Subgroups — #6404642

Order 512.

1851 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3400	C₂	1	1	yes	maximal, characteristic
2	#34500	C₂	1	1	yes	maximal, characteristic
3	#34488	C₂	1	1	yes	maximal, characteristic, complemented
4	#23192	C₂	1	1	yes	maximal, characteristic, complemented
5	#23192	C₂	1	1	yes	maximal, characteristic, complemented
6	#23190	C₂	1	1	yes	maximal, characteristic
7	#23014	C₂	1	1	yes	maximal, characteristic, complemented
8	#23012	C₂	1	1	yes	maximal, characteristic, complemented
9	#23010	C₂	1	1	yes	maximal, characteristic
10	#23009	C₂	1	1	yes	maximal, characteristic, complemented
11	#23006	C₂	1	1	yes	maximal, characteristic, complemented
12	#23002	C₂	1	1	yes	maximal, characteristic, complemented
13	#22731	C₂	1	1	yes	maximal, characteristic, complemented
14	#22678	C₂	1	1	yes	maximal, characteristic, complemented
15	#22677	C₂	1	1	yes	maximal, characteristic, complemented
16	#22675	C₂	1	1	yes	maximal, characteristic, complemented
17	#22549	C₂	1	1	yes	maximal, characteristic
18	#22547	C₂	1	1	yes	maximal, characteristic, complemented
19	#22164	C₂	1	1	yes	maximal, characteristic, complemented
20	#22163	C₂	1	1	yes	maximal, characteristic, complemented
21	#22162	C₂	1	1	yes	maximal, characteristic, complemented
22	#22160	C₂	1	1	yes	maximal, characteristic
23	#22156	C₂	1	1	yes	maximal, characteristic, complemented
24	#22152	C₂	1	1	yes	maximal, characteristic, complemented
25	#21703	C₂	1	1	yes	maximal, characteristic, complemented
26	#21702	C₂	1	1	yes	maximal, characteristic, complemented
27	#21695	C₂	1	1	yes	maximal, characteristic
28	#21291	C₂	1	1	yes	maximal, characteristic, complemented
29	#21288	C₂	1	1	yes	maximal, characteristic, complemented
30	#21281	C₂	1	1	yes	maximal, characteristic, complemented
31	#20518	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#559	C₂²	1	1	yes	characteristic
33	C₂×#557	C₂²	1	1	yes	characteristic
34	#3400	C₄	1	16	yes	complemented
35	C₂×#497	C₂²	1	1	yes	characteristic
36	C₂×#497	C₂²	1	1	yes	characteristic
37	C₂×#492	C₂²	1	1	yes	characteristic
38	C₂×#464	C₂²	1	1	yes	characteristic
39	C₂×#464	C₂²	1	1	yes	characteristic
40	C₂×#462	C₂²	1	1	yes	characteristic
41	C₂×#460	C₂²	1	1	yes	characteristic
42	C₂×#461	C₂²	1	1	yes	characteristic
43	C₂×#461	C₂²	1	1	yes	characteristic
44	C₂×#446	C₂²	1	1	yes	characteristic
45	C₂×#446	C₂²	1	1	yes	characteristic
46	C₂×#441	C₂²	1	1	yes	characteristic
47	C₂×#441	C₂²	1	1	yes	characteristic
48	C₂×#441	C₂²	1	1	yes	characteristic
49	C₂×#440	C₂²	1	1	yes	characteristic
50	C₂×#440	C₂²	1	1	yes	characteristic
51	C₂×#440	C₂²	1	1	yes	characteristic
52	C₂×#440	C₂²	1	1	yes	characteristic
53	C₂×#440	C₂²	1	1	yes	characteristic
54	C₂×#440	C₂²	1	1	yes	characteristic
55	C₂×#440	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
58	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
59	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
61	#2382	—	2	1	no	—
62	#2382	—	2	1	no	—
63	#2379	—	2	1	no	—
64	#2376	—	2	1	no	—
65	#2370	—	2	1	no	—
66	#2367	C₂²	1	1	yes	characteristic
67	#2367	C₂²	1	1	yes	characteristic
68	#2366	C₂²	1	1	yes	characteristic
69	#2365	C₂²	1	1	yes	characteristic
70	#2365	C₂²	1	1	yes	characteristic
71	#2365	C₂²	1	1	yes	characteristic
72	#2359	—	2	1	no	—
73	#2355	—	2	1	no	—
74	#2355	C₂²	1	1	yes	characteristic
75	#2355	C₂²	1	1	yes	characteristic
76	#2352	—	2	1	no	—
77	#2351	C₂²	1	1	yes	characteristic
78	#2351	C₂²	1	1	yes	characteristic
79	#2351	C₂²	1	1	yes	characteristic
80	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#2349	C₂²	1	1	yes	characteristic
82	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	#2337	—	2	1	no	—
84	#2336	—	2	1	no	—
85	#2336	—	2	1	no	—
86	#2335	—	2	1	no	—
87	#2330	—	2	1	no	—
88	#2328	C₂²	1	1	yes	characteristic
89	#2327	C₂²	1	1	yes	characteristic
90	#2327	C₂²	1	1	yes	characteristic
91	#2326	C₂²	1	1	yes	characteristic
92	#2322	—	2	1	no	—
93	#2320	—	2	1	no	—
94	#2320	C₂²	1	1	yes	characteristic
95	#2320	C₂²	1	1	yes	characteristic
96	#2320	C₂²	1	1	yes	characteristic
97	#2319	C₂²	1	1	yes	characteristic
98	#2318	—	2	1	no	—
99	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
100	C₄×#124	C₂²	1	1	yes	characteristic
101	#2295	C₂²	1	1	yes	characteristic
102	#2295	C₂²	1	1	yes	characteristic
103	#2293	C₂²	1	1	yes	characteristic
104	#1983	C₂²	1	1	yes	characteristic
105	#1983	C₂²	1	1	yes	characteristic
106	#1982	C₂²	1	1	yes	characteristic
107	#1981	C₂²	1	1	yes	characteristic
108	#1981	C₂²	1	1	yes	characteristic
109	#1981	C₂²	1	1	yes	characteristic
110	#1973	C₂²	1	1	yes	characteristic
111	#1973	C₂²	1	1	yes	characteristic
112	#1973	C₂²	1	1	yes	characteristic
113	#1973	C₂²	1	1	yes	characteristic
114	#1973	C₂²	1	1	yes	characteristic
115	#1971	C₂²	1	1	yes	characteristic
116	#1969	C₂²	1	1	yes	characteristic
117	#1969	C₂²	1	1	yes	characteristic
118	#1969	C₂²	1	1	yes	characteristic
119	#1968	C₂²	1	1	yes	characteristic
120	#1968	C₂²	1	1	yes	characteristic
121	#1968	C₂²	1	1	yes	characteristic
122	#1961	C₂²	1	1	yes	characteristic
123	#1960	C₂²	1	1	yes	characteristic
124	#1960	C₂²	1	1	yes	characteristic
125	#1959	C₂²	1	1	yes	characteristic
126	#1958	C₂²	1	1	yes	characteristic
127	#1956	C₂²	1	1	yes	characteristic
128	#1949	C₂²	1	1	yes	characteristic
129	#1949	C₂²	1	1	yes	characteristic
130	#1949	C₂²	1	1	yes	characteristic
131	#1949	C₂²	1	1	yes	characteristic
132	#1947	C₂²	1	1	yes	characteristic
133	#1947	C₂²	1	1	yes	characteristic
134	#1943	C₂²	1	1	yes	characteristic
135	#1943	C₂²	1	1	yes	characteristic
136	#1942	C₂²	1	1	yes	characteristic
137	#1942	C₂²	1	1	yes	characteristic
138	#1936	C₂²	1	1	yes	characteristic
139	#1936	C₂²	1	1	yes	characteristic
140	#1935	C₂²	1	1	yes	characteristic
141	#1935	C₂²	1	1	yes	characteristic
142	#1935	C₂²	1	1	yes	characteristic
143	#1935	C₂²	1	1	yes	characteristic
144	#1935	C₂²	1	1	yes	characteristic
145	#1935	C₂²	1	1	yes	characteristic
146	#1934	C₂²	1	1	yes	characteristic
147	#1934	C₂²	1	1	yes	characteristic
148	#1933	C₂²	1	1	yes	characteristic
149	#1933	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	#1880	C₂²	1	1	yes	characteristic
154	#1878	C₂²	1	1	yes	characteristic
155	#1878	C₂²	1	1	yes	characteristic
156	#1878	C₂²	1	1	yes	characteristic
157	#1878	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	#1877	C₂²	1	1	yes	characteristic
162	#1865	C₂²	1	1	yes	characteristic
163	#1865	C₂²	1	1	yes	characteristic
164	#1864	C₂²	1	1	yes	characteristic
165	#1864	C₂²	1	1	yes	characteristic
166	#1863	C₂²	1	1	yes	characteristic
167	#1863	C₂²	1	1	yes	characteristic
168	#1863	C₂²	1	1	yes	characteristic
169	#1863	C₂²	1	1	yes	characteristic
170	#1863	C₂²	1	1	yes	characteristic
171	#1863	C₂²	1	1	yes	characteristic
172	#1862	C₂²	1	1	yes	characteristic
173	#1862	C₂²	1	1	yes	characteristic
174	#1847	C₂²	1	1	yes	characteristic
175	#1847	C₂²	1	1	yes	characteristic
176	#1846	C₂²	1	1	yes	characteristic
177	#1805	C₂²	1	1	yes	characteristic
178	#1805	C₂²	1	1	yes	characteristic
179	#1805	C₂²	1	1	yes	characteristic
180	#1804	C₂²	1	1	yes	characteristic
181	#1803	C₂²	1	1	yes	characteristic
182	#1802	C₂²	1	1	yes	characteristic
183	#1776	C₂²	1	1	yes	characteristic
184	#1776	C₂²	1	1	yes	characteristic
185	C₄×#107	C₂²	1	1	yes	characteristic
186	#1771	C₂²	1	1	yes	characteristic
187	#1771	C₂²	1	1	yes	characteristic
188	#1771	C₂²	1	1	yes	characteristic
189	#1771	C₂²	1	1	yes	characteristic
190	#1770	C₂²	1	1	yes	characteristic
191	#1770	C₂²	1	1	yes	characteristic
192	#1768	C₂²	1	1	yes	characteristic
193	#1768	C₂²	1	1	yes	characteristic
194	#1767	C₂²	1	1	yes	characteristic
195	#1763	C₂²	1	1	yes	characteristic
196	#1763	C₂²	1	1	yes	characteristic
197	#1763	C₂²	1	1	yes	characteristic
198	#1762	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	C₄×#102	C₂²	1	1	yes	characteristic
201	#1726	C₂²	1	1	yes	characteristic
202	#1726	C₂²	1	1	yes	characteristic
203	C₄×#97	C₂²	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
212	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
213	#559	—	2	4	no	—
214	#559	C₂×C₄	1	8	yes	—
215	#557	—	2	4	no	—
216	#557	C₂×C₄	1	8	yes	complemented
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×#127	C₂³	1	1	yes	characteristic
221	C₂×#125	—	2	1	no	—
222	C₂×#125	—	2	1	no	—
223	C₂×#125	—	2	1	no	—
224	C₂×#124	—	2	1	no	—
225	C₂×#124	C₂³	1	1	yes	characteristic
226	C₂×#124	C₂³	1	1	yes	characteristic
227	C₂×#123	—	2	1	no	—
228	C₂×#123	—	2	1	no	—
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₄	—	2	1	no	—
244	C₂×C₄×D₄	—	2	1	no	—
245	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
251	C₂×#117	—	2	1	no	—
252	C₂²×C₄⋊C₄	—	2	1	no	—
253	#497	C₂×C₄	1	8	yes	complemented
254	#497	C₂×C₄	1	8	yes	complemented
255	#492	C₂×C₄	1	8	yes	—
256	#464	C₂×C₄	1	8	yes	complemented
257	#464	C₂×C₄	1	8	yes	complemented
258	#462	C₂×C₄	1	8	yes	complemented
259	#461	C₂×C₄	1	8	yes	complemented
260	#461	C₂×C₄	1	8	yes	complemented
261	#460	C₂×C₄	1	8	yes	—
262	#446	—	2	4	no	—
263	#446	C₂×C₄	1	8	yes	complemented
264	#441	—	4	2	no	—
265	#441	—	4	2	no	—
266	#441	—	4	2	no	—
267	#440	—	4	2	no	—
268	#440	—	4	2	no	—
269	#440	—	4	2	no	—
270	#440	—	4	2	no	—
271	#440	—	4	2	no	—
272	#440	C₂×C₄	1	8	yes	complemented
273	#440	C₂×C₄	1	8	yes	complemented
274	C₄×Q₁₆	—	4	2	no	—
275	C₄×Q₁₆	C₂×C₄	1	8	yes	complemented
276	C₄×SD₁₆	—	4	2	no	—
277	C₄×SD₁₆	—	4	2	no	—
278	C₄×SD₁₆	—	4	2	no	—
279	C₂×#107	C₂³	1	1	yes	characteristic
280	C₂×#107	C₂³	1	1	yes	characteristic
281	C₂×#107	C₂³	1	1	yes	characteristic
282	C₂×#107	C₂³	1	1	yes	characteristic
283	C₂×#107	C₂³	1	1	yes	characteristic
284	C₂×#107	C₂³	1	1	yes	characteristic
285	C₂×#107	C₂³	1	1	yes	characteristic
286	C₂×#106	C₂³	1	1	yes	characteristic
287	C₂×#106	C₂³	1	1	yes	characteristic
288	C₂×#106	C₂³	1	1	yes	characteristic
289	C₂×#106	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#103	C₂³	1	1	yes	characteristic
302	C₂×#103	C₂³	1	1	yes	characteristic
303	C₂×#103	C₂³	1	1	yes	characteristic
304	C₂×#103	C₂³	1	1	yes	characteristic
305	C₂×#103	C₂³	1	1	yes	characteristic
306	C₂×#103	C₂³	1	1	yes	characteristic
307	C₂×#103	C₂³	1	1	yes	characteristic
308	C₂×#103	C₂³	1	1	yes	characteristic
309	C₂×#103	C₂³	1	1	yes	characteristic
310	C₂×#103	C₂³	1	1	yes	characteristic
311	C₂×#103	C₂³	1	1	yes	characteristic
312	C₂×#103	C₂³	1	1	yes	characteristic
313	C₂×#103	C₂³	1	1	yes	characteristic
314	C₂×#103	C₂³	1	1	yes	characteristic
315	C₂×#103	C₂³	1	1	yes	characteristic
316	C₂×#102	C₂³	1	1	yes	characteristic
317	C₂×#102	C₂³	1	1	yes	characteristic
318	C₂×#102	C₂³	1	1	yes	characteristic
319	C₂×#102	C₂³	1	1	yes	characteristic
320	C₂×#102	C₂³	1	1	yes	characteristic
321	C₂×#102	C₂³	1	1	yes	characteristic
322	C₂×#102	C₂³	1	1	yes	characteristic
323	C₂×#102	C₂³	1	1	yes	characteristic
324	C₂×#102	C₂³	1	1	yes	characteristic
325	C₂×#102	C₂³	1	1	yes	characteristic
326	C₂×#97	C₂³	1	1	yes	characteristic
327	C₂×#97	C₂³	1	1	yes	characteristic
328	C₂×#97	C₂³	1	1	yes	characteristic
329	C₂×#97	C₂³	1	1	yes	characteristic
330	C₂×#97	C₂³	1	1	yes	characteristic
331	C₂×#97	C₂³	1	1	yes	characteristic
332	C₂×#97	C₂³	1	1	yes	characteristic
333	C₂×#97	C₂³	1	1	yes	characteristic
334	C₂×#97	C₂³	1	1	yes	characteristic
335	C₂×#97	C₂³	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
337	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
342	#391	—	2	1	no	—
343	#391	—	2	1	no	—
344	#391	D₄	1	1	yes	characteristic
345	#391	D₄	1	1	yes	characteristic
346	#391	C₂³	1	1	yes	characteristic
347	#391	C₂³	1	1	yes	characteristic
348	#391	C₂³	1	1	yes	characteristic
349	#391	C₂³	1	1	yes	characteristic
350	#391	C₂³	1	1	yes	characteristic
351	#391	C₂³	1	1	yes	characteristic
352	#391	C₂³	1	1	yes	characteristic
353	#391	C₂³	1	1	yes	characteristic
354	#390	—	2	1	no	—
355	#390	C₂³	1	1	yes	characteristic
356	#390	C₂³	1	1	yes	characteristic
357	#390	C₂³	1	1	yes	characteristic
358	#390	C₂³	1	1	yes	characteristic
359	#389	—	2	1	no	—
360	#389	—	2	1	no	—
361	#389	—	2	1	no	—
362	#389	—	2	1	no	—
363	#389	—	2	1	no	—
364	#389	—	2	1	no	—
365	#389	—	2	1	no	—
366	#389	—	2	1	no	—
367	#389	—	2	1	no	—
368	#389	—	2	1	no	—
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	—	2	1	no	—
372	#389	D₄	1	1	yes	characteristic
373	#389	D₄	1	1	yes	characteristic
374	#389	C₂³	1	1	yes	characteristic
375	#389	C₂³	1	1	yes	characteristic
376	#389	C₂³	1	1	yes	characteristic
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#389	C₂³	1	1	yes	characteristic
381	#389	C₂³	1	1	yes	characteristic
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#387	—	2	1	no	—
413	#387	—	2	1	no	—
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	D₄	1	1	yes	characteristic
421	#387	D₄	1	1	yes	characteristic
422	#387	D₄	1	1	yes	characteristic
423	#387	D₄	1	1	yes	characteristic
424	#386	—	2	1	no	—
425	#386	—	2	1	no	—
426	#386	—	2	1	no	—
427	#386	—	2	1	no	—
428	#386	—	2	1	no	—
429	#386	—	2	1	no	—
430	#385	—	2	1	no	—
431	#385	—	2	1	no	—
432	#385	—	2	1	no	—
433	#385	—	2	1	no	—
434	#385	—	2	1	no	—
435	#385	—	2	1	no	—
436	#385	—	2	1	no	—
437	#385	—	2	1	no	—
438	#384	—	2	1	no	—
439	#384	C₂³	1	1	yes	characteristic
440	#384	C₂³	1	1	yes	characteristic
441	#383	—	2	1	no	—
442	#383	—	2	1	no	—
443	#383	—	2	1	no	—
444	#382	—	2	1	no	—
445	#382	—	2	1	no	—
446	#382	—	2	1	no	—
447	#382	—	2	1	no	—
448	#382	—	2	1	no	—
449	#382	—	2	1	no	—
450	#382	C₂³	1	1	yes	characteristic
451	#382	C₂³	1	1	yes	characteristic
452	#382	C₂³	1	1	yes	characteristic
453	#382	C₂³	1	1	yes	characteristic
454	#381	—	2	1	no	—
455	#380	—	2	1	no	—
456	#380	—	2	1	no	—
457	#380	—	2	1	no	—
458	C₄×C₄⋊C₄	—	2	1	no	—
459	C₄×C₄⋊C₄	—	2	1	no	—
460	C₄×C₄⋊C₄	—	2	1	no	—
461	C₄×C₄⋊C₄	—	2	1	no	—
462	C₄×C₄⋊C₄	—	2	1	no	—
463	C₄×C₄⋊C₄	—	2	1	no	—
464	C₄×C₄⋊C₄	—	2	1	no	—
465	C₄×C₄⋊C₄	—	2	1	no	—
466	C₄×C₄⋊C₄	—	2	1	no	—
467	C₄×C₄⋊C₄	—	2	1	no	—
468	C₄×C₄⋊C₄	—	2	1	no	—
469	C₄×C₄⋊C₄	—	2	1	no	—
470	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
472	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	—	2	1	no	—
480	C₄×C₂²⋊C₄	—	2	1	no	—
481	C₄×C₂²⋊C₄	—	2	1	no	—
482	C₄×C₂²⋊C₄	—	2	1	no	—
483	C₄×C₂²⋊C₄	—	2	1	no	—
484	#376	—	2	1	no	—
485	#376	C₂³	1	1	yes	characteristic
486	#376	C₂³	1	1	yes	characteristic
487	C₂×#95	—	2	1	no	—
488	C₄³	C₂³	1	1	yes	characteristic
489	#340	C₂³	1	1	yes	characteristic
490	#340	C₂³	1	1	yes	characteristic
491	#340	C₂³	1	1	yes	characteristic
492	#340	C₂³	1	1	yes	characteristic
493	#340	C₂³	1	1	yes	characteristic
494	#340	C₂³	1	1	yes	characteristic
495	#340	C₂³	1	1	yes	characteristic
496	#340	C₂³	1	1	yes	characteristic
497	#340	C₂³	1	1	yes	characteristic
498	#340	C₂³	1	1	yes	characteristic
499	#340	C₂³	1	1	yes	characteristic
500	#340	C₂³	1	1	yes	characteristic
501	#340	C₂³	1	1	yes	characteristic
502	#340	C₂³	1	1	yes	characteristic
503	#336	C₂³	1	1	yes	characteristic
504	#336	C₂³	1	1	yes	characteristic
505	#336	C₂³	1	1	yes	characteristic
506	#336	C₂³	1	1	yes	characteristic
507	#336	C₂³	1	1	yes	characteristic
508	#336	C₂³	1	1	yes	characteristic
509	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
510	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
511	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
512	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
513	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	C₂⁴	1	1	yes	characteristic
517	C₂²×D₄	C₂⁴	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂×Q₁₆	—	2	2	no	—
525	C₂×Q₁₆	—	2	2	no	—
526	C₂×Q₁₆	—	4	1	no	—
527	C₂×Q₁₆	—	4	1	no	—
528	C₂×Q₁₆	—	4	1	no	—
529	C₂×Q₁₆	—	4	1	no	—
530	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
531	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
532	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	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×SD₁₆	—	4	1	no	—
543	C₂×SD₁₆	—	4	1	no	—
544	C₂×SD₁₆	—	4	1	no	—
545	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
546	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
547	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
548	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
549	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
550	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
551	C₂²×C₈	C₂⁴	1	1	yes	characteristic
552	C₂²×C₈	C₂⁴	1	1	yes	characteristic
553	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
563	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
564	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
565	#127	—	2	2	no	—
566	#127	C₂²×C₄	1	4	yes	—
567	#125	—	2	8	no	—
568	#125	—	2	8	no	—
569	#125	—	2	8	no	—
570	#124	—	2	8	no	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	C₂²×C₄	1	4	yes	—
574	#124	C₂²×C₄	1	4	yes	—
575	#123	—	2	8	no	—
576	#123	—	2	8	no	—
577	C₄×Q₈	—	2	8	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	4	1	no	—
583	C₄×Q₈	—	4	1	no	—
584	C₄×Q₈	—	4	1	no	—
585	C₄×Q₈	—	4	1	no	—
586	C₄×Q₈	—	4	1	no	—
587	C₄×Q₈	—	4	1	no	—
588	C₄×Q₈	—	4	1	no	—
589	C₄×Q₈	—	4	1	no	—
590	C₄×Q₈	—	4	1	no	—
591	C₄×Q₈	—	4	1	no	—
592	C₄×Q₈	—	4	1	no	—
593	C₄×Q₈	—	4	1	no	—
594	C₄×Q₈	—	4	1	no	—
595	C₄×Q₈	—	4	1	no	—
596	C₄×Q₈	—	4	1	no	—
597	C₄×Q₈	—	4	1	no	—
598	C₄×Q₈	C₂²×C₄	1	4	yes	—
599	C₄×Q₈	C₂²×C₄	1	4	yes	—
600	C₄×Q₈	C₂²×C₄	1	4	yes	—
601	C₄×Q₈	C₂²×C₄	1	4	yes	—
602	C₄×Q₈	C₂²×C₄	1	4	yes	—
603	C₄×Q₈	#41	1	4	yes	—
604	C₄×D₄	—	2	8	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	4	1	no	—
608	C₄×D₄	—	4	1	no	—
609	C₄×D₄	—	4	1	no	—
610	C₄×D₄	—	4	1	no	—
611	C₄×D₄	—	4	1	no	—
612	C₄×D₄	—	4	1	no	—
613	C₄×D₄	—	4	1	no	—
614	C₄×D₄	—	4	1	no	—
615	C₄×D₄	—	8	2	no	—
616	C₄×D₄	C₂²×C₄	1	4	yes	—
617	C₄×D₄	C₂²×C₄	1	4	yes	—
618	#117	—	8	2	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	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	1	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	—	8	2	no	—
650	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	2	1	no	—
696	C₂×C₄²	—	2	1	no	—
697	C₂×C₄²	—	2	1	no	—
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	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
706	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
707	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
708	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
709	C₂×C₄²	C₂⁴	1	1	yes	characteristic
710	C₂×C₄²	C₂⁴	1	1	yes	characteristic
711	C₂×C₄²	C₂⁴	1	1	yes	characteristic
712	C₂×C₄²	C₂⁴	1	1	yes	characteristic
713	C₂×C₄²	C₂⁴	1	1	yes	characteristic
714	C₂×C₄²	C₂⁴	1	1	yes	characteristic
715	C₂×C₄²	C₂⁴	1	1	yes	characteristic
716	#107	—	2	2	no	—
717	#107	—	2	2	no	—
718	#107	—	4	1	no	—
719	#107	—	4	1	no	—
720	#107	—	4	1	no	—
721	#107	—	4	1	no	—
722	#107	C₂²×C₄	1	4	yes	—
723	#106	—	2	2	no	—
724	#106	—	2	2	no	—
725	#106	—	4	1	no	—
726	#106	—	4	1	no	—
727	C₄⋊C₈	—	2	2	no	—
728	C₄⋊C₈	—	2	2	no	—
729	C₄⋊C₈	—	2	2	no	—
730	C₄⋊C₈	C₂²×C₄	1	4	yes	—
731	C₄⋊C₈	C₂²×C₄	1	4	yes	—
732	C₄⋊C₈	C₂²×C₄	1	4	yes	—
733	#103	—	2	2	no	—
734	#103	—	2	2	no	—
735	#103	—	2	2	no	—
736	#103	—	2	2	no	—
737	#103	—	4	1	no	—
738	#103	—	4	1	no	—
739	#103	—	4	1	no	—
740	#103	—	4	1	no	—
741	#103	—	4	1	no	—
742	#103	—	4	1	no	—
743	#103	—	4	1	no	—
744	#103	—	4	1	no	—
745	#103	—	4	1	no	—
746	#103	—	4	1	no	—
747	#103	—	4	1	no	—
748	#103	—	4	1	no	—
749	#103	C₂²×C₄	1	4	yes	—
750	#103	C₂²×C₄	1	4	yes	—
751	#103	C₂²×C₄	1	4	yes	—
752	#103	C₂²×C₄	1	4	yes	—
753	#102	—	2	2	no	—
754	#102	—	2	2	no	—
755	#102	—	4	1	no	—
756	#102	—	4	1	no	—
757	#102	—	4	1	no	—
758	#102	—	4	1	no	—
759	#102	—	4	1	no	—
760	#102	—	4	1	no	—
761	#102	C₂²×C₄	1	4	yes	—
762	#102	C₂²×C₄	1	4	yes	—
763	#97	—	2	2	no	—
764	#97	—	2	2	no	—
765	#97	—	2	2	no	—
766	#97	—	2	2	no	—
767	#97	—	2	2	no	—
768	#97	—	2	2	no	—
769	#97	—	4	1	no	—
770	#97	—	4	1	no	—
771	#97	C₂²×C₄	1	4	yes	—
772	#97	C₂²×C₄	1	4	yes	—
773	C₄×C₈	—	2	2	no	—
774	C₄×C₈	—	2	2	no	—
775	C₄×C₈	—	2	2	no	—
776	C₄×C₈	—	2	2	no	—
777	C₄×C₈	—	4	1	no	—
778	C₄×C₈	C₂²×C₄	1	4	yes	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	—	2	1	no	—
797	#95	—	2	1	no	—
798	#95	—	2	1	no	—
799	#95	—	2	1	no	—
800	#95	—	2	1	no	—
801	#95	—	2	1	no	—
802	#95	—	2	1	no	—
803	#95	—	2	1	no	—
804	#95	—	2	1	no	—
805	#95	—	2	1	no	—
806	#95	—	2	1	no	—
807	#95	—	2	1	no	—
808	#95	—	2	1	no	—
809	#95	—	2	1	no	—
810	#95	—	2	1	no	—
811	#95	—	2	1	no	—
812	#95	—	2	1	no	—
813	#95	—	2	1	no	—
814	#95	—	2	1	no	—
815	#95	—	2	1	no	—
816	#95	—	2	1	no	—
817	#95	C₂×D₄	1	1	yes	characteristic
818	#95	C₂×D₄	1	1	yes	characteristic
819	#95	C₂×D₄	1	1	yes	characteristic
820	#95	C₂×D₄	1	1	yes	characteristic
821	#95	C₂×D₄	1	1	yes	characteristic
822	#95	C₂×D₄	1	1	yes	characteristic
823	#95	C₂×D₄	1	1	yes	characteristic
824	#95	C₂×D₄	1	1	yes	characteristic
825	#95	C₂×D₄	1	1	yes	characteristic
826	#95	C₂×D₄	1	1	yes	characteristic
827	#95	C₂×D₄	1	1	yes	characteristic
828	#95	C₂×D₄	1	1	yes	characteristic
829	#95	C₂×D₄	1	1	yes	characteristic
830	#95	C₂×D₄	1	1	yes	characteristic
831	C₂⁴	—	2	1	no	—
832	C₂⁴	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	4	1	no	—
854	C₂×Q₈	—	4	1	no	—
855	C₂×Q₈	C₄×D₄	1	4	yes	—
856	C₂×Q₈	C₂³×C₄	1	2	yes	—
857	C₂×Q₈	C₂³×C₄	1	2	yes	—
858	C₂×Q₈	C₂³×C₄	1	2	yes	—
859	C₂×Q₈	C₂³×C₄	1	2	yes	—
860	C₂×D₄	—	2	4	no	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	1	no	—
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	8	1	no	—
873	C₂×D₄	—	8	1	no	—
874	C₂×D₄	—	8	1	no	—
875	C₂×D₄	—	8	1	no	—
876	C₂×D₄	C₂³×C₄	1	2	yes	—
877	C₂×D₄	C₂³×C₄	1	2	yes	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
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	4	no	—
885	C₂²×C₄	—	2	4	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	—	4	2	no	—
895	C₂²×C₄	—	8	1	no	—
896	C₂²×C₄	—	8	1	no	—
897	C₂²×C₄	—	8	1	no	—
898	C₂²×C₄	—	8	1	no	—
899	C₂²×C₄	—	8	1	no	—
900	C₂²×C₄	—	8	1	no	—
901	C₂²×C₄	—	8	1	no	—
902	C₂²×C₄	—	8	1	no	—
903	C₂²×C₄	—	8	1	no	—
904	C₂²×C₄	—	8	1	no	—
905	C₂²×C₄	—	8	1	no	—
906	C₂²×C₄	—	8	1	no	—
907	C₂²×C₄	—	8	1	no	—
908	C₂²×C₄	—	8	1	no	—
909	C₂²×C₄	—	8	1	no	—
910	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
911	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
912	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
913	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
914	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
915	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
916	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
917	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
918	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
919	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
920	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
925	Q₁₆	—	2	8	no	—
926	Q₁₆	—	4	4	no	—
927	Q₁₆	—	4	4	no	—
928	SD₁₆	—	2	8	no	—
929	SD₁₆	—	2	8	no	—
930	SD₁₆	—	4	4	no	—
931	SD₁₆	—	4	4	no	—
932	SD₁₆	—	4	4	no	—
933	SD₁₆	—	4	4	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	2	1	no	—
936	C₂×C₈	—	2	1	no	—
937	C₂×C₈	—	2	1	no	—
938	C₂×C₈	—	2	1	no	—
939	C₂×C₈	—	2	1	no	—
940	C₂×C₈	—	2	1	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	C₂³×C₄	1	2	yes	—
952	C₂×C₈	C₂³×C₄	1	2	yes	—
953	C₂×C₈	C₂³×C₄	1	2	yes	—
954	C₂×C₈	C₂³×C₄	1	2	yes	—
955	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
956	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
957	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
958	C₄⋊C₄	—	2	4	no	—
959	C₄⋊C₄	—	2	4	no	—
960	C₄⋊C₄	—	2	4	no	—
961	C₄⋊C₄	—	2	4	no	—
962	C₄⋊C₄	—	2	4	no	—
963	C₄⋊C₄	—	2	4	no	—
964	C₄⋊C₄	—	2	4	no	—
965	C₄⋊C₄	—	2	4	no	—
966	C₄⋊C₄	—	2	4	no	—
967	C₄⋊C₄	—	2	4	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	1	no	—
987	C₄⋊C₄	—	4	1	no	—
988	C₄⋊C₄	—	4	1	no	—
989	C₄⋊C₄	—	4	1	no	—
990	C₄⋊C₄	—	4	1	no	—
991	C₄⋊C₄	—	4	1	no	—
992	C₄⋊C₄	—	4	2	no	—
993	C₄⋊C₄	—	4	2	no	—
994	C₄⋊C₄	—	4	2	no	—
995	C₄⋊C₄	—	8	1	no	—
996	C₄⋊C₄	—	8	1	no	—
997	C₄⋊C₄	—	8	1	no	—
998	C₄⋊C₄	—	8	1	no	—
999	C₄⋊C₄	—	8	1	no	—
1000	C₄⋊C₄	—	8	1	no	—
1001	C₄⋊C₄	—	8	1	no	—
1002	C₄⋊C₄	—	8	1	no	—
1003	C₄⋊C₄	—	8	1	no	—
1004	C₄⋊C₄	—	8	1	no	—
1005	C₄⋊C₄	—	8	1	no	—
1006	C₄⋊C₄	—	8	1	no	—
1007	C₄⋊C₄	—	8	1	no	—
1008	C₄⋊C₄	—	8	1	no	—
1009	C₄⋊C₄	—	8	1	no	—
1010	C₄⋊C₄	—	8	1	no	—
1011	C₄⋊C₄	—	8	1	no	—
1012	C₄⋊C₄	C₄×D₄	1	4	yes	—
1013	C₄⋊C₄	C₄×D₄	1	4	yes	—
1014	C₄⋊C₄	C₄×D₄	1	4	yes	—
1015	C₄⋊C₄	C₂³×C₄	1	2	yes	—
1016	C₄⋊C₄	C₂³×C₄	1	2	yes	—
1017	C₂²⋊C₄	—	2	4	no	—
1018	C₂²⋊C₄	—	2	4	no	—
1019	C₂²⋊C₄	—	2	4	no	—
1020	C₂²⋊C₄	—	2	4	no	—
1021	C₂²⋊C₄	—	2	4	no	—
1022	C₂²⋊C₄	—	2	4	no	—
1023	C₂²⋊C₄	—	4	2	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	—	8	1	no	—
1027	C₂²⋊C₄	—	8	1	no	—
1028	C₂²⋊C₄	—	8	1	no	—
1029	C₂²⋊C₄	—	8	1	no	—
1030	C₂²⋊C₄	—	8	1	no	—
1031	C₂²⋊C₄	—	8	1	no	—
1032	C₂²⋊C₄	—	8	1	no	—
1033	C₂²⋊C₄	—	8	1	no	—
1034	C₂²⋊C₄	—	8	1	no	—
1035	C₄²	—	2	4	no	—
1036	C₄²	—	2	4	no	—
1037	C₄²	—	2	4	no	—
1038	C₄²	—	2	4	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	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	4	1	no	—
1048	C₄²	—	4	1	no	—
1049	C₄²	—	4	1	no	—
1050	C₄²	—	4	1	no	—
1051	C₄²	—	4	2	no	—
1052	C₄²	—	8	1	no	—
1053	C₄²	—	8	1	no	—
1054	C₄²	—	8	1	no	—
1055	C₄²	—	8	1	no	—
1056	C₄²	—	8	1	no	—
1057	C₄²	—	8	1	no	—
1058	C₄²	—	8	1	no	—
1059	C₄²	—	8	1	no	—
1060	C₄²	—	8	1	no	—
1061	C₄²	—	8	1	no	—
1062	C₄²	—	8	1	no	—
1063	C₄²	—	8	1	no	—
1064	C₄²	—	8	1	no	—
1065	C₄²	C₂³×C₄	1	2	yes	—
1066	C₄²	C₂³×C₄	1	2	yes	—
1067	C₄²	C₂³×C₄	1	2	yes	—
1068	C₄²	C₂×#41	1	2	yes	—
1069	C₄²	C₂×#41	1	2	yes	—
1070	C₄²	C₂×#41	1	2	yes	—
1071	C₂³	—	2	2	no	—
1072	C₂³	—	2	2	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	4	1	no	—
1077	C₂³	—	4	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	—	4	1	no	—
1081	C₂³	—	4	1	no	—
1082	C₂³	—	4	1	no	—
1083	C₂³	—	4	1	no	—
1084	C₂³	—	4	1	no	—
1085	C₂³	C₂³×D₄	1	1	yes	characteristic
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	4	1	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	1	no	—
1098	Q₈	—	4	1	no	—
1099	Q₈	—	4	1	no	—
1100	Q₈	—	4	1	no	—
1101	Q₈	—	4	1	no	—
1102	Q₈	—	4	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	2	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	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	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	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	8	4	no	—
1192	C₂×C₄	—	8	4	no	—
1193	C₂×C₄	—	16	2	no	—
1194	C₂×C₄	—	16	2	no	—
1195	C₂×C₄	—	16	2	no	—
1196	C₂×C₄	—	16	2	no	—
1197	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1198	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1199	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1200	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1201	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1202	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1203	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1204	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1205	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1206	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1207	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1208	C₂×C₄	#585	1	1	yes	characteristic
1209	C₈	—	2	2	no	—
1210	C₈	—	2	2	no	—
1211	C₈	—	2	2	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	4	1	no	—
1214	C₈	—	4	1	no	—
1215	C₈	—	4	1	no	—
1216	C₈	#520	1	4	yes	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	—	8	1	no	—
1229	C₂²	—	8	1	no	—
1230	C₂²	—	8	1	no	—
1231	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1232	C₂²	#3497	1	1	yes	characteristic
1233	C₂²	#3498	1	1	yes	characteristic
1234	C₂²	#3585	1	1	yes	characteristic
1235	C₂²	#3586	1	1	yes	characteristic
1236	C₂²	#3586	1	1	yes	characteristic
1237	C₂²	#3586	1	1	yes	characteristic
1238	C₄	—	2	2	no	—
1239	C₄	—	2	2	no	—
1240	C₄	—	2	2	no	—
1241	C₄	—	2	2	no	—
1242	C₄	—	2	2	no	—
1243	C₄	—	2	2	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	2	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	—	8	1	no	—
1266	C₄	C₂×#520	1	1	yes	characteristic
1267	C₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1268	C₄	#3517	1	1	yes	characteristic
1269	C₄	#3522	1	1	yes	characteristic
1270	C₂	—	8	2	no	—
1271	C₂	—	8	2	no	—
1272	C₂	#34313	1	1	yes	characteristic
1273	C₂	#60169	1	1	yes	characteristic
1274	C₂	#60174	1	1	yes	characteristic
1275	C₂	#62388	1	1	yes	characteristic
1276	C₂	#62390	1	1	yes	characteristic
1277	C₂	#62442	1	1	yes	characteristic
1278	C₂	#62445	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#127	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2295 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #34488	C₂	semidirect
4. #23192	C₂	semidirect
5. #23192	C₂	semidirect
7. #23014	C₂	semidirect
8. #23012	C₂	semidirect
10. #23009	C₂	semidirect
11. #23006	C₂	semidirect
12. #23002	C₂	semidirect
13. #22731	C₂	semidirect
14. #22678	C₂	semidirect
15. #22677	C₂	semidirect
16. #22675	C₂	semidirect
18. #22547	C₂	semidirect
19. #22164	C₂	semidirect
20. #22163	C₂	semidirect
21. #22162	C₂	semidirect
23. #22156	C₂	semidirect
24. #22152	C₂	semidirect
25. #21703	C₂	semidirect
26. #21702	C₂	semidirect
28. #21291	C₂	semidirect
29. #21288	C₂	semidirect
30. #21281	C₂	semidirect
31. #20518	C₂	semidirect
34. #3400	C₄	semidirect
216. #557	C₂×C₄	semidirect
253. #497	C₂×C₄	semidirect
254. #497	C₂×C₄	semidirect
256. #464	C₂×C₄	semidirect
257. #464	C₂×C₄	semidirect
258. #462	C₂×C₄	semidirect
259. #461	C₂×C₄	semidirect
260. #461	C₂×C₄	semidirect
263. #446	C₂×C₄	semidirect
272. #440	C₂×C₄	semidirect
273. #440	C₂×C₄	semidirect
275. C₄×Q₁₆	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3400	2
#34500	2
#34488	2
#23192	2
#23190	2
#23014	2
#23012	2
#23010	2
#23009	2
#23006	2
#23002	2
#22731	2
#22678	2
#22677	2
#22675	2
#22549	2
#22547	2
#22164	2
#22163	2
#22162	2
#22160	2
#22156	2
#22152	2
#21703	2
#21702	2
#21695	2
#21291	2
#21288	2
#21281	2
#20518	2