Subgroups — #6571935

Order 512.

1524 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#38056	C₂	1	1	yes	maximal, characteristic
2	#34378	C₂	1	1	yes	maximal, characteristic, complemented
3	#30161	C₂	1	1	yes	maximal, characteristic, complemented
4	#30071	C₂	1	1	yes	maximal, characteristic, complemented
5	#29640	C₂	1	1	yes	maximal, characteristic, complemented
6	#29529	C₂	1	1	yes	maximal, characteristic, complemented
7	#29404	C₂	1	1	yes	maximal, characteristic, complemented
8	#29360	C₂	1	1	yes	maximal, characteristic, complemented
9	#29265	C₂	1	1	yes	maximal, characteristic, complemented
10	#27856	C₂	1	1	yes	maximal, characteristic, complemented
11	#27585	C₂	1	1	yes	maximal, characteristic, complemented
12	#27157	C₂	1	1	yes	maximal, characteristic, complemented
13	#27136	C₂	1	1	yes	maximal, characteristic, complemented
14	#27023	C₂	1	1	yes	maximal, characteristic, complemented
15	#27010	C₂	1	1	yes	maximal, characteristic, complemented
16	#26716	C₂	1	1	yes	maximal, characteristic, complemented
17	#26712	C₂	1	1	yes	maximal, characteristic, complemented
18	#26701	C₂	1	1	yes	maximal, characteristic, complemented
19	#26697	C₂	1	1	yes	maximal, characteristic, complemented
20	#26002	C₂	1	1	yes	maximal, characteristic, complemented
21	#25996	C₂	1	1	yes	maximal, characteristic, complemented
22	#24478	C₂	1	1	yes	maximal, characteristic
23	#24476	C₂	1	1	yes	maximal, characteristic
24	#23830	C₂	1	1	yes	maximal, characteristic, complemented
25	#23790	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#2025	C₂	1	1	yes	maximal, characteristic, complemented
27	#22938	C₂	1	1	yes	maximal, characteristic, complemented
28	#22918	C₂	1	1	yes	maximal, characteristic, complemented
29	#22595	C₂	1	1	yes	maximal, characteristic, complemented
30	#22570	C₂	1	1	yes	maximal, characteristic, complemented
31	#22566	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#125	C₂²	1	1	yes	characteristic
33	C₂×#481	C₂²	1	1	yes	characteristic
34	C₂×#480	C₂²	1	1	yes	characteristic
35	C₂²×#102	C₂²	1	1	yes	characteristic
36	C₂²×#102	C₂²	1	1	yes	characteristic
37	#2854	C₂²	1	1	yes	characteristic
38	#2756	—	2	1	no	—
39	#2753	—	2	1	no	—
40	#2749	—	2	1	no	—
41	#2706	—	2	1	no	—
42	#2644	C₂²	1	1	yes	characteristic
43	#2641	C₂²	1	1	yes	characteristic
44	#2534	—	2	1	no	—
45	#2513	C₂²	1	1	yes	characteristic
46	#2454	C₂²	1	1	yes	characteristic
47	#2445	C₂²	1	1	yes	characteristic
48	#2445	C₂²	1	1	yes	characteristic
49	#2442	C₂²	1	1	yes	characteristic
50	#2433	C₂²	1	1	yes	characteristic
51	#2418	—	2	1	no	—
52	#2412	—	2	1	no	—
53	#2412	—	2	1	no	—
54	#2382	—	2	1	no	—
55	#2382	—	2	1	no	—
56	#2370	C₂²	1	1	yes	characteristic, complemented
57	#2370	C₂²	1	1	yes	characteristic, complemented
58	#2370	C₂²	1	1	yes	characteristic, complemented
59	#2370	C₂²	1	1	yes	characteristic, complemented
60	#2361	C₂²	1	1	yes	characteristic
61	#2345	C₂²	1	1	yes	characteristic
62	#2345	C₂²	1	1	yes	characteristic
63	#2344	—	2	1	no	—
64	#2344	—	2	1	no	—
65	#2344	C₂²	1	1	yes	characteristic
66	#2344	C₂²	1	1	yes	characteristic
67	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	#2336	—	2	1	no	—
69	#2336	—	2	1	no	—
70	#2330	C₂²	1	1	yes	characteristic, complemented
71	#2330	C₂²	1	1	yes	characteristic, complemented
72	#2330	C₂²	1	1	yes	characteristic, complemented
73	#2330	C₂²	1	1	yes	characteristic, complemented
74	#2328	C₂²	1	1	yes	characteristic
75	#2319	C₂²	1	1	yes	characteristic
76	#2316	—	2	1	no	—
77	#2313	—	2	1	no	—
78	C₂×#390	C₂²	1	1	yes	characteristic
79	#2285	C₂²	1	1	yes	characteristic
80	#2283	C₂²	1	1	yes	characteristic
81	#2101	C₂²	1	1	yes	characteristic, complemented
82	#2101	C₂²	1	1	yes	characteristic, complemented
83	#2099	C₂²	1	1	yes	characteristic, complemented
84	#2094	C₂²	1	1	yes	characteristic
85	#2094	C₂²	1	1	yes	characteristic
86	#2093	C₂²	1	1	yes	characteristic, complemented
87	#2088	C₂²	1	1	yes	characteristic, complemented
88	#2088	C₂²	1	1	yes	characteristic, complemented
89	#2087	C₂²	1	1	yes	characteristic, complemented
90	#2086	C₂²	1	1	yes	characteristic, complemented
91	#2083	C₂²	1	1	yes	characteristic, complemented
92	#2071	C₂²	1	1	yes	characteristic
93	#2071	C₂²	1	1	yes	characteristic
94	#2071	C₂²	1	1	yes	characteristic, complemented
95	#2067	C₂²	1	1	yes	characteristic
96	#2067	C₂²	1	1	yes	characteristic
97	#2065	C₂²	1	1	yes	characteristic
98	#2065	C₂²	1	1	yes	characteristic
99	#2059	C₂²	1	1	yes	characteristic, complemented
100	#2059	C₂²	1	1	yes	characteristic, complemented
101	#2059	C₂²	1	1	yes	characteristic, complemented
102	#2059	C₂²	1	1	yes	characteristic, complemented
103	#2059	C₂²	1	1	yes	characteristic, complemented
104	#2059	C₂²	1	1	yes	characteristic, complemented
105	#2041	C₂²	1	1	yes	characteristic
106	#2041	C₂²	1	1	yes	characteristic
107	#2041	C₂²	1	1	yes	characteristic
108	#2041	C₂²	1	1	yes	characteristic
109	#2025	C₂²	1	1	yes	characteristic
110	#2025	C₂²	1	1	yes	characteristic
111	#2025	C₂²	1	1	yes	characteristic
112	#2025	C₂²	1	1	yes	characteristic
113	#2025	C₂²	1	1	yes	characteristic
114	#2025	C₂²	1	1	yes	characteristic
115	#2025	C₂²	1	1	yes	characteristic
116	#2025	C₂²	1	1	yes	characteristic
117	#2025	C₂²	1	1	yes	characteristic, complemented
118	#2025	C₂²	1	1	yes	characteristic, complemented
119	#2025	C₂²	1	1	yes	characteristic, complemented
120	#2025	C₂²	1	1	yes	characteristic, complemented
121	#1989	C₂²	1	1	yes	characteristic, complemented
122	#1989	C₂²	1	1	yes	characteristic, complemented
123	#1982	C₂²	1	1	yes	characteristic
124	#1982	C₂²	1	1	yes	characteristic
125	#1982	C₂²	1	1	yes	characteristic
126	#1982	C₂²	1	1	yes	characteristic
127	#1949	C₂²	1	1	yes	characteristic, complemented
128	#1949	C₂²	1	1	yes	characteristic, complemented
129	#1943	C₂²	1	1	yes	characteristic, complemented
130	#1941	C₂²	1	1	yes	characteristic, complemented
131	#1936	C₂²	1	1	yes	characteristic
132	#1936	C₂²	1	1	yes	characteristic
133	#1936	C₂²	1	1	yes	characteristic, complemented
134	#1934	C₂²	1	1	yes	characteristic
135	#1934	C₂²	1	1	yes	characteristic
136	#1934	C₂²	1	1	yes	characteristic, complemented
137	#1926	C₂²	1	1	yes	characteristic
138	#1926	C₂²	1	1	yes	characteristic
139	#1926	C₂²	1	1	yes	characteristic
140	#1926	C₂²	1	1	yes	characteristic
141	#1926	C₂²	1	1	yes	characteristic
142	#1926	C₂²	1	1	yes	characteristic
143	#1926	C₂²	1	1	yes	characteristic, complemented
144	#1926	C₂²	1	1	yes	characteristic, complemented
145	#1925	C₂²	1	1	yes	characteristic
146	#1925	C₂²	1	1	yes	characteristic
147	#1925	C₂²	1	1	yes	characteristic
148	#1925	C₂²	1	1	yes	characteristic
149	#1925	C₂²	1	1	yes	characteristic
150	#1925	C₂²	1	1	yes	characteristic
151	#1925	C₂²	1	1	yes	characteristic, complemented
152	#1925	C₂²	1	1	yes	characteristic, complemented
153	#1921	C₂²	1	1	yes	characteristic, complemented
154	#1921	C₂²	1	1	yes	characteristic, complemented
155	#1921	C₂²	1	1	yes	characteristic, complemented
156	#1920	C₂²	1	1	yes	characteristic, complemented
157	#1920	C₂²	1	1	yes	characteristic, complemented
158	#1919	C₂²	1	1	yes	characteristic, complemented
159	#1919	C₂²	1	1	yes	characteristic, complemented
160	#1918	C₂²	1	1	yes	characteristic, complemented
161	#1918	C₂²	1	1	yes	characteristic, complemented
162	#1918	C₂²	1	1	yes	characteristic, complemented
163	#1917	C₂²	1	1	yes	characteristic, complemented
164	#1917	C₂²	1	1	yes	characteristic, complemented
165	#1916	C₂²	1	1	yes	characteristic, complemented
166	#1916	C₂²	1	1	yes	characteristic, complemented
167	#1893	C₂²	1	1	yes	characteristic
168	#1893	C₂²	1	1	yes	characteristic
169	#1864	C₂²	1	1	yes	characteristic, complemented
170	#1864	C₂²	1	1	yes	characteristic, complemented
171	#1862	C₂²	1	1	yes	characteristic
172	#1862	C₂²	1	1	yes	characteristic
173	#1862	C₂²	1	1	yes	characteristic
174	#1862	C₂²	1	1	yes	characteristic
175	#1853	C₂²	1	1	yes	characteristic
176	#1853	C₂²	1	1	yes	characteristic
177	#1850	C₂²	1	1	yes	characteristic
178	#1850	C₂²	1	1	yes	characteristic
179	#1840	C₂²	1	1	yes	characteristic, complemented
180	#1832	C₂²	1	1	yes	characteristic, complemented
181	#1824	C₂²	1	1	yes	characteristic
182	#1823	C₂²	1	1	yes	characteristic
183	#1817	C₂²	1	1	yes	characteristic
184	#1808	C₂²	1	1	yes	characteristic
185	#1808	C₂²	1	1	yes	characteristic
186	#1786	C₂²	1	1	yes	characteristic
187	#1786	C₂²	1	1	yes	characteristic
188	#1776	C₂²	1	1	yes	characteristic, complemented
189	C₄×#106	C₂²	1	1	yes	characteristic, complemented
190	#1768	C₂²	1	1	yes	characteristic, complemented
191	#1762	C₂²	1	1	yes	characteristic
192	#1762	C₂²	1	1	yes	characteristic
193	#1762	C₂²	1	1	yes	characteristic, complemented
194	C₄×#102	C₂²	1	1	yes	characteristic
195	C₄×#102	C₂²	1	1	yes	characteristic
196	C₄×#102	C₂²	1	1	yes	characteristic, complemented
197	#1752	C₂²	1	1	yes	characteristic
198	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
199	#1746	C₂²	1	1	yes	characteristic, complemented
200	C₂×#340	C₂²	1	1	yes	characteristic
201	C₂×#340	C₂²	1	1	yes	characteristic
202	C₂×#336	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂³×C₈	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂×#127	C₂³	1	1	yes	characteristic
207	C₂×#127	C₂³	1	1	yes	characteristic
208	C₂×#125	—	2	4	no	—
209	C₂×#125	—	2	4	no	—
210	C₂×#125	—	2	1	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#125	C₂³	1	1	yes	characteristic
214	C₂×#125	C₂³	1	1	yes	characteristic
215	C₂×#125	C₂³	1	1	yes	characteristic
216	C₂×#125	C₂³	1	1	yes	characteristic
217	C₂×#123	—	2	1	no	—
218	C₂×#123	—	2	1	no	—
219	C₂×#123	—	2	1	no	—
220	C₂×#121	C₂³	1	1	yes	characteristic
221	C₂×#120	—	2	1	no	—
222	C₂×#120	—	2	1	no	—
223	C₂×C₄×D₄	—	2	1	no	—
224	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₂×#117	—	2	1	no	—
228	C₂×#117	—	2	1	no	—
229	C₂×#117	—	2	1	no	—
230	C₂²×C₄⋊C₄	—	2	1	no	—
231	C₂²×C₄⋊C₄	—	2	1	no	—
232	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₂²⋊C₄	—	2	1	no	—
237	C₂²×C₂²⋊C₄	—	2	1	no	—
238	C₂²×C₄²	C₂³	1	1	yes	characteristic
239	#481	—	2	4	no	—
240	#480	—	2	4	no	—
241	C₂×#107	C₂³	1	1	yes	characteristic
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#107	C₂³	1	1	yes	characteristic
244	C₂×#107	C₂³	1	1	yes	characteristic
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×#106	C₂³	1	1	yes	characteristic
249	C₂×#106	C₂³	1	1	yes	characteristic
250	C₂×#106	C₂³	1	1	yes	characteristic
251	C₂×#106	C₂³	1	1	yes	characteristic
252	C₂×#106	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₂×#102	—	2	4	no	—
258	C₂×#102	—	2	4	no	—
259	C₂×#102	C₂³	1	1	yes	characteristic
260	C₂×#102	C₂³	1	1	yes	characteristic
261	C₂×#102	C₂³	1	1	yes	characteristic
262	C₂×#102	C₂³	1	1	yes	characteristic
263	C₂×#102	C₂³	1	1	yes	characteristic
264	C₂×#102	C₂³	1	1	yes	characteristic
265	C₂×#102	C₂³	1	1	yes	characteristic
266	C₂×#102	C₂³	1	1	yes	characteristic
267	C₂×#102	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×#97	C₂³	1	1	yes	characteristic
286	C₂×#97	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
289	#400	—	2	1	no	—
290	#399	—	2	1	no	—
291	#398	—	2	1	no	—
292	#397	—	2	1	no	—
293	#397	—	2	1	no	—
294	#397	—	2	1	no	—
295	#397	—	2	1	no	—
296	#397	—	2	1	no	—
297	#396	—	2	1	no	—
298	#396	—	2	1	no	—
299	#394	—	2	1	no	—
300	#394	—	2	1	no	—
301	#394	—	2	1	no	—
302	#394	—	2	1	no	—
303	#394	—	2	1	no	—
304	#394	—	2	1	no	—
305	#394	—	2	1	no	—
306	#394	—	2	1	no	—
307	#392	—	2	1	no	—
308	#392	—	2	1	no	—
309	#390	—	2	1	no	—
310	#390	—	2	1	no	—
311	#390	C₂³	1	1	yes	characteristic
312	#390	C₂³	1	1	yes	characteristic
313	#390	C₂³	1	1	yes	characteristic
314	#390	C₂³	1	1	yes	characteristic
315	#390	C₂³	1	1	yes	characteristic
316	#390	C₂³	1	1	yes	characteristic
317	#390	C₂³	1	1	yes	characteristic
318	#390	C₂³	1	1	yes	characteristic
319	#390	C₂³	1	1	yes	characteristic
320	#390	C₂³	1	1	yes	characteristic
321	#390	C₂³	1	1	yes	characteristic
322	#389	—	2	1	no	—
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
335	#389	C₂³	1	1	yes	characteristic
336	#389	C₂³	1	1	yes	characteristic
337	#389	C₂³	1	1	yes	characteristic
338	#389	C₂³	1	1	yes	characteristic
339	#389	C₂³	1	1	yes	characteristic
340	#389	C₂³	1	1	yes	characteristic
341	#389	C₂³	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	#389	C₂³	1	1	yes	characteristic
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	#387	—	2	1	no	—
355	#387	—	2	1	no	—
356	#387	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	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	#386	—	2	1	no	—
379	#386	—	2	1	no	—
380	#386	—	2	1	no	—
381	#386	—	2	1	no	—
382	#386	—	2	1	no	—
383	#386	—	2	1	no	—
384	#386	—	2	1	no	—
385	#386	—	2	1	no	—
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#385	—	2	1	no	—
389	#385	—	2	1	no	—
390	#385	—	2	1	no	—
391	#384	C₂³	1	1	yes	characteristic
392	#384	C₂³	1	1	yes	characteristic
393	#383	D₄	1	1	yes	characteristic
394	#383	D₄	1	1	yes	characteristic
395	#382	—	2	1	no	—
396	#382	D₄	1	1	yes	characteristic
397	#382	D₄	1	1	yes	characteristic
398	#382	C₂³	1	1	yes	characteristic
399	#381	—	2	1	no	—
400	#381	—	2	1	no	—
401	#381	—	2	1	no	—
402	#381	D₄	1	1	yes	characteristic
403	#381	D₄	1	1	yes	characteristic
404	#380	—	2	1	no	—
405	#380	—	2	1	no	—
406	#380	—	2	1	no	—
407	#380	—	2	1	no	—
408	#380	—	2	1	no	—
409	#380	—	2	1	no	—
410	#380	D₄	1	1	yes	characteristic
411	#380	D₄	1	1	yes	characteristic
412	#380	C₂³	1	1	yes	characteristic
413	#380	C₂³	1	1	yes	characteristic
414	#380	C₂³	1	1	yes	characteristic
415	#379	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	—	2	1	no	—
418	C₄×C₄⋊C₄	—	2	1	no	—
419	C₄×C₄⋊C₄	—	2	1	no	—
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
438	#376	C₂³	1	1	yes	characteristic
439	#376	C₂³	1	1	yes	characteristic
440	#340	C₂³	1	1	yes	characteristic
441	#340	C₂³	1	1	yes	characteristic
442	#340	C₂³	1	1	yes	characteristic
443	#340	C₂³	1	1	yes	characteristic
444	#340	C₂³	1	1	yes	characteristic
445	#340	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
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	#336	C₂³	1	1	yes	characteristic
469	#336	C₂³	1	1	yes	characteristic
470	#336	C₂³	1	1	yes	characteristic
471	#336	C₂³	1	1	yes	characteristic
472	#336	C₂³	1	1	yes	characteristic
473	#336	C₂³	1	1	yes	characteristic
474	#336	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#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	C₂⁵	—	2	1	no	—
485	C₂²×D₄	—	2	2	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	4	1	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	C₂⁴	1	1	yes	characteristic
498	C₂²×D₄	C₂⁴	1	1	yes	characteristic
499	C₂²×D₄	C₂⁴	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	2	2	no	—
511	C₂²×C₈	—	4	1	no	—
512	C₂²×C₈	—	4	1	no	—
513	C₂²×C₈	—	4	1	no	—
514	C₂²×C₈	—	4	1	no	—
515	C₂²×C₈	C₂⁴	1	1	yes	characteristic
516	C₂²×C₈	C₂⁴	1	1	yes	characteristic
517	C₂²×C₈	C₂⁴	1	1	yes	characteristic
518	C₂²×C₈	C₂⁴	1	1	yes	characteristic
519	C₂²×C₈	C₂⁴	1	1	yes	characteristic
520	C₂²×C₈	C₂⁴	1	1	yes	characteristic
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	#127	—	2	2	no	—
524	#127	—	4	1	no	—
525	#127	—	4	1	no	—
526	#127	—	4	1	no	—
527	#125	—	2	8	no	—
528	#125	—	2	8	no	—
529	#125	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	2	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	4	1	no	—
538	#125	—	4	1	no	—
539	#123	—	8	2	no	—
540	#123	—	8	2	no	—
541	#123	—	8	2	no	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#120	—	8	2	no	—
545	#120	—	8	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	4	1	no	—
548	C₄×D₄	—	4	1	no	—
549	C₄×D₄	—	4	1	no	—
550	C₄×D₄	—	4	1	no	—
551	C₄×D₄	—	4	1	no	—
552	C₄×D₄	—	8	2	no	—
553	#117	—	8	2	no	—
554	#117	—	8	2	no	—
555	#117	—	8	2	no	—
556	C₂×C₄⋊C₄	—	2	8	no	—
557	C₂×C₄⋊C₄	—	2	8	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	2	no	—
569	C₂×C₄⋊C₄	—	2	2	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
591	C₂×C₄⋊C₄	—	4	1	no	—
592	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	#41	1	4	yes	—
597	C₂×C₄⋊C₄	#41	1	4	yes	—
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	8	2	no	—
641	C₂×C₂²⋊C₄	—	8	2	no	—
642	C₂×C₂²⋊C₄	—	8	2	no	—
643	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂×C₄²	—	2	2	no	—
648	C₂×C₄²	—	2	2	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	1	yes	characteristic
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	C₂×C₄²	C₂⁴	1	1	yes	characteristic
668	#107	—	2	2	no	—
669	#107	—	2	2	no	—
670	#107	—	4	1	no	—
671	#107	—	4	1	no	—
672	#107	—	4	1	no	—
673	#107	—	4	1	no	—
674	#106	—	2	2	no	—
675	#106	—	2	2	no	—
676	#106	—	4	1	no	—
677	#106	—	4	1	no	—
678	#106	—	4	1	no	—
679	#106	—	4	1	no	—
680	C₄⋊C₈	—	4	1	no	—
681	C₄⋊C₈	—	4	1	no	—
682	C₄⋊C₈	—	4	1	no	—
683	C₄⋊C₈	—	4	1	no	—
684	#102	—	2	2	no	—
685	#102	—	2	2	no	—
686	#102	—	2	2	no	—
687	#102	—	2	2	no	—
688	#102	—	2	2	no	—
689	#102	—	2	2	no	—
690	#102	—	2	2	no	—
691	#102	—	2	2	no	—
692	#102	—	2	2	no	—
693	#102	—	2	2	no	—
694	#102	—	2	2	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	4	1	no	—
699	#102	—	4	1	no	—
700	#102	—	4	1	no	—
701	#102	—	4	1	no	—
702	#102	—	4	1	no	—
703	#102	—	4	1	no	—
704	#102	—	4	1	no	—
705	#102	—	4	1	no	—
706	#102	—	4	1	no	—
707	#102	—	4	1	no	—
708	C₂²⋊C₈	—	2	2	no	—
709	C₂²⋊C₈	—	2	2	no	—
710	#97	—	4	1	no	—
711	#97	—	4	1	no	—
712	C₄×C₈	—	4	1	no	—
713	C₄×C₈	—	4	1	no	—
714	#95	—	2	1	no	—
715	#95	—	2	1	no	—
716	#95	—	2	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	C₂×D₄	1	1	yes	characteristic
744	#95	C₂×D₄	1	1	yes	characteristic
745	#95	C₂×D₄	1	1	yes	characteristic
746	#95	C₂×D₄	1	1	yes	characteristic
747	#95	C₂×D₄	1	1	yes	characteristic
748	#95	C₂×D₄	1	1	yes	characteristic
749	#95	C₂×D₄	1	1	yes	characteristic
750	#95	C₂×D₄	1	1	yes	characteristic
751	#95	C₂×D₄	1	1	yes	characteristic
752	#95	C₂×D₄	1	1	yes	characteristic
753	#95	C₂×D₄	1	1	yes	characteristic
754	#95	C₂×D₄	1	1	yes	characteristic
755	#95	C₂×D₄	1	1	yes	characteristic
756	#95	C₂×D₄	1	1	yes	characteristic
757	#95	C₂×D₄	1	1	yes	characteristic
758	#95	C₂×D₄	1	1	yes	characteristic
759	C₂⁴	—	2	1	no	—
760	C₂⁴	—	2	1	no	—
761	C₂⁴	—	2	1	no	—
762	C₂⁴	—	4	2	no	—
763	C₂⁴	—	4	2	no	—
764	C₂⁴	—	4	2	no	—
765	C₂⁴	—	4	2	no	—
766	C₂⁴	—	8	1	no	—
767	C₂⁴	—	8	1	no	—
768	C₂⁴	—	8	1	no	—
769	C₂⁴	C₂²×D₄	1	1	yes	characteristic
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	1	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	4	4	no	—
788	C₂×D₄	—	4	4	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	8	2	no	—
797	C₂×D₄	—	8	2	no	—
798	C₂×D₄	—	8	1	no	—
799	C₂×D₄	—	8	1	no	—
800	C₂×D₄	—	8	1	no	—
801	C₂×D₄	—	8	1	no	—
802	C₂×D₄	—	8	1	no	—
803	C₂×D₄	—	8	1	no	—
804	C₂×D₄	—	8	1	no	—
805	C₂×D₄	—	8	1	no	—
806	C₂×D₄	—	8	1	no	—
807	C₂×D₄	—	8	1	no	—
808	C₂×D₄	—	8	1	no	—
809	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
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	—	4	1	no	—
834	C₂²×C₄	—	4	1	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
841	C₂²×C₄	—	8	1	no	—
842	C₂²×C₄	—	8	1	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	—	8	1	no	—
845	C₂²×C₄	—	8	1	no	—
846	C₂²×C₄	—	8	1	no	—
847	C₂²×C₄	—	8	1	no	—
848	C₂²×C₄	—	8	1	no	—
849	C₂²×C₄	—	8	1	no	—
850	C₂²×C₄	—	8	1	no	—
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂×#41	1	2	yes	—
865	C₂²×C₄	C₂×#41	1	2	yes	—
866	C₂²×C₄	C₂⁵	1	1	yes	characteristic
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	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	—	8	2	no	—
892	C₂×C₈	—	8	2	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	4	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	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	—	4	1	no	—
926	C₄⋊C₄	—	4	1	no	—
927	C₄⋊C₄	—	4	1	no	—
928	C₄⋊C₄	—	4	1	no	—
929	C₄⋊C₄	—	8	1	no	—
930	C₄⋊C₄	—	8	1	no	—
931	C₄⋊C₄	—	8	1	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	—	8	1	no	—
945	C₄⋊C₄	—	8	1	no	—
946	C₄⋊C₄	—	8	1	no	—
947	C₄⋊C₄	—	8	1	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	C₂×#41	1	2	yes	—
950	C₄⋊C₄	C₂×#41	1	2	yes	—
951	C₄⋊C₄	C₂×#41	1	2	yes	—
952	C₄⋊C₄	C₂×#41	1	2	yes	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	8	1	no	—
966	C₂²⋊C₄	—	8	1	no	—
967	C₂²⋊C₄	—	8	1	no	—
968	C₂²⋊C₄	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₂²⋊C₄	—	8	1	no	—
978	C₂²⋊C₄	—	8	1	no	—
979	C₂²⋊C₄	—	8	1	no	—
980	C₂²⋊C₄	—	8	1	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	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	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	—	8	1	no	—
1001	C₄²	—	8	1	no	—
1002	C₄²	—	8	1	no	—
1003	C₄²	—	8	1	no	—
1004	C₄²	—	8	1	no	—
1005	C₄²	—	8	1	no	—
1006	C₄²	—	8	1	no	—
1007	C₄²	—	8	1	no	—
1008	C₄²	—	8	1	no	—
1009	C₄²	—	8	1	no	—
1010	C₄²	—	8	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	1	no	—
1030	C₂³	—	4	1	no	—
1031	C₂³	—	4	1	no	—
1032	C₂³	—	4	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	8	4	no	—
1037	C₂³	—	8	4	no	—
1038	C₂³	—	8	4	no	—
1039	C₂³	—	8	4	no	—
1040	C₂³	—	16	2	no	—
1041	C₂³	—	16	2	no	—
1042	C₂³	—	16	2	no	—
1043	C₂³	#525	1	2	yes	—
1044	C₂³	#576	1	2	yes	—
1045	C₂³	#577	1	2	yes	—
1046	C₂³	C₂³×D₄	1	1	yes	characteristic
1047	D₄	—	2	2	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	4	1	no	—
1050	D₄	—	4	1	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	4	1	no	—
1053	D₄	—	4	1	no	—
1054	D₄	—	4	1	no	—
1055	D₄	—	4	1	no	—
1056	D₄	—	4	1	no	—
1057	D₄	—	4	1	no	—
1058	D₄	—	4	1	no	—
1059	D₄	—	8	4	no	—
1060	D₄	—	8	4	no	—
1061	D₄	—	16	2	no	—
1062	D₄	—	16	2	no	—
1063	D₄	—	16	2	no	—
1064	D₄	—	16	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	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	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	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	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	—	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	—	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	4	no	—
1116	C₂×C₄	—	4	8	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	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	4	no	—
1150	C₂×C₄	—	16	2	no	—
1151	C₂×C₄	—	16	2	no	—
1152	C₂×C₄	—	16	2	no	—
1153	C₂×C₄	—	16	2	no	—
1154	C₂×C₄	#525	1	2	yes	—
1155	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1156	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1157	C₂×C₄	C₂×2₋¹⁺⁴	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	—	4	1	no	—
1162	C₈	—	4	1	no	—
1163	C₈	—	4	1	no	—
1164	C₈	—	4	1	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	—	2	2	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	8	1	no	—
1179	C₂²	—	8	1	no	—
1180	C₂²	—	8	1	no	—
1181	C₂²	—	8	1	no	—
1182	C₂²	—	8	1	no	—
1183	C₂²	—	8	1	no	—
1184	C₂²	—	8	1	no	—
1185	C₂²	—	8	1	no	—
1186	C₂²	—	8	1	no	—
1187	C₂²	—	8	1	no	—
1188	C₂²	—	8	1	no	—
1189	C₂²	—	8	1	no	—
1190	C₂²	—	8	1	no	—
1191	C₂²	—	8	1	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	8	1	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	1	no	—
1196	C₂²	—	16	8	no	—
1197	C₂²	#3119	1	4	yes	—
1198	C₂²	C₂×#525	1	1	yes	characteristic
1199	C₂²	#3489	1	1	yes	characteristic
1200	C₂²	#3500	1	1	yes	characteristic
1201	C₂²	C₂×#576	1	1	yes	characteristic
1202	C₂²	C₂×#577	1	1	yes	characteristic
1203	C₂²	#3584	1	1	yes	characteristic
1204	C₂²	#3585	1	1	yes	characteristic
1205	C₄	—	2	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	8	1	no	—
1223	C₄	—	8	1	no	—
1224	C₄	—	8	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	—	8	1	no	—
1228	C₄	—	8	1	no	—
1229	C₄	—	8	1	no	—
1230	C₄	—	8	1	no	—
1231	C₄	#3495	1	1	yes	characteristic
1232	C₄	#3495	1	1	yes	characteristic
1233	C₄	#3510	1	1	yes	characteristic
1234	C₄	#3510	1	1	yes	characteristic
1235	C₂	—	2	4	no	—
1236	C₂	—	8	2	no	—
1237	C₂	—	16	1	no	—
1238	C₂	—	16	1	no	—
1239	C₂	#36079	1	1	yes	characteristic
1240	C₂	C₂×#3119	1	1	yes	characteristic
1241	C₂	#60580	1	1	yes	characteristic
1242	C₂	#62163	1	1	yes	characteristic
1243	C₂	#62212	1	1	yes	characteristic
1244	C₂	#62558	1	1	yes	characteristic
1245	C₂	#62596	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2433	C₂²
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. #34378	C₂	semidirect
3. #30161	C₂	semidirect
4. #30071	C₂	semidirect
5. #29640	C₂	semidirect
6. #29529	C₂	semidirect
7. #29404	C₂	semidirect
8. #29360	C₂	semidirect
9. #29265	C₂	semidirect
10. #27856	C₂	semidirect
11. #27585	C₂	semidirect
12. #27157	C₂	semidirect
13. #27136	C₂	semidirect
14. #27023	C₂	semidirect
15. #27010	C₂	semidirect
16. #26716	C₂	semidirect
17. #26712	C₂	semidirect
18. #26701	C₂	semidirect
19. #26697	C₂	semidirect
20. #26002	C₂	semidirect
21. #25996	C₂	semidirect
24. #23830	C₂	semidirect
25. #23790	C₂	semidirect
26. C₂×#2025	C₂	semidirect
27. #22938	C₂	semidirect
28. #22918	C₂	semidirect
29. #22595	C₂	semidirect
30. #22570	C₂	semidirect
31. #22566	C₂	semidirect
56. #2370	C₂²	semidirect
57. #2370	C₂²	semidirect
58. #2370	C₂²	semidirect
59. #2370	C₂²	semidirect
70. #2330	C₂²	semidirect
71. #2330	C₂²	semidirect
72. #2330	C₂²	semidirect
73. #2330	C₂²	semidirect
81. #2101	C₂²	semidirect
82. #2101	C₂²	semidirect
83. #2099	C₂²	semidirect
86. #2093	C₂²	semidirect
87. #2088	C₂²	semidirect
88. #2088	C₂²	semidirect
89. #2087	C₂²	semidirect
90. #2086	C₂²	semidirect
91. #2083	C₂²	semidirect
94. #2071	C₂²	semidirect
99. #2059	C₂²	semidirect
100. #2059	C₂²	semidirect
101. #2059	C₂²	semidirect
102. #2059	C₂²	semidirect
103. #2059	C₂²	semidirect
104. #2059	C₂²	semidirect
117. #2025	C₂²	semidirect
118. #2025	C₂²	semidirect
119. #2025	C₂²	semidirect
120. #2025	C₂²	semidirect
121. #1989	C₂²	semidirect
122. #1989	C₂²	semidirect
127. #1949	C₂²	semidirect
128. #1949	C₂²	semidirect
129. #1943	C₂²	semidirect
130. #1941	C₂²	semidirect
133. #1936	C₂²	semidirect
136. #1934	C₂²	semidirect
143. #1926	C₂²	semidirect
144. #1926	C₂²	semidirect
151. #1925	C₂²	semidirect
152. #1925	C₂²	semidirect
153. #1921	C₂²	semidirect
154. #1921	C₂²	semidirect
155. #1921	C₂²	semidirect
156. #1920	C₂²	semidirect
157. #1920	C₂²	semidirect
158. #1919	C₂²	semidirect
159. #1919	C₂²	semidirect
160. #1918	C₂²	semidirect
161. #1918	C₂²	semidirect
162. #1918	C₂²	semidirect
163. #1917	C₂²	semidirect
164. #1917	C₂²	semidirect
165. #1916	C₂²	semidirect
166. #1916	C₂²	semidirect
169. #1864	C₂²	semidirect
170. #1864	C₂²	semidirect
179. #1840	C₂²	semidirect
180. #1832	C₂²	semidirect
188. #1776	C₂²	semidirect
189. C₄×#106	C₂²	semidirect
190. #1768	C₂²	semidirect
193. #1762	C₂²	semidirect
196. C₄×#102	C₂²	semidirect
199. #1746	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#38056	2
#34378	2
#30161	2
#30071	2
#29640	2
#29529	2
#29404	2
#29360	2
#29265	2
#27856	2
#27585	2
#27157	2
#27136	2
#27023	2
#27010	2
#26716	2
#26712	2
#26701	2
#26697	2
#26002	2
#25996	2
#24478	2
#24476	2
#23830	2
#23790	2
C₂×#2025	2
#22938	2
#22918	2
#22595	2
#22570	2
#22566	2