Subgroups — #6569851

Order 512.

2124 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3357	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#3348	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#3323	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#3314	C₂	1	1	yes	maximal, characteristic, complemented
5	#38090	C₂	1	1	yes	maximal, characteristic
6	#37865	C₂	1	1	yes	maximal, characteristic, complemented
7	#30289	C₂	1	1	yes	maximal, characteristic, complemented
8	#30252	C₂	1	1	yes	maximal, characteristic, complemented
9	#30248	C₂	1	1	yes	maximal, characteristic, complemented
10	#28545	C₂	1	1	yes	maximal, characteristic, complemented
11	#28540	C₂	1	1	yes	maximal, characteristic, complemented
12	#28525	C₂	1	1	yes	maximal, characteristic, complemented
13	#28436	C₂	1	1	yes	maximal, characteristic, complemented
14	#28412	C₂	1	1	yes	maximal, characteristic, complemented
15	#28396	C₂	1	1	yes	maximal, characteristic, complemented
16	#28366	C₂	1	1	yes	maximal, characteristic, complemented
17	#28365	C₂	1	1	yes	maximal, characteristic, complemented
18	#28360	C₂	1	1	yes	maximal, characteristic, complemented
19	#28344	C₂	1	1	yes	maximal, characteristic, complemented
20	#28320	C₂	1	1	yes	maximal, characteristic, complemented
21	#28317	C₂	1	1	yes	maximal, characteristic, complemented
22	#27946	C₂	1	1	yes	maximal, characteristic, complemented
23	#27945	C₂	1	1	yes	maximal, characteristic, complemented
24	#27943	C₂	1	1	yes	maximal, characteristic, complemented
25	#27936	C₂	1	1	yes	maximal, characteristic, complemented
26	#27921	C₂	1	1	yes	maximal, characteristic, complemented
27	#27918	C₂	1	1	yes	maximal, characteristic, complemented
28	#23811	C₂	1	1	yes	maximal, characteristic, complemented
29	#23735	C₂	1	1	yes	maximal, characteristic, complemented
30	#23733	C₂	1	1	yes	maximal, characteristic, complemented
31	#20564	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#555	C₂²	1	1	yes	characteristic
33	C₂×#554	C₂²	1	1	yes	characteristic
34	C₂×#552	C₂²	1	1	yes	characteristic
35	C₂×#546	C₂²	1	1	yes	characteristic
36	#3357	—	2	8	no	—
37	#3348	—	2	8	no	—
38	#3323	—	2	8	no	—
39	#3314	—	2	8	no	—
40	C₂×#501	C₂²	1	1	yes	characteristic, complemented
41	C₂×#500	C₂²	1	1	yes	characteristic, complemented
42	C₂×#489	C₂²	1	1	yes	characteristic
43	C₂×#488	C₂²	1	1	yes	characteristic
44	C₂×#484	C₂²	1	1	yes	characteristic
45	C₂×#481	C₂²	1	1	yes	characteristic
46	C₂×#481	C₂²	1	1	yes	characteristic, complemented
47	C₂×#485	C₂²	1	1	yes	characteristic
48	C₂×#485	C₂²	1	1	yes	characteristic
49	C₂×#485	C₂²	1	1	yes	characteristic
50	C₂×#485	C₂²	1	1	yes	characteristic, complemented
51	C₂×#485	C₂²	1	1	yes	characteristic, complemented
52	C₂×#482	C₂²	1	1	yes	characteristic
53	C₂×#480	C₂²	1	1	yes	characteristic
54	C₂×#480	C₂²	1	1	yes	characteristic
55	C₂×#480	C₂²	1	1	yes	characteristic, complemented
56	C₂×#477	C₂²	1	1	yes	characteristic, complemented
57	C₂×#475	C₂²	1	1	yes	characteristic, complemented
58	C₂×#478	C₂²	1	1	yes	characteristic
59	C₂×#478	C₂²	1	1	yes	characteristic, complemented
60	C₂×#476	C₂²	1	1	yes	characteristic, complemented
61	C₂×#474	C₂²	1	1	yes	characteristic
62	C₂×#470	C₂²	1	1	yes	characteristic
63	C₂×#468	C₂²	1	1	yes	characteristic
64	C₂×#468	C₂²	1	1	yes	characteristic
65	C₂×#468	C₂²	1	1	yes	characteristic
66	C₂×#468	C₂²	1	1	yes	characteristic, complemented
67	C₂×#468	C₂²	1	1	yes	characteristic, complemented
68	C₂×#467	C₂²	1	1	yes	characteristic
69	C₂×#465	C₂²	1	1	yes	characteristic
70	C₂×#464	C₂²	1	1	yes	characteristic
71	C₂×#464	C₂²	1	1	yes	characteristic
72	C₂×#452	C₂²	1	1	yes	characteristic
73	C₂×#452	C₂²	1	1	yes	characteristic
74	C₂×#450	C₂²	1	1	yes	characteristic
75	C₂×#450	C₂²	1	1	yes	characteristic
76	C₂×#440	C₂²	1	1	yes	characteristic
77	C₂×#440	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
79	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
80	C₂×#436	C₂²	1	1	yes	characteristic
81	C₂×#435	C₂²	1	1	yes	characteristic
82	C₂×#428	C₂²	1	1	yes	characteristic
83	C₂×#428	C₂²	1	1	yes	characteristic, complemented
84	C₂×#428	C₂²	1	1	yes	characteristic, complemented
85	C₂×#427	C₂²	1	1	yes	characteristic
86	C₂×#417	C₂²	1	1	yes	characteristic
87	C₂×#417	C₂²	1	1	yes	characteristic
88	C₂×#418	C₂²	1	1	yes	characteristic
89	C₂²×#102	C₂²	1	1	yes	characteristic
90	#2857	C₂²	1	1	yes	characteristic, complemented
91	#2856	C₂²	1	1	yes	characteristic
92	#2719	—	2	2	no	—
93	#2698	—	2	2	no	—
94	#2676	—	2	2	no	—
95	#2668	—	2	2	no	—
96	#2660	C₂²	1	1	yes	characteristic, complemented
97	#2640	C₂²	1	1	yes	characteristic
98	#2621	C₂²	1	1	yes	characteristic
99	#2620	C₂²	1	1	yes	characteristic
100	#2568	C₂²	1	1	yes	characteristic, complemented
101	#2565	C₂²	1	1	yes	characteristic, complemented
102	#2544	C₂²	1	1	yes	characteristic
103	#2542	C₂²	1	1	yes	characteristic
104	#2503	C₂²	1	1	yes	characteristic
105	#2503	C₂²	1	1	yes	characteristic, complemented
106	#2502	C₂²	1	1	yes	characteristic, complemented
107	#2500	C₂²	1	1	yes	characteristic
108	#2499	C₂²	1	1	yes	characteristic
109	#2499	C₂²	1	1	yes	characteristic
110	#2472	—	2	2	no	—
111	#2471	—	2	2	no	—
112	#2438	—	2	2	no	—
113	#2433	C₂²	1	1	yes	characteristic
114	#2431	C₂²	1	1	yes	characteristic
115	#2419	—	2	2	no	—
116	#2328	C₂²	1	1	yes	characteristic
117	#2327	C₂²	1	1	yes	characteristic, complemented
118	#2317	C₂²	1	1	yes	characteristic
119	#2309	C₂²	1	1	yes	characteristic
120	#2297	C₂²	1	1	yes	characteristic
121	#2290	C₂²	1	1	yes	characteristic
122	C₂×#382	C₂²	1	1	yes	characteristic, complemented
123	#2097	C₂²	1	1	yes	characteristic, complemented
124	#2097	C₂²	1	1	yes	characteristic, complemented
125	#2097	C₂²	1	1	yes	characteristic, complemented
126	#2097	C₂²	1	1	yes	characteristic, complemented
127	#2097	C₂²	1	1	yes	characteristic, complemented
128	#2097	C₂²	1	1	yes	characteristic, complemented
129	#2097	C₂²	1	1	yes	characteristic, complemented
130	#2096	C₂²	1	1	yes	characteristic, complemented
131	#2095	C₂²	1	1	yes	characteristic, complemented
132	#2095	C₂²	1	1	yes	characteristic, complemented
133	#2095	C₂²	1	1	yes	characteristic, complemented
134	#2095	C₂²	1	1	yes	characteristic, complemented
135	#2095	C₂²	1	1	yes	characteristic, complemented
136	#2094	C₂²	1	1	yes	characteristic
137	#2094	C₂²	1	1	yes	characteristic
138	#2093	C₂²	1	1	yes	characteristic
139	#2093	C₂²	1	1	yes	characteristic
140	#2093	C₂²	1	1	yes	characteristic
141	#2093	C₂²	1	1	yes	characteristic, complemented
142	#2092	C₂²	1	1	yes	characteristic
143	#2092	C₂²	1	1	yes	characteristic
144	#2092	C₂²	1	1	yes	characteristic
145	#2092	C₂²	1	1	yes	characteristic
146	#2092	C₂²	1	1	yes	characteristic
147	#2092	C₂²	1	1	yes	characteristic
148	#2092	C₂²	1	1	yes	characteristic
149	#2092	C₂²	1	1	yes	characteristic
150	#2092	C₂²	1	1	yes	characteristic
151	#2092	C₂²	1	1	yes	characteristic, complemented
152	#2092	C₂²	1	1	yes	characteristic, complemented
153	#2016	C₂²	1	1	yes	characteristic, complemented
154	#2015	C₂²	1	1	yes	characteristic, complemented
155	#2015	C₂²	1	1	yes	characteristic, complemented
156	#2014	C₂²	1	1	yes	characteristic
157	#2014	C₂²	1	1	yes	characteristic
158	#2014	C₂²	1	1	yes	characteristic
159	#2014	C₂²	1	1	yes	characteristic
160	#2013	C₂²	1	1	yes	characteristic
161	#2013	C₂²	1	1	yes	characteristic
162	#2013	C₂²	1	1	yes	characteristic, complemented
163	#1973	C₂²	1	1	yes	characteristic
164	#1973	C₂²	1	1	yes	characteristic
165	#1973	C₂²	1	1	yes	characteristic
166	#1973	C₂²	1	1	yes	characteristic
167	#1973	C₂²	1	1	yes	characteristic
168	#1971	C₂²	1	1	yes	characteristic, complemented
169	#1971	C₂²	1	1	yes	characteristic, complemented
170	#1971	C₂²	1	1	yes	characteristic, complemented
171	#1969	C₂²	1	1	yes	characteristic, complemented
172	#1968	C₂²	1	1	yes	characteristic
173	#1968	C₂²	1	1	yes	characteristic
174	#1968	C₂²	1	1	yes	characteristic
175	#1961	C₂²	1	1	yes	characteristic
176	#1961	C₂²	1	1	yes	characteristic
177	#1961	C₂²	1	1	yes	characteristic
178	#1959	C₂²	1	1	yes	characteristic, complemented
179	#1958	C₂²	1	1	yes	characteristic, complemented
180	#1957	C₂²	1	1	yes	characteristic
181	#1847	C₂²	1	1	yes	characteristic, complemented
182	#1847	C₂²	1	1	yes	characteristic, complemented
183	#1847	C₂²	1	1	yes	characteristic, complemented
184	#1847	C₂²	1	1	yes	characteristic, complemented
185	#1846	C₂²	1	1	yes	characteristic, complemented
186	#1845	C₂²	1	1	yes	characteristic, complemented
187	#1771	C₂²	1	1	yes	characteristic, complemented
188	#1770	C₂²	1	1	yes	characteristic, complemented
189	#1768	C₂²	1	1	yes	characteristic, complemented
190	#1753	C₂²	1	1	yes	characteristic
191	#1753	C₂²	1	1	yes	characteristic, complemented
192	#1753	C₂²	1	1	yes	characteristic, complemented
193	#1752	C₂²	1	1	yes	characteristic
194	#1750	C₂²	1	1	yes	characteristic
195	#1749	C₂²	1	1	yes	characteristic, complemented
196	#1746	C₂²	1	1	yes	characteristic, complemented
197	#1729	C₂²	1	1	yes	characteristic
198	#1728	C₂²	1	1	yes	characteristic, complemented
199	C₂²×#41	C₂³	1	1	yes	characteristic
200	C₂³×D₄	C₂³	1	1	yes	characteristic
201	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
202	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
203	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
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	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×M₁₆	C₂³	1	1	yes	characteristic
210	C₂²×M₁₆	C₂³	1	1	yes	characteristic
211	C₂²×M₁₆	C₂³	1	1	yes	characteristic
212	C₂³×C₈	C₂³	1	1	yes	characteristic
213	#555	—	2	4	no	—
214	#555	—	2	4	no	—
215	#554	—	2	4	no	—
216	#554	—	2	4	no	—
217	#552	—	2	4	no	—
218	#552	—	2	4	no	—
219	#546	—	2	4	no	—
220	#546	—	2	4	no	—
221	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂×#127	C₂³	1	1	yes	characteristic
225	C₂×#127	C₂³	1	1	yes	characteristic
226	C₂×#126	—	2	1	no	—
227	C₂×#125	—	2	1	no	—
228	C₂×#125	—	2	1	no	—
229	C₂×#125	C₂³	1	1	yes	characteristic
230	C₂×#124	—	2	1	no	—
231	C₂×#124	—	2	1	no	—
232	C₂×#124	C₂³	1	1	yes	characteristic
233	C₂×#124	C₂³	1	1	yes	characteristic
234	C₂×#123	—	2	1	no	—
235	C₂×#123	—	2	1	no	—
236	C₂×C₂²⋊Q₈	—	2	2	no	—
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
244	C₂×#121	—	2	1	no	—
245	C₂×#121	—	2	2	no	—
246	C₂×#121	—	2	1	no	—
247	C₂×#121	C₂³	1	1	yes	characteristic
248	C₂×#121	C₂³	1	1	yes	characteristic
249	C₂×#121	C₂³	1	1	yes	characteristic
250	C₂×#120	—	2	1	no	—
251	C₂×#120	—	2	2	no	—
252	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₄	—	2	1	no	—
255	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
258	C₂×#117	—	2	1	no	—
259	C₂×#117	—	2	1	no	—
260	C₂×#117	C₂³	1	1	yes	characteristic
261	C₂×#117	C₂³	1	1	yes	characteristic
262	C₂×#117	C₂³	1	1	yes	characteristic
263	C₂×#117	C₂³	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	—	2	1	no	—
268	C₂²×C₄²	C₂³	1	1	yes	characteristic
269	#501	—	2	4	no	—
270	#500	—	2	4	no	—
271	#489	—	2	4	no	—
272	#488	—	2	4	no	—
273	#485	—	2	4	no	—
274	#485	—	2	4	no	—
275	#485	—	2	4	no	—
276	#485	—	2	4	no	—
277	#485	—	2	4	no	—
278	#484	—	2	4	no	—
279	#482	—	2	4	no	—
280	#481	—	2	4	no	—
281	#481	—	2	4	no	—
282	#480	—	2	4	no	—
283	#480	—	2	4	no	—
284	#480	—	2	4	no	—
285	#478	—	2	4	no	—
286	#478	—	2	4	no	—
287	#477	—	2	4	no	—
288	#476	—	2	4	no	—
289	#475	—	2	4	no	—
290	#474	—	2	4	no	—
291	#470	—	2	4	no	—
292	#468	—	2	4	no	—
293	#468	—	2	4	no	—
294	#468	—	2	4	no	—
295	#468	—	2	4	no	—
296	#468	—	2	4	no	—
297	#467	—	2	4	no	—
298	#465	—	2	4	no	—
299	#464	—	2	4	no	—
300	#464	—	2	4	no	—
301	#452	—	2	4	no	—
302	#452	—	2	4	no	—
303	#450	—	2	4	no	—
304	#450	—	2	4	no	—
305	#440	—	2	4	no	—
306	#440	—	2	4	no	—
307	C₄×SD₁₆	—	2	4	no	—
308	C₄×SD₁₆	—	2	4	no	—
309	#436	D₄	1	8	yes	complemented
310	#435	D₄	1	8	yes	complemented
311	#428	—	2	4	no	—
312	#428	—	2	4	no	—
313	#428	—	2	4	no	—
314	#427	—	2	4	no	—
315	C₂×#107	C₂³	1	1	yes	characteristic
316	C₂×#107	C₂³	1	1	yes	characteristic
317	C₂×#107	C₂³	1	1	yes	characteristic
318	C₂×#107	C₂³	1	1	yes	characteristic
319	C₂×#107	C₂³	1	1	yes	characteristic
320	C₂×#107	C₂³	1	1	yes	characteristic
321	C₂×#107	C₂³	1	1	yes	characteristic
322	C₂×#107	C₂³	1	1	yes	characteristic
323	C₂×#107	C₂³	1	1	yes	characteristic
324	C₂×#107	C₂³	1	1	yes	characteristic
325	C₂×#107	C₂³	1	1	yes	characteristic
326	C₂×#107	C₂³	1	1	yes	characteristic
327	C₂×#107	C₂³	1	1	yes	characteristic
328	C₂×#107	C₂³	1	1	yes	characteristic
329	C₂×#106	C₂³	1	1	yes	characteristic
330	C₂×#106	C₂³	1	1	yes	characteristic
331	C₂×#106	C₂³	1	1	yes	characteristic
332	C₂×#106	C₂³	1	1	yes	characteristic
333	C₂×#106	C₂³	1	1	yes	characteristic
334	C₂×#106	C₂³	1	1	yes	characteristic
335	C₂×#106	C₂³	1	1	yes	characteristic
336	C₂×#106	C₂³	1	1	yes	characteristic
337	C₂×#106	C₂³	1	1	yes	characteristic
338	C₂×#106	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
341	#418	—	2	4	no	—
342	#417	—	2	4	no	—
343	#417	—	2	4	no	—
344	C₂×#103	C₂³	1	1	yes	characteristic
345	C₂×#103	C₂³	1	1	yes	characteristic
346	C₂×#103	C₂³	1	1	yes	characteristic
347	C₂×#103	C₂³	1	1	yes	characteristic
348	C₂×#103	C₂³	1	1	yes	characteristic
349	C₂×#103	C₂³	1	1	yes	characteristic
350	C₂×#103	C₂³	1	1	yes	characteristic
351	C₂×#103	C₂³	1	1	yes	characteristic
352	C₂×#103	C₂³	1	1	yes	characteristic
353	C₂×#103	C₂³	1	1	yes	characteristic
354	C₂×#103	C₂³	1	1	yes	characteristic
355	C₂×#103	C₂³	1	1	yes	characteristic
356	C₂×#103	C₂³	1	1	yes	characteristic
357	C₂×#103	C₂³	1	1	yes	characteristic
358	C₂×#102	—	2	4	no	—
359	C₂×#102	C₂³	1	1	yes	characteristic
360	C₂×#102	C₂³	1	1	yes	characteristic
361	C₂×#102	C₂³	1	1	yes	characteristic
362	C₂×#102	C₂³	1	1	yes	characteristic
363	C₂×#102	C₂³	1	1	yes	characteristic
364	C₂×#102	C₂³	1	1	yes	characteristic
365	C₂×#102	C₂³	1	1	yes	characteristic
366	C₂×#102	C₂³	1	1	yes	characteristic
367	C₂×#102	C₂³	1	1	yes	characteristic
368	C₂×#102	C₂³	1	1	yes	characteristic
369	C₂×#102	C₂³	1	1	yes	characteristic
370	C₂×#102	C₂³	1	1	yes	characteristic
371	C₂×#102	C₂³	1	1	yes	characteristic
372	C₂×#102	C₂³	1	1	yes	characteristic
373	C₂×#102	C₂³	1	1	yes	characteristic
374	C₂×#102	C₂³	1	1	yes	characteristic
375	C₂×#102	C₂³	1	1	yes	characteristic
376	C₂×#102	C₂³	1	1	yes	characteristic
377	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
378	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
380	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
381	C₂×#97	C₂³	1	1	yes	characteristic
382	C₂×#97	C₂³	1	1	yes	characteristic
383	C₂×#97	C₂³	1	1	yes	characteristic
384	C₂×#97	C₂³	1	1	yes	characteristic
385	C₂×#97	C₂³	1	1	yes	characteristic
386	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
387	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
388	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
389	#400	—	2	2	no	—
390	#400	—	2	2	no	—
391	#400	—	2	2	no	—
392	#399	—	2	2	no	—
393	#398	—	2	2	no	—
394	#398	—	2	2	no	—
395	#398	—	2	2	no	—
396	#398	—	2	2	no	—
397	#397	—	2	2	no	—
398	#397	—	2	2	no	—
399	#397	—	2	2	no	—
400	#397	—	2	2	no	—
401	#396	—	2	2	no	—
402	#395	—	2	2	no	—
403	#394	—	2	2	no	—
404	#394	—	2	2	no	—
405	#394	—	2	2	no	—
406	#393	—	2	2	no	—
407	#392	—	2	2	no	—
408	#392	—	2	2	no	—
409	#391	—	2	2	no	—
410	#391	C₂³	1	1	yes	characteristic
411	#391	C₂³	1	1	yes	characteristic
412	#391	C₂³	1	1	yes	characteristic
413	#391	C₂³	1	1	yes	characteristic
414	#391	C₂³	1	1	yes	characteristic
415	#391	C₂³	1	1	yes	characteristic
416	#391	C₂³	1	1	yes	characteristic
417	#391	C₂³	1	1	yes	characteristic
418	#391	C₂³	1	1	yes	characteristic
419	#390	—	2	2	no	—
420	#390	—	2	2	no	—
421	#390	C₂³	1	1	yes	characteristic
422	#390	C₂³	1	1	yes	characteristic
423	#390	C₂³	1	1	yes	characteristic
424	#390	C₂³	1	1	yes	characteristic
425	#390	C₂³	1	1	yes	characteristic
426	#390	C₂³	1	1	yes	characteristic
427	#390	C₂³	1	1	yes	characteristic
428	#389	—	2	2	no	—
429	#389	—	2	2	no	—
430	#388	—	2	2	no	—
431	#388	D₄	1	2	yes	—
432	#387	—	2	2	no	—
433	#387	—	2	2	no	—
434	#387	—	2	2	no	—
435	#387	—	2	2	no	—
436	#387	—	2	2	no	—
437	#387	D₄	1	2	yes	—
438	#386	—	2	2	no	—
439	#386	—	2	2	no	—
440	#386	—	2	2	no	—
441	#386	—	2	2	no	—
442	#386	—	2	2	no	—
443	#386	D₄	1	2	yes	—
444	#385	—	2	2	no	—
445	#385	—	2	2	no	—
446	#385	D₄	1	2	yes	—
447	#384	C₂³	1	1	yes	characteristic
448	#384	C₂³	1	1	yes	characteristic
449	#384	C₂³	1	1	yes	characteristic
450	#384	C₂³	1	1	yes	characteristic
451	#384	C₂³	1	1	yes	characteristic
452	#382	—	2	2	no	—
453	#382	C₂³	1	1	yes	characteristic
454	#382	C₂³	1	1	yes	characteristic
455	#382	C₂³	1	1	yes	characteristic
456	#382	C₂³	1	1	yes	characteristic
457	#382	C₂³	1	1	yes	characteristic
458	#382	C₂³	1	1	yes	characteristic
459	#382	C₂³	1	1	yes	characteristic
460	#381	—	2	2	no	—
461	#381	—	2	2	no	—
462	#380	—	2	2	no	—
463	#379	—	2	2	no	—
464	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	—	2	2	no	—
466	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
467	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
468	#376	C₂³	1	1	yes	characteristic
469	C₂×#95	—	2	2	no	—
470	#336	C₂³	1	1	yes	characteristic
471	#336	C₂³	1	1	yes	characteristic
472	#336	C₂³	1	1	yes	characteristic
473	#336	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	C₂⁵	—	2	1	no	—
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	2	2	no	—
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	4	1	no	—
485	C₂×#41	—	4	1	no	—
486	C₂×#41	—	4	1	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
490	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	4	1	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	—	4	1	no	—
505	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
506	C₂²×D₄	C₂⁴	1	1	yes	characteristic
507	C₂²×D₄	C₂⁴	1	1	yes	characteristic
508	C₂²×D₄	C₂⁴	1	1	yes	characteristic
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	C₂×D₄	1	2	yes	—
516	C₂³×C₄	C₂⁴	1	1	yes	characteristic
517	C₂³×C₄	C₂⁴	1	1	yes	characteristic
518	C₂×Q₁₆	—	2	2	no	—
519	C₂×Q₁₆	—	2	2	no	—
520	C₂×Q₁₆	—	4	1	no	—
521	C₂×Q₁₆	—	4	1	no	—
522	C₂×Q₁₆	—	4	1	no	—
523	C₂×Q₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	2	2	no	—
527	C₂×SD₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×SD₁₆	—	2	2	no	—
531	C₂×SD₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	4	1	no	—
533	C₂×SD₁₆	—	4	1	no	—
534	C₂×SD₁₆	—	4	1	no	—
535	C₂×SD₁₆	—	4	1	no	—
536	C₂×SD₁₆	—	4	1	no	—
537	C₂×SD₁₆	—	4	1	no	—
538	C₂×SD₁₆	—	4	1	no	—
539	C₂×SD₁₆	—	4	1	no	—
540	C₂×SD₁₆	—	4	1	no	—
541	C₂×SD₁₆	—	4	1	no	—
542	C₂×M₁₆	—	4	1	no	—
543	C₂×M₁₆	—	4	1	no	—
544	C₂×M₁₆	—	4	1	no	—
545	C₂×M₁₆	—	4	1	no	—
546	C₂×M₁₆	—	4	1	no	—
547	C₂×M₁₆	—	4	1	no	—
548	C₂×M₁₆	C₂×D₄	1	4	yes	—
549	C₂×M₁₆	C₂×D₄	1	4	yes	—
550	C₂×M₁₆	C₂×D₄	1	4	yes	—
551	C₂²×C₈	—	4	1	no	—
552	C₂²×C₈	—	4	1	no	—
553	C₂²×C₈	C₂×D₄	1	4	yes	—
554	C₂²×C₈	C₂⁴	1	1	yes	characteristic
555	C₂²×C₈	C₂⁴	1	1	yes	characteristic
556	C₂²×C₈	C₂⁴	1	1	yes	characteristic
557	C₂²×C₈	C₂⁴	1	1	yes	characteristic
558	C₂²×C₈	C₂⁴	1	1	yes	characteristic
559	C₂²×C₈	C₂⁴	1	1	yes	characteristic
560	C₂²×C₈	C₂⁴	1	1	yes	characteristic
561	C₂²×C₈	C₂⁴	1	1	yes	characteristic
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	—	2	2	no	—
564	C₄⋊Q₈	—	2	2	no	—
565	C₄⋊Q₈	—	2	2	no	—
566	C₄⋊Q₈	—	4	1	no	—
567	C₄⋊Q₈	—	4	1	no	—
568	#127	—	2	2	no	—
569	#127	—	4	1	no	—
570	#127	—	4	1	no	—
571	#127	—	4	1	no	—
572	#126	—	4	4	no	—
573	#125	—	2	2	no	—
574	#125	—	2	2	no	—
575	#125	—	4	4	no	—
576	#125	—	4	4	no	—
577	#124	—	2	2	no	—
578	#124	—	2	2	no	—
579	#124	—	4	1	no	—
580	#124	—	4	1	no	—
581	#124	—	4	4	no	—
582	#124	—	4	4	no	—
583	#123	—	4	4	no	—
584	#123	—	4	4	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	4	4	no	—
596	C₂²⋊Q₈	—	4	4	no	—
597	C₂²⋊Q₈	—	8	4	no	—
598	#121	—	2	2	no	—
599	#121	—	2	2	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	4	4	no	—
605	#121	—	4	4	no	—
606	#121	—	8	4	no	—
607	#120	—	4	4	no	—
608	#120	—	8	4	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	4	4	no	—
618	C₄×D₄	C₂×D₄	1	4	yes	—
619	C₄×D₄	C₂×D₄	1	4	yes	—
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	4	1	no	—
627	#117	—	4	1	no	—
628	#117	—	4	4	no	—
629	#117	—	4	4	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	2	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	—	2	2	no	—
654	C₂×C₄⋊C₄	—	2	2	no	—
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
657	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
658	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	2	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	2	no	—
686	C₂×C₂²⋊C₄	—	2	2	no	—
687	C₂×C₂²⋊C₄	—	2	2	no	—
688	C₂×C₂²⋊C₄	—	2	2	no	—
689	C₂×C₂²⋊C₄	—	2	2	no	—
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₂²⋊C₄	—	2	2	no	—
692	C₂×C₂²⋊C₄	—	4	4	no	—
693	C₂×C₂²⋊C₄	C₂×D₄	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂×D₄	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂×D₄	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
698	C₂×C₄²	—	2	1	no	—
699	C₂×C₄²	—	2	1	no	—
700	C₂×C₄²	—	2	1	no	—
701	C₂×C₄²	—	2	1	no	—
702	C₂×C₄²	—	2	1	no	—
703	C₂×C₄²	—	4	1	no	—
704	C₂×C₄²	—	4	1	no	—
705	C₂×C₄²	C₂×D₄	1	2	yes	—
706	C₂×C₄²	C₂⁴	1	1	yes	characteristic
707	C₂×C₄²	C₂⁴	1	1	yes	characteristic
708	C₂×C₄²	C₂⁴	1	1	yes	characteristic
709	C₂×C₄²	C₂⁴	1	1	yes	characteristic
710	C₂×C₄²	C₂⁴	1	1	yes	characteristic
711	#107	—	2	2	no	—
712	#107	—	2	2	no	—
713	#107	—	2	2	no	—
714	#107	—	2	2	no	—
715	#107	—	2	2	no	—
716	#107	—	2	2	no	—
717	#107	—	2	2	no	—
718	#107	—	2	2	no	—
719	#107	—	2	2	no	—
720	#107	—	2	2	no	—
721	#107	—	2	2	no	—
722	#107	—	2	2	no	—
723	#107	—	2	2	no	—
724	#107	—	2	2	no	—
725	#106	—	2	2	no	—
726	#106	—	2	2	no	—
727	#106	—	2	2	no	—
728	#106	—	2	2	no	—
729	#106	—	2	2	no	—
730	#106	—	2	2	no	—
731	#106	—	2	2	no	—
732	#106	—	2	2	no	—
733	#106	—	2	2	no	—
734	#106	—	2	2	no	—
735	C₄⋊C₈	C₂×D₄	1	4	yes	—
736	C₄⋊C₈	C₂×D₄	1	4	yes	—
737	#103	—	2	2	no	—
738	#103	—	2	2	no	—
739	#103	—	2	2	no	—
740	#103	—	2	2	no	—
741	#103	—	2	2	no	—
742	#103	—	2	2	no	—
743	#103	—	2	2	no	—
744	#103	—	2	2	no	—
745	#103	—	2	2	no	—
746	#103	—	2	2	no	—
747	#103	—	2	2	no	—
748	#103	—	2	2	no	—
749	#103	—	2	2	no	—
750	#103	—	2	2	no	—
751	#102	—	2	2	no	—
752	#102	—	2	2	no	—
753	#102	—	2	2	no	—
754	#102	—	2	2	no	—
755	#102	—	2	2	no	—
756	#102	—	2	2	no	—
757	#102	—	2	2	no	—
758	#102	—	2	2	no	—
759	#102	—	2	2	no	—
760	#102	—	2	2	no	—
761	#102	—	2	2	no	—
762	#102	—	2	2	no	—
763	#102	—	2	2	no	—
764	#102	—	2	2	no	—
765	#102	—	2	2	no	—
766	#102	—	2	2	no	—
767	#102	—	2	2	no	—
768	#102	—	2	2	no	—
769	C₂²⋊C₈	C₂×D₄	1	4	yes	—
770	C₂²⋊C₈	C₂×D₄	1	4	yes	—
771	C₂²⋊C₈	C₂×D₄	1	4	yes	—
772	C₂²⋊C₈	C₂×D₄	1	4	yes	—
773	#97	—	4	1	no	—
774	#97	—	4	1	no	—
775	#97	—	4	1	no	—
776	#97	—	4	1	no	—
777	#97	C₂×D₄	1	4	yes	—
778	C₄×C₈	—	4	1	no	—
779	C₄×C₈	—	4	1	no	—
780	C₄×C₈	C₂×D₄	1	4	yes	—
781	#95	—	2	2	no	—
782	#95	—	2	2	no	—
783	#95	—	2	2	no	—
784	#95	—	2	2	no	—
785	#95	—	2	2	no	—
786	#95	—	2	2	no	—
787	#95	—	2	2	no	—
788	#95	—	2	2	no	—
789	#95	—	2	2	no	—
790	#95	—	2	2	no	—
791	#95	—	2	2	no	—
792	#95	—	2	2	no	—
793	#95	—	2	2	no	—
794	#95	—	2	2	no	—
795	#95	—	2	2	no	—
796	#95	—	2	2	no	—
797	#95	C₂×D₄	1	2	yes	—
798	#95	C₂×D₄	1	2	yes	—
799	#95	C₂×D₄	1	2	yes	—
800	#95	C₂×D₄	1	2	yes	—
801	#95	C₂×D₄	1	2	yes	—
802	C₂⁴	—	2	1	no	—
803	C₂⁴	—	2	1	no	—
804	C₂⁴	—	2	1	no	—
805	C₂⁴	—	4	2	no	—
806	C₂⁴	—	4	2	no	—
807	C₂⁴	—	8	1	no	—
808	C₂⁴	—	8	2	no	—
809	C₂⁴	—	8	2	no	—
810	C₂⁴	C₂²×D₄	1	1	yes	characteristic
811	C₂⁴	C₂²×D₄	1	1	yes	characteristic
812	#41	—	4	4	no	—
813	#41	—	4	4	no	—
814	#41	—	8	2	no	—
815	#41	—	8	2	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	1	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	4	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	8	2	no	—
837	C₂×Q₈	—	8	2	no	—
838	C₂×D₄	—	2	1	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	—	4	4	no	—
856	C₂×D₄	—	4	4	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	4	no	—
860	C₂×D₄	—	4	4	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	8	2	no	—
868	C₂×D₄	—	8	2	no	—
869	C₂×D₄	—	8	1	no	—
870	C₂×D₄	—	8	2	no	—
871	C₂×D₄	—	8	2	no	—
872	C₂×D₄	—	8	2	no	—
873	C₂×D₄	—	8	2	no	—
874	C₂×D₄	—	8	1	no	—
875	C₂×D₄	—	8	2	no	—
876	C₂×D₄	—	8	2	no	—
877	C₂×D₄	—	8	2	no	—
878	C₂×D₄	#127	1	4	yes	—
879	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	2	no	—
903	C₂²×C₄	—	4	2	no	—
904	C₂²×C₄	—	4	2	no	—
905	C₂²×C₄	—	4	4	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	8	2	no	—
913	C₂²×C₄	—	8	1	no	—
914	C₂²×C₄	—	8	2	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	—	8	2	no	—
917	C₂²×C₄	C₂²×D₄	1	2	yes	—
918	C₂²×C₄	C₂²×D₄	1	2	yes	—
919	C₂²×C₄	C₂²×D₄	1	2	yes	—
920	C₂²×C₄	C₂²×D₄	1	2	yes	—
921	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
922	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
923	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
924	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
925	C₂²×C₄	C₂²×D₄	1	2	yes	—
926	C₂²×C₄	C₂²×D₄	1	2	yes	—
927	C₂²×C₄	C₂²×D₄	1	2	yes	—
928	C₂²×C₄	C₂²×D₄	1	2	yes	—
929	C₂²×C₄	C₂⁵	1	1	yes	characteristic
930	Q₁₆	—	8	2	no	—
931	Q₁₆	—	8	2	no	—
932	SD₁₆	—	4	4	no	—
933	SD₁₆	—	4	4	no	—
934	SD₁₆	—	4	4	no	—
935	SD₁₆	—	4	4	no	—
936	SD₁₆	—	8	2	no	—
937	SD₁₆	—	8	2	no	—
938	M₁₆	—	4	4	no	—
939	M₁₆	—	4	4	no	—
940	M₁₆	—	4	4	no	—
941	C₂×C₈	—	2	1	no	—
942	C₂×C₈	—	2	1	no	—
943	C₂×C₈	—	2	1	no	—
944	C₂×C₈	—	2	1	no	—
945	C₂×C₈	—	2	1	no	—
946	C₂×C₈	—	2	1	no	—
947	C₂×C₈	—	2	1	no	—
948	C₂×C₈	—	2	1	no	—
949	C₂×C₈	—	2	1	no	—
950	C₂×C₈	—	2	1	no	—
951	C₂×C₈	—	2	1	no	—
952	C₂×C₈	—	2	1	no	—
953	C₂×C₈	—	2	1	no	—
954	C₂×C₈	—	2	1	no	—
955	C₂×C₈	—	2	1	no	—
956	C₂×C₈	—	2	1	no	—
957	C₂×C₈	—	4	4	no	—
958	C₂×C₈	C₂²×D₄	1	2	yes	—
959	C₂×C₈	C₂²×D₄	1	2	yes	—
960	C₂×C₈	C₂²×D₄	1	2	yes	—
961	C₂×C₈	C₂²×D₄	1	2	yes	—
962	C₂×C₈	C₂²×D₄	1	2	yes	—
963	C₂×C₈	C₂²×D₄	1	2	yes	—
964	C₂×C₈	C₂²×D₄	1	2	yes	—
965	C₂×C₈	C₂²×D₄	1	2	yes	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₄⋊C₄	—	4	4	no	—
989	C₄⋊C₄	—	4	4	no	—
990	C₄⋊C₄	—	4	2	no	—
991	C₄⋊C₄	—	4	2	no	—
992	C₄⋊C₄	—	4	2	no	—
993	C₄⋊C₄	—	4	2	no	—
994	C₄⋊C₄	—	4	2	no	—
995	C₄⋊C₄	—	4	2	no	—
996	C₄⋊C₄	—	4	2	no	—
997	C₄⋊C₄	—	4	2	no	—
998	C₄⋊C₄	—	4	2	no	—
999	C₄⋊C₄	—	4	2	no	—
1000	C₄⋊C₄	—	4	2	no	—
1001	C₄⋊C₄	—	4	2	no	—
1002	C₄⋊C₄	—	4	2	no	—
1003	C₄⋊C₄	—	4	2	no	—
1004	C₄⋊C₄	—	8	2	no	—
1005	C₄⋊C₄	—	8	2	no	—
1006	C₄⋊C₄	—	8	2	no	—
1007	C₄⋊C₄	—	8	2	no	—
1008	C₄⋊C₄	#127	1	4	yes	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	4	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	—	4	2	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	4	2	no	—
1022	C₂²⋊C₄	—	4	2	no	—
1023	C₂²⋊C₄	—	4	2	no	—
1024	C₂²⋊C₄	—	4	2	no	—
1025	C₂²⋊C₄	—	4	2	no	—
1026	C₂²⋊C₄	—	4	2	no	—
1027	C₂²⋊C₄	—	4	2	no	—
1028	C₂²⋊C₄	—	8	2	no	—
1029	C₂²⋊C₄	—	8	2	no	—
1030	C₂²⋊C₄	—	8	2	no	—
1031	C₂²⋊C₄	—	8	2	no	—
1032	C₂²⋊C₄	—	8	2	no	—
1033	C₂²⋊C₄	—	8	2	no	—
1034	C₂²⋊C₄	—	8	2	no	—
1035	C₂²⋊C₄	#127	1	4	yes	—
1036	C₂²⋊C₄	#127	1	4	yes	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	4	2	no	—
1046	C₄²	—	4	2	no	—
1047	C₄²	—	4	2	no	—
1048	C₄²	—	4	2	no	—
1049	C₄²	—	4	2	no	—
1050	C₄²	—	4	2	no	—
1051	C₄²	C₂²×D₄	1	2	yes	—
1052	C₄²	C₂²×D₄	1	2	yes	—
1053	C₂³	—	2	2	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	4	2	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	4	2	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	8	4	no	—
1077	C₂³	—	8	4	no	—
1078	C₂³	—	16	2	no	—
1079	C₂³	—	16	4	no	—
1080	C₂³	—	16	4	no	—
1081	C₂³	C₂×#127	1	2	yes	—
1082	C₂³	C₂×#127	1	2	yes	—
1083	C₂³	C₂³×D₄	1	1	yes	characteristic
1084	Q₈	—	4	1	no	—
1085	Q₈	—	4	1	no	—
1086	Q₈	—	4	1	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	1	no	—
1095	Q₈	—	4	1	no	—
1096	Q₈	—	16	2	no	—
1097	Q₈	—	16	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	4	4	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	4	1	no	—
1103	D₄	—	4	1	no	—
1104	D₄	—	4	1	no	—
1105	D₄	—	4	1	no	—
1106	D₄	—	4	1	no	—
1107	D₄	—	4	1	no	—
1108	D₄	—	4	1	no	—
1109	D₄	—	4	1	no	—
1110	D₄	—	4	1	no	—
1111	D₄	—	8	4	no	—
1112	D₄	—	8	4	no	—
1113	D₄	—	16	4	no	—
1114	D₄	—	16	4	no	—
1115	D₄	—	16	2	no	—
1116	D₄	—	16	2	no	—
1117	D₄	—	16	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	2	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	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	—	4	1	no	—
1173	C₂×C₄	—	8	4	no	—
1174	C₂×C₄	—	8	4	no	—
1175	C₂×C₄	—	8	4	no	—
1176	C₂×C₄	—	8	4	no	—
1177	C₂×C₄	—	16	2	no	—
1178	C₂×C₄	—	16	2	no	—
1179	C₂×C₄	—	16	2	no	—
1180	C₂×C₄	C₂×#127	1	2	yes	—
1181	C₂×C₄	C₂×#127	1	2	yes	—
1182	C₂×C₄	C₂×#127	1	2	yes	—
1183	C₂×C₄	C₂×#127	1	2	yes	—
1184	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1185	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1186	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1187	C₂×C₄	#585	1	1	yes	characteristic
1188	C₂×C₄	#585	1	1	yes	characteristic
1189	C₂×C₄	#585	1	1	yes	characteristic
1190	C₈	—	2	2	no	—
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	2	2	no	—
1194	C₈	—	2	2	no	—
1195	C₈	—	2	2	no	—
1196	C₈	—	2	2	no	—
1197	C₈	—	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	—	2	2	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	2	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	4	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	8	2	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	8	2	no	—
1214	C₂²	—	8	2	no	—
1215	C₂²	—	8	2	no	—
1216	C₂²	—	8	2	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	8	1	no	—
1222	C₂²	—	8	1	no	—
1223	C₂²	—	16	8	no	—
1224	C₂²	C₂²×#127	1	1	yes	characteristic
1225	C₂²	#3485	1	1	yes	characteristic
1226	C₂²	#3489	1	1	yes	characteristic
1227	C₂²	#3585	1	2	yes	—
1228	C₂²	#3586	1	2	yes	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	4	2	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	—	8	1	no	—
1249	C₄	—	8	1	no	—
1250	C₄	#3485	1	1	yes	characteristic
1251	C₄	#3485	1	1	yes	characteristic
1252	C₄	#3489	1	1	yes	characteristic
1253	C₄	#3489	1	1	yes	characteristic
1254	C₂	—	4	2	no	—
1255	C₂	—	4	2	no	—
1256	C₂	—	8	2	no	—
1257	C₂	—	16	1	no	—
1258	C₂	—	16	1	no	—
1259	C₂	#36060	1	1	yes	characteristic
1260	C₂	#60645	1	1	yes	characteristic
1261	C₂	#60650	1	1	yes	characteristic
1262	C₂	#61780	1	2	yes	—
1263	C₂	#62236	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#38090	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2290 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#3357	C₂	semidirect
2. C₂×#3348	C₂	semidirect
3. C₂×#3323	C₂	semidirect
4. C₂×#3314	C₂	semidirect
6. #37865	C₂	semidirect
7. #30289	C₂	semidirect
8. #30252	C₂	semidirect
9. #30248	C₂	semidirect
10. #28545	C₂	semidirect
11. #28540	C₂	semidirect
12. #28525	C₂	semidirect
13. #28436	C₂	semidirect
14. #28412	C₂	semidirect
15. #28396	C₂	semidirect
16. #28366	C₂	semidirect
17. #28365	C₂	semidirect
18. #28360	C₂	semidirect
19. #28344	C₂	semidirect
20. #28320	C₂	semidirect
21. #28317	C₂	semidirect
22. #27946	C₂	semidirect
23. #27945	C₂	semidirect
24. #27943	C₂	semidirect
25. #27936	C₂	semidirect
26. #27921	C₂	semidirect
27. #27918	C₂	semidirect
28. #23811	C₂	semidirect
29. #23735	C₂	semidirect
30. #23733	C₂	semidirect
31. #20564	C₂	semidirect
40. C₂×#501	C₂²	semidirect
41. C₂×#500	C₂²	semidirect
46. C₂×#481	C₂²	semidirect
50. C₂×#485	C₂²	semidirect
51. C₂×#485	C₂²	semidirect
55. C₂×#480	C₂²	semidirect
56. C₂×#477	C₂²	semidirect
57. C₂×#475	C₂²	semidirect
59. C₂×#478	C₂²	semidirect
60. C₂×#476	C₂²	semidirect
66. C₂×#468	C₂²	semidirect
67. C₂×#468	C₂²	semidirect
77. C₂×#440	C₂²	semidirect
79. C₂×C₄×SD₁₆	C₂²	semidirect
83. C₂×#428	C₂²	semidirect
84. C₂×#428	C₂²	semidirect
90. #2857	C₂²	semidirect
96. #2660	C₂²	semidirect
100. #2568	C₂²	semidirect
101. #2565	C₂²	semidirect
105. #2503	C₂²	semidirect
106. #2502	C₂²	semidirect
117. #2327	C₂²	semidirect
122. C₂×#382	C₂²	semidirect
123. #2097	C₂²	semidirect
124. #2097	C₂²	semidirect
125. #2097	C₂²	semidirect
126. #2097	C₂²	semidirect
127. #2097	C₂²	semidirect
128. #2097	C₂²	semidirect
129. #2097	C₂²	semidirect
130. #2096	C₂²	semidirect
131. #2095	C₂²	semidirect
132. #2095	C₂²	semidirect
133. #2095	C₂²	semidirect
134. #2095	C₂²	semidirect
135. #2095	C₂²	semidirect
141. #2093	C₂²	semidirect
151. #2092	C₂²	semidirect
152. #2092	C₂²	semidirect
153. #2016	C₂²	semidirect
154. #2015	C₂²	semidirect
155. #2015	C₂²	semidirect
162. #2013	C₂²	semidirect
168. #1971	C₂²	semidirect
169. #1971	C₂²	semidirect
170. #1971	C₂²	semidirect
171. #1969	C₂²	semidirect
178. #1959	C₂²	semidirect
179. #1958	C₂²	semidirect
181. #1847	C₂²	semidirect
182. #1847	C₂²	semidirect
183. #1847	C₂²	semidirect
184. #1847	C₂²	semidirect
185. #1846	C₂²	semidirect
186. #1845	C₂²	semidirect
187. #1771	C₂²	semidirect
188. #1770	C₂²	semidirect
189. #1768	C₂²	semidirect
191. #1753	C₂²	semidirect
192. #1753	C₂²	semidirect
195. #1749	C₂²	semidirect
196. #1746	C₂²	semidirect
198. #1728	C₂²	semidirect
309. #436	D₄	semidirect
310. #435	D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3357	2
C₂×#3348	2
C₂×#3323	2
C₂×#3314	2
#38090	2
#37865	2
#30289	2
#30252	2
#30248	2
#28545	2
#28540	2
#28525	2
#28436	2
#28412	2
#28396	2
#28366	2
#28365	2
#28360	2
#28344	2
#28320	2
#28317	2
#27946	2
#27945	2
#27943	2
#27936	2
#27921	2
#27918	2
#23811	2
#23735	2
#23733	2
#20564	2