Subgroups — #6388255

Order 512.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3120	C₂	1	1	yes	maximal, characteristic
2	#34420	C₂	1	1	yes	maximal, characteristic, complemented
3	#34252	C₂	1	1	yes	maximal, characteristic
4	#23112	C₂	1	1	yes	maximal, characteristic, complemented
5	#23110	C₂	1	1	yes	maximal, characteristic, complemented
6	#23102	C₂	1	1	yes	maximal, characteristic, complemented
7	#23100	C₂	1	1	yes	maximal, characteristic, complemented
8	#23074	C₂	1	1	yes	maximal, characteristic, complemented
9	#23072	C₂	1	1	yes	maximal, characteristic, complemented
10	#23071	C₂	1	1	yes	maximal, characteristic, complemented
11	#23070	C₂	1	1	yes	maximal, characteristic, complemented
12	#22820	C₂	1	1	yes	maximal, characteristic, complemented
13	#22818	C₂	1	1	yes	maximal, characteristic, complemented
14	#22815	C₂	1	1	yes	maximal, characteristic, complemented
15	#22812	C₂	1	1	yes	maximal, characteristic, complemented
16	#22779	C₂	1	1	yes	maximal, characteristic, complemented
17	#22775	C₂	1	1	yes	maximal, characteristic, complemented
18	#22763	C₂	1	1	yes	maximal, characteristic, complemented
19	#22759	C₂	1	1	yes	maximal, characteristic, complemented
20	#22059	C₂	1	1	yes	maximal, characteristic
21	#22057	C₂	1	1	yes	maximal, characteristic
22	#22048	C₂	1	1	yes	maximal, characteristic
23	#22048	C₂	1	1	yes	maximal, characteristic
24	#21992	C₂	1	1	yes	maximal, characteristic, complemented
25	#21873	C₂	1	1	yes	maximal, characteristic, complemented
26	#21587	C₂	1	1	yes	maximal, characteristic, complemented
27	#21585	C₂	1	1	yes	maximal, characteristic, complemented
28	#21581	C₂	1	1	yes	maximal, characteristic, complemented
29	#21579	C₂	1	1	yes	maximal, characteristic, complemented
30	#20746	C₂	1	1	yes	maximal, characteristic
31	#20542	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#541	C₂²	1	1	yes	characteristic
33	C₂×#520	C₂²	1	1	yes	characteristic
34	#3120	C₄	1	16	yes	complemented
35	C₂×#484	C₂²	1	1	yes	characteristic
36	C₂×#483	C₂²	1	1	yes	characteristic
37	C₂×#479	C₂²	1	1	yes	characteristic
38	C₂×#478	C₂²	1	1	yes	characteristic
39	C₂×#462	C₂²	1	1	yes	characteristic
40	C₂×#461	C₂²	1	1	yes	characteristic
41	C₂×#452	C₂²	1	1	yes	characteristic
42	C₂×#452	C₂²	1	1	yes	characteristic
43	C₂×#441	C₂²	1	1	yes	characteristic
44	C₂×#440	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
46	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
47	C₂×#433	C₂²	1	1	yes	characteristic
48	C₂×#433	C₂²	1	1	yes	characteristic
49	#2383	—	2	1	no	—
50	#2383	—	2	1	no	—
51	#2373	—	2	1	no	—
52	#2373	—	2	1	no	—
53	#2370	C₂²	1	1	yes	characteristic
54	#2370	C₂²	1	1	yes	characteristic
55	#2365	C₂²	1	1	yes	characteristic
56	#2365	C₂²	1	1	yes	characteristic
57	#2357	C₂²	1	1	yes	characteristic
58	#2357	C₂²	1	1	yes	characteristic
59	#2356	C₂²	1	1	yes	characteristic
60	#2356	C₂²	1	1	yes	characteristic
61	#2356	C₂²	1	1	yes	characteristic
62	#2356	C₂²	1	1	yes	characteristic
63	#2355	C₂²	1	1	yes	characteristic
64	#2355	C₂²	1	1	yes	characteristic
65	#2354	C₂²	1	1	yes	characteristic
66	#2354	C₂²	1	1	yes	characteristic
67	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	#2347	—	2	1	no	—
70	#2346	—	2	1	no	—
71	#2345	—	2	1	no	—
72	#2344	—	2	1	no	—
73	#2336	—	2	1	no	—
74	#2336	—	2	1	no	—
75	#2330	—	2	1	no	—
76	#2330	—	2	1	no	—
77	#2323	C₂²	1	1	yes	characteristic
78	#2323	C₂²	1	1	yes	characteristic
79	#2318	—	2	1	no	—
80	#2318	—	2	1	no	—
81	#2317	C₂²	1	1	yes	characteristic
82	#2314	C₂²	1	1	yes	characteristic
83	#2311	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
86	#2297	C₂²	1	1	yes	characteristic
87	#2296	C₂²	1	1	yes	characteristic
88	#2290	—	2	1	no	—
89	#2290	—	2	1	no	—
90	#2274	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	#1992	C₂²	1	1	yes	characteristic
93	#1991	C₂²	1	1	yes	characteristic
94	#1973	C₂²	1	1	yes	characteristic
95	#1973	C₂²	1	1	yes	characteristic
96	#1973	C₂²	1	1	yes	characteristic
97	#1971	C₂²	1	1	yes	characteristic
98	#1971	C₂²	1	1	yes	characteristic
99	#1971	C₂²	1	1	yes	characteristic
100	#1969	C₂²	1	1	yes	characteristic
101	#1968	C₂²	1	1	yes	characteristic
102	#1960	C₂²	1	1	yes	characteristic
103	#1956	C₂²	1	1	yes	characteristic
104	#1949	C₂²	1	1	yes	characteristic
105	#1949	C₂²	1	1	yes	characteristic
106	#1948	C₂²	1	1	yes	characteristic
107	#1947	C₂²	1	1	yes	characteristic
108	#1936	C₂²	1	1	yes	characteristic
109	#1936	C₂²	1	1	yes	characteristic
110	#1936	C₂²	1	1	yes	characteristic
111	#1935	C₂²	1	1	yes	characteristic
112	#1935	C₂²	1	1	yes	characteristic
113	#1935	C₂²	1	1	yes	characteristic
114	#1934	C₂²	1	1	yes	characteristic
115	#1933	C₂²	1	1	yes	characteristic
116	#1928	C₂²	1	1	yes	characteristic
117	#1928	C₂²	1	1	yes	characteristic
118	#1928	C₂²	1	1	yes	characteristic
119	#1928	C₂²	1	1	yes	characteristic
120	#1928	C₂²	1	1	yes	characteristic
121	#1928	C₂²	1	1	yes	characteristic
122	#1928	C₂²	1	1	yes	characteristic
123	#1927	C₂²	1	1	yes	characteristic
124	#1927	C₂²	1	1	yes	characteristic
125	#1927	C₂²	1	1	yes	characteristic
126	#1927	C₂²	1	1	yes	characteristic
127	#1927	C₂²	1	1	yes	characteristic
128	#1926	C₂²	1	1	yes	characteristic
129	#1926	C₂²	1	1	yes	characteristic
130	#1926	C₂²	1	1	yes	characteristic
131	#1925	C₂²	1	1	yes	characteristic
132	#1921	C₂²	1	1	yes	characteristic
133	#1920	C₂²	1	1	yes	characteristic
134	#1919	C₂²	1	1	yes	characteristic
135	#1919	C₂²	1	1	yes	characteristic
136	#1919	C₂²	1	1	yes	characteristic
137	#1918	C₂²	1	1	yes	characteristic
138	#1918	C₂²	1	1	yes	characteristic
139	#1918	C₂²	1	1	yes	characteristic
140	#1880	C₂²	1	1	yes	characteristic
141	#1880	C₂²	1	1	yes	characteristic
142	#1880	C₂²	1	1	yes	characteristic
143	#1880	C₂²	1	1	yes	characteristic
144	#1878	C₂²	1	1	yes	characteristic
145	#1878	C₂²	1	1	yes	characteristic
146	#1878	C₂²	1	1	yes	characteristic
147	#1878	C₂²	1	1	yes	characteristic
148	#1873	C₂²	1	1	yes	characteristic
149	#1873	C₂²	1	1	yes	characteristic
150	#1872	C₂²	1	1	yes	characteristic
151	#1872	C₂²	1	1	yes	characteristic
152	#1854	C₂²	1	1	yes	characteristic
153	#1854	C₂²	1	1	yes	characteristic
154	#1853	C₂²	1	1	yes	characteristic
155	#1852	C₂²	1	1	yes	characteristic
156	#1847	C₂²	1	1	yes	characteristic
157	#1846	C₂²	1	1	yes	characteristic
158	#1836	C₂²	1	1	yes	characteristic
159	#1834	C₂²	1	1	yes	characteristic
160	#1824	C₂²	1	1	yes	characteristic
161	#1823	C₂²	1	1	yes	characteristic
162	#1805	C₂²	1	1	yes	characteristic
163	#1805	C₂²	1	1	yes	characteristic
164	#1805	C₂²	1	1	yes	characteristic
165	#1804	C₂²	1	1	yes	characteristic
166	#1803	C₂²	1	1	yes	characteristic
167	#1803	C₂²	1	1	yes	characteristic
168	#1803	C₂²	1	1	yes	characteristic
169	#1802	C₂²	1	1	yes	characteristic
170	#1788	C₂²	1	1	yes	characteristic
171	#1788	C₂²	1	1	yes	characteristic
172	#1776	C₂²	1	1	yes	characteristic
173	#1776	C₂²	1	1	yes	characteristic
174	#1776	C₂²	1	1	yes	characteristic
175	#1776	C₂²	1	1	yes	characteristic
176	#1776	C₂²	1	1	yes	characteristic
177	#1776	C₂²	1	1	yes	characteristic
178	C₄×#107	C₂²	1	1	yes	characteristic
179	C₄×#106	C₂²	1	1	yes	characteristic
180	#1771	C₂²	1	1	yes	characteristic
181	#1771	C₂²	1	1	yes	characteristic
182	#1771	C₂²	1	1	yes	characteristic
183	#1771	C₂²	1	1	yes	characteristic
184	#1770	C₂²	1	1	yes	characteristic
185	#1770	C₂²	1	1	yes	characteristic
186	#1770	C₂²	1	1	yes	characteristic
187	#1770	C₂²	1	1	yes	characteristic
188	#1763	C₂²	1	1	yes	characteristic
189	#1763	C₂²	1	1	yes	characteristic
190	#1763	C₂²	1	1	yes	characteristic
191	#1763	C₂²	1	1	yes	characteristic
192	#1763	C₂²	1	1	yes	characteristic
193	#1763	C₂²	1	1	yes	characteristic
194	#1763	C₂²	1	1	yes	characteristic
195	#1762	C₂²	1	1	yes	characteristic
196	C₄×#103	C₂²	1	1	yes	characteristic
197	C₄×#103	C₂²	1	1	yes	characteristic
198	C₄×#103	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	#1750	C₂²	1	1	yes	characteristic
201	#1750	C₂²	1	1	yes	characteristic
202	#1749	C₂²	1	1	yes	characteristic
203	#1749	C₂²	1	1	yes	characteristic
204	C₂²×#41	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	#541	—	2	4	no	—
210	#541	C₂×C₄	1	8	yes	—
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×#126	—	2	1	no	—
213	C₂×#126	—	2	1	no	—
214	C₂×#125	—	2	1	no	—
215	C₂×#125	—	2	1	no	—
216	C₂×#125	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	#520	—	2	4	no	—
220	#520	C₂×C₄	1	8	yes	—
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×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
233	C₂×#117	—	2	1	no	—
234	C₂×#117	—	2	1	no	—
235	C₂×#117	—	2	1	no	—
236	C₂×#117	C₂³	1	1	yes	characteristic
237	C₂×#117	C₂³	1	1	yes	characteristic
238	C₂×#117	C₂³	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	—	2	1	no	—
240	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂²×C₄²	—	2	1	no	—
243	C₂²×C₄²	C₂³	1	1	yes	characteristic
244	#484	C₂×C₄	1	8	yes	—
245	#483	C₂×C₄	1	8	yes	—
246	#479	C₂×C₄	1	8	yes	complemented
247	#478	C₂×C₄	1	8	yes	complemented
248	#462	C₂×C₄	1	8	yes	complemented
249	#461	C₂×C₄	1	8	yes	complemented
250	#452	C₂×C₄	1	8	yes	—
251	#452	C₂×C₄	1	8	yes	—
252	#441	C₂×C₄	1	8	yes	complemented
253	#440	C₂×C₄	1	8	yes	complemented
254	C₄×Q₁₆	C₂×C₄	1	8	yes	complemented
255	C₄×SD₁₆	C₂×C₄	1	8	yes	complemented
256	#433	—	2	4	no	—
257	#433	C₂×C₄	1	8	yes	—
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#107	C₂³	1	1	yes	characteristic
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#106	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
302	C₂×#97	C₂³	1	1	yes	characteristic
303	C₂×#97	C₂³	1	1	yes	characteristic
304	C₂×#97	C₂³	1	1	yes	characteristic
305	C₂×#97	C₂³	1	1	yes	characteristic
306	C₂×#97	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×#97	C₂³	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
314	#391	C₂³	1	1	yes	characteristic
315	#391	C₂³	1	1	yes	characteristic
316	#391	C₂³	1	1	yes	characteristic
317	#391	C₂³	1	1	yes	characteristic
318	#391	C₂³	1	1	yes	characteristic
319	#391	C₂³	1	1	yes	characteristic
320	#391	C₂³	1	1	yes	characteristic
321	#391	C₂³	1	1	yes	characteristic
322	#390	C₂³	1	1	yes	characteristic
323	#390	C₂³	1	1	yes	characteristic
324	#390	C₂³	1	1	yes	characteristic
325	#390	C₂³	1	1	yes	characteristic
326	#389	—	2	1	no	—
327	#389	—	2	1	no	—
328	#389	—	2	1	no	—
329	#389	—	2	1	no	—
330	#389	—	2	1	no	—
331	#389	—	2	1	no	—
332	#389	—	2	1	no	—
333	#389	—	2	1	no	—
334	#389	—	2	1	no	—
335	#389	—	2	1	no	—
336	#389	—	2	1	no	—
337	#389	—	2	1	no	—
338	#389	D₄	1	1	yes	characteristic
339	#389	D₄	1	1	yes	characteristic
340	#389	D₄	1	1	yes	characteristic
341	#389	D₄	1	1	yes	characteristic
342	#389	C₂³	1	1	yes	characteristic
343	#389	C₂³	1	1	yes	characteristic
344	#389	C₂³	1	1	yes	characteristic
345	#389	C₂³	1	1	yes	characteristic
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#388	—	2	1	no	—
349	#388	—	2	1	no	—
350	#388	—	2	1	no	—
351	#388	—	2	1	no	—
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#387	—	2	1	no	—
369	#387	—	2	1	no	—
370	#387	—	2	1	no	—
371	#387	—	2	1	no	—
372	#387	—	2	1	no	—
373	#387	—	2	1	no	—
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#386	—	2	1	no	—
389	#386	—	2	1	no	—
390	#385	—	2	1	no	—
391	#385	—	2	1	no	—
392	#385	—	2	1	no	—
393	#385	—	2	1	no	—
394	#385	D₄	1	1	yes	characteristic
395	#385	D₄	1	1	yes	characteristic
396	#385	D₄	1	1	yes	characteristic
397	#385	D₄	1	1	yes	characteristic
398	#384	—	2	1	no	—
399	#384	—	2	1	no	—
400	#384	C₂³	1	1	yes	characteristic
401	#384	C₂³	1	1	yes	characteristic
402	#384	C₂³	1	1	yes	characteristic
403	#383	—	2	1	no	—
404	#383	—	2	1	no	—
405	#383	—	2	1	no	—
406	#383	—	2	1	no	—
407	#382	—	2	1	no	—
408	#382	—	2	1	no	—
409	#382	C₂³	1	1	yes	characteristic
410	#382	C₂³	1	1	yes	characteristic
411	#382	C₂³	1	1	yes	characteristic
412	#381	—	2	1	no	—
413	#381	—	2	1	no	—
414	#380	—	2	1	no	—
415	#380	—	2	1	no	—
416	#380	—	2	1	no	—
417	#380	—	2	1	no	—
418	#380	C₂³	1	1	yes	characteristic
419	#380	C₂³	1	1	yes	characteristic
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	—	2	1	no	—
422	C₄×C₄⋊C₄	—	2	1	no	—
423	C₄×C₄⋊C₄	—	2	1	no	—
424	C₄×C₄⋊C₄	—	2	1	no	—
425	C₄×C₄⋊C₄	—	2	1	no	—
426	C₄×C₄⋊C₄	—	2	1	no	—
427	C₄×C₄⋊C₄	—	2	1	no	—
428	C₄×C₄⋊C₄	—	2	1	no	—
429	C₄×C₄⋊C₄	—	2	1	no	—
430	C₄×C₄⋊C₄	—	2	1	no	—
431	C₄×C₄⋊C₄	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	C₄×C₂²⋊C₄	—	2	1	no	—
457	C₄×C₂²⋊C₄	—	2	1	no	—
458	C₄×C₂²⋊C₄	—	2	1	no	—
459	C₄×C₂²⋊C₄	—	2	1	no	—
460	#376	—	2	1	no	—
461	#376	—	2	1	no	—
462	#376	—	2	1	no	—
463	#376	—	2	1	no	—
464	C₂×#95	—	2	1	no	—
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	C₂³	1	1	yes	characteristic
486	#340	C₂³	1	1	yes	characteristic
487	#340	C₂³	1	1	yes	characteristic
488	#340	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	#336	C₂³	1	1	yes	characteristic
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	4	1	no	—
499	C₂×#41	—	4	1	no	—
500	C₂×#41	—	4	1	no	—
501	C₂×#41	—	4	1	no	—
502	C₂×#41	C₂²×C₄	1	4	yes	—
503	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
504	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
505	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	C₂⁴	1	1	yes	characteristic
508	C₂³×C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
515	C₂³×C₄	C₂⁴	1	1	yes	characteristic
516	C₂×Q₁₆	—	4	1	no	—
517	C₂×Q₁₆	—	4	1	no	—
518	C₂×Q₁₆	—	4	1	no	—
519	C₂×Q₁₆	—	4	1	no	—
520	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
521	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
527	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
538	#126	—	2	8	no	—
539	#126	—	2	8	no	—
540	#125	—	2	8	no	—
541	#125	—	2	8	no	—
542	#125	—	2	2	no	—
543	#125	C₂²×C₄	1	4	yes	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
547	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	4	1	no	—
553	C₄×Q₈	—	4	1	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	4	1	no	—
557	C₄×Q₈	—	4	1	no	—
558	C₄×Q₈	—	4	1	no	—
559	C₄×Q₈	—	4	1	no	—
560	C₄×Q₈	C₂²×C₄	1	4	yes	—
561	C₄×Q₈	C₂²×C₄	1	4	yes	—
562	C₄×Q₈	C₂²×C₄	1	4	yes	—
563	C₄×Q₈	C₂²×C₄	1	4	yes	—
564	C₄×D₄	—	2	8	no	—
565	C₄×D₄	—	2	8	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	C₂²×C₄	1	4	yes	—
569	C₄×D₄	C₂²×C₄	1	4	yes	—
570	#117	—	2	8	no	—
571	#117	—	4	1	no	—
572	#117	—	4	1	no	—
573	#117	—	4	1	no	—
574	#117	—	4	1	no	—
575	#117	—	8	2	no	—
576	#117	—	8	2	no	—
577	#117	C₂²×C₄	1	4	yes	—
578	#117	#41	1	4	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	—	2	8	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	4	1	no	—
608	C₂×C₄⋊C₄	—	4	1	no	—
609	C₂×C₄⋊C₄	C₂²×C₄	1	4	yes	—
610	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	1	no	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	4	1	no	—
677	C₂×C₄²	—	4	1	no	—
678	C₂×C₄²	—	8	2	no	—
679	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
680	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
681	C₂×C₄²	C₂⁴	1	1	yes	characteristic
682	C₂×C₄²	C₂⁴	1	1	yes	characteristic
683	C₂×C₄²	C₂⁴	1	1	yes	characteristic
684	C₂×C₄²	C₂⁴	1	1	yes	characteristic
685	C₂×C₄²	C₂⁴	1	1	yes	characteristic
686	C₂×C₄²	C₂⁴	1	1	yes	characteristic
687	#107	—	4	1	no	—
688	#107	—	4	1	no	—
689	#107	—	4	1	no	—
690	#107	—	4	1	no	—
691	#107	C₂²×C₄	1	4	yes	—
692	#107	C₂²×C₄	1	4	yes	—
693	#106	—	4	1	no	—
694	#106	—	4	1	no	—
695	#106	—	4	1	no	—
696	#106	—	4	1	no	—
697	#106	C₂²×C₄	1	4	yes	—
698	#106	C₂²×C₄	1	4	yes	—
699	C₄⋊C₈	—	2	2	no	—
700	C₄⋊C₈	—	2	2	no	—
701	C₄⋊C₈	C₂²×C₄	1	4	yes	—
702	C₄⋊C₈	C₂²×C₄	1	4	yes	—
703	#103	—	4	1	no	—
704	#103	—	4	1	no	—
705	#103	—	4	1	no	—
706	#103	—	4	1	no	—
707	#103	—	4	1	no	—
708	#103	—	4	1	no	—
709	#103	—	4	1	no	—
710	#103	—	4	1	no	—
711	#103	—	4	1	no	—
712	#103	—	4	1	no	—
713	#103	—	4	1	no	—
714	#103	—	4	1	no	—
715	#103	C₂²×C₄	1	4	yes	—
716	#103	C₂²×C₄	1	4	yes	—
717	#103	C₂²×C₄	1	4	yes	—
718	#103	C₂²×C₄	1	4	yes	—
719	#103	C₂²×C₄	1	4	yes	—
720	#103	C₂²×C₄	1	4	yes	—
721	#102	—	4	1	no	—
722	#102	—	4	1	no	—
723	#102	—	4	1	no	—
724	#102	—	4	1	no	—
725	#102	C₂²×C₄	1	4	yes	—
726	#102	C₂²×C₄	1	4	yes	—
727	C₂²⋊C₈	—	2	2	no	—
728	C₂²⋊C₈	—	2	2	no	—
729	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
730	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
731	#97	—	2	2	no	—
732	#97	—	4	1	no	—
733	#97	—	4	1	no	—
734	#97	—	4	1	no	—
735	#97	—	4	1	no	—
736	#97	—	4	1	no	—
737	#97	—	4	1	no	—
738	#97	C₂²×C₄	1	4	yes	—
739	C₄×C₈	—	2	2	no	—
740	C₄×C₈	—	4	1	no	—
741	C₄×C₈	—	4	1	no	—
742	C₄×C₈	C₂²×C₄	1	4	yes	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	#95	C₂×D₄	1	1	yes	characteristic
792	#95	C₂×D₄	1	1	yes	characteristic
793	C₂⁴	—	2	1	no	—
794	C₂⁴	C₂²×D₄	1	1	yes	characteristic
795	#41	—	4	4	no	—
796	#41	—	4	4	no	—
797	#41	—	4	4	no	—
798	#41	—	4	4	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	C₂³×C₄	1	2	yes	—
815	C₂×Q₈	C₂³×C₄	1	2	yes	—
816	C₂×Q₈	C₂³×C₄	1	2	yes	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	C₂³×C₄	1	2	yes	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	8	1	no	—
859	C₂²×C₄	—	8	1	no	—
860	C₂²×C₄	—	8	1	no	—
861	C₂²×C₄	—	8	1	no	—
862	C₂²×C₄	—	8	1	no	—
863	C₂²×C₄	—	8	1	no	—
864	C₂²×C₄	—	8	1	no	—
865	C₂²×C₄	—	8	1	no	—
866	C₂²×C₄	C₂³×C₄	1	2	yes	—
867	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
868	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
869	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	C₂×#41	1	2	yes	—
881	C₂²×C₄	C₂⁵	1	1	yes	characteristic
882	Q₁₆	—	4	4	no	—
883	Q₁₆	—	4	4	no	—
884	SD₁₆	—	4	4	no	—
885	SD₁₆	—	4	4	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	C₂³×C₄	1	2	yes	—
907	C₂×C₈	C₂³×C₄	1	2	yes	—
908	C₂×C₈	C₂³×C₄	1	2	yes	—
909	C₂×C₈	C₂³×C₄	1	2	yes	—
910	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	4	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	4	no	—
919	C₄⋊C₄	—	2	4	no	—
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	—	4	1	no	—
943	C₄⋊C₄	—	4	1	no	—
944	C₄⋊C₄	—	4	1	no	—
945	C₄⋊C₄	—	4	1	no	—
946	C₄⋊C₄	—	4	1	no	—
947	C₄⋊C₄	—	4	1	no	—
948	C₄⋊C₄	—	4	1	no	—
949	C₄⋊C₄	—	4	1	no	—
950	C₄⋊C₄	—	4	1	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	no	—
958	C₄⋊C₄	—	8	1	no	—
959	C₄⋊C₄	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₄⋊C₄	—	8	1	no	—
962	C₄⋊C₄	—	8	1	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	C₄×D₄	1	4	yes	—
967	C₄⋊C₄	C₄×D₄	1	4	yes	—
968	C₄⋊C₄	C₂³×C₄	1	2	yes	—
969	C₄⋊C₄	C₂³×C₄	1	2	yes	—
970	C₄⋊C₄	C₂³×C₄	1	2	yes	—
971	C₄⋊C₄	C₂³×C₄	1	2	yes	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	4	1	no	—
977	C₂²⋊C₄	—	4	1	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	—	8	1	no	—
984	C₂²⋊C₄	—	8	1	no	—
985	C₂²⋊C₄	—	8	1	no	—
986	C₂²⋊C₄	—	8	1	no	—
987	C₂²⋊C₄	—	8	1	no	—
988	C₂²⋊C₄	—	8	1	no	—
989	C₂²⋊C₄	C₄×D₄	1	4	yes	—
990	C₂²⋊C₄	C₄×D₄	1	4	yes	—
991	C₄²	—	2	4	no	—
992	C₄²	—	2	4	no	—
993	C₄²	—	2	4	no	—
994	C₄²	—	2	4	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	4	1	no	—
1004	C₄²	—	4	1	no	—
1005	C₄²	—	4	2	no	—
1006	C₄²	—	4	2	no	—
1007	C₄²	—	4	2	no	—
1008	C₄²	—	4	2	no	—
1009	C₄²	—	4	2	no	—
1010	C₄²	—	8	1	no	—
1011	C₄²	—	8	1	no	—
1012	C₄²	—	8	1	no	—
1013	C₄²	—	8	1	no	—
1014	C₄²	—	8	1	no	—
1015	C₄²	—	8	1	no	—
1016	C₄²	—	8	1	no	—
1017	C₄²	—	8	1	no	—
1018	C₄²	—	8	1	no	—
1019	C₄²	—	8	1	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	1	no	—
1024	C₄²	C₂³×C₄	1	2	yes	—
1025	C₄²	C₂³×C₄	1	2	yes	—
1026	C₄²	C₂×#41	1	2	yes	—
1027	C₄²	C₂×#41	1	2	yes	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	C₂×C₄×D₄	1	2	yes	—
1042	C₂³	C₂³×D₄	1	1	yes	characteristic
1043	Q₈	—	2	2	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	4	1	no	—
1050	Q₈	—	4	1	no	—
1051	Q₈	—	4	1	no	—
1052	Q₈	—	4	1	no	—
1053	Q₈	—	4	1	no	—
1054	Q₈	—	4	1	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	4	8	no	—
1058	D₄	—	4	1	no	—
1059	D₄	—	4	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	4	8	no	—
1106	C₂×C₄	—	4	4	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	8	4	no	—
1146	C₂×C₄	—	8	4	no	—
1147	C₂×C₄	—	8	4	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	4	no	—
1150	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1151	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1152	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1153	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1154	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1155	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1156	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1157	C₂×C₄	#585	1	1	yes	characteristic
1158	C₂×C₄	#585	1	1	yes	characteristic
1159	C₂×C₄	#585	1	1	yes	characteristic
1160	C₂×C₄	#585	1	1	yes	characteristic
1161	C₈	—	2	2	no	—
1162	C₈	—	2	2	no	—
1163	C₈	—	2	2	no	—
1164	C₈	—	2	2	no	—
1165	C₈	—	4	1	no	—
1166	C₈	—	4	1	no	—
1167	C₈	—	4	1	no	—
1168	C₈	—	4	1	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	8	1	no	—
1180	C₂²	—	8	1	no	—
1181	C₂²	—	8	1	no	—
1182	C₂²	—	8	1	no	—
1183	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1184	C₂²	#3485	1	1	yes	characteristic
1185	C₂²	#3487	1	1	yes	characteristic
1186	C₂²	#3585	1	1	yes	characteristic
1187	C₂²	#3586	1	1	yes	characteristic
1188	C₂²	#3586	1	1	yes	characteristic
1189	C₂²	#3586	1	1	yes	characteristic
1190	C₄	—	2	2	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	4	2	no	—
1196	C₄	—	4	2	no	—
1197	C₄	—	4	2	no	—
1198	C₄	—	4	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	—	8	1	no	—
1213	C₄	—	8	1	no	—
1214	C₄	—	8	1	no	—
1215	C₄	—	8	1	no	—
1216	C₄	—	8	1	no	—
1217	C₄	—	8	1	no	—
1218	C₄	#3428	1	1	yes	characteristic
1219	C₄	#3428	1	1	yes	characteristic
1220	C₄	#3493	1	1	yes	characteristic
1221	C₄	#3493	1	1	yes	characteristic
1222	C₂	—	4	2	no	—
1223	C₂	—	8	2	no	—
1224	C₂	#34201	1	1	yes	characteristic
1225	C₂	#60174	1	1	yes	characteristic
1226	C₂	#60175	1	1	yes	characteristic
1227	C₂	#61774	1	1	yes	characteristic
1228	C₂	#61779	1	1	yes	characteristic
1229	C₂	#61939	1	1	yes	characteristic
1230	C₂	#61941	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2296 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #34420	C₂	semidirect
4. #23112	C₂	semidirect
5. #23110	C₂	semidirect
6. #23102	C₂	semidirect
7. #23100	C₂	semidirect
8. #23074	C₂	semidirect
9. #23072	C₂	semidirect
10. #23071	C₂	semidirect
11. #23070	C₂	semidirect
12. #22820	C₂	semidirect
13. #22818	C₂	semidirect
14. #22815	C₂	semidirect
15. #22812	C₂	semidirect
16. #22779	C₂	semidirect
17. #22775	C₂	semidirect
18. #22763	C₂	semidirect
19. #22759	C₂	semidirect
24. #21992	C₂	semidirect
25. #21873	C₂	semidirect
26. #21587	C₂	semidirect
27. #21585	C₂	semidirect
28. #21581	C₂	semidirect
29. #21579	C₂	semidirect
31. #20542	C₂	semidirect
34. #3120	C₄	semidirect
246. #479	C₂×C₄	semidirect
247. #478	C₂×C₄	semidirect
248. #462	C₂×C₄	semidirect
249. #461	C₂×C₄	semidirect
252. #441	C₂×C₄	semidirect
253. #440	C₂×C₄	semidirect
254. C₄×Q₁₆	C₂×C₄	semidirect
255. C₄×SD₁₆	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×#3120	2
#34420	2
#34252	2
#23112	2
#23110	2
#23102	2
#23100	2
#23074	2
#23072	2
#23071	2
#23070	2
#22820	2
#22818	2
#22815	2
#22812	2
#22779	2
#22775	2
#22763	2
#22759	2
#22059	2
#22057	2
#22048	2
#21992	2
#21873	2
#21587	2
#21585	2
#21581	2
#21579	2
#20746	2
#20542	2