Subgroups — #6358000

Order 512.

1709 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62536	C₂	1	1	yes	maximal, characteristic
2	#62482	C₂	1	1	yes	maximal, characteristic
3	#62482	C₂	1	1	yes	maximal, characteristic
4	#62478	C₂	1	1	yes	maximal, characteristic
5	#61013	C₂	1	1	yes	maximal, characteristic
6	#60878	C₂	1	1	yes	maximal, characteristic
7	#19751	C₂	1	1	yes	maximal, characteristic, complemented
8	#19751	C₂	1	1	yes	maximal, characteristic, complemented
9	#19736	C₂	1	1	yes	maximal, characteristic, complemented
10	#19736	C₂	1	1	yes	maximal, characteristic, complemented
11	#19736	C₂	1	1	yes	maximal, characteristic, complemented
12	#19736	C₂	1	1	yes	maximal, characteristic, complemented
13	#19732	C₂	1	1	yes	maximal, characteristic, complemented
14	#19732	C₂	1	1	yes	maximal, characteristic, complemented
15	#19720	C₂	1	1	yes	maximal, characteristic, complemented
16	#19720	C₂	1	1	yes	maximal, characteristic, complemented
17	#19720	C₂	1	1	yes	maximal, characteristic, complemented
18	#19720	C₂	1	1	yes	maximal, characteristic, complemented
19	#19711	C₂	1	1	yes	maximal, characteristic, complemented
20	#19706	C₂	1	1	yes	maximal, characteristic, complemented
21	#19690	C₂	1	1	yes	maximal, characteristic, complemented
22	#19690	C₂	1	1	yes	maximal, characteristic, complemented
23	#19681	C₂	1	1	yes	maximal, characteristic, complemented
24	#19680	C₂	1	1	yes	maximal, characteristic, complemented
25	#19668	C₂	1	1	yes	maximal, characteristic, complemented
26	#19663	C₂	1	1	yes	maximal, characteristic, complemented
27	#19648	C₂	1	1	yes	maximal, characteristic, complemented
28	#19648	C₂	1	1	yes	maximal, characteristic, complemented
29	#19634	C₂	1	1	yes	maximal, characteristic, complemented
30	#19634	C₂	1	1	yes	maximal, characteristic, complemented
31	#17340	C₂	1	1	yes	maximal, characteristic
32	#3509	C₂²	1	1	yes	characteristic
33	#3509	C₂²	1	1	yes	characteristic
34	#3509	C₂²	1	1	yes	characteristic
35	#3503	C₂²	1	1	yes	characteristic
36	#3390	—	2	2	no	—
37	#3390	—	2	2	no	—
38	#3387	—	2	2	no	—
39	#3374	—	2	2	no	—
40	#3356	—	2	2	no	—
41	#3352	—	2	2	no	—
42	#3352	—	2	2	no	—
43	#3349	—	2	2	no	—
44	#3349	—	2	2	no	—
45	#3349	—	2	2	no	—
46	#3349	—	2	2	no	—
47	#3344	—	2	2	no	—
48	#3344	—	2	2	no	—
49	#3328	—	2	2	no	—
50	#3312	—	2	2	no	—
51	#3312	—	2	2	no	—
52	#3261	—	2	2	no	—
53	#3242	—	2	2	no	—
54	#3242	—	2	2	no	—
55	#3231	C₂²	1	1	yes	characteristic
56	#3231	C₂²	1	1	yes	characteristic
57	#3231	C₂²	1	1	yes	characteristic
58	#3231	C₂²	1	1	yes	characteristic
59	#3231	C₂²	1	1	yes	characteristic
60	#3231	C₂²	1	1	yes	characteristic
61	#3231	C₂²	1	1	yes	characteristic
62	#3231	C₂²	1	1	yes	characteristic
63	#3231	C₂²	1	1	yes	characteristic
64	#3231	C₂²	1	1	yes	characteristic
65	#3231	C₂²	1	1	yes	characteristic
66	#3231	C₂²	1	1	yes	characteristic
67	#3231	C₂²	1	1	yes	characteristic
68	#3231	C₂²	1	1	yes	characteristic
69	#3231	C₂²	1	1	yes	characteristic
70	#3231	C₂²	1	1	yes	characteristic
71	#3231	C₂²	1	1	yes	characteristic
72	#3231	C₂²	1	1	yes	characteristic
73	#3231	C₂²	1	1	yes	characteristic
74	#3231	C₂²	1	1	yes	characteristic
75	#3230	C₂²	1	1	yes	characteristic
76	#3230	C₂²	1	1	yes	characteristic
77	#3230	C₂²	1	1	yes	characteristic
78	#3230	C₂²	1	1	yes	characteristic
79	#3230	C₂²	1	1	yes	characteristic
80	#3230	C₂²	1	1	yes	characteristic
81	#3230	C₂²	1	1	yes	characteristic
82	#3229	C₂²	1	1	yes	characteristic
83	#3229	C₂²	1	1	yes	characteristic
84	#3229	C₂²	1	1	yes	characteristic
85	#3229	C₂²	1	1	yes	characteristic
86	#3229	C₂²	1	1	yes	characteristic
87	#3229	C₂²	1	1	yes	characteristic
88	#3209	C₂²	1	1	yes	characteristic
89	#3209	C₂²	1	1	yes	characteristic
90	#3209	C₂²	1	1	yes	characteristic
91	#3209	C₂²	1	1	yes	characteristic
92	#3209	C₂²	1	1	yes	characteristic
93	#3209	C₂²	1	1	yes	characteristic
94	#3209	C₂²	1	1	yes	characteristic
95	#3202	—	2	2	no	—
96	#3185	C₂²	1	1	yes	characteristic
97	#3185	C₂²	1	1	yes	characteristic
98	#3185	C₂²	1	1	yes	characteristic
99	#3185	C₂²	1	1	yes	characteristic
100	#3185	C₂²	1	1	yes	characteristic
101	#3185	C₂²	1	1	yes	characteristic
102	#3185	C₂²	1	1	yes	characteristic
103	#3185	C₂²	1	1	yes	characteristic
104	#3185	C₂²	1	1	yes	characteristic
105	#3185	C₂²	1	1	yes	characteristic
106	#3170	C₂²	1	1	yes	characteristic
107	#3170	C₂²	1	1	yes	characteristic
108	#3170	C₂²	1	1	yes	characteristic
109	#3170	C₂²	1	1	yes	characteristic
110	#3170	C₂²	1	1	yes	characteristic
111	#3170	C₂²	1	1	yes	characteristic
112	#3165	C₂²	1	1	yes	characteristic
113	#3165	C₂²	1	1	yes	characteristic
114	#3165	C₂²	1	1	yes	characteristic
115	#3165	C₂²	1	1	yes	characteristic
116	#3165	C₂²	1	1	yes	characteristic
117	#3165	C₂²	1	1	yes	characteristic
118	#3165	C₂²	1	1	yes	characteristic
119	#3160	C₂²	1	1	yes	characteristic
120	#3160	C₂²	1	1	yes	characteristic
121	#3160	C₂²	1	1	yes	characteristic
122	C₂×#498	C₂²	1	1	yes	characteristic
123	#3139	C₂²	1	1	yes	characteristic
124	#3139	C₂²	1	1	yes	characteristic
125	#3139	C₂²	1	1	yes	characteristic
126	C₂×#487	C₂²	1	1	yes	characteristic
127	C₂×#487	C₂²	1	1	yes	characteristic
128	#3127	—	2	2	no	—
129	#3127	—	2	2	no	—
130	#3097	—	2	2	no	—
131	#3082	—	2	2	no	—
132	#2965	C₂²	1	1	yes	characteristic
133	#2965	C₂²	1	1	yes	characteristic
134	#2922	C₂²	1	1	yes	characteristic
135	#1723	C₂²	1	1	yes	characteristic
136	#1723	C₂²	1	1	yes	characteristic
137	#1723	C₂²	1	1	yes	characteristic
138	#1723	C₂²	1	1	yes	characteristic
139	#1723	C₂²	1	1	yes	characteristic
140	#1723	C₂²	1	1	yes	characteristic
141	#1723	C₂²	1	1	yes	characteristic
142	#1723	C₂²	1	1	yes	characteristic
143	#1723	C₂²	1	1	yes	characteristic
144	#1723	C₂²	1	1	yes	characteristic
145	#1723	C₂²	1	1	yes	characteristic
146	#1723	C₂²	1	1	yes	characteristic
147	#1723	C₂²	1	1	yes	characteristic
148	#1723	C₂²	1	1	yes	characteristic
149	#1723	C₂²	1	1	yes	characteristic
150	#1723	C₂²	1	1	yes	characteristic
151	#1723	C₂²	1	1	yes	characteristic
152	#1723	C₂²	1	1	yes	characteristic
153	#1718	C₂²	1	1	yes	characteristic
154	#1718	C₂²	1	1	yes	characteristic
155	#1718	C₂²	1	1	yes	characteristic
156	#1718	C₂²	1	1	yes	characteristic
157	#1718	C₂²	1	1	yes	characteristic
158	#1718	C₂²	1	1	yes	characteristic
159	#1718	C₂²	1	1	yes	characteristic
160	#1718	C₂²	1	1	yes	characteristic
161	#1718	C₂²	1	1	yes	characteristic
162	#1718	C₂²	1	1	yes	characteristic
163	#1718	C₂²	1	1	yes	characteristic
164	#1718	C₂²	1	1	yes	characteristic
165	#1718	C₂²	1	1	yes	characteristic
166	#1718	C₂²	1	1	yes	characteristic
167	#1718	C₂²	1	1	yes	characteristic
168	#1718	C₂²	1	1	yes	characteristic
169	#1718	C₂²	1	1	yes	characteristic
170	#1718	C₂²	1	1	yes	characteristic
171	#1718	C₂²	1	1	yes	characteristic
172	#1718	C₂²	1	1	yes	characteristic
173	#1716	C₂²	1	1	yes	characteristic
174	#1716	C₂²	1	1	yes	characteristic
175	#1716	C₂²	1	1	yes	characteristic
176	#1716	C₂²	1	1	yes	characteristic
177	#1716	C₂²	1	1	yes	characteristic
178	#1716	C₂²	1	1	yes	characteristic
179	#1716	C₂²	1	1	yes	characteristic
180	#1716	C₂²	1	1	yes	characteristic
181	#1716	C₂²	1	1	yes	characteristic
182	#1716	C₂²	1	1	yes	characteristic
183	#1713	C₂²	1	1	yes	characteristic
184	#1710	C₂²	1	1	yes	characteristic
185	#1710	C₂²	1	1	yes	characteristic
186	#1710	C₂²	1	1	yes	characteristic
187	#1710	C₂²	1	1	yes	characteristic
188	#1710	C₂²	1	1	yes	characteristic
189	#1707	C₂²	1	1	yes	characteristic
190	#1707	C₂²	1	1	yes	characteristic
191	#1707	C₂²	1	1	yes	characteristic
192	#1707	C₂²	1	1	yes	characteristic
193	#1707	C₂²	1	1	yes	characteristic
194	#1707	C₂²	1	1	yes	characteristic
195	#1707	C₂²	1	1	yes	characteristic
196	#1707	C₂²	1	1	yes	characteristic
197	#1707	C₂²	1	1	yes	characteristic
198	#1707	C₂²	1	1	yes	characteristic
199	#1455	C₂²	1	1	yes	characteristic
200	#1454	C₂²	1	1	yes	characteristic
201	#1454	C₂²	1	1	yes	characteristic
202	#1453	C₂²	1	1	yes	characteristic
203	#1453	C₂²	1	1	yes	characteristic
204	#1453	C₂²	1	1	yes	characteristic
205	#1452	C₂²	1	1	yes	characteristic
206	#1451	C₂²	1	1	yes	characteristic
207	#1451	C₂²	1	1	yes	characteristic
208	#1450	C₂²	1	1	yes	characteristic
209	C₈×M₁₆	C₂²	1	1	yes	characteristic
210	C₈×M₁₆	C₂²	1	1	yes	characteristic
211	Q₈²	—	2	1	no	—
212	#557	—	2	1	no	—
213	#557	—	2	1	no	—
214	#557	—	2	1	no	—
215	#557	—	2	1	no	—
216	#557	—	2	1	no	—
217	#557	—	2	1	no	—
218	#557	—	2	1	no	—
219	#556	—	2	1	no	—
220	#556	—	2	1	no	—
221	#556	—	2	1	no	—
222	#556	—	2	1	no	—
223	#556	—	2	1	no	—
224	#556	—	2	1	no	—
225	#554	—	2	1	no	—
226	#554	—	2	1	no	—
227	#554	—	2	1	no	—
228	#552	—	2	1	no	—
229	#552	—	2	1	no	—
230	#552	—	2	1	no	—
231	#552	—	2	1	no	—
232	#552	—	2	1	no	—
233	#552	—	2	1	no	—
234	#552	—	2	1	no	—
235	#552	—	2	1	no	—
236	#552	—	2	1	no	—
237	#552	—	2	1	no	—
238	#552	—	2	1	no	—
239	#552	—	2	1	no	—
240	D₄×Q₈	—	2	1	no	—
241	D₄×Q₈	—	2	1	no	—
242	D₄×Q₈	—	2	1	no	—
243	#544	—	2	1	no	—
244	#544	—	2	1	no	—
245	#544	—	2	1	no	—
246	#541	—	2	1	no	—
247	#541	—	2	1	no	—
248	#541	—	2	1	no	—
249	#541	—	2	1	no	—
250	#541	—	2	1	no	—
251	#541	—	2	1	no	—
252	#536	—	2	1	no	—
253	#536	—	2	1	no	—
254	#536	—	2	1	no	—
255	#533	C₂³	1	1	yes	characteristic
256	#533	C₂³	1	1	yes	characteristic
257	#533	C₂³	1	1	yes	characteristic
258	#533	C₂³	1	1	yes	characteristic
259	#533	C₂³	1	1	yes	characteristic
260	#533	C₂³	1	1	yes	characteristic
261	#533	C₂³	1	1	yes	characteristic
262	#533	C₂³	1	1	yes	characteristic
263	#533	C₂³	1	1	yes	characteristic
264	#533	C₂³	1	1	yes	characteristic
265	#533	C₂³	1	1	yes	characteristic
266	#533	C₂³	1	1	yes	characteristic
267	#533	C₂³	1	1	yes	characteristic
268	#533	C₂³	1	1	yes	characteristic
269	#533	C₂³	1	1	yes	characteristic
270	#533	C₂³	1	1	yes	characteristic
271	#533	C₂³	1	1	yes	characteristic
272	#533	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
279	#520	—	2	1	no	—
280	#519	—	2	1	no	—
281	#519	—	2	1	no	—
282	#519	—	2	1	no	—
283	C₄×#41	C₂³	1	1	yes	characteristic
284	#501	—	2	2	no	—
285	#501	—	2	2	no	—
286	#501	—	2	2	no	—
287	#501	—	2	2	no	—
288	#501	—	2	2	no	—
289	#501	—	2	2	no	—
290	#501	—	2	2	no	—
291	#500	C₂³	1	1	yes	characteristic
292	#500	C₂³	1	1	yes	characteristic
293	#500	C₂³	1	1	yes	characteristic
294	#500	C₂³	1	1	yes	characteristic
295	#500	C₂³	1	1	yes	characteristic
296	#500	C₂³	1	1	yes	characteristic
297	#500	C₂³	1	1	yes	characteristic
298	#500	C₂³	1	1	yes	characteristic
299	#500	C₂³	1	1	yes	characteristic
300	#500	C₂³	1	1	yes	characteristic
301	#500	C₂³	1	1	yes	characteristic
302	#500	C₂³	1	1	yes	characteristic
303	#500	C₂³	1	1	yes	characteristic
304	#500	C₂³	1	1	yes	characteristic
305	#500	C₂³	1	1	yes	characteristic
306	#500	C₂³	1	1	yes	characteristic
307	#500	C₂³	1	1	yes	characteristic
308	#500	C₂³	1	1	yes	characteristic
309	#500	C₂³	1	1	yes	characteristic
310	#500	C₂³	1	1	yes	characteristic
311	#499	—	2	2	no	—
312	#499	—	2	2	no	—
313	#499	—	2	2	no	—
314	#498	—	2	2	no	—
315	#498	C₂³	1	1	yes	characteristic
316	#498	C₂³	1	1	yes	characteristic
317	#498	C₂³	1	1	yes	characteristic
318	#498	C₂³	1	1	yes	characteristic
319	#498	C₂³	1	1	yes	characteristic
320	#498	C₂³	1	1	yes	characteristic
321	#498	C₂³	1	1	yes	characteristic
322	#498	C₂³	1	1	yes	characteristic
323	#498	C₂³	1	1	yes	characteristic
324	#498	C₂³	1	1	yes	characteristic
325	#498	C₂³	1	1	yes	characteristic
326	#498	C₂³	1	1	yes	characteristic
327	#498	C₂³	1	1	yes	characteristic
328	#498	C₂³	1	1	yes	characteristic
329	#498	C₂³	1	1	yes	characteristic
330	#498	C₂³	1	1	yes	characteristic
331	#498	C₂³	1	1	yes	characteristic
332	#498	C₂³	1	1	yes	characteristic
333	#498	C₂³	1	1	yes	characteristic
334	#498	C₂³	1	1	yes	characteristic
335	#498	C₂³	1	1	yes	characteristic
336	#498	C₂³	1	1	yes	characteristic
337	#494	C₂³	1	1	yes	characteristic
338	#494	C₂³	1	1	yes	characteristic
339	#494	C₂³	1	1	yes	characteristic
340	#494	C₂³	1	1	yes	characteristic
341	#494	C₂³	1	1	yes	characteristic
342	#494	C₂³	1	1	yes	characteristic
343	#494	C₂³	1	1	yes	characteristic
344	#494	C₂³	1	1	yes	characteristic
345	#494	C₂³	1	1	yes	characteristic
346	#494	C₂³	1	1	yes	characteristic
347	#491	—	2	2	no	—
348	#491	—	2	2	no	—
349	#491	—	2	2	no	—
350	#487	—	2	2	no	—
351	#487	—	2	2	no	—
352	#487	C₂³	1	1	yes	characteristic
353	#487	C₂³	1	1	yes	characteristic
354	#487	C₂³	1	1	yes	characteristic
355	#487	C₂³	1	1	yes	characteristic
356	#487	C₂³	1	1	yes	characteristic
357	#487	C₂³	1	1	yes	characteristic
358	#487	C₂³	1	1	yes	characteristic
359	#487	C₂³	1	1	yes	characteristic
360	#487	C₂³	1	1	yes	characteristic
361	#487	C₂³	1	1	yes	characteristic
362	#487	C₂³	1	1	yes	characteristic
363	#487	C₂³	1	1	yes	characteristic
364	#487	C₂³	1	1	yes	characteristic
365	#487	C₂³	1	1	yes	characteristic
366	#487	C₂³	1	1	yes	characteristic
367	#487	C₂³	1	1	yes	characteristic
368	#487	C₂³	1	1	yes	characteristic
369	#487	C₂³	1	1	yes	characteristic
370	#487	C₂³	1	1	yes	characteristic
371	#487	C₂³	1	1	yes	characteristic
372	#487	C₂³	1	1	yes	characteristic
373	#487	C₂³	1	1	yes	characteristic
374	#487	C₂³	1	1	yes	characteristic
375	#487	C₂³	1	1	yes	characteristic
376	#487	C₂³	1	1	yes	characteristic
377	#487	C₂³	1	1	yes	characteristic
378	#487	C₂³	1	1	yes	characteristic
379	#487	C₂³	1	1	yes	characteristic
380	#487	C₂³	1	1	yes	characteristic
381	#487	C₂³	1	1	yes	characteristic
382	#487	C₂³	1	1	yes	characteristic
383	#487	C₂³	1	1	yes	characteristic
384	#487	C₂³	1	1	yes	characteristic
385	#487	C₂³	1	1	yes	characteristic
386	#487	C₂³	1	1	yes	characteristic
387	#487	C₂³	1	1	yes	characteristic
388	#487	C₂³	1	1	yes	characteristic
389	#487	C₂³	1	1	yes	characteristic
390	#487	C₂³	1	1	yes	characteristic
391	#487	C₂³	1	1	yes	characteristic
392	#487	C₂³	1	1	yes	characteristic
393	#487	C₂³	1	1	yes	characteristic
394	#487	C₂³	1	1	yes	characteristic
395	#487	C₂³	1	1	yes	characteristic
396	#485	—	2	2	no	—
397	#485	—	2	2	no	—
398	#485	—	2	2	no	—
399	#485	—	2	2	no	—
400	#485	—	2	2	no	—
401	#485	—	2	2	no	—
402	#485	—	2	2	no	—
403	#485	—	2	2	no	—
404	#485	—	2	2	no	—
405	#485	—	2	2	no	—
406	#485	—	2	2	no	—
407	#485	—	2	2	no	—
408	#485	—	2	2	no	—
409	#485	—	2	2	no	—
410	#485	—	2	2	no	—
411	#485	—	2	2	no	—
412	#485	—	2	2	no	—
413	#485	—	2	2	no	—
414	#485	—	2	2	no	—
415	#485	—	2	2	no	—
416	#484	—	2	2	no	—
417	#484	—	2	2	no	—
418	#484	—	2	2	no	—
419	#484	—	2	2	no	—
420	#484	—	2	2	no	—
421	#484	—	2	2	no	—
422	#484	—	2	2	no	—
423	#483	—	2	2	no	—
424	#483	—	2	2	no	—
425	#483	—	2	2	no	—
426	#483	—	2	2	no	—
427	#483	—	2	2	no	—
428	#483	—	2	2	no	—
429	#479	—	2	2	no	—
430	#479	—	2	2	no	—
431	#479	—	2	2	no	—
432	#479	—	2	2	no	—
433	#479	—	2	2	no	—
434	#479	—	2	2	no	—
435	#479	—	2	2	no	—
436	#479	—	2	2	no	—
437	#479	—	2	2	no	—
438	#479	—	2	2	no	—
439	#479	—	2	2	no	—
440	#479	—	2	2	no	—
441	#479	—	2	2	no	—
442	#479	—	2	2	no	—
443	#479	—	2	2	no	—
444	#479	—	2	2	no	—
445	#479	—	2	2	no	—
446	#479	—	2	2	no	—
447	#479	—	2	2	no	—
448	#479	—	2	2	no	—
449	#477	—	2	2	no	—
450	#477	—	2	2	no	—
451	#477	—	2	2	no	—
452	#477	—	2	2	no	—
453	#477	—	2	2	no	—
454	#477	—	2	2	no	—
455	#477	—	2	2	no	—
456	#475	—	2	2	no	—
457	#475	—	2	2	no	—
458	#475	—	2	2	no	—
459	#475	—	2	2	no	—
460	#475	—	2	2	no	—
461	#475	—	2	2	no	—
462	#470	—	2	2	no	—
463	#470	—	2	2	no	—
464	#470	—	2	2	no	—
465	#470	—	2	2	no	—
466	#470	—	2	2	no	—
467	#470	—	2	2	no	—
468	#470	—	2	2	no	—
469	#470	—	2	2	no	—
470	#470	—	2	2	no	—
471	#470	—	2	2	no	—
472	#467	—	2	2	no	—
473	#467	—	2	2	no	—
474	#467	—	2	2	no	—
475	#467	—	2	2	no	—
476	#467	—	2	2	no	—
477	#467	—	2	2	no	—
478	#462	—	2	2	no	—
479	#462	—	2	2	no	—
480	#462	—	2	2	no	—
481	#462	—	2	2	no	—
482	#462	—	2	2	no	—
483	#462	—	2	2	no	—
484	#462	—	2	2	no	—
485	#451	—	2	2	no	—
486	#451	—	2	2	no	—
487	#451	—	2	2	no	—
488	#451	—	2	2	no	—
489	#451	—	2	2	no	—
490	#451	—	2	2	no	—
491	#451	—	2	2	no	—
492	#446	D₄	1	2	yes	—
493	#446	D₄	1	2	yes	—
494	#441	—	2	2	no	—
495	#441	—	2	2	no	—
496	#441	—	2	2	no	—
497	#441	—	2	2	no	—
498	#441	—	2	2	no	—
499	#441	—	2	2	no	—
500	#441	—	2	2	no	—
501	#441	—	2	2	no	—
502	#441	—	2	2	no	—
503	#441	—	2	2	no	—
504	C₄×Q₁₆	—	2	2	no	—
505	C₄×Q₁₆	—	2	2	no	—
506	C₄×Q₁₆	—	2	2	no	—
507	C₄×Q₁₆	—	2	2	no	—
508	C₄×Q₁₆	—	2	2	no	—
509	C₄×Q₁₆	—	2	2	no	—
510	#436	D₄	1	2	yes	—
511	#436	D₄	1	2	yes	—
512	#435	D₄	1	2	yes	—
513	#435	D₄	1	2	yes	—
514	#435	D₄	1	2	yes	—
515	#435	D₄	1	2	yes	—
516	#433	D₄	1	2	yes	—
517	#433	D₄	1	2	yes	—
518	#431	C₂³	1	1	yes	characteristic
519	#431	C₂³	1	1	yes	characteristic
520	#431	C₂³	1	1	yes	characteristic
521	#431	C₂³	1	1	yes	characteristic
522	#431	C₂³	1	1	yes	characteristic
523	#431	C₂³	1	1	yes	characteristic
524	#431	C₂³	1	1	yes	characteristic
525	#431	C₂³	1	1	yes	characteristic
526	#431	C₂³	1	1	yes	characteristic
527	#431	C₂³	1	1	yes	characteristic
528	#428	—	2	2	no	—
529	#428	—	2	2	no	—
530	#428	—	2	2	no	—
531	#428	—	2	2	no	—
532	#428	—	2	2	no	—
533	#428	—	2	2	no	—
534	#428	—	2	2	no	—
535	#427	—	2	2	no	—
536	#427	—	2	2	no	—
537	#427	—	2	2	no	—
538	C₂×#106	—	2	2	no	—
539	#424	D₄	1	2	yes	—
540	#419	—	2	2	no	—
541	#419	—	2	2	no	—
542	#419	—	2	2	no	—
543	C₂×#103	—	2	2	no	—
544	C₂×#103	—	2	2	no	—
545	#408	D₄	1	2	yes	—
546	C₄×M₁₆	C₂³	1	1	yes	characteristic
547	C₄×M₁₆	C₂³	1	1	yes	characteristic
548	C₄×M₁₆	C₂³	1	1	yes	characteristic
549	C₄×M₁₆	C₂³	1	1	yes	characteristic
550	C₄×M₁₆	C₂³	1	1	yes	characteristic
551	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
552	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
553	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
554	#322	C₂³	1	1	yes	characteristic
555	#322	C₂³	1	1	yes	characteristic
556	#322	C₂³	1	1	yes	characteristic
557	#322	C₂³	1	1	yes	characteristic
558	#322	C₂³	1	1	yes	characteristic
559	#322	C₂³	1	1	yes	characteristic
560	#322	C₂³	1	1	yes	characteristic
561	#322	C₂³	1	1	yes	characteristic
562	#322	C₂³	1	1	yes	characteristic
563	#322	C₂³	1	1	yes	characteristic
564	#322	C₂³	1	1	yes	characteristic
565	#322	C₂³	1	1	yes	characteristic
566	C₈²	C₂³	1	1	yes	characteristic
567	C₈²	C₂³	1	1	yes	characteristic
568	C₈²	C₂³	1	1	yes	characteristic
569	C₈²	C₂³	1	1	yes	characteristic
570	C₂×#41	C₂×D₄	1	1	yes	characteristic
571	C₂²×Q₈	—	2	1	no	—
572	C₂²×Q₈	—	2	1	no	—
573	C₂²×Q₈	—	2	1	no	—
574	C₂²×Q₈	—	2	1	no	—
575	C₂²×Q₈	—	2	1	no	—
576	C₂²×Q₈	—	2	1	no	—
577	C₂×Q₁₆	—	2	2	no	—
578	C₂×Q₁₆	—	2	2	no	—
579	C₂×Q₁₆	—	2	2	no	—
580	C₂×Q₁₆	—	2	2	no	—
581	C₂×Q₁₆	—	2	2	no	—
582	C₂×Q₁₆	—	2	2	no	—
583	C₂×Q₁₆	—	2	2	no	—
584	C₂×Q₁₆	—	2	2	no	—
585	C₂×Q₁₆	—	2	2	no	—
586	C₂×Q₁₆	—	2	2	no	—
587	C₂×M₁₆	C₂×D₄	1	2	yes	—
588	C₂×M₁₆	C₂×D₄	1	2	yes	—
589	C₂×M₁₆	C₂×D₄	1	2	yes	—
590	C₂×M₁₆	C₂×D₄	1	2	yes	—
591	C₂×M₁₆	C₂×D₄	1	2	yes	—
592	C₂²×C₈	C₂×D₄	1	2	yes	—
593	C₂²×C₈	C₂×D₄	1	2	yes	—
594	C₂²×C₈	C₂×D₄	1	2	yes	—
595	C₄⋊Q₈	—	2	1	no	—
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	—	2	1	no	—
598	C₄⋊Q₈	—	2	1	no	—
599	C₄⋊Q₈	—	2	1	no	—
600	C₄⋊Q₈	—	2	1	no	—
601	C₄⋊Q₈	—	2	1	no	—
602	C₄⋊Q₈	—	2	1	no	—
603	C₄⋊Q₈	—	2	1	no	—
604	C₄⋊Q₈	—	2	1	no	—
605	C₄⋊Q₈	—	2	1	no	—
606	C₄⋊Q₈	—	2	1	no	—
607	C₄⋊Q₈	—	2	1	no	—
608	C₄⋊Q₈	—	2	1	no	—
609	C₄⋊Q₈	—	2	1	no	—
610	C₄⋊Q₈	—	2	1	no	—
611	C₄⋊Q₈	—	2	1	no	—
612	C₄⋊Q₈	—	2	1	no	—
613	C₄⋊Q₈	—	4	1	no	—
614	C₄⋊Q₈	—	4	1	no	—
615	C₄⋊Q₈	—	4	1	no	—
616	C₄⋊Q₈	—	4	1	no	—
617	C₄⋊Q₈	—	4	1	no	—
618	C₄⋊Q₈	—	4	1	no	—
619	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
620	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
621	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
622	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
623	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
624	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
625	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
626	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
627	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
628	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
629	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
630	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
631	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
632	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
633	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
634	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
635	#126	—	4	1	no	—
636	#126	—	4	1	no	—
637	#126	—	4	1	no	—
638	#126	—	4	1	no	—
639	#126	—	4	1	no	—
640	#126	—	4	1	no	—
641	#126	—	4	1	no	—
642	#126	—	4	1	no	—
643	#126	—	4	1	no	—
644	#126	—	4	1	no	—
645	#126	—	4	1	no	—
646	#126	—	4	1	no	—
647	#125	—	2	1	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	—	2	1	no	—
654	#125	—	2	1	no	—
655	#125	—	2	1	no	—
656	#125	—	2	1	no	—
657	#125	—	2	1	no	—
658	#125	—	2	1	no	—
659	#125	—	2	1	no	—
660	#125	—	2	1	no	—
661	#125	—	2	1	no	—
662	#125	—	2	1	no	—
663	#125	—	2	1	no	—
664	#125	—	2	1	no	—
665	#125	—	4	1	no	—
666	#125	—	4	1	no	—
667	#125	—	4	1	no	—
668	#125	—	4	1	no	—
669	#125	—	4	1	no	—
670	#125	—	4	1	no	—
671	#125	—	4	1	no	—
672	#125	—	4	1	no	—
673	#125	—	4	1	no	—
674	#125	—	4	1	no	—
675	#125	—	4	1	no	—
676	#125	—	4	1	no	—
677	#125	—	4	1	no	—
678	#125	—	4	1	no	—
679	#125	—	4	1	no	—
680	#124	—	4	1	no	—
681	#124	—	4	1	no	—
682	#124	—	4	1	no	—
683	#123	—	4	1	no	—
684	#123	—	4	1	no	—
685	#123	—	4	1	no	—
686	#123	—	4	1	no	—
687	#123	—	4	1	no	—
688	#123	—	4	1	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	—	2	1	no	—
696	C₂²⋊Q₈	—	2	1	no	—
697	C₂²⋊Q₈	—	2	1	no	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	1	no	—
700	C₂²⋊Q₈	—	2	1	no	—
701	C₂²⋊Q₈	—	2	1	no	—
702	C₂²⋊Q₈	—	2	1	no	—
703	C₂²⋊Q₈	—	2	1	no	—
704	C₂²⋊Q₈	—	2	1	no	—
705	C₂²⋊Q₈	—	2	1	no	—
706	C₂²⋊Q₈	—	2	1	no	—
707	C₂²⋊Q₈	—	2	1	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	1	no	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	1	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	1	no	—
715	C₂²⋊Q₈	—	2	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	2	1	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	4	1	no	—
726	C₂²⋊Q₈	—	4	1	no	—
727	C₂²⋊Q₈	—	4	1	no	—
728	C₂²⋊Q₈	—	4	1	no	—
729	C₂²⋊Q₈	—	4	1	no	—
730	C₂²⋊Q₈	—	4	1	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	—	2	1	no	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	4	1	no	—
768	C₄×Q₈	—	4	1	no	—
769	C₄×Q₈	—	4	1	no	—
770	C₄×Q₈	—	4	1	no	—
771	C₄×Q₈	—	4	1	no	—
772	C₄×Q₈	—	4	1	no	—
773	C₄×Q₈	—	4	1	no	—
774	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
775	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
776	C₄×D₄	—	4	1	no	—
777	C₄×D₄	—	4	1	no	—
778	C₄×D₄	—	4	1	no	—
779	C₄×D₄	C₂×D₄	1	1	yes	characteristic
780	C₄×D₄	C₂×D₄	1	1	yes	characteristic
781	C₄×D₄	C₂×D₄	1	1	yes	characteristic
782	C₄×D₄	C₂×D₄	1	1	yes	characteristic
783	C₄×D₄	C₂×D₄	1	1	yes	characteristic
784	C₄×D₄	C₂×D₄	1	1	yes	characteristic
785	#117	—	2	1	no	—
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	—	2	1	no	—
789	#117	—	2	1	no	—
790	#117	—	2	1	no	—
791	#117	—	2	1	no	—
792	#117	—	2	1	no	—
793	#117	—	2	1	no	—
794	#117	—	2	1	no	—
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	4	1	no	—
804	#117	—	4	1	no	—
805	#117	—	4	1	no	—
806	#117	—	4	1	no	—
807	#117	—	4	1	no	—
808	#117	—	4	1	no	—
809	#117	C₂×D₄	1	1	yes	characteristic
810	#117	C₂×D₄	1	1	yes	characteristic
811	#117	C₂×D₄	1	1	yes	characteristic
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	—	2	1	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄²	C₂⁴	1	1	yes	characteristic
825	C₂×C₄²	C₂⁴	1	1	yes	characteristic
826	C₂×C₄²	C₂⁴	1	1	yes	characteristic
827	#107	—	2	2	no	—
828	#107	—	2	2	no	—
829	#107	—	2	2	no	—
830	#107	—	2	2	no	—
831	#107	—	2	2	no	—
832	#107	—	2	2	no	—
833	#107	—	2	2	no	—
834	#107	—	2	2	no	—
835	#107	—	2	2	no	—
836	#107	—	2	2	no	—
837	#107	—	2	2	no	—
838	#107	—	2	2	no	—
839	#107	—	2	2	no	—
840	#107	—	2	2	no	—
841	#107	—	2	2	no	—
842	#107	—	2	2	no	—
843	#107	—	2	2	no	—
844	#107	—	2	2	no	—
845	#107	—	2	2	no	—
846	#107	—	2	2	no	—
847	#106	—	2	2	no	—
848	#106	—	2	2	no	—
849	#106	—	2	2	no	—
850	#106	—	2	2	no	—
851	#106	—	2	2	no	—
852	#106	—	2	2	no	—
853	#106	—	2	2	no	—
854	#106	—	2	2	no	—
855	#106	—	2	2	no	—
856	#106	—	2	2	no	—
857	#106	—	2	2	no	—
858	#106	—	2	2	no	—
859	#106	—	2	2	no	—
860	#106	—	2	2	no	—
861	#106	—	2	2	no	—
862	#106	—	2	2	no	—
863	#106	—	2	2	no	—
864	#106	—	2	2	no	—
865	#106	—	2	2	no	—
866	#106	—	2	2	no	—
867	#106	—	2	2	no	—
868	#106	—	2	2	no	—
869	C₄⋊C₈	C₂×D₄	1	2	yes	—
870	C₄⋊C₈	C₂×D₄	1	2	yes	—
871	C₄⋊C₈	C₂×D₄	1	2	yes	—
872	C₄⋊C₈	C₂×D₄	1	2	yes	—
873	C₄⋊C₈	C₂×D₄	1	2	yes	—
874	C₄⋊C₈	C₂×D₄	1	2	yes	—
875	C₄⋊C₈	C₂×D₄	1	2	yes	—
876	C₄⋊C₈	C₂×D₄	1	2	yes	—
877	C₄⋊C₈	C₂×D₄	1	2	yes	—
878	C₄⋊C₈	C₂×D₄	1	2	yes	—
879	#103	—	2	2	no	—
880	#103	—	2	2	no	—
881	#103	—	2	2	no	—
882	#103	—	2	2	no	—
883	#103	—	2	2	no	—
884	#103	—	2	2	no	—
885	#103	—	2	2	no	—
886	#103	—	2	2	no	—
887	#103	—	2	2	no	—
888	#103	—	2	2	no	—
889	#103	—	2	2	no	—
890	#103	—	2	2	no	—
891	#103	—	2	2	no	—
892	#103	—	2	2	no	—
893	#103	—	2	2	no	—
894	#103	—	2	2	no	—
895	#103	—	2	2	no	—
896	#103	—	2	2	no	—
897	#103	—	2	2	no	—
898	#103	—	2	2	no	—
899	#103	—	2	2	no	—
900	#103	—	2	2	no	—
901	#103	—	2	2	no	—
902	#103	—	2	2	no	—
903	#103	—	2	2	no	—
904	#103	—	2	2	no	—
905	#103	—	2	2	no	—
906	#103	—	2	2	no	—
907	#103	—	2	2	no	—
908	#103	—	2	2	no	—
909	#103	—	2	2	no	—
910	#103	—	2	2	no	—
911	#103	—	2	2	no	—
912	#103	—	2	2	no	—
913	#103	—	2	2	no	—
914	#103	—	2	2	no	—
915	#103	—	2	2	no	—
916	#103	—	2	2	no	—
917	#103	—	2	2	no	—
918	#103	—	2	2	no	—
919	#103	—	2	2	no	—
920	#103	—	2	2	no	—
921	#103	—	2	2	no	—
922	#103	—	2	2	no	—
923	C₂²⋊C₈	C₂×D₄	1	2	yes	—
924	C₂²⋊C₈	C₂×D₄	1	2	yes	—
925	C₂²⋊C₈	C₂×D₄	1	2	yes	—
926	C₂²⋊C₈	C₂×D₄	1	2	yes	—
927	C₂²⋊C₈	C₂×D₄	1	2	yes	—
928	C₂²⋊C₈	C₂×D₄	1	2	yes	—
929	C₂²⋊C₈	C₂×D₄	1	2	yes	—
930	C₂²⋊C₈	C₂×D₄	1	2	yes	—
931	C₂²⋊C₈	C₂×D₄	1	2	yes	—
932	C₂²⋊C₈	C₂×D₄	1	2	yes	—
933	#97	C₂×D₄	1	2	yes	—
934	#97	C₂×D₄	1	2	yes	—
935	#97	C₂×D₄	1	2	yes	—
936	#97	C₂×D₄	1	2	yes	—
937	#97	C₂×D₄	1	2	yes	—
938	C₄×C₈	C₂×D₄	1	2	yes	—
939	C₄×C₈	C₂×D₄	1	2	yes	—
940	C₄×C₈	C₂×D₄	1	2	yes	—
941	C₄×C₈	C₂⁴	1	1	yes	characteristic
942	C₄×C₈	C₂⁴	1	1	yes	characteristic
943	C₄×C₈	C₂⁴	1	1	yes	characteristic
944	C₄×C₈	C₂⁴	1	1	yes	characteristic
945	C₄×C₈	C₂⁴	1	1	yes	characteristic
946	C₄×C₈	C₂⁴	1	1	yes	characteristic
947	C₄×C₈	C₂⁴	1	1	yes	characteristic
948	C₄×C₈	C₂⁴	1	1	yes	characteristic
949	C₄×C₈	C₂⁴	1	1	yes	characteristic
950	C₄×C₈	C₂⁴	1	1	yes	characteristic
951	C₄×C₈	C₂⁴	1	1	yes	characteristic
952	C₄×C₈	C₂⁴	1	1	yes	characteristic
953	#41	—	4	2	no	—
954	C₂×Q₈	—	2	1	no	—
955	C₂×Q₈	—	2	1	no	—
956	C₂×Q₈	—	2	1	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	1	no	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	1	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	1	no	—
964	C₂×Q₈	—	2	1	no	—
965	C₂×Q₈	—	2	1	no	—
966	C₂×Q₈	—	2	1	no	—
967	C₂×Q₈	—	2	1	no	—
968	C₂×Q₈	—	2	1	no	—
969	C₂×Q₈	—	2	1	no	—
970	C₂×Q₈	—	4	4	no	—
971	C₂×Q₈	—	4	1	no	—
972	C₂×Q₈	—	4	1	no	—
973	C₂×Q₈	—	4	1	no	—
974	C₂×Q₈	—	4	1	no	—
975	C₂×Q₈	—	4	1	no	—
976	C₂×Q₈	—	4	1	no	—
977	C₂×Q₈	—	8	2	no	—
978	C₂×Q₈	—	8	2	no	—
979	C₂×Q₈	—	8	2	no	—
980	C₂×Q₈	—	8	2	no	—
981	C₂×Q₈	—	8	2	no	—
982	C₂×Q₈	#127	1	1	yes	characteristic
983	C₂×D₄	#127	1	1	yes	characteristic
984	C₂×D₄	#127	1	1	yes	characteristic
985	C₂×D₄	#127	1	1	yes	characteristic
986	C₂²×C₄	—	4	1	no	—
987	C₂²×C₄	—	4	1	no	—
988	C₂²×C₄	—	4	1	no	—
989	C₂²×C₄	—	4	1	no	—
990	C₂²×C₄	—	4	1	no	—
991	C₂²×C₄	—	4	1	no	—
992	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
993	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
994	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
995	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
996	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
997	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
998	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
999	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1000	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1001	Q₁₆	—	4	4	no	—
1002	Q₁₆	—	4	4	no	—
1003	Q₁₆	—	4	4	no	—
1004	Q₁₆	—	8	2	no	—
1005	Q₁₆	—	8	2	no	—
1006	Q₁₆	—	8	2	no	—
1007	Q₁₆	—	8	2	no	—
1008	Q₁₆	—	8	2	no	—
1009	Q₁₆	—	8	2	no	—
1010	Q₁₆	—	8	2	no	—
1011	M₁₆	—	2	4	no	—
1012	M₁₆	—	2	4	no	—
1013	M₁₆	—	4	2	no	—
1014	M₁₆	—	4	2	no	—
1015	M₁₆	—	4	2	no	—
1016	C₂×C₈	—	2	4	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	C₂²×D₄	1	2	yes	—
1020	C₂×C₈	C₂²×D₄	1	2	yes	—
1021	C₂×C₈	C₂²×D₄	1	2	yes	—
1022	C₂×C₈	C₂²×D₄	1	2	yes	—
1023	C₂×C₈	C₂²×D₄	1	2	yes	—
1024	C₂×C₈	C₂²×D₄	1	2	yes	—
1025	C₂×C₈	C₂²×D₄	1	2	yes	—
1026	C₂×C₈	C₂²×D₄	1	2	yes	—
1027	C₂×C₈	C₂²×D₄	1	2	yes	—
1028	C₂×C₈	C₂²×D₄	1	2	yes	—
1029	C₂×C₈	C₂²×D₄	1	2	yes	—
1030	C₂×C₈	C₂²×D₄	1	2	yes	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	4	1	no	—
1064	C₄⋊C₄	—	4	1	no	—
1065	C₄⋊C₄	—	4	1	no	—
1066	C₄⋊C₄	—	4	1	no	—
1067	C₄⋊C₄	—	4	1	no	—
1068	C₄⋊C₄	—	4	1	no	—
1069	C₄⋊C₄	—	4	1	no	—
1070	C₄⋊C₄	—	4	1	no	—
1071	C₄⋊C₄	—	4	1	no	—
1072	C₄⋊C₄	—	4	1	no	—
1073	C₄⋊C₄	—	4	1	no	—
1074	C₄⋊C₄	—	4	1	no	—
1075	C₄⋊C₄	—	4	1	no	—
1076	C₄⋊C₄	—	4	1	no	—
1077	C₄⋊C₄	—	4	1	no	—
1078	C₄⋊C₄	—	4	1	no	—
1079	C₄⋊C₄	—	4	1	no	—
1080	C₄⋊C₄	—	4	1	no	—
1081	C₄⋊C₄	—	4	1	no	—
1082	C₄⋊C₄	—	4	1	no	—
1083	C₄⋊C₄	—	4	1	no	—
1084	C₄⋊C₄	—	4	1	no	—
1085	C₄⋊C₄	—	4	1	no	—
1086	C₄⋊C₄	—	4	1	no	—
1087	C₄⋊C₄	—	4	1	no	—
1088	C₄⋊C₄	—	4	1	no	—
1089	C₄⋊C₄	—	4	1	no	—
1090	C₄⋊C₄	—	4	1	no	—
1091	C₄⋊C₄	—	4	1	no	—
1092	C₄⋊C₄	—	4	1	no	—
1093	C₄⋊C₄	—	4	1	no	—
1094	C₄⋊C₄	—	4	1	no	—
1095	C₄⋊C₄	—	4	1	no	—
1096	C₄⋊C₄	—	4	1	no	—
1097	C₄⋊C₄	—	4	1	no	—
1098	C₄⋊C₄	—	4	1	no	—
1099	C₄⋊C₄	—	4	1	no	—
1100	C₄⋊C₄	—	4	1	no	—
1101	C₄⋊C₄	—	4	1	no	—
1102	C₄⋊C₄	—	4	1	no	—
1103	C₄⋊C₄	—	4	1	no	—
1104	C₄⋊C₄	—	4	1	no	—
1105	C₄⋊C₄	—	4	1	no	—
1106	C₄⋊C₄	—	4	1	no	—
1107	C₄⋊C₄	—	4	1	no	—
1108	C₄⋊C₄	—	4	1	no	—
1109	C₄⋊C₄	—	4	1	no	—
1110	C₄⋊C₄	—	4	1	no	—
1111	C₄⋊C₄	#127	1	1	yes	characteristic
1112	C₄⋊C₄	#127	1	1	yes	characteristic
1113	C₄⋊C₄	#127	1	1	yes	characteristic
1114	C₄⋊C₄	#127	1	1	yes	characteristic
1115	C₄⋊C₄	#127	1	1	yes	characteristic
1116	C₄⋊C₄	#127	1	1	yes	characteristic
1117	C₂²⋊C₄	—	4	1	no	—
1118	C₂²⋊C₄	—	4	1	no	—
1119	C₂²⋊C₄	—	4	1	no	—
1120	C₂²⋊C₄	—	4	1	no	—
1121	C₂²⋊C₄	—	4	1	no	—
1122	C₂²⋊C₄	—	4	1	no	—
1123	C₂²⋊C₄	—	4	1	no	—
1124	C₂²⋊C₄	—	4	1	no	—
1125	C₂²⋊C₄	—	4	1	no	—
1126	C₂²⋊C₄	—	4	1	no	—
1127	C₂²⋊C₄	—	4	1	no	—
1128	C₂²⋊C₄	—	4	1	no	—
1129	C₂²⋊C₄	—	4	1	no	—
1130	C₂²⋊C₄	—	4	1	no	—
1131	C₂²⋊C₄	—	4	1	no	—
1132	C₂²⋊C₄	—	4	1	no	—
1133	C₂²⋊C₄	—	4	1	no	—
1134	C₂²⋊C₄	—	4	1	no	—
1135	C₂²⋊C₄	#127	1	1	yes	characteristic
1136	C₂²⋊C₄	#127	1	1	yes	characteristic
1137	C₂²⋊C₄	#127	1	1	yes	characteristic
1138	C₂²⋊C₄	#127	1	1	yes	characteristic
1139	C₂²⋊C₄	#127	1	1	yes	characteristic
1140	C₂²⋊C₄	#127	1	1	yes	characteristic
1141	C₄²	—	4	1	no	—
1142	C₄²	—	4	1	no	—
1143	C₄²	—	4	1	no	—
1144	C₄²	—	4	1	no	—
1145	C₄²	—	4	1	no	—
1146	C₄²	—	4	1	no	—
1147	C₄²	—	4	1	no	—
1148	C₄²	—	4	1	no	—
1149	C₄²	—	4	1	no	—
1150	C₄²	—	4	1	no	—
1151	C₄²	—	4	1	no	—
1152	C₄²	—	4	1	no	—
1153	C₄²	—	4	1	no	—
1154	C₄²	—	4	1	no	—
1155	C₄²	—	4	1	no	—
1156	C₄²	—	4	1	no	—
1157	C₄²	—	4	1	no	—
1158	C₄²	—	4	1	no	—
1159	C₄²	C₂²×D₄	1	1	yes	characteristic
1160	C₄²	C₂²×D₄	1	1	yes	characteristic
1161	C₄²	C₂²×D₄	1	1	yes	characteristic
1162	C₄²	C₂²×D₄	1	1	yes	characteristic
1163	C₄²	C₂²×D₄	1	1	yes	characteristic
1164	C₄²	C₂²×D₄	1	1	yes	characteristic
1165	C₄²	C₂²×D₄	1	1	yes	characteristic
1166	C₄²	C₂²×D₄	1	1	yes	characteristic
1167	C₄²	C₂²×D₄	1	1	yes	characteristic
1168	C₄²	C₂⁵	1	1	yes	characteristic
1169	C₂³	C₂×#127	1	1	yes	characteristic
1170	C₂³	C₂×#127	1	1	yes	characteristic
1171	C₂³	C₂×#127	1	1	yes	characteristic
1172	Q₈	—	4	1	no	—
1173	Q₈	—	4	2	no	—
1174	Q₈	—	4	2	no	—
1175	Q₈	—	4	2	no	—
1176	Q₈	—	4	2	no	—
1177	Q₈	—	4	2	no	—
1178	Q₈	—	4	2	no	—
1179	Q₈	—	4	2	no	—
1180	Q₈	—	4	2	no	—
1181	Q₈	—	4	2	no	—
1182	Q₈	—	4	2	no	—
1183	Q₈	—	4	2	no	—
1184	Q₈	—	4	2	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	4	2	no	—
1187	Q₈	—	4	2	no	—
1188	Q₈	—	4	2	no	—
1189	Q₈	—	8	2	no	—
1190	Q₈	—	8	2	no	—
1191	Q₈	—	8	2	no	—
1192	Q₈	—	16	1	no	—
1193	Q₈	—	16	1	no	—
1194	Q₈	—	16	1	no	—
1195	D₄	—	4	1	no	—
1196	D₄	—	4	1	no	—
1197	D₄	—	4	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	4	1	no	—
1208	C₂×C₄	—	4	1	no	—
1209	C₂×C₄	—	4	1	no	—
1210	C₂×C₄	—	4	1	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	1	no	—
1213	C₂×C₄	—	4	1	no	—
1214	C₂×C₄	—	4	1	no	—
1215	C₂×C₄	—	4	1	no	—
1216	C₂×C₄	—	4	1	no	—
1217	C₂×C₄	—	4	1	no	—
1218	C₂×C₄	—	4	1	no	—
1219	C₂×C₄	—	4	1	no	—
1220	C₂×C₄	—	4	1	no	—
1221	C₂×C₄	—	4	1	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	—	8	2	no	—
1225	C₂×C₄	—	8	2	no	—
1226	C₂×C₄	—	16	1	no	—
1227	C₂×C₄	—	16	1	no	—
1228	C₂×C₄	—	16	1	no	—
1229	C₂×C₄	C₂×#127	1	1	yes	characteristic
1230	C₂×C₄	C₂×#127	1	1	yes	characteristic
1231	C₂×C₄	C₂×#127	1	1	yes	characteristic
1232	C₂×C₄	C₂×#127	1	1	yes	characteristic
1233	C₂×C₄	C₂×#127	1	1	yes	characteristic
1234	C₂×C₄	C₂×#127	1	1	yes	characteristic
1235	C₂×C₄	C₂×#127	1	1	yes	characteristic
1236	C₂×C₄	C₂×#127	1	1	yes	characteristic
1237	C₂×C₄	C₂×#127	1	1	yes	characteristic
1238	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1239	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1240	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1241	C₈	—	2	2	no	—
1242	C₈	—	2	2	no	—
1243	C₈	—	2	2	no	—
1244	C₈	—	2	2	no	—
1245	C₈	—	2	2	no	—
1246	C₈	—	2	2	no	—
1247	C₈	—	2	2	no	—
1248	C₈	—	2	2	no	—
1249	C₈	—	2	2	no	—
1250	C₈	—	2	2	no	—
1251	C₈	—	2	2	no	—
1252	C₈	#578	1	4	yes	—
1253	C₂²	—	2	1	no	—
1254	C₂²	—	2	1	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	C₂²×#127	1	1	yes	characteristic
1263	C₄	—	2	1	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	8	1	no	—
1273	C₄	—	8	1	no	—
1274	C₄	—	8	1	no	—
1275	C₄	—	8	1	no	—
1276	C₄	—	8	1	no	—
1277	C₄	—	8	1	no	—
1278	C₄	—	8	1	no	—
1279	C₄	—	8	1	no	—
1280	C₄	—	8	1	no	—
1281	C₄	—	8	1	no	—
1282	C₄	—	8	1	no	—
1283	C₄	—	8	1	no	—
1284	C₄	—	8	1	no	—
1285	C₄	—	8	1	no	—
1286	C₄	—	8	1	no	—
1287	C₄	—	8	1	no	—
1288	C₄	C₂×#578	1	2	yes	—
1289	C₄	#3586	1	2	yes	—
1290	C₄	#3586	1	2	yes	—
1291	C₂	—	4	1	no	—
1292	C₂	—	4	1	no	—
1293	C₂	—	4	1	no	—
1294	C₂	#60645	1	1	yes	characteristic
1295	C₂	#60648	1	1	yes	characteristic
1296	C₂	#60651	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#127
commutator, Frattini, cosocle	C₄²	C₂⁵
prime radical	C₂×#41	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
7. #19751	C₂	semidirect
8. #19751	C₂	semidirect
9. #19736	C₂	semidirect
10. #19736	C₂	semidirect
11. #19736	C₂	semidirect
12. #19736	C₂	semidirect
13. #19732	C₂	semidirect
14. #19732	C₂	semidirect
15. #19720	C₂	semidirect
16. #19720	C₂	semidirect
17. #19720	C₂	semidirect
18. #19720	C₂	semidirect
19. #19711	C₂	semidirect
20. #19706	C₂	semidirect
21. #19690	C₂	semidirect
22. #19690	C₂	semidirect
23. #19681	C₂	semidirect
24. #19680	C₂	semidirect
25. #19668	C₂	semidirect
26. #19663	C₂	semidirect
27. #19648	C₂	semidirect
28. #19648	C₂	semidirect
29. #19634	C₂	semidirect
30. #19634	C₂	semidirect

Maximal subgroups

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

subgroup	index
#62536	2
#62482	2
#62478	2
#61013	2
#60878	2
#19751	2
#19736	2
#19732	2
#19720	2
#19711	2
#19706	2
#19690	2
#19681	2
#19680	2
#19668	2
#19663	2
#19648	2
#19634	2
#17340	2