Subgroups — #7086888

Order 512.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59712	C₂	1	1	yes	maximal, characteristic, complemented
2	#40176	C₂	1	1	yes	maximal, characteristic
3	#32226	C₂	1	1	yes	maximal, characteristic, complemented
4	#32191	C₂	1	1	yes	maximal, characteristic, complemented
5	#32165	C₂	1	1	yes	maximal, characteristic, complemented
6	#32118	C₂	1	1	yes	maximal, characteristic, complemented
7	#31810	C₂	1	1	yes	maximal, characteristic, complemented
8	#31081	C₂	1	1	yes	maximal, characteristic, complemented
9	#30543	C₂	1	1	yes	maximal, characteristic, complemented
10	#30527	C₂	1	1	yes	maximal, characteristic
11	#29557	C₂	1	1	yes	maximal, characteristic, complemented
12	#29352	C₂	1	1	yes	maximal, characteristic, complemented
13	#29052	C₂	1	1	yes	maximal, characteristic, complemented
14	#28977	C₂	1	1	yes	maximal, characteristic, complemented
15	#28025	C₂	1	1	yes	maximal, characteristic, complemented
16	#27783	C₂	1	1	yes	maximal, characteristic, complemented
17	#27541	C₂	1	1	yes	maximal, characteristic, complemented
18	#27348	C₂	1	1	yes	maximal, characteristic, complemented
19	#27254	C₂	1	1	yes	maximal, characteristic
20	#27018	C₂	1	1	yes	maximal, characteristic, complemented
21	#26915	C₂	1	1	yes	maximal, characteristic, complemented
22	#26832	C₂	1	1	yes	maximal, characteristic, complemented
23	#26709	C₂	1	1	yes	maximal, characteristic, complemented
24	#26645	C₂	1	1	yes	maximal, characteristic, complemented
25	#25277	C₂	1	1	yes	maximal, characteristic, complemented
26	#24479	C₂	1	1	yes	maximal, characteristic, complemented
27	#23684	C₂	1	1	yes	maximal, characteristic, complemented
28	#23282	C₂	1	1	yes	maximal, characteristic, complemented
29	#23230	C₂	1	1	yes	maximal, characteristic, complemented
30	#22854	C₂	1	1	yes	maximal, characteristic, complemented
31	#22220	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#489	C₂²	1	1	yes	characteristic
33	C₂×#486	C₂²	1	1	yes	characteristic
34	C₂×#486	C₂²	1	1	yes	characteristic
35	C₂×#484	C₂²	1	1	yes	characteristic
36	C₂×#477	C₂²	1	1	yes	characteristic, complemented
37	C₂×#450	C₂²	1	1	yes	characteristic
38	C₂×#440	C₂²	1	1	yes	characteristic
39	C₂×#440	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#102	C₂²	1	1	yes	characteristic
41	#2861	C₂²	1	1	yes	characteristic
42	#2805	—	2	1	no	—
43	#2797	—	2	1	no	—
44	#2788	—	2	1	no	—
45	#2756	—	2	1	no	—
46	#2685	—	2	1	no	—
47	#2685	—	2	1	no	—
48	#2630	—	2	1	no	—
49	#2605	—	2	1	no	—
50	#2588	—	2	1	no	—
51	#2551	C₂²	1	1	yes	characteristic, complemented
52	#2548	C₂²	1	1	yes	characteristic
53	#2544	C₂²	1	1	yes	characteristic
54	#2512	C₂²	1	1	yes	characteristic
55	#2511	C₂²	1	1	yes	characteristic, complemented
56	#2511	C₂²	1	1	yes	characteristic, complemented
57	#2497	C₂²	1	1	yes	characteristic
58	#2492	—	2	1	no	—
59	#2492	C₂²	1	1	yes	characteristic
60	#2492	C₂²	1	1	yes	characteristic
61	#2490	C₂²	1	1	yes	characteristic
62	#2467	—	2	1	no	—
63	#2465	—	2	1	no	—
64	#2454	C₂²	1	1	yes	characteristic
65	#2451	C₂²	1	1	yes	characteristic, complemented
66	#2446	—	2	1	no	—
67	#2445	C₂²	1	1	yes	characteristic
68	#2440	C₂²	1	1	yes	characteristic
69	#2435	C₂²	1	1	yes	characteristic
70	#2433	C₂²	1	1	yes	characteristic
71	#2427	C₂²	1	1	yes	characteristic
72	#2423	C₂²	1	1	yes	characteristic
73	#2418	—	2	1	no	—
74	#2373	—	2	1	no	—
75	#2369	C₂²	1	1	yes	characteristic, complemented
76	#2369	C₂²	1	1	yes	characteristic, complemented
77	#2367	C₂²	1	1	yes	characteristic
78	#2360	C₂²	1	1	yes	characteristic
79	#2345	C₂²	1	1	yes	characteristic
80	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	#2321	—	2	1	no	—
82	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₄×#127	C₂²	1	1	yes	characteristic
84	C₄×#126	C₂²	1	1	yes	characteristic
85	#2295	C₂²	1	1	yes	characteristic, complemented
86	#2099	C₂²	1	1	yes	characteristic, complemented
87	#2087	C₂²	1	1	yes	characteristic, complemented
88	#2083	C₂²	1	1	yes	characteristic, complemented
89	#2076	C₂²	1	1	yes	characteristic
90	#2076	C₂²	1	1	yes	characteristic
91	#2072	C₂²	1	1	yes	characteristic, complemented
92	#2072	C₂²	1	1	yes	characteristic, complemented
93	#2071	C₂²	1	1	yes	characteristic
94	#2071	C₂²	1	1	yes	characteristic
95	#2068	C₂²	1	1	yes	characteristic, complemented
96	#2067	C₂²	1	1	yes	characteristic
97	#2067	C₂²	1	1	yes	characteristic
98	#2067	C₂²	1	1	yes	characteristic
99	#2067	C₂²	1	1	yes	characteristic, complemented
100	#2059	C₂²	1	1	yes	characteristic, complemented
101	#2057	C₂²	1	1	yes	characteristic, complemented
102	#2055	C₂²	1	1	yes	characteristic
103	#2055	C₂²	1	1	yes	characteristic
104	#2055	C₂²	1	1	yes	characteristic, complemented
105	#2055	C₂²	1	1	yes	characteristic, complemented
106	#2042	C₂²	1	1	yes	characteristic
107	#2042	C₂²	1	1	yes	characteristic
108	#2042	C₂²	1	1	yes	characteristic, complemented
109	#2041	C₂²	1	1	yes	characteristic
110	#2041	C₂²	1	1	yes	characteristic
111	#2036	C₂²	1	1	yes	characteristic
112	#2034	C₂²	1	1	yes	characteristic
113	#2026	C₂²	1	1	yes	characteristic, complemented
114	#2024	C₂²	1	1	yes	characteristic, complemented
115	#2023	C₂²	1	1	yes	characteristic
116	#2023	C₂²	1	1	yes	characteristic
117	#2023	C₂²	1	1	yes	characteristic
118	#2023	C₂²	1	1	yes	characteristic, complemented
119	#2015	C₂²	1	1	yes	characteristic
120	#2015	C₂²	1	1	yes	characteristic
121	#2015	C₂²	1	1	yes	characteristic, complemented
122	#2014	C₂²	1	1	yes	characteristic
123	#2014	C₂²	1	1	yes	characteristic
124	#2001	C₂²	1	1	yes	characteristic
125	#2000	C₂²	1	1	yes	characteristic
126	#1990	C₂²	1	1	yes	characteristic, complemented
127	#1989	C₂²	1	1	yes	characteristic, complemented
128	#1989	C₂²	1	1	yes	characteristic, complemented
129	#1988	C₂²	1	1	yes	characteristic, complemented
130	#1983	C₂²	1	1	yes	characteristic
131	#1983	C₂²	1	1	yes	characteristic
132	#1983	C₂²	1	1	yes	characteristic
133	#1983	C₂²	1	1	yes	characteristic, complemented
134	#1982	C₂²	1	1	yes	characteristic
135	#1973	C₂²	1	1	yes	characteristic
136	#1973	C₂²	1	1	yes	characteristic
137	#1969	C₂²	1	1	yes	characteristic, complemented
138	#1968	C₂²	1	1	yes	characteristic
139	#1959	C₂²	1	1	yes	characteristic, complemented
140	#1957	C₂²	1	1	yes	characteristic
141	#1943	C₂²	1	1	yes	characteristic, complemented
142	#1939	C₂²	1	1	yes	characteristic, complemented
143	#1936	C₂²	1	1	yes	characteristic
144	#1936	C₂²	1	1	yes	characteristic
145	#1936	C₂²	1	1	yes	characteristic, complemented
146	#1935	C₂²	1	1	yes	characteristic, complemented
147	#1935	C₂²	1	1	yes	characteristic, complemented
148	#1934	C₂²	1	1	yes	characteristic
149	#1934	C₂²	1	1	yes	characteristic
150	#1933	C₂²	1	1	yes	characteristic, complemented
151	#1933	C₂²	1	1	yes	characteristic, complemented
152	#1928	C₂²	1	1	yes	characteristic, complemented
153	#1927	C₂²	1	1	yes	characteristic, complemented
154	#1926	C₂²	1	1	yes	characteristic
155	#1925	C₂²	1	1	yes	characteristic
156	#1925	C₂²	1	1	yes	characteristic
157	#1925	C₂²	1	1	yes	characteristic
158	#1925	C₂²	1	1	yes	characteristic
159	#1925	C₂²	1	1	yes	characteristic
160	#1925	C₂²	1	1	yes	characteristic, complemented
161	#1925	C₂²	1	1	yes	characteristic, complemented
162	#1925	C₂²	1	1	yes	characteristic, complemented
163	#1924	C₂²	1	1	yes	characteristic
164	#1924	C₂²	1	1	yes	characteristic
165	#1923	C₂²	1	1	yes	characteristic
166	#1921	C₂²	1	1	yes	characteristic, complemented
167	#1918	C₂²	1	1	yes	characteristic, complemented
168	#1918	C₂²	1	1	yes	characteristic, complemented
169	#1917	C₂²	1	1	yes	characteristic, complemented
170	#1917	C₂²	1	1	yes	characteristic, complemented
171	#1916	C₂²	1	1	yes	characteristic, complemented
172	#1893	C₂²	1	1	yes	characteristic
173	#1892	C₂²	1	1	yes	characteristic
174	#1892	C₂²	1	1	yes	characteristic
175	#1880	C₂²	1	1	yes	characteristic
176	#1878	C₂²	1	1	yes	characteristic, complemented
177	#1878	C₂²	1	1	yes	characteristic, complemented
178	#1877	C₂²	1	1	yes	characteristic
179	#1874	C₂²	1	1	yes	characteristic
180	#1863	C₂²	1	1	yes	characteristic, complemented
181	#1862	C₂²	1	1	yes	characteristic
182	#1862	C₂²	1	1	yes	characteristic
183	#1862	C₂²	1	1	yes	characteristic
184	#1862	C₂²	1	1	yes	characteristic, complemented
185	#1862	C₂²	1	1	yes	characteristic, complemented
186	#1852	C₂²	1	1	yes	characteristic
187	#1850	C₂²	1	1	yes	characteristic
188	#1845	C₂²	1	1	yes	characteristic, complemented
189	#1802	C₂²	1	1	yes	characteristic
190	#1786	C₂²	1	1	yes	characteristic
191	#1786	C₂²	1	1	yes	characteristic
192	#1776	C₂²	1	1	yes	characteristic, complemented
193	#1771	C₂²	1	1	yes	characteristic, complemented
194	#1771	C₂²	1	1	yes	characteristic, complemented
195	#1767	C₂²	1	1	yes	characteristic, complemented
196	#1762	C₂²	1	1	yes	characteristic
197	#1762	C₂²	1	1	yes	characteristic
198	#1762	C₂²	1	1	yes	characteristic, complemented
199	C₄×#103	C₂²	1	1	yes	characteristic, complemented
200	#1752	C₂²	1	1	yes	characteristic
201	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
202	#1744	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	—	2	1	no	—
210	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×#127	C₂³	1	1	yes	characteristic
214	C₂×#127	C₂³	1	1	yes	characteristic
215	C₂×#126	—	2	1	no	—
216	C₂×#126	D₄	1	1	yes	characteristic
217	C₂×#125	C₂³	1	1	yes	characteristic
218	C₂×#124	C₂³	1	1	yes	characteristic
219	C₂×#124	C₂³	1	1	yes	characteristic
220	C₂×#124	C₂³	1	1	yes	characteristic
221	C₂×#123	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×#121	C₂³	1	1	yes	characteristic
226	C₂×#120	—	2	1	no	—
227	C₂×#120	—	2	1	no	—
228	C₂×C₄×Q₈	—	2	1	no	—
229	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	—	2	1	no	—
238	#489	—	2	4	no	—
239	#486	—	2	4	no	—
240	#486	—	4	2	no	—
241	#484	—	4	2	no	—
242	#477	—	4	2	no	—
243	#450	—	2	4	no	—
244	#440	—	4	2	no	—
245	#440	—	4	2	no	—
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#107	C₂³	1	1	yes	characteristic
253	C₂×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#102	—	4	2	no	—
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×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×#97	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×#97	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
302	#400	—	2	1	no	—
303	#400	—	2	1	no	—
304	#400	—	2	1	no	—
305	#400	—	2	1	no	—
306	#400	—	2	1	no	—
307	#400	—	2	1	no	—
308	#400	—	2	1	no	—
309	#399	—	2	1	no	—
310	#399	—	2	1	no	—
311	#398	—	2	1	no	—
312	#398	—	2	1	no	—
313	#398	—	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	#395	—	2	1	no	—
322	#395	—	2	1	no	—
323	#395	—	2	1	no	—
324	#394	—	2	1	no	—
325	#394	—	2	1	no	—
326	#394	—	2	1	no	—
327	#394	—	2	1	no	—
328	#394	—	2	1	no	—
329	#394	—	2	1	no	—
330	#394	—	2	1	no	—
331	#394	—	2	1	no	—
332	#394	—	2	1	no	—
333	#394	—	2	1	no	—
334	#393	—	2	1	no	—
335	#393	—	2	1	no	—
336	#392	—	2	1	no	—
337	#392	—	2	1	no	—
338	#391	—	2	1	no	—
339	#391	—	2	1	no	—
340	#391	—	2	1	no	—
341	#391	—	2	1	no	—
342	#391	—	2	1	no	—
343	#391	—	2	1	no	—
344	#391	—	2	1	no	—
345	#391	—	2	1	no	—
346	#391	C₂³	1	1	yes	characteristic
347	#391	C₂³	1	1	yes	characteristic
348	#391	C₂³	1	1	yes	characteristic
349	#391	C₂³	1	1	yes	characteristic
350	#391	C₂³	1	1	yes	characteristic
351	#391	C₂³	1	1	yes	characteristic
352	#391	C₂³	1	1	yes	characteristic
353	#390	—	2	1	no	—
354	#390	—	2	1	no	—
355	#390	—	2	1	no	—
356	#390	—	2	1	no	—
357	#390	—	2	1	no	—
358	#390	C₂³	1	1	yes	characteristic
359	#390	C₂³	1	1	yes	characteristic
360	#390	C₂³	1	1	yes	characteristic
361	#390	C₂³	1	1	yes	characteristic
362	#390	C₂³	1	1	yes	characteristic
363	#390	C₂³	1	1	yes	characteristic
364	#390	C₂³	1	1	yes	characteristic
365	#390	C₂³	1	1	yes	characteristic
366	#389	—	2	1	no	—
367	#389	—	2	1	no	—
368	#389	—	2	1	no	—
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	C₂³	1	1	yes	characteristic
372	#389	C₂³	1	1	yes	characteristic
373	#389	C₂³	1	1	yes	characteristic
374	#389	C₂³	1	1	yes	characteristic
375	#389	C₂³	1	1	yes	characteristic
376	#389	C₂³	1	1	yes	characteristic
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	D₄	1	1	yes	characteristic
393	#388	D₄	1	1	yes	characteristic
394	#388	D₄	1	1	yes	characteristic
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	D₄	1	1	yes	characteristic
408	#387	D₄	1	1	yes	characteristic
409	#387	D₄	1	1	yes	characteristic
410	#386	—	2	1	no	—
411	#386	—	2	1	no	—
412	#386	—	2	1	no	—
413	#386	—	2	1	no	—
414	#386	—	2	1	no	—
415	#386	—	2	1	no	—
416	#385	—	2	1	no	—
417	#385	—	2	1	no	—
418	#385	—	2	1	no	—
419	#385	—	2	1	no	—
420	#384	C₂³	1	1	yes	characteristic
421	#384	C₂³	1	1	yes	characteristic
422	#384	C₂³	1	1	yes	characteristic
423	#383	D₄	1	1	yes	characteristic
424	#380	—	2	1	no	—
425	#380	—	2	1	no	—
426	#380	—	2	1	no	—
427	#380	C₂³	1	1	yes	characteristic
428	#380	C₂³	1	1	yes	characteristic
429	#380	C₂³	1	1	yes	characteristic
430	#379	—	2	1	no	—
431	#379	—	2	1	no	—
432	#379	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
453	#376	—	2	1	no	—
454	C₄³	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	#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	#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	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	—	4	1	no	—
502	C₂²×D₄	—	4	1	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	—	4	1	no	—
505	C₂²×D₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
512	C₂³×C₄	C₂⁴	1	1	yes	characteristic
513	C₂×Q₁₆	—	4	1	no	—
514	C₂×Q₁₆	—	4	1	no	—
515	C₂×Q₁₆	—	4	1	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	4	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂²×C₈	—	4	1	no	—
526	C₂²×C₈	—	4	1	no	—
527	C₂²×C₈	—	4	1	no	—
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	—	2	2	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	4	1	no	—
540	C₄⋊Q₈	—	4	1	no	—
541	C₄⋊Q₈	—	4	1	no	—
542	C₄⋊Q₈	—	8	2	no	—
543	#127	—	2	2	no	—
544	#127	—	4	1	no	—
545	#127	—	4	1	no	—
546	#127	—	4	1	no	—
547	#126	—	2	4	no	—
548	#126	—	8	2	no	—
549	#125	—	4	1	no	—
550	#125	—	4	1	no	—
551	#124	—	2	2	no	—
552	#124	—	4	1	no	—
553	#124	—	4	1	no	—
554	#124	—	4	1	no	—
555	#124	—	4	1	no	—
556	#124	—	4	1	no	—
557	#123	—	8	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	4	1	no	—
560	C₂²⋊Q₈	—	4	1	no	—
561	C₂²⋊Q₈	—	4	1	no	—
562	C₂²⋊Q₈	—	8	2	no	—
563	#121	—	4	1	no	—
564	#121	—	4	1	no	—
565	#120	—	4	4	no	—
566	#120	—	8	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	4	1	no	—
569	C₄×Q₈	—	4	1	no	—
570	C₄×Q₈	—	4	1	no	—
571	C₄×Q₈	—	8	2	no	—
572	C₄×D₄	—	4	1	no	—
573	C₄×D₄	—	4	1	no	—
574	C₄×D₄	—	4	1	no	—
575	C₄×D₄	—	4	1	no	—
576	C₄×D₄	—	4	1	no	—
577	C₄×D₄	—	4	1	no	—
578	C₄×D₄	—	8	2	no	—
579	C₄×D₄	—	8	2	no	—
580	C₂×C₄⋊C₄	—	2	2	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	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	—	4	1	no	—
607	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	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	—	8	2	no	—
656	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	C₂×C₄²	C₂⁴	1	1	yes	characteristic
678	C₂×C₄²	C₂⁴	1	1	yes	characteristic
679	C₂×C₄²	C₂⁴	1	1	yes	characteristic
680	C₂×C₄²	C₂⁴	1	1	yes	characteristic
681	#107	—	2	2	no	—
682	#107	—	2	2	no	—
683	#107	—	4	1	no	—
684	#107	—	4	1	no	—
685	#107	—	4	1	no	—
686	#107	—	4	1	no	—
687	#107	—	4	1	no	—
688	#106	—	4	1	no	—
689	C₄⋊C₈	—	4	1	no	—
690	C₄⋊C₈	—	4	1	no	—
691	C₄⋊C₈	—	4	1	no	—
692	C₄⋊C₈	—	4	1	no	—
693	C₄⋊C₈	—	4	1	no	—
694	#103	—	2	2	no	—
695	#103	—	2	2	no	—
696	#103	—	2	2	no	—
697	#103	—	4	1	no	—
698	#103	—	4	1	no	—
699	#103	—	4	1	no	—
700	#103	—	4	1	no	—
701	#103	—	4	1	no	—
702	#103	—	4	1	no	—
703	#103	—	4	1	no	—
704	#103	—	4	1	no	—
705	#102	—	2	2	no	—
706	#102	—	2	2	no	—
707	#102	—	2	2	no	—
708	#102	—	2	2	no	—
709	#102	—	2	2	no	—
710	#102	—	2	2	no	—
711	#102	—	2	2	no	—
712	#102	—	2	2	no	—
713	#102	—	4	1	no	—
714	#102	—	4	1	no	—
715	#102	—	4	1	no	—
716	#102	—	4	1	no	—
717	#102	—	4	1	no	—
718	#102	—	4	1	no	—
719	#102	—	4	1	no	—
720	#102	—	4	1	no	—
721	#102	—	4	1	no	—
722	#102	—	4	1	no	—
723	#102	—	4	1	no	—
724	#102	—	4	1	no	—
725	#102	#41	1	4	yes	—
726	C₂²⋊C₈	—	2	2	no	—
727	C₂²⋊C₈	—	4	1	no	—
728	C₂²⋊C₈	—	4	1	no	—
729	#97	—	2	2	no	—
730	#97	—	4	1	no	—
731	#97	—	4	1	no	—
732	#97	—	4	1	no	—
733	C₄×C₈	—	2	2	no	—
734	C₄×C₈	—	4	1	no	—
735	C₄×C₈	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	#95	C₂×D₄	1	1	yes	characteristic
773	#95	C₂×D₄	1	1	yes	characteristic
774	#95	C₂×D₄	1	1	yes	characteristic
775	#95	C₂×D₄	1	1	yes	characteristic
776	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	—	2	1	no	—
782	C₂⁴	—	2	1	no	—
783	C₂⁴	—	2	1	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	2	no	—
786	C₂⁴	—	8	1	no	—
787	C₂⁴	—	8	1	no	—
788	C₂⁴	—	8	1	no	—
789	C₂⁴	—	8	1	no	—
790	C₂⁴	—	8	1	no	—
791	C₂⁴	C₂²×D₄	1	1	yes	characteristic
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	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	—	4	2	no	—
805	C₂×Q₈	—	4	2	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	8	1	no	—
809	C₂×Q₈	—	8	1	no	—
810	C₂×Q₈	—	8	1	no	—
811	C₂×Q₈	—	8	1	no	—
812	C₂×Q₈	—	8	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	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	—	2	1	no	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	4	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	8	1	no	—
839	C₂×D₄	—	8	1	no	—
840	C₂×D₄	—	8	1	no	—
841	C₂×D₄	—	8	1	no	—
842	C₂×D₄	—	8	1	no	—
843	C₂×D₄	—	8	1	no	—
844	C₂×D₄	—	8	1	no	—
845	C₂×D₄	—	8	1	no	—
846	C₂×D₄	—	8	1	no	—
847	C₂×D₄	—	8	2	no	—
848	C₂×D₄	—	8	2	no	—
849	C₂×D₄	—	8	2	no	—
850	C₂×D₄	—	8	1	no	—
851	C₂×D₄	—	8	1	no	—
852	C₂×D₄	C₂×#41	1	2	yes	—
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	1	no	—
859	C₂²×C₄	—	2	1	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	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	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	—	8	1	no	—
881	C₂²×C₄	—	8	1	no	—
882	C₂²×C₄	—	8	1	no	—
883	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂⁵	1	1	yes	characteristic
898	Q₁₆	—	8	2	no	—
899	SD₁₆	—	4	4	no	—
900	SD₁₆	—	4	4	no	—
901	SD₁₆	—	8	2	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	—	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	—	8	2	no	—
926	C₂×C₈	C₂×#41	1	2	yes	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	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	—	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	—	4	1	no	—
952	C₄⋊C₄	—	4	1	no	—
953	C₄⋊C₄	—	4	2	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	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	—	8	1	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	—	8	1	no	—
977	C₄⋊C₄	—	8	1	no	—
978	C₄⋊C₄	C₂×#41	1	2	yes	—
979	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	4	1	no	—
984	C₂²⋊C₄	—	4	1	no	—
985	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	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	C₂²⋊C₄	—	8	1	no	—
1013	C₂²⋊C₄	—	8	1	no	—
1014	C₂²⋊C₄	—	8	1	no	—
1015	C₂²⋊C₄	—	8	1	no	—
1016	C₂²⋊C₄	#137	1	4	yes	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	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	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	4	1	no	—
1032	C₄²	—	4	1	no	—
1033	C₄²	—	4	2	no	—
1034	C₄²	—	8	1	no	—
1035	C₄²	—	8	1	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	C₂³	—	2	1	no	—
1043	C₂³	—	2	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	2	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	4	1	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	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	8	4	no	—
1070	C₂³	—	8	4	no	—
1071	C₂³	—	16	2	no	—
1072	C₂³	—	16	2	no	—
1073	C₂³	—	16	2	no	—
1074	C₂³	—	16	2	no	—
1075	C₂³	—	16	2	no	—
1076	C₂³	C₂×#137	1	2	yes	—
1077	C₂³	C₂³×D₄	1	1	yes	characteristic
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	—	4	1	no	—
1086	Q₈	—	8	4	no	—
1087	Q₈	—	16	2	no	—
1088	Q₈	—	16	2	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	4	1	no	—
1092	D₄	—	4	1	no	—
1093	D₄	—	4	1	no	—
1094	D₄	—	4	1	no	—
1095	D₄	—	4	1	no	—
1096	D₄	—	4	1	no	—
1097	D₄	—	4	1	no	—
1098	D₄	—	4	1	no	—
1099	D₄	—	4	1	no	—
1100	D₄	—	4	1	no	—
1101	D₄	—	8	4	no	—
1102	D₄	—	8	4	no	—
1103	D₄	—	8	4	no	—
1104	D₄	—	16	2	no	—
1105	D₄	—	16	2	no	—
1106	D₄	—	16	2	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	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	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	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	16	2	no	—
1187	C₂×C₄	—	16	2	no	—
1188	C₂×C₄	—	16	2	no	—
1189	C₂×C₄	—	16	2	no	—
1190	C₂×C₄	C₂×#137	1	2	yes	—
1191	C₂×C₄	C₂×#137	1	2	yes	—
1192	C₂×C₄	#576	1	2	yes	—
1193	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1194	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1195	C₂×C₄	#585	1	1	yes	characteristic
1196	C₂×C₄	#585	1	1	yes	characteristic
1197	C₂×C₄	#585	1	1	yes	characteristic
1198	C₂×C₄	#585	1	1	yes	characteristic
1199	C₈	—	2	2	no	—
1200	C₈	—	4	1	no	—
1201	C₈	—	4	1	no	—
1202	C₈	—	4	1	no	—
1203	C₈	—	4	1	no	—
1204	C₈	—	4	1	no	—
1205	C₈	—	4	1	no	—
1206	C₈	—	4	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	8	1	no	—
1222	C₂²	—	8	1	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	—	8	1	no	—
1229	C₂²	—	8	1	no	—
1230	C₂²	—	8	1	no	—
1231	C₂²	—	8	1	no	—
1232	C₂²	—	8	1	no	—
1233	C₂²	—	8	1	no	—
1234	C₂²	—	8	1	no	—
1235	C₂²	—	16	8	no	—
1236	C₂²	D₄×#41	1	1	yes	characteristic
1237	C₂²	#3488	1	1	yes	characteristic
1238	C₂²	#3500	1	1	yes	characteristic
1239	C₂²	C₂²×#137	1	1	yes	characteristic
1240	C₂²	C₂×#576	1	1	yes	characteristic
1241	C₂²	#3584	1	1	yes	characteristic
1242	C₂²	#3585	1	1	yes	characteristic
1243	C₄	—	2	2	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	2	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	—	8	1	no	—
1266	C₄	—	8	1	no	—
1267	C₄	—	8	1	no	—
1268	C₄	—	8	1	no	—
1269	C₄	#3506	1	1	yes	characteristic
1270	C₄	#3521	1	1	yes	characteristic
1271	C₄	#3540	1	1	yes	characteristic
1272	C₄	#3568	1	1	yes	characteristic
1273	C₂	—	4	2	no	—
1274	C₂	—	8	2	no	—
1275	C₂	—	16	1	no	—
1276	C₂	—	16	1	no	—
1277	C₂	#44182	1	1	yes	characteristic
1278	C₂	#61453	1	1	yes	characteristic
1279	C₂	#61489	1	1	yes	characteristic
1280	C₂	#61991	1	1	yes	characteristic
1281	C₂	#62031	1	1	yes	characteristic
1282	C₂	#62537	1	1	yes	characteristic
1283	C₂	#62607	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 ◁ C₄×#126 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #59712	C₂	semidirect
3. #32226	C₂	semidirect
4. #32191	C₂	semidirect
5. #32165	C₂	semidirect
6. #32118	C₂	semidirect
7. #31810	C₂	semidirect
8. #31081	C₂	semidirect
9. #30543	C₂	semidirect
11. #29557	C₂	semidirect
12. #29352	C₂	semidirect
13. #29052	C₂	semidirect
14. #28977	C₂	semidirect
15. #28025	C₂	semidirect
16. #27783	C₂	semidirect
17. #27541	C₂	semidirect
18. #27348	C₂	semidirect
20. #27018	C₂	semidirect
21. #26915	C₂	semidirect
22. #26832	C₂	semidirect
23. #26709	C₂	semidirect
24. #26645	C₂	semidirect
25. #25277	C₂	semidirect
26. #24479	C₂	semidirect
27. #23684	C₂	semidirect
28. #23282	C₂	semidirect
29. #23230	C₂	semidirect
30. #22854	C₂	semidirect
31. #22220	C₂	semidirect
36. C₂×#477	C₂²	semidirect
39. C₂×#440	C₂²	semidirect
51. #2551	C₂²	semidirect
55. #2511	C₂²	semidirect
56. #2511	C₂²	semidirect
65. #2451	C₂²	semidirect
75. #2369	C₂²	semidirect
76. #2369	C₂²	semidirect
82. C₄×C₄⋊Q₈	C₂²	semidirect
85. #2295	C₂²	semidirect
86. #2099	C₂²	semidirect
87. #2087	C₂²	semidirect
88. #2083	C₂²	semidirect
91. #2072	C₂²	semidirect
92. #2072	C₂²	semidirect
95. #2068	C₂²	semidirect
99. #2067	C₂²	semidirect
100. #2059	C₂²	semidirect
101. #2057	C₂²	semidirect
104. #2055	C₂²	semidirect
105. #2055	C₂²	semidirect
108. #2042	C₂²	semidirect
113. #2026	C₂²	semidirect
114. #2024	C₂²	semidirect
118. #2023	C₂²	semidirect
121. #2015	C₂²	semidirect
126. #1990	C₂²	semidirect
127. #1989	C₂²	semidirect
128. #1989	C₂²	semidirect
129. #1988	C₂²	semidirect
133. #1983	C₂²	semidirect
137. #1969	C₂²	semidirect
139. #1959	C₂²	semidirect
141. #1943	C₂²	semidirect
142. #1939	C₂²	semidirect
145. #1936	C₂²	semidirect
146. #1935	C₂²	semidirect
147. #1935	C₂²	semidirect
150. #1933	C₂²	semidirect
151. #1933	C₂²	semidirect
152. #1928	C₂²	semidirect
153. #1927	C₂²	semidirect
160. #1925	C₂²	semidirect
161. #1925	C₂²	semidirect
162. #1925	C₂²	semidirect
166. #1921	C₂²	semidirect
167. #1918	C₂²	semidirect
168. #1918	C₂²	semidirect
169. #1917	C₂²	semidirect
170. #1917	C₂²	semidirect
171. #1916	C₂²	semidirect
176. #1878	C₂²	semidirect
177. #1878	C₂²	semidirect
180. #1863	C₂²	semidirect
184. #1862	C₂²	semidirect
185. #1862	C₂²	semidirect
188. #1845	C₂²	semidirect
192. #1776	C₂²	semidirect
193. #1771	C₂²	semidirect
194. #1771	C₂²	semidirect
195. #1767	C₂²	semidirect
198. #1762	C₂²	semidirect
199. C₄×#103	C₂²	semidirect
202. #1744	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#59712	2
#40176	2
#32226	2
#32191	2
#32165	2
#32118	2
#31810	2
#31081	2
#30543	2
#30527	2
#29557	2
#29352	2
#29052	2
#28977	2
#28025	2
#27783	2
#27541	2
#27348	2
#27254	2
#27018	2
#26915	2
#26832	2
#26709	2
#26645	2
#25277	2
#24479	2
#23684	2
#23282	2
#23230	2
#22854	2
#22220	2