Subgroups — #6602560

Order 512.

1591 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#38054	C₂	1	1	yes	maximal, characteristic
2	#34231	C₂	1	1	yes	maximal, characteristic, complemented
3	#33101	C₂	1	1	yes	maximal, characteristic, complemented
4	#33087	C₂	1	1	yes	maximal, characteristic, complemented
5	#33035	C₂	1	1	yes	maximal, characteristic, complemented
6	#29571	C₂	1	1	yes	maximal, characteristic, complemented
7	#29548	C₂	1	1	yes	maximal, characteristic, complemented
8	#29442	C₂	1	1	yes	maximal, characteristic, complemented
9	#29383	C₂	1	1	yes	maximal, characteristic, complemented
10	#27147	C₂	1	1	yes	maximal, characteristic, complemented
11	#27066	C₂	1	1	yes	maximal, characteristic, complemented
12	#27002	C₂	1	1	yes	maximal, characteristic, complemented
13	#26919	C₂	1	1	yes	maximal, characteristic, complemented
14	#26710	C₂	1	1	yes	maximal, characteristic, complemented
15	#26693	C₂	1	1	yes	maximal, characteristic, complemented
16	#26604	C₂	1	1	yes	maximal, characteristic, complemented
17	#26591	C₂	1	1	yes	maximal, characteristic, complemented
18	#26429	C₂	1	1	yes	maximal, characteristic, complemented
19	#26355	C₂	1	1	yes	maximal, characteristic, complemented
20	#25504	C₂	1	1	yes	maximal, characteristic, complemented
21	#25105	C₂	1	1	yes	maximal, characteristic
22	#25105	C₂	1	1	yes	maximal, characteristic
23	#23933	C₂	1	1	yes	maximal, characteristic
24	#23139	C₂	1	1	yes	maximal, characteristic, complemented
25	#23036	C₂	1	1	yes	maximal, characteristic, complemented
26	#22864	C₂	1	1	yes	maximal, characteristic
27	#22864	C₂	1	1	yes	maximal, characteristic
28	#22596	C₂	1	1	yes	maximal, characteristic, complemented
29	#21512	C₂	1	1	yes	maximal, characteristic, complemented
30	#21128	C₂	1	1	yes	maximal, characteristic, complemented
31	#21060	C₂	1	1	yes	maximal, characteristic
32	C₂×#533	C₂²	1	1	yes	characteristic
33	C₂×#477	C₂²	1	1	yes	characteristic, complemented
34	C₂×#470	C₂²	1	1	yes	characteristic
35	C₂×#470	C₂²	1	1	yes	characteristic
36	C₂×#464	C₂²	1	1	yes	characteristic
37	C₂×#464	C₂²	1	1	yes	characteristic
38	C₂×#450	C₂²	1	1	yes	characteristic
39	C₂×#450	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×#440	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₂×#428	C₂²	1	1	yes	characteristic
44	C₂×#418	C₂²	1	1	yes	characteristic
45	C₂×#418	C₂²	1	1	yes	characteristic
46	#2855	C₂²	1	1	yes	characteristic
47	#2761	—	2	1	no	—
48	#2757	—	2	1	no	—
49	#2737	—	2	1	no	—
50	#2723	—	2	1	no	—
51	#2644	C₂²	1	1	yes	characteristic
52	#2640	C₂²	1	1	yes	characteristic
53	#2561	—	2	1	no	—
54	#2512	C₂²	1	1	yes	characteristic
55	#2483	—	2	1	no	—
56	#2480	—	2	1	no	—
57	#2452	C₂²	1	1	yes	characteristic
58	#2448	C₂²	1	1	yes	characteristic
59	#2447	C₂²	1	1	yes	characteristic
60	#2440	C₂²	1	1	yes	characteristic
61	#2437	—	2	1	no	—
62	#2435	C₂²	1	1	yes	characteristic
63	#2369	C₂²	1	1	yes	characteristic, complemented
64	#2369	C₂²	1	1	yes	characteristic, complemented
65	#2365	C₂²	1	1	yes	characteristic, complemented
66	#2365	C₂²	1	1	yes	characteristic, complemented
67	#2362	C₂²	1	1	yes	characteristic
68	#2362	C₂²	1	1	yes	characteristic
69	#2362	C₂²	1	1	yes	characteristic
70	#2362	C₂²	1	1	yes	characteristic
71	#2360	C₂²	1	1	yes	characteristic
72	#2356	—	2	1	no	—
73	#2356	—	2	1	no	—
74	#2347	—	2	1	no	—
75	#2346	—	2	1	no	—
76	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
77	#2332	—	2	1	no	—
78	#2332	—	2	1	no	—
79	#2326	C₂²	1	1	yes	characteristic
80	#2320	C₂²	1	1	yes	characteristic, complemented
81	#2320	C₂²	1	1	yes	characteristic, complemented
82	#2319	C₂²	1	1	yes	characteristic
83	C₄×#125	—	2	1	no	—
84	C₄×#125	—	2	1	no	—
85	C₂×#390	C₂²	1	1	yes	characteristic
86	#2283	C₂²	1	1	yes	characteristic
87	#2276	C₂²	1	1	yes	characteristic, complemented
88	#2276	C₂²	1	1	yes	characteristic, complemented
89	C₄×#117	C₂²	1	1	yes	characteristic
90	#2100	C₂²	1	1	yes	characteristic, complemented
91	#2096	C₂²	1	1	yes	characteristic, complemented
92	#2088	C₂²	1	1	yes	characteristic, complemented
93	#2088	C₂²	1	1	yes	characteristic, complemented
94	#2066	C₂²	1	1	yes	characteristic, complemented
95	#2066	C₂²	1	1	yes	characteristic, complemented
96	#2065	C₂²	1	1	yes	characteristic
97	#2065	C₂²	1	1	yes	characteristic
98	#2058	C₂²	1	1	yes	characteristic, complemented
99	#2058	C₂²	1	1	yes	characteristic, complemented
100	#2055	C₂²	1	1	yes	characteristic
101	#2055	C₂²	1	1	yes	characteristic
102	#2043	C₂²	1	1	yes	characteristic, complemented
103	#2042	C₂²	1	1	yes	characteristic
104	#2042	C₂²	1	1	yes	characteristic
105	#2024	C₂²	1	1	yes	characteristic, complemented
106	#2024	C₂²	1	1	yes	characteristic, complemented
107	#2023	C₂²	1	1	yes	characteristic
108	#2023	C₂²	1	1	yes	characteristic
109	#2016	C₂²	1	1	yes	characteristic, complemented
110	#2015	C₂²	1	1	yes	characteristic
111	#2015	C₂²	1	1	yes	characteristic
112	#2013	C₂²	1	1	yes	characteristic
113	#2013	C₂²	1	1	yes	characteristic
114	#1988	C₂²	1	1	yes	characteristic, complemented
115	#1983	C₂²	1	1	yes	characteristic
116	#1983	C₂²	1	1	yes	characteristic
117	#1971	C₂²	1	1	yes	characteristic, complemented
118	#1968	C₂²	1	1	yes	characteristic
119	#1968	C₂²	1	1	yes	characteristic
120	#1947	C₂²	1	1	yes	characteristic, complemented
121	#1941	C₂²	1	1	yes	characteristic, complemented
122	#1936	C₂²	1	1	yes	characteristic
123	#1936	C₂²	1	1	yes	characteristic
124	#1935	C₂²	1	1	yes	characteristic, complemented
125	#1933	C₂²	1	1	yes	characteristic, complemented
126	#1928	C₂²	1	1	yes	characteristic, complemented
127	#1928	C₂²	1	1	yes	characteristic, complemented
128	#1928	C₂²	1	1	yes	characteristic, complemented
129	#1927	C₂²	1	1	yes	characteristic, complemented
130	#1927	C₂²	1	1	yes	characteristic, complemented
131	#1927	C₂²	1	1	yes	characteristic, complemented
132	#1926	C₂²	1	1	yes	characteristic
133	#1926	C₂²	1	1	yes	characteristic
134	#1926	C₂²	1	1	yes	characteristic
135	#1926	C₂²	1	1	yes	characteristic
136	#1926	C₂²	1	1	yes	characteristic
137	#1926	C₂²	1	1	yes	characteristic
138	#1925	C₂²	1	1	yes	characteristic
139	#1925	C₂²	1	1	yes	characteristic
140	#1925	C₂²	1	1	yes	characteristic
141	#1925	C₂²	1	1	yes	characteristic
142	#1925	C₂²	1	1	yes	characteristic
143	#1925	C₂²	1	1	yes	characteristic
144	#1921	C₂²	1	1	yes	characteristic, complemented
145	#1920	C₂²	1	1	yes	characteristic, complemented
146	#1919	C₂²	1	1	yes	characteristic, complemented
147	#1919	C₂²	1	1	yes	characteristic, complemented
148	#1919	C₂²	1	1	yes	characteristic, complemented
149	#1918	C₂²	1	1	yes	characteristic, complemented
150	#1918	C₂²	1	1	yes	characteristic, complemented
151	#1918	C₂²	1	1	yes	characteristic, complemented
152	#1917	C₂²	1	1	yes	characteristic, complemented
153	#1917	C₂²	1	1	yes	characteristic, complemented
154	#1916	C₂²	1	1	yes	characteristic, complemented
155	#1916	C₂²	1	1	yes	characteristic, complemented
156	#1894	C₂²	1	1	yes	characteristic
157	#1894	C₂²	1	1	yes	characteristic
158	#1880	C₂²	1	1	yes	characteristic
159	#1880	C₂²	1	1	yes	characteristic
160	#1880	C₂²	1	1	yes	characteristic
161	#1880	C₂²	1	1	yes	characteristic
162	#1880	C₂²	1	1	yes	characteristic
163	#1880	C₂²	1	1	yes	characteristic
164	#1880	C₂²	1	1	yes	characteristic
165	#1880	C₂²	1	1	yes	characteristic
166	#1878	C₂²	1	1	yes	characteristic, complemented
167	#1878	C₂²	1	1	yes	characteristic, complemented
168	#1878	C₂²	1	1	yes	characteristic, complemented
169	#1878	C₂²	1	1	yes	characteristic, complemented
170	#1877	C₂²	1	1	yes	characteristic
171	#1877	C₂²	1	1	yes	characteristic
172	#1873	C₂²	1	1	yes	characteristic
173	#1873	C₂²	1	1	yes	characteristic
174	#1872	C₂²	1	1	yes	characteristic
175	#1872	C₂²	1	1	yes	characteristic
176	#1865	C₂²	1	1	yes	characteristic, complemented
177	#1865	C₂²	1	1	yes	characteristic, complemented
178	#1865	C₂²	1	1	yes	characteristic, complemented
179	#1864	C₂²	1	1	yes	characteristic
180	#1864	C₂²	1	1	yes	characteristic
181	#1863	C₂²	1	1	yes	characteristic, complemented
182	#1863	C₂²	1	1	yes	characteristic, complemented
183	#1863	C₂²	1	1	yes	characteristic, complemented
184	#1854	C₂²	1	1	yes	characteristic
185	#1854	C₂²	1	1	yes	characteristic
186	#1851	C₂²	1	1	yes	characteristic
187	#1851	C₂²	1	1	yes	characteristic
188	#1840	C₂²	1	1	yes	characteristic, complemented
189	#1832	C₂²	1	1	yes	characteristic, complemented
190	#1817	C₂²	1	1	yes	characteristic
191	#1803	C₂²	1	1	yes	characteristic, complemented
192	#1776	C₂²	1	1	yes	characteristic, complemented
193	#1768	C₂²	1	1	yes	characteristic, complemented
194	#1763	C₂²	1	1	yes	characteristic, complemented
195	C₄×#103	C₂²	1	1	yes	characteristic, complemented
196	C₄×#102	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	#1753	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	#1746	C₂²	1	1	yes	characteristic, complemented
201	#1736	C₂²	1	1	yes	characteristic
202	#1728	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	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×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂²×M₁₆	C₂³	1	1	yes	characteristic
211	C₂²×M₁₆	C₂³	1	1	yes	characteristic
212	#533	—	2	4	no	—
213	#533	—	2	4	no	—
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×#126	—	2	1	no	—
218	C₂×#125	—	2	1	no	—
219	C₂×#124	C₂³	1	1	yes	characteristic
220	C₂×#124	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	—	2	1	no	—
224	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	—	2	1	no	—
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×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×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×#117	—	2	1	no	—
238	C₂×#117	C₂³	1	1	yes	characteristic
239	C₂×#117	C₂³	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	—	2	1	no	—
242	C₂²×C₂²⋊C₄	—	2	1	no	—
243	C₂²×C₂²⋊C₄	—	2	1	no	—
244	C₂²×C₄²	C₂³	1	1	yes	characteristic
245	#477	—	4	2	no	—
246	#470	—	2	4	no	—
247	#470	—	2	4	no	—
248	#464	—	2	4	no	—
249	#464	—	4	2	no	—
250	#450	—	2	4	no	—
251	#450	—	2	4	no	—
252	#440	—	2	4	no	—
253	#440	—	4	2	no	—
254	C₄×Q₁₆	—	4	2	no	—
255	#428	—	4	2	no	—
256	C₂×#107	C₂³	1	1	yes	characteristic
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	C₂×#106	C₂³	1	1	yes	characteristic
262	C₂×#106	C₂³	1	1	yes	characteristic
263	C₂×#106	C₂³	1	1	yes	characteristic
264	C₂×#106	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	#418	—	2	4	no	—
271	#418	—	4	2	no	—
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#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×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#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×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	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×C₄×C₈	C₂³	1	1	yes	characteristic
305	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
306	#399	—	2	1	no	—
307	#398	—	2	1	no	—
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#397	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	2	1	no	—
317	#396	—	2	1	no	—
318	#396	—	2	1	no	—
319	#396	—	2	1	no	—
320	#395	—	2	1	no	—
321	#394	—	2	1	no	—
322	#394	—	2	1	no	—
323	#393	—	2	1	no	—
324	#393	—	2	1	no	—
325	#393	—	2	1	no	—
326	#391	—	2	1	no	—
327	#391	—	2	1	no	—
328	#391	—	2	1	no	—
329	#391	—	2	1	no	—
330	#391	C₂³	1	1	yes	characteristic
331	#391	C₂³	1	1	yes	characteristic
332	#391	C₂³	1	1	yes	characteristic
333	#391	C₂³	1	1	yes	characteristic
334	#391	C₂³	1	1	yes	characteristic
335	#391	C₂³	1	1	yes	characteristic
336	#391	C₂³	1	1	yes	characteristic
337	#390	—	2	1	no	—
338	#390	—	2	1	no	—
339	#390	C₂³	1	1	yes	characteristic
340	#390	C₂³	1	1	yes	characteristic
341	#390	C₂³	1	1	yes	characteristic
342	#390	C₂³	1	1	yes	characteristic
343	#390	C₂³	1	1	yes	characteristic
344	#390	C₂³	1	1	yes	characteristic
345	#390	C₂³	1	1	yes	characteristic
346	#390	C₂³	1	1	yes	characteristic
347	#389	—	2	1	no	—
348	#389	—	2	1	no	—
349	#389	—	2	1	no	—
350	#389	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	C₂³	1	1	yes	characteristic
353	#389	C₂³	1	1	yes	characteristic
354	#389	C₂³	1	1	yes	characteristic
355	#389	C₂³	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#389	C₂³	1	1	yes	characteristic
360	#389	C₂³	1	1	yes	characteristic
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	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	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#386	—	2	1	no	—
392	#386	—	2	1	no	—
393	#385	—	2	1	no	—
394	#385	—	2	1	no	—
395	#385	—	2	1	no	—
396	#385	—	2	1	no	—
397	#385	—	2	1	no	—
398	#385	—	2	1	no	—
399	#385	—	2	1	no	—
400	#384	C₂³	1	1	yes	characteristic
401	#383	—	2	1	no	—
402	#383	—	2	1	no	—
403	#383	D₄	1	1	yes	characteristic
404	#383	D₄	1	1	yes	characteristic
405	#382	—	2	1	no	—
406	#382	—	2	1	no	—
407	#382	D₄	1	1	yes	characteristic
408	#382	D₄	1	1	yes	characteristic
409	#381	—	2	1	no	—
410	#381	—	2	1	no	—
411	#381	—	2	1	no	—
412	#381	D₄	1	1	yes	characteristic
413	#381	D₄	1	1	yes	characteristic
414	#380	—	2	1	no	—
415	#380	D₄	1	1	yes	characteristic
416	#380	D₄	1	1	yes	characteristic
417	#380	C₂³	1	1	yes	characteristic
418	#379	—	2	1	no	—
419	#379	—	2	1	no	—
420	#379	—	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	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	#376	—	2	1	no	—
452	#376	—	2	1	no	—
453	#376	—	2	1	no	—
454	#376	C₂³	1	1	yes	characteristic
455	#376	C₂³	1	1	yes	characteristic
456	C₄³	—	2	1	no	—
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	C₂⁵	—	2	1	no	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
498	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	—	4	1	no	—
505	C₂²×D₄	—	4	1	no	—
506	C₂²×D₄	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂⁴	1	1	yes	characteristic
514	C₂×Q₁₆	—	2	2	no	—
515	C₂×Q₁₆	—	2	2	no	—
516	C₂×Q₁₆	—	2	2	no	—
517	C₂×Q₁₆	—	4	1	no	—
518	C₂×Q₁₆	—	4	1	no	—
519	C₂×Q₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	2	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×SD₁₆	—	4	1	no	—
528	C₂×SD₁₆	—	4	1	no	—
529	C₂×SD₁₆	—	4	1	no	—
530	C₂×SD₁₆	—	4	1	no	—
531	C₂×SD₁₆	—	4	1	no	—
532	C₂×M₁₆	—	2	2	no	—
533	C₂×M₁₆	—	2	2	no	—
534	C₂×M₁₆	—	2	2	no	—
535	C₂×M₁₆	—	4	1	no	—
536	C₂×M₁₆	—	4	1	no	—
537	C₂×M₁₆	—	4	1	no	—
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	2	2	no	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	—	4	1	no	—
551	C₄⋊Q₈	—	4	1	no	—
552	#126	—	8	2	no	—
553	#125	—	2	8	no	—
554	#124	—	2	2	no	—
555	#124	—	4	1	no	—
556	#124	—	4	1	no	—
557	#124	—	4	1	no	—
558	C₂²⋊Q₈	—	2	8	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	8	2	no	—
564	C₂²⋊Q₈	—	8	2	no	—
565	C₂²⋊Q₈	#41	1	4	yes	—
566	C₂²⋊Q₈	#41	1	4	yes	—
567	C₄×Q₈	—	2	8	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	4	1	no	—
577	C₄×Q₈	—	4	1	no	—
578	C₄×Q₈	—	4	1	no	—
579	C₄×Q₈	—	4	1	no	—
580	C₄×Q₈	—	4	1	no	—
581	C₄×Q₈	—	4	1	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	4	1	no	—
584	C₄×D₄	—	4	1	no	—
585	C₄×D₄	—	4	1	no	—
586	#117	—	2	8	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	—	4	1	no	—
590	#117	—	4	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	4	1	no	—
618	C₂×C₄⋊C₄	—	4	1	no	—
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	C₂×D₄	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	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	8	2	no	—
663	C₂×C₂²⋊C₄	—	8	2	no	—
664	C₂×C₂²⋊C₄	—	8	2	no	—
665	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	2	no	—
672	C₂×C₄²	—	2	2	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
690	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
691	C₂×C₄²	C₂⁴	1	1	yes	characteristic
692	C₂×C₄²	C₂⁴	1	1	yes	characteristic
693	C₂×C₄²	C₂⁴	1	1	yes	characteristic
694	C₂×C₄²	C₂⁴	1	1	yes	characteristic
695	C₂×C₄²	C₂⁴	1	1	yes	characteristic
696	C₂×C₄²	C₂⁴	1	1	yes	characteristic
697	#107	—	2	2	no	—
698	#107	—	2	2	no	—
699	#107	—	2	2	no	—
700	#107	—	2	2	no	—
701	#106	—	2	2	no	—
702	#106	—	2	2	no	—
703	#106	—	4	1	no	—
704	#106	—	4	1	no	—
705	#106	—	4	1	no	—
706	#106	—	4	1	no	—
707	C₄⋊C₈	—	2	2	no	—
708	C₄⋊C₈	—	4	1	no	—
709	C₄⋊C₈	—	4	1	no	—
710	C₄⋊C₈	—	4	1	no	—
711	#103	—	2	2	no	—
712	#103	—	2	2	no	—
713	#103	—	2	2	no	—
714	#103	—	2	2	no	—
715	#103	—	2	2	no	—
716	#103	—	2	2	no	—
717	#103	—	2	2	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#103	—	4	1	no	—
724	#103	—	4	1	no	—
725	#103	—	4	1	no	—
726	#103	—	4	1	no	—
727	#102	—	2	2	no	—
728	#102	—	2	2	no	—
729	#102	—	2	2	no	—
730	#102	—	2	2	no	—
731	#102	—	2	2	no	—
732	#102	—	2	2	no	—
733	#102	—	2	2	no	—
734	#102	—	2	2	no	—
735	#102	—	2	2	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	#41	1	4	yes	—
739	C₂²⋊C₈	—	2	2	no	—
740	C₂²⋊C₈	—	2	2	no	—
741	#97	—	2	2	no	—
742	#97	—	4	1	no	—
743	C₄×C₈	—	4	1	no	—
744	C₄×C₈	—	4	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	C₂×D₄	1	1	yes	characteristic
779	#95	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
781	#95	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
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	#95	C₂×D₄	1	1	yes	characteristic
794	C₂⁴	—	2	1	no	—
795	C₂⁴	—	2	1	no	—
796	C₂⁴	—	4	2	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	—	4	2	no	—
800	C₂⁴	—	8	1	no	—
801	C₂⁴	—	8	1	no	—
802	C₂⁴	—	8	1	no	—
803	C₂⁴	C₂²×D₄	1	1	yes	characteristic
804	C₂×Q₈	—	2	4	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	—	2	1	no	—
815	C₂×Q₈	—	2	1	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	—	8	1	no	—
822	C₂×Q₈	—	8	1	no	—
823	C₂×Q₈	—	8	1	no	—
824	C₂×Q₈	—	8	1	no	—
825	C₂×Q₈	—	8	1	no	—
826	C₂×Q₈	C₂×#41	1	2	yes	—
827	C₂×Q₈	C₂×#41	1	2	yes	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	1	no	—
838	C₂×D₄	—	2	1	no	—
839	C₂×D₄	—	4	4	no	—
840	C₂×D₄	—	4	4	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	8	2	no	—
844	C₂×D₄	—	8	2	no	—
845	C₂×D₄	—	8	1	no	—
846	C₂×D₄	C₂×#41	1	2	yes	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	1	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	8	1	no	—
874	C₂²×C₄	—	8	1	no	—
875	C₂²×C₄	—	8	1	no	—
876	C₂²×C₄	—	8	1	no	—
877	C₂²×C₄	—	8	1	no	—
878	C₂²×C₄	—	8	1	no	—
879	C₂²×C₄	—	8	1	no	—
880	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂×#41	1	2	yes	—
894	C₂²×C₄	C₂×#41	1	2	yes	—
895	C₂²×C₄	C₂⁵	1	1	yes	characteristic
896	Q₁₆	—	4	4	no	—
897	Q₁₆	—	8	2	no	—
898	SD₁₆	—	4	4	no	—
899	SD₁₆	—	4	4	no	—
900	SD₁₆	—	8	2	no	—
901	SD₁₆	—	8	2	no	—
902	M₁₆	—	4	4	no	—
903	M₁₆	—	8	2	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	C₂×#41	1	2	yes	—
928	C₄⋊C₄	—	2	4	no	—
929	C₄⋊C₄	—	2	4	no	—
930	C₄⋊C₄	—	2	4	no	—
931	C₄⋊C₄	—	2	4	no	—
932	C₄⋊C₄	—	2	4	no	—
933	C₄⋊C₄	—	2	4	no	—
934	C₄⋊C₄	—	2	4	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	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	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	4	1	no	—
956	C₄⋊C₄	—	4	1	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	4	2	no	—
959	C₄⋊C₄	—	4	2	no	—
960	C₄⋊C₄	—	4	2	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	—	8	1	no	—
967	C₄⋊C₄	—	8	1	no	—
968	C₄⋊C₄	—	8	1	no	—
969	C₄⋊C₄	—	8	1	no	—
970	C₄⋊C₄	—	8	1	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	—	8	1	no	—
973	C₄⋊C₄	—	8	1	no	—
974	C₄⋊C₄	—	8	1	no	—
975	C₄⋊C₄	—	8	1	no	—
976	C₄⋊C₄	C₂×#41	1	2	yes	—
977	C₄⋊C₄	C₂×#41	1	2	yes	—
978	C₄⋊C₄	C₂×#41	1	2	yes	—
979	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	4	1	no	—
983	C₂²⋊C₄	—	4	1	no	—
984	C₂²⋊C₄	—	4	1	no	—
985	C₂²⋊C₄	—	4	1	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	1	no	—
1006	C₂²⋊C₄	—	8	1	no	—
1007	C₂²⋊C₄	—	8	1	no	—
1008	C₂²⋊C₄	—	8	1	no	—
1009	C₂²⋊C₄	—	8	1	no	—
1010	C₂²⋊C₄	—	8	1	no	—
1011	C₂²⋊C₄	—	8	1	no	—
1012	C₄²	—	2	4	no	—
1013	C₄²	—	2	4	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	4	2	no	—
1029	C₄²	—	4	2	no	—
1030	C₄²	—	4	2	no	—
1031	C₄²	—	4	2	no	—
1032	C₄²	—	4	2	no	—
1033	C₄²	—	4	2	no	—
1034	C₄²	—	4	2	no	—
1035	C₄²	—	4	2	no	—
1036	C₄²	—	8	1	no	—
1037	C₄²	—	8	1	no	—
1038	C₄²	—	8	1	no	—
1039	C₄²	—	8	1	no	—
1040	C₄²	—	8	1	no	—
1041	C₄²	—	8	1	no	—
1042	C₄²	—	8	1	no	—
1043	C₄²	—	8	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	1	no	—
1055	C₂³	—	4	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	4	1	no	—
1060	C₂³	—	4	1	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	1	no	—
1063	C₂³	—	4	1	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	—	8	4	no	—
1067	C₂³	—	8	4	no	—
1068	C₂³	—	16	2	no	—
1069	C₂³	—	16	2	no	—
1070	C₂³	—	16	2	no	—
1071	C₂³	#525	1	2	yes	—
1072	C₂³	C₂³×D₄	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	2	no	—
1077	Q₈	—	4	1	no	—
1078	Q₈	—	4	1	no	—
1079	Q₈	—	4	1	no	—
1080	Q₈	—	4	1	no	—
1081	Q₈	—	4	1	no	—
1082	Q₈	—	4	1	no	—
1083	Q₈	—	4	1	no	—
1084	Q₈	—	4	1	no	—
1085	Q₈	—	8	4	no	—
1086	Q₈	—	16	2	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	2	no	—
1089	D₄	—	4	1	no	—
1090	D₄	—	4	1	no	—
1091	D₄	—	4	1	no	—
1092	D₄	—	4	1	no	—
1093	D₄	—	4	1	no	—
1094	D₄	—	4	1	no	—
1095	D₄	—	8	4	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	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	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	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	2	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	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	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	—	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	—	8	2	no	—
1181	C₂×C₄	—	16	2	no	—
1182	C₂×C₄	—	16	2	no	—
1183	C₂×C₄	—	16	2	no	—
1184	C₂×C₄	#525	1	2	yes	—
1185	C₂×C₄	#577	1	2	yes	—
1186	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1187	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1188	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1189	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂×C₄	#585	1	1	yes	characteristic
1191	C₂×C₄	#585	1	1	yes	characteristic
1192	C₈	—	2	2	no	—
1193	C₈	—	4	1	no	—
1194	C₈	—	4	1	no	—
1195	C₈	—	4	1	no	—
1196	C₈	—	4	1	no	—
1197	C₈	—	4	1	no	—
1198	C₈	—	4	1	no	—
1199	C₈	—	4	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	8	1	no	—
1214	C₂²	—	8	1	no	—
1215	C₂²	—	8	1	no	—
1216	C₂²	—	8	1	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	16	8	no	—
1222	C₂²	C₂×#525	1	1	yes	characteristic
1223	C₂²	D₄×#41	1	1	yes	characteristic
1224	C₂²	#3488	1	1	yes	characteristic
1225	C₂²	C₂×#577	1	1	yes	characteristic
1226	C₂²	#3585	1	1	yes	characteristic
1227	C₂²	#3586	1	1	yes	characteristic
1228	C₂²	#3586	1	1	yes	characteristic
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	2	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	2	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	2	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	8	1	no	—
1249	C₄	—	8	1	no	—
1250	C₄	—	8	1	no	—
1251	C₄	—	8	1	no	—
1252	C₄	—	8	1	no	—
1253	C₄	—	8	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	#3475	1	1	yes	characteristic
1257	C₄	#3481	1	1	yes	characteristic
1258	C₄	#3514	1	1	yes	characteristic
1259	C₄	#3521	1	1	yes	characteristic
1260	C₂	—	4	2	no	—
1261	C₂	—	8	2	no	—
1262	C₂	—	16	1	no	—
1263	C₂	#36226	1	1	yes	characteristic
1264	C₂	#60567	1	1	yes	characteristic
1265	C₂	#60582	1	1	yes	characteristic
1266	C₂	#61509	1	1	yes	characteristic
1267	C₂	#61557	1	1	yes	characteristic
1268	C₂	#62033	1	1	yes	characteristic
1269	C₂	#62091	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2283 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #34231	C₂	semidirect
3. #33101	C₂	semidirect
4. #33087	C₂	semidirect
5. #33035	C₂	semidirect
6. #29571	C₂	semidirect
7. #29548	C₂	semidirect
8. #29442	C₂	semidirect
9. #29383	C₂	semidirect
10. #27147	C₂	semidirect
11. #27066	C₂	semidirect
12. #27002	C₂	semidirect
13. #26919	C₂	semidirect
14. #26710	C₂	semidirect
15. #26693	C₂	semidirect
16. #26604	C₂	semidirect
17. #26591	C₂	semidirect
18. #26429	C₂	semidirect
19. #26355	C₂	semidirect
20. #25504	C₂	semidirect
24. #23139	C₂	semidirect
25. #23036	C₂	semidirect
28. #22596	C₂	semidirect
29. #21512	C₂	semidirect
30. #21128	C₂	semidirect
33. C₂×#477	C₂²	semidirect
42. C₂×C₄×Q₁₆	C₂²	semidirect
63. #2369	C₂²	semidirect
64. #2369	C₂²	semidirect
65. #2365	C₂²	semidirect
66. #2365	C₂²	semidirect
80. #2320	C₂²	semidirect
81. #2320	C₂²	semidirect
87. #2276	C₂²	semidirect
88. #2276	C₂²	semidirect
90. #2100	C₂²	semidirect
91. #2096	C₂²	semidirect
92. #2088	C₂²	semidirect
93. #2088	C₂²	semidirect
94. #2066	C₂²	semidirect
95. #2066	C₂²	semidirect
98. #2058	C₂²	semidirect
99. #2058	C₂²	semidirect
102. #2043	C₂²	semidirect
105. #2024	C₂²	semidirect
106. #2024	C₂²	semidirect
109. #2016	C₂²	semidirect
114. #1988	C₂²	semidirect
117. #1971	C₂²	semidirect
120. #1947	C₂²	semidirect
121. #1941	C₂²	semidirect
124. #1935	C₂²	semidirect
125. #1933	C₂²	semidirect
126. #1928	C₂²	semidirect
127. #1928	C₂²	semidirect
128. #1928	C₂²	semidirect
129. #1927	C₂²	semidirect
130. #1927	C₂²	semidirect
131. #1927	C₂²	semidirect
144. #1921	C₂²	semidirect
145. #1920	C₂²	semidirect
146. #1919	C₂²	semidirect
147. #1919	C₂²	semidirect
148. #1919	C₂²	semidirect
149. #1918	C₂²	semidirect
150. #1918	C₂²	semidirect
151. #1918	C₂²	semidirect
152. #1917	C₂²	semidirect
153. #1917	C₂²	semidirect
154. #1916	C₂²	semidirect
155. #1916	C₂²	semidirect
166. #1878	C₂²	semidirect
167. #1878	C₂²	semidirect
168. #1878	C₂²	semidirect
169. #1878	C₂²	semidirect
176. #1865	C₂²	semidirect
177. #1865	C₂²	semidirect
178. #1865	C₂²	semidirect
181. #1863	C₂²	semidirect
182. #1863	C₂²	semidirect
183. #1863	C₂²	semidirect
188. #1840	C₂²	semidirect
189. #1832	C₂²	semidirect
191. #1803	C₂²	semidirect
192. #1776	C₂²	semidirect
193. #1768	C₂²	semidirect
194. #1763	C₂²	semidirect
195. C₄×#103	C₂²	semidirect
200. #1746	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#38054	2
#34231	2
#33101	2
#33087	2
#33035	2
#29571	2
#29548	2
#29442	2
#29383	2
#27147	2
#27066	2
#27002	2
#26919	2
#26710	2
#26693	2
#26604	2
#26591	2
#26429	2
#26355	2
#25504	2
#25105	2
#23933	2
#23139	2
#23036	2
#22864	2
#22596	2
#21512	2
#21128	2
#21060	2