51	#2337	—	2	1	no	—
52	#2333	—	2	1	no	—
53	#2333	—	2	1	no	—
54	#2331	C₂²	1	1	yes	characteristic
55	#2331	C₂²	1	1	yes	characteristic
56	#2330	C₂²	1	1	yes	characteristic
57	#2328	C₂²	1	1	yes	characteristic
58	#2328	C₂²	1	1	yes	characteristic
59	#2327	C₂²	1	1	yes	characteristic
60	#2324	C₂²	1	1	yes	characteristic
61	#2324	C₂²	1	1	yes	characteristic
62	#2324	C₂²	1	1	yes	characteristic
63	#2324	C₂²	1	1	yes	characteristic
64	#2323	C₂²	1	1	yes	characteristic
65	#2323	C₂²	1	1	yes	characteristic
66	#2314	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
68	C₄×#125	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	#2297	—	2	1	no	—
72	#2297	—	2	1	no	—
73	#2295	C₂²	1	1	yes	characteristic
74	#2295	C₂²	1	1	yes	characteristic
75	#2293	C₂²	1	1	yes	characteristic
76	#2293	C₂²	1	1	yes	characteristic
77	#2290	—	2	1	no	—
78	#2290	—	2	1	no	—
79	#2283	C₂²	1	1	yes	characteristic
80	#2276	C₂²	1	1	yes	characteristic
81	#2276	C₂²	1	1	yes	characteristic
82	C₄²×D₄	C₂²	1	1	yes	characteristic
83	C₄²×D₄	C₂²	1	1	yes	characteristic
84	C₄×#117	C₂²	1	1	yes	characteristic
85	#2100	C₂²	1	1	yes	characteristic
86	#2099	C₂²	1	1	yes	characteristic
87	#2094	C₂²	1	1	yes	characteristic
88	#2093	C₂²	1	1	yes	characteristic
89	#2085	C₂²	1	1	yes	characteristic
90	#2085	C₂²	1	1	yes	characteristic
91	#2077	C₂²	1	1	yes	characteristic
92	#2077	C₂²	1	1	yes	characteristic
93	#2076	C₂²	1	1	yes	characteristic
94	#2075	C₂²	1	1	yes	characteristic
95	#2073	C₂²	1	1	yes	characteristic
96	#2073	C₂²	1	1	yes	characteristic
97	#2059	C₂²	1	1	yes	characteristic
98	#2059	C₂²	1	1	yes	characteristic
99	#2043	C₂²	1	1	yes	characteristic
100	#2043	C₂²	1	1	yes	characteristic
101	#2036	C₂²	1	1	yes	characteristic
102	#2036	C₂²	1	1	yes	characteristic
103	#2035	C₂²	1	1	yes	characteristic
104	#2035	C₂²	1	1	yes	characteristic
105	#2034	C₂²	1	1	yes	characteristic
106	#2034	C₂²	1	1	yes	characteristic
107	#2033	C₂²	1	1	yes	characteristic
108	#2033	C₂²	1	1	yes	characteristic
109	#2025	C₂²	1	1	yes	characteristic
110	#2025	C₂²	1	1	yes	characteristic
111	#2013	C₂²	1	1	yes	characteristic
112	#2013	C₂²	1	1	yes	characteristic
113	#2000	C₂²	1	1	yes	characteristic
114	#2000	C₂²	1	1	yes	characteristic
115	#2000	C₂²	1	1	yes	characteristic
116	#2000	C₂²	1	1	yes	characteristic
117	#1988	C₂²	1	1	yes	characteristic
118	#1987	C₂²	1	1	yes	characteristic
119	#1982	C₂²	1	1	yes	characteristic
120	#1982	C₂²	1	1	yes	characteristic
121	#1949	C₂²	1	1	yes	characteristic
122	#1949	C₂²	1	1	yes	characteristic
123	#1949	C₂²	1	1	yes	characteristic
124	#1949	C₂²	1	1	yes	characteristic
125	#1928	C₂²	1	1	yes	characteristic
126	#1928	C₂²	1	1	yes	characteristic
127	#1928	C₂²	1	1	yes	characteristic
128	#1928	C₂²	1	1	yes	characteristic
129	#1927	C₂²	1	1	yes	characteristic
130	#1927	C₂²	1	1	yes	characteristic
131	#1927	C₂²	1	1	yes	characteristic
132	#1927	C₂²	1	1	yes	characteristic
133	#1926	C₂²	1	1	yes	characteristic
134	#1926	C₂²	1	1	yes	characteristic
135	#1925	C₂²	1	1	yes	characteristic
136	#1925	C₂²	1	1	yes	characteristic
137	#1921	C₂²	1	1	yes	characteristic
138	#1921	C₂²	1	1	yes	characteristic
139	#1921	C₂²	1	1	yes	characteristic
140	#1920	C₂²	1	1	yes	characteristic
141	#1920	C₂²	1	1	yes	characteristic
142	#1920	C₂²	1	1	yes	characteristic
143	#1919	C₂²	1	1	yes	characteristic
144	#1919	C₂²	1	1	yes	characteristic
145	#1919	C₂²	1	1	yes	characteristic
146	#1918	C₂²	1	1	yes	characteristic
147	#1918	C₂²	1	1	yes	characteristic
148	#1918	C₂²	1	1	yes	characteristic
149	#1880	C₂²	1	1	yes	characteristic
150	#1880	C₂²	1	1	yes	characteristic
151	#1880	C₂²	1	1	yes	characteristic
152	#1880	C₂²	1	1	yes	characteristic
153	#1877	C₂²	1	1	yes	characteristic
154	#1877	C₂²	1	1	yes	characteristic
155	#1877	C₂²	1	1	yes	characteristic
156	#1877	C₂²	1	1	yes	characteristic
157	#1877	C₂²	1	1	yes	characteristic
158	#1877	C₂²	1	1	yes	characteristic
159	#1877	C₂²	1	1	yes	characteristic
160	#1877	C₂²	1	1	yes	characteristic
161	#1865	C₂²	1	1	yes	characteristic
162	#1865	C₂²	1	1	yes	characteristic
163	#1864	C₂²	1	1	yes	characteristic
164	#1864	C₂²	1	1	yes	characteristic
165	#1864	C₂²	1	1	yes	characteristic
166	#1864	C₂²	1	1	yes	characteristic
167	#1863	C₂²	1	1	yes	characteristic
168	#1863	C₂²	1	1	yes	characteristic
169	#1862	C₂²	1	1	yes	characteristic
170	#1862	C₂²	1	1	yes	characteristic
171	#1862	C₂²	1	1	yes	characteristic
172	#1862	C₂²	1	1	yes	characteristic
173	#1839	C₂²	1	1	yes	characteristic
174	#1839	C₂²	1	1	yes	characteristic
175	#1832	C₂²	1	1	yes	characteristic
176	#1832	C₂²	1	1	yes	characteristic
177	#1818	C₂²	1	1	yes	characteristic
178	#1818	C₂²	1	1	yes	characteristic
179	#1805	C₂²	1	1	yes	characteristic
180	#1805	C₂²	1	1	yes	characteristic
181	#1805	C₂²	1	1	yes	characteristic
182	#1805	C₂²	1	1	yes	characteristic
183	#1797	C₂²	1	1	yes	characteristic
184	#1797	C₂²	1	1	yes	characteristic
185	#1776	C₂²	1	1	yes	characteristic
186	#1776	C₂²	1	1	yes	characteristic
187	C₄×#107	C₂²	1	1	yes	characteristic
188	C₄×#106	C₂²	1	1	yes	characteristic
189	#1768	C₂²	1	1	yes	characteristic
190	#1768	C₂²	1	1	yes	characteristic
191	#1763	C₂²	1	1	yes	characteristic
192	#1763	C₂²	1	1	yes	characteristic
193	#1762	C₂²	1	1	yes	characteristic
194	#1762	C₂²	1	1	yes	characteristic
195	C₄×#103	C₂²	1	1	yes	characteristic
196	C₄×#103	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	#1750	C₂²	1	1	yes	characteristic
200	#1750	C₂²	1	1	yes	characteristic
201	#1745	C₂²	1	1	yes	characteristic
202	#1744	C₂²	1	1	yes	characteristic
203	C₂²×#41	—	2	1	no	—
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	#541	—	2	4	no	—
209	#541	—	2	4	no	—
210	#532	—	2	4	no	—
211	#532	—	2	4	no	—
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×#127	C₂³	1	1	yes	characteristic
215	C₂×#126	—	2	1	no	—
216	C₂×#126	—	2	1	no	—
217	C₂×#125	—	2	1	no	—
218	C₂×#125	—	2	1	no	—
219	C₂×#125	C₂³	1	1	yes	characteristic
220	C₂×#124	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×#121	—	2	1	no	—
224	C₂×#121	C₂³	1	1	yes	characteristic
225	C₂×#121	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×#117	—	2	1	no	—
240	C₂×#117	—	2	1	no	—
241	C₂×#117	C₂³	1	1	yes	characteristic
242	C₂×#117	C₂³	1	1	yes	characteristic
243	C₂²×C₄²	—	2	1	no	—
244	C₂²×C₄²	—	2	1	no	—
245	C₂²×C₄²	C₂³	1	1	yes	characteristic
246	#477	—	2	4	no	—
247	#475	—	2	4	no	—
248	#460	—	2	4	no	—
249	#460	—	2	4	no	—
250	#440	—	2	4	no	—
251	#440	—	2	4	no	—
252	C₄×SD₁₆	—	2	4	no	—
253	C₄×SD₁₆	—	2	4	no	—
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#107	C₂³	1	1	yes	characteristic
256	C₂×#107	C₂³	1	1	yes	characteristic
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	C₂×#106	C₂³	1	1	yes	characteristic
262	C₂×#106	C₂³	1	1	yes	characteristic
263	C₂×#106	C₂³	1	1	yes	characteristic
264	C₂×#106	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×#97	C₂³	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
302	#391	—	2	1	no	—
303	#391	—	2	1	no	—
304	#391	—	2	1	no	—
305	#391	—	2	1	no	—
306	#391	C₂³	1	1	yes	characteristic
307	#391	C₂³	1	1	yes	characteristic
308	#391	C₂³	1	1	yes	characteristic
309	#391	C₂³	1	1	yes	characteristic
310	#390	—	2	1	no	—
311	#390	—	2	1	no	—
312	#390	—	2	1	no	—
313	#390	—	2	1	no	—
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	#389	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
333	#388	—	2	1	no	—
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	#387	—	2	1	no	—
347	#387	—	2	1	no	—
348	#387	—	2	1	no	—
349	#387	—	2	1	no	—
350	#387	—	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	#386	—	2	1	no	—
376	#386	—	2	1	no	—
377	#386	—	2	1	no	—
378	#386	—	2	1	no	—
379	#386	—	2	1	no	—
380	#385	—	2	1	no	—
381	#385	—	2	1	no	—
382	#385	—	2	1	no	—
383	#385	—	2	1	no	—
384	#385	—	2	1	no	—
385	#385	—	2	1	no	—
386	#384	C₂³	1	1	yes	characteristic
387	#383	—	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	#380	C₂³	1	1	yes	characteristic
393	#380	C₂³	1	1	yes	characteristic
394	#380	C₂³	1	1	yes	characteristic
395	#380	C₂³	1	1	yes	characteristic
396	C₄×C₄⋊C₄	—	2	1	no	—
397	C₄×C₄⋊C₄	—	2	1	no	—
398	C₄×C₄⋊C₄	—	2	1	no	—
399	C₄×C₄⋊C₄	—	2	1	no	—
400	C₄×C₄⋊C₄	—	2	1	no	—
401	C₄×C₄⋊C₄	—	2	1	no	—
402	C₄×C₄⋊C₄	—	2	1	no	—
403	C₄×C₄⋊C₄	—	2	1	no	—
404	C₄×C₄⋊C₄	—	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	D₄	1	1	yes	characteristic
413	C₄×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	#376	—	2	1	no	—
442	#376	—	2	1	no	—
443	#376	—	2	1	no	—
444	#376	—	2	1	no	—
445	#376	—	2	1	no	—
446	#376	C₂³	1	1	yes	characteristic
447	#376	C₂³	1	1	yes	characteristic
448	C₄³	C₂³	1	1	yes	characteristic
449	C₄³	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	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂×#41	—	2	8	no	—
491	C₂×#41	—	8	2	no	—
492	C₂×#41	—	8	2	no	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	2	2	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	#41	1	4	yes	—
535	#127	—	2	2	no	—
536	#127	#41	1	4	yes	—
537	#126	—	2	8	no	—
538	#126	—	2	8	no	—
539	#125	—	2	8	no	—
540	#125	—	2	8	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#124	—	2	8	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	#121	—	2	8	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	4	1	no	—
560	C₄×Q₈	—	4	1	no	—
561	C₄×Q₈	—	4	1	no	—
562	C₄×Q₈	—	4	1	no	—
563	C₄×Q₈	#41	1	4	yes	complemented
564	C₄×Q₈	#41	1	4	yes	complemented
565	C₄×D₄	—	2	8	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	4	1	no	—
575	C₄×D₄	—	4	1	no	—
576	C₄×D₄	—	4	1	no	—
577	C₄×D₄	—	4	1	no	—
578	#117	—	2	2	no	—
579	#117	—	2	2	no	—
580	#117	—	4	1	no	—
581	#117	—	4	1	no	—
582	#117	—	8	2	no	—
583	#117	—	8	2	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	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
645	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	2	no	—
652	C₂×C₄²	—	2	2	no	—
653	C₂×C₄²	—	2	1	no	—
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	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	8	2	no	—
670	C₂×C₄²	—	8	2	no	—
671	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
677	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
678	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
679	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
680	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
681	C₂×C₄²	C₂⁴	1	1	yes	characteristic
682	C₂×C₄²	C₂⁴	1	1	yes	characteristic
683	C₂×C₄²	C₂⁴	1	1	yes	characteristic
684	C₂×C₄²	C₂⁴	1	1	yes	characteristic
685	C₂×C₄²	C₂⁴	1	1	yes	characteristic
686	C₂×C₄²	C₂⁴	1	1	yes	characteristic
687	#107	—	2	2	no	—
688	#107	—	2	2	no	—
689	#107	—	2	2	no	—
690	#107	—	2	2	no	—
691	#107	—	4	1	no	—
692	#107	—	4	1	no	—
693	#106	—	2	2	no	—
694	#106	—	2	2	no	—
695	#106	—	2	2	no	—
696	#106	—	2	2	no	—
697	#106	—	4	1	no	—
698	#106	—	4	1	no	—
699	C₄⋊C₈	—	2	2	no	—
700	C₄⋊C₈	—	2	2	no	—
701	C₄⋊C₈	—	2	2	no	—
702	C₄⋊C₈	—	2	2	no	—
703	#103	—	2	2	no	—
704	#103	—	2	2	no	—
705	#103	—	2	2	no	—
706	#103	—	2	2	no	—
707	#103	—	2	2	no	—
708	#103	—	2	2	no	—
709	#103	—	2	2	no	—
710	#103	—	2	2	no	—
711	#103	—	4	1	no	—
712	#103	—	4	1	no	—
713	#103	—	4	1	no	—
714	#103	—	4	1	no	—
715	#102	—	2	2	no	—
716	#102	—	2	2	no	—
717	#102	—	2	2	no	—
718	#102	—	2	2	no	—
719	#102	—	2	2	no	—
720	#102	—	2	2	no	—
721	#102	—	2	2	no	—
722	#102	—	2	2	no	—
723	#102	—	4	1	no	—
724	#102	—	4	1	no	—
725	#102	—	4	1	no	—
726	#102	—	4	1	no	—
727	C₂²⋊C₈	—	4	1	no	—
728	C₂²⋊C₈	—	4	1	no	—
729	C₂²⋊C₈	—	4	1	no	—
730	C₂²⋊C₈	—	4	1	no	—
731	#97	—	2	2	no	—
732	#97	—	2	2	no	—
733	C₄×C₈	—	2	2	no	—
734	C₄×C₈	—	2	2	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	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	C₂×D₄	1	1	yes	characteristic
774	#95	C₂×D₄	1	1	yes	characteristic
775	#95	C₂×D₄	1	1	yes	characteristic
776	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
778	#95	C₂×D₄	1	1	yes	characteristic
779	#95	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
781	C₂⁴	—	2	1	no	—
782	C₂⁴	—	2	1	no	—
783	C₂⁴	C₂²×D₄	1	1	yes	characteristic
784	#41	—	8	16	no	—
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	8	1	no	—
797	C₂×Q₈	—	8	1	no	—
798	C₂×Q₈	C₂×#41	1	2	yes	—
799	C₂×Q₈	C₂×#41	1	2	yes	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	8	1	no	—
815	C₂×D₄	—	8	1	no	—
816	C₂×D₄	—	8	1	no	—
817	C₂×D₄	—	8	1	no	—
818	C₂×D₄	—	8	1	no	—
819	C₂×D₄	—	8	1	no	—
820	C₂×D₄	—	8	1	no	—
821	C₂×D₄	—	8	1	no	—
822	C₂×D₄	C₂×#41	1	2	yes	—
823	C₂×D₄	C₂×#41	1	2	yes	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	4	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	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	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	2	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	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂⁵	1	1	yes	characteristic
882	SD₁₆	—	4	4	no	—
883	SD₁₆	—	4	4	no	—
884	SD₁₆	—	4	4	no	—
885	SD₁₆	—	4	4	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	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	4	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	4	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	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	—	4	1	no	—
942	C₄⋊C₄	—	4	1	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	—	4	2	no	—
948	C₄⋊C₄	—	4	2	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	C₂×#41	1	2	yes	—
958	C₄⋊C₄	C₂×#41	1	2	yes	—
959	C₄⋊C₄	C₂×#41	1	2	yes	—
960	C₄⋊C₄	C₂×#41	1	2	yes	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	2	4	no	—
963	C₂²⋊C₄	—	2	4	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	2	4	no	—
966	C₂²⋊C₄	—	2	4	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	4	1	no	—
970	C₂²⋊C₄	—	4	1	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	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₂²⋊C₄	—	8	1	no	—
978	C₂²⋊C₄	—	8	1	no	—
979	C₂²⋊C₄	—	8	1	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	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	4	no	—
990	C₄²	—	2	4	no	—
991	C₄²	—	2	2	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	2	no	—
1008	C₄²	—	4	2	no	—
1009	C₄²	—	4	2	no	—
1010	C₄²	—	4	2	no	—
1011	C₄²	—	4	2	no	—
1012	C₄²	—	4	2	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	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	C₂×#41	1	2	yes	—
1024	C₄²	C₂×#41	1	2	yes	—
1025	C₄²	C₂×#41	1	2	yes	—
1026	C₄²	C₂×#41	1	2	yes	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	1	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	C₂³×D₄	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	4	1	no	—
1054	Q₈	—	4	1	no	—
1055	Q₈	—	4	1	no	—
1056	Q₈	—	4	1	no	—
1057	Q₈	—	8	4	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	4	1	no	—
1063	D₄	—	4	1	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	4	1	no	—
1066	D₄	—	8	4	no	—
1067	D₄	—	8	4	no	—
1068	D₄	—	8	4	no	—
1069	D₄	—	8	4	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	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	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	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	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	—	4	4	no	—
1111	C₂×C₄	—	4	8	no	—
1112	C₂×C₄	—	4	8	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	—	8	2	no	—
1154	C₂×C₄	—	8	4	no	—
1155	C₂×C₄	—	8	4	no	—
1156	C₂×C₄	—	8	4	no	—
1157	C₂×C₄	—	8	4	no	—
1158	C₂×C₄	#525	1	2	yes	—
1159	C₂×C₄	#525	1	2	yes	—
1160	C₂×C₄	#525	1	2	yes	—
1161	C₂×C₄	#525	1	2	yes	—
1162	C₂×C₄	#577	1	2	yes	—
1163	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1164	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1165	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1166	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1167	C₂×C₄	#585	1	1	yes	characteristic
1168	C₂×C₄	#585	1	1	yes	characteristic
1169	C₈	—	4	1	no	—
1170	C₈	—	4	1	no	—
1171	C₈	—	4	1	no	—
1172	C₈	—	4	1	no	—
1173	C₈	—	4	1	no	—
1174	C₈	—	4	1	no	—
1175	C₈	—	4	1	no	—
1176	C₈	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	8	1	no	—
1191	C₂²	—	8	1	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	8	1	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	1	no	—
1196	C₂²	—	8	1	no	—
1197	C₂²	—	8	1	no	—
1198	C₂²	C₂×#525	1	1	yes	characteristic
1199	C₂²	C₂×#525	1	1	yes	characteristic
1200	C₂²	#3449	1	1	yes	characteristic
1201	C₂²	C₂×#577	1	1	yes	characteristic
1202	C₂²	#3584	1	1	yes	characteristic
1203	C₂²	#3585	1	1	yes	characteristic
1204	C₂²	#3586	1	1	yes	characteristic
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	8	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	—	8	1	no	—
1228	C₄	—	8	1	no	—
1229	C₄	—	8	1	no	—
1230	C₄	—	8	1	no	—
1231	C₄	—	8	1	no	—
1232	C₄	#3475	1	1	yes	characteristic
1233	C₄	#3475	1	1	yes	characteristic
1234	C₄	#3480	1	1	yes	characteristic
1235	C₄	#3480	1	1	yes	characteristic
1236	C₂	—	8	1	no	—
1237	C₂	—	8	2	no	—
1238	C₂	—	8	2	no	—
1239	C₂	#34909	1	1	yes	characteristic
1240	C₂	#60572	1	1	yes	characteristic
1241	C₂	#60576	1	1	yes	characteristic
1242	C₂	#60579	1	1	yes	characteristic
1243	C₂	#60581	1	1	yes	characteristic
1244	C₂	#60991	1	1	yes	characteristic
1245	C₂	#60997	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #34281	C₂	semidirect
3. #29424	C₂	semidirect
4. #29423	C₂	semidirect
5. #29420	C₂	semidirect
6. #29419	C₂	semidirect
7. #29397	C₂	semidirect
8. #29396	C₂	semidirect
9. #29369	C₂	semidirect
10. #29368	C₂	semidirect
11. #29282	C₂	semidirect
12. #29265	C₂	semidirect
13. #28213	C₂	semidirect
14. #28169	C₂	semidirect
15. #27635	C₂	semidirect
16. #27634	C₂	semidirect
19. #23770	C₂	semidirect
20. #23766	C₂	semidirect
21. #23584	C₂	semidirect
22. #23584	C₂	semidirect
23. #21626	C₂	semidirect
24. #21625	C₂	semidirect
25. #21515	C₂	semidirect
26. #21515	C₂	semidirect
27. #21121	C₂	semidirect
28. #21121	C₂	semidirect
29. #21117	C₂	semidirect
30. #21114	C₂	semidirect
31. #20785	C₂	semidirect
563. C₄×Q₈	#41	semidirect
564. C₄×Q₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#34281	2
#34086	2
#29424	2
#29423	2
#29420	2
#29419	2
#29397	2
#29396	2
#29369	2
#29368	2
#29282	2
#29265	2
#28213	2
#28169	2
#27635	2
#27634	2
#24156	2
#24154	2
#23770	2
#23766	2
#23584	2
#21626	2
#21625	2
#21515	2
#21121	2
#21117	2
#21114	2
#20785	2