Subgroups — #6916731

Order 512.

1466 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36165	C₂	1	1	yes	maximal, characteristic, complemented
2	#35025	C₂	1	1	yes	maximal, characteristic
3	#32836	C₂	1	1	yes	maximal, characteristic, complemented
4	#32778	C₂	1	1	yes	maximal, characteristic, complemented
5	#32389	C₂	1	1	yes	maximal, characteristic, complemented
6	#32385	C₂	1	1	yes	maximal, characteristic, complemented
7	#31583	C₂	1	1	yes	maximal, characteristic, complemented
8	#31579	C₂	1	1	yes	maximal, characteristic, complemented
9	#30783	C₂	1	1	yes	maximal, characteristic, complemented
10	#30781	C₂	1	1	yes	maximal, characteristic, complemented
11	#30643	C₂	1	1	yes	maximal, characteristic, complemented
12	#30641	C₂	1	1	yes	maximal, characteristic, complemented
13	#30360	C₂	1	1	yes	maximal, characteristic, complemented
14	#30282	C₂	1	1	yes	maximal, characteristic, complemented
15	#30065	C₂	1	1	yes	maximal, characteristic, complemented
16	#29956	C₂	1	1	yes	maximal, characteristic, complemented
17	#29912	C₂	1	1	yes	maximal, characteristic, complemented
18	#29516	C₂	1	1	yes	maximal, characteristic, complemented
19	#29158	C₂	1	1	yes	maximal, characteristic, complemented
20	#27912	C₂	1	1	yes	maximal, characteristic, complemented
21	#27686	C₂	1	1	yes	maximal, characteristic, complemented
22	#27256	C₂	1	1	yes	maximal, characteristic, complemented
23	#27256	C₂	1	1	yes	maximal, characteristic, complemented
24	#26132	C₂	1	1	yes	maximal, characteristic, complemented
25	#26128	C₂	1	1	yes	maximal, characteristic, complemented
26	#26067	C₂	1	1	yes	maximal, characteristic, complemented
27	#26062	C₂	1	1	yes	maximal, characteristic, complemented
28	#24865	C₂	1	1	yes	maximal, characteristic
29	#24861	C₂	1	1	yes	maximal, characteristic
30	C₂×#2092	C₂	1	1	yes	maximal, characteristic, complemented
31	#22785	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#499	C₂²	1	1	yes	characteristic, complemented
33	C₂×#499	C₂²	1	1	yes	characteristic, complemented
34	C₂×#488	C₂²	1	1	yes	characteristic
35	C₂×#488	C₂²	1	1	yes	characteristic
36	C₂×#484	C₂²	1	1	yes	characteristic, complemented
37	C₂×#481	C₂²	1	1	yes	characteristic
38	C₂×#483	C₂²	1	1	yes	characteristic, complemented
39	C₂×#480	C₂²	1	1	yes	characteristic
40	C₂²×#107	C₂²	1	1	yes	characteristic
41	C₂²×#106	C₂²	1	1	yes	characteristic
42	C₂²×#102	C₂²	1	1	yes	characteristic
43	C₂²×#102	C₂²	1	1	yes	characteristic
44	#2861	C₂²	1	1	yes	characteristic
45	#2860	C₂²	1	1	yes	characteristic
46	#2859	C₂²	1	1	yes	characteristic, complemented
47	#2854	C₂²	1	1	yes	characteristic
48	#2851	C₂²	1	1	yes	characteristic
49	#2851	C₂²	1	1	yes	characteristic, complemented
50	#2850	C₂²	1	1	yes	characteristic
51	#2651	—	2	1	no	—
52	#2648	—	2	1	no	—
53	#2593	—	2	1	no	—
54	#2571	C₂²	1	1	yes	characteristic, complemented
55	#2571	C₂²	1	1	yes	characteristic, complemented
56	#2554	—	2	1	no	—
57	#2513	C₂²	1	1	yes	characteristic
58	#2508	—	2	1	no	—
59	#2508	—	2	1	no	—
60	#2505	—	2	1	no	—
61	#2505	—	2	1	no	—
62	#2505	—	2	1	no	—
63	#2505	—	2	1	no	—
64	#2490	C₂²	1	1	yes	characteristic
65	#2480	—	2	1	no	—
66	#2448	C₂²	1	1	yes	characteristic
67	#2442	C₂²	1	1	yes	characteristic
68	#2442	C₂²	1	1	yes	characteristic
69	#2442	C₂²	1	1	yes	characteristic
70	#2442	C₂²	1	1	yes	characteristic, complemented
71	#2442	C₂²	1	1	yes	characteristic, complemented
72	#2435	C₂²	1	1	yes	characteristic
73	#2426	C₂²	1	1	yes	characteristic
74	#2418	—	2	1	no	—
75	#2417	C₂²	1	1	yes	characteristic
76	#2408	C₂²	1	1	yes	characteristic
77	#2349	—	2	1	no	—
78	#2349	—	2	1	no	—
79	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#2321	—	2	1	no	—
82	#2312	—	2	1	no	—
83	C₄×#125	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
85	C₂×#390	C₂²	1	1	yes	characteristic
86	C₂×#382	C₂²	1	1	yes	characteristic
87	C₂×#382	C₂²	1	1	yes	characteristic, complemented
88	C₄²×D₄	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic, complemented
90	#2101	C₂²	1	1	yes	characteristic, complemented
91	#2101	C₂²	1	1	yes	characteristic, complemented
92	#2097	C₂²	1	1	yes	characteristic, complemented
93	#2097	C₂²	1	1	yes	characteristic, complemented
94	#2097	C₂²	1	1	yes	characteristic, complemented
95	#2096	C₂²	1	1	yes	characteristic, complemented
96	#2095	C₂²	1	1	yes	characteristic, complemented
97	#2094	C₂²	1	1	yes	characteristic
98	#2093	C₂²	1	1	yes	characteristic
99	#2092	C₂²	1	1	yes	characteristic
100	#2092	C₂²	1	1	yes	characteristic
101	#2092	C₂²	1	1	yes	characteristic
102	#2092	C₂²	1	1	yes	characteristic
103	#2092	C₂²	1	1	yes	characteristic
104	#2092	C₂²	1	1	yes	characteristic
105	#2092	C₂²	1	1	yes	characteristic
106	#2092	C₂²	1	1	yes	characteristic
107	#2092	C₂²	1	1	yes	characteristic
108	#2092	C₂²	1	1	yes	characteristic
109	#2085	C₂²	1	1	yes	characteristic, complemented
110	#2085	C₂²	1	1	yes	characteristic, complemented
111	#2085	C₂²	1	1	yes	characteristic, complemented
112	#2085	C₂²	1	1	yes	characteristic, complemented
113	#2084	C₂²	1	1	yes	characteristic, complemented
114	#2083	C₂²	1	1	yes	characteristic, complemented
115	#2077	C₂²	1	1	yes	characteristic, complemented
116	#2076	C₂²	1	1	yes	characteristic, complemented
117	#2073	C₂²	1	1	yes	characteristic
118	#2073	C₂²	1	1	yes	characteristic
119	#2071	C₂²	1	1	yes	characteristic
120	#2071	C₂²	1	1	yes	characteristic
121	#2067	C₂²	1	1	yes	characteristic
122	#2067	C₂²	1	1	yes	characteristic
123	#2065	C₂²	1	1	yes	characteristic
124	#2065	C₂²	1	1	yes	characteristic
125	#2059	C₂²	1	1	yes	characteristic, complemented
126	#2059	C₂²	1	1	yes	characteristic, complemented
127	#2059	C₂²	1	1	yes	characteristic, complemented
128	#2059	C₂²	1	1	yes	characteristic, complemented
129	#2059	C₂²	1	1	yes	characteristic, complemented
130	#2042	C₂²	1	1	yes	characteristic
131	#2042	C₂²	1	1	yes	characteristic
132	#2042	C₂²	1	1	yes	characteristic
133	#2042	C₂²	1	1	yes	characteristic
134	#2036	C₂²	1	1	yes	characteristic, complemented
135	#2035	C₂²	1	1	yes	characteristic, complemented
136	#2034	C₂²	1	1	yes	characteristic
137	#2034	C₂²	1	1	yes	characteristic
138	#2033	C₂²	1	1	yes	characteristic
139	#2033	C₂²	1	1	yes	characteristic
140	#2026	C₂²	1	1	yes	characteristic, complemented
141	#2025	C₂²	1	1	yes	characteristic
142	#2025	C₂²	1	1	yes	characteristic
143	#2025	C₂²	1	1	yes	characteristic
144	#2025	C₂²	1	1	yes	characteristic
145	#1958	C₂²	1	1	yes	characteristic
146	#1958	C₂²	1	1	yes	characteristic
147	#1949	C₂²	1	1	yes	characteristic, complemented
148	#1949	C₂²	1	1	yes	characteristic, complemented
149	#1942	C₂²	1	1	yes	characteristic, complemented
150	#1942	C₂²	1	1	yes	characteristic, complemented
151	#1941	C₂²	1	1	yes	characteristic, complemented
152	#1941	C₂²	1	1	yes	characteristic, complemented
153	#1934	C₂²	1	1	yes	characteristic
154	#1934	C₂²	1	1	yes	characteristic
155	#1934	C₂²	1	1	yes	characteristic
156	#1934	C₂²	1	1	yes	characteristic
157	#1928	C₂²	1	1	yes	characteristic, complemented
158	#1927	C₂²	1	1	yes	characteristic, complemented
159	#1926	C₂²	1	1	yes	characteristic
160	#1926	C₂²	1	1	yes	characteristic
161	#1925	C₂²	1	1	yes	characteristic
162	#1925	C₂²	1	1	yes	characteristic
163	#1923	C₂²	1	1	yes	characteristic, complemented
164	#1923	C₂²	1	1	yes	characteristic, complemented
165	#1921	C₂²	1	1	yes	characteristic, complemented
166	#1920	C₂²	1	1	yes	characteristic, complemented
167	#1920	C₂²	1	1	yes	characteristic, complemented
168	#1918	C₂²	1	1	yes	characteristic, complemented
169	#1916	C₂²	1	1	yes	characteristic, complemented
170	#1916	C₂²	1	1	yes	characteristic, complemented
171	#1892	C₂²	1	1	yes	characteristic
172	#1892	C₂²	1	1	yes	characteristic
173	#1874	C₂²	1	1	yes	characteristic
174	#1874	C₂²	1	1	yes	characteristic
175	#1872	C₂²	1	1	yes	characteristic
176	#1872	C₂²	1	1	yes	characteristic
177	#1869	C₂²	1	1	yes	characteristic
178	#1869	C₂²	1	1	yes	characteristic
179	#1865	C₂²	1	1	yes	characteristic, complemented
180	#1863	C₂²	1	1	yes	characteristic, complemented
181	#1853	C₂²	1	1	yes	characteristic
182	#1853	C₂²	1	1	yes	characteristic
183	#1853	C₂²	1	1	yes	characteristic, complemented
184	#1852	C₂²	1	1	yes	characteristic
185	#1852	C₂²	1	1	yes	characteristic
186	#1852	C₂²	1	1	yes	characteristic, complemented
187	#1846	C₂²	1	1	yes	characteristic, complemented
188	#1846	C₂²	1	1	yes	characteristic, complemented
189	#1839	C₂²	1	1	yes	characteristic, complemented
190	#1817	C₂²	1	1	yes	characteristic, complemented
191	#1808	C₂²	1	1	yes	characteristic
192	#1807	C₂²	1	1	yes	characteristic
193	#1805	C₂²	1	1	yes	characteristic, complemented
194	#1805	C₂²	1	1	yes	characteristic, complemented
195	#1797	C₂²	1	1	yes	characteristic
196	#1786	C₂²	1	1	yes	characteristic
197	#1786	C₂²	1	1	yes	characteristic
198	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
200	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
201	#1744	C₂²	1	1	yes	characteristic, complemented
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×#126	—	2	1	no	—
207	C₂×#125	C₂³	1	1	yes	characteristic
208	C₂×#125	C₂³	1	1	yes	characteristic
209	C₂×#125	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×#124	C₂³	1	1	yes	characteristic
212	C₂×#124	C₂³	1	1	yes	characteristic
213	C₂×#123	—	2	1	no	—
214	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×#121	C₂³	1	1	yes	characteristic
218	C₂×#120	—	2	1	no	—
219	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	D₄	1	1	yes	characteristic
223	C₂×C₄×D₄	D₄	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂²×C₂²⋊C₄	—	2	1	no	—
232	C₂²×C₄²	C₂³	1	1	yes	characteristic
233	C₂²×C₄²	C₂³	1	1	yes	characteristic
234	#499	—	4	2	no	—
235	#499	—	4	2	no	—
236	#488	—	4	2	no	—
237	#488	—	4	2	no	—
238	#484	—	4	2	no	—
239	#483	—	4	2	no	—
240	#481	—	4	2	no	—
241	#480	—	4	2	no	—
242	C₂×#107	—	4	2	no	—
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×#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	—	4	2	no	—
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	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×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#102	—	4	2	no	—
275	C₂×#102	—	4	2	no	—
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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
298	C₂×C₄×C₈	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	#400	—	2	1	no	—
310	#400	—	2	1	no	—
311	#399	—	2	1	no	—
312	#398	—	2	1	no	—
313	#398	—	2	1	no	—
314	#398	—	2	1	no	—
315	#398	—	2	1	no	—
316	#398	—	2	1	no	—
317	#398	—	2	1	no	—
318	#397	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#396	—	2	1	no	—
323	#396	—	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	#392	—	2	1	no	—
330	#391	C₂³	1	1	yes	characteristic
331	#391	C₂³	1	1	yes	characteristic
332	#390	—	2	1	no	—
333	#390	—	2	1	no	—
334	#390	—	2	1	no	—
335	#390	—	2	1	no	—
336	#390	C₂³	1	1	yes	characteristic
337	#390	C₂³	1	1	yes	characteristic
338	#390	C₂³	1	1	yes	characteristic
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	#389	—	2	1	no	—
345	#389	—	2	1	no	—
346	#389	—	2	1	no	—
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	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#388	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#386	—	2	1	no	—
389	#386	—	2	1	no	—
390	#385	—	2	1	no	—
391	#385	—	2	1	no	—
392	#385	—	2	1	no	—
393	#385	—	2	1	no	—
394	#385	—	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	#385	—	2	1	no	—
401	#385	—	2	1	no	—
402	#385	—	2	1	no	—
403	#385	—	2	1	no	—
404	#384	C₂³	1	1	yes	characteristic
405	#384	C₂³	1	1	yes	characteristic
406	#382	—	2	1	no	—
407	#382	—	2	1	no	—
408	#382	—	2	1	no	—
409	#382	—	2	1	no	—
410	#382	—	2	1	no	—
411	#382	—	2	1	no	—
412	#382	C₂³	1	1	yes	characteristic
413	#382	C₂³	1	1	yes	characteristic
414	#382	C₂³	1	1	yes	characteristic
415	#382	C₂³	1	1	yes	characteristic
416	#382	C₂³	1	1	yes	characteristic
417	#382	C₂³	1	1	yes	characteristic
418	#382	C₂³	1	1	yes	characteristic
419	#382	C₂³	1	1	yes	characteristic
420	#380	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	—	2	1	no	—
423	#380	—	2	1	no	—
424	#380	—	2	1	no	—
425	#380	—	2	1	no	—
426	#380	C₂³	1	1	yes	characteristic
427	#380	C₂³	1	1	yes	characteristic
428	#380	C₂³	1	1	yes	characteristic
429	#380	C₂³	1	1	yes	characteristic
430	#380	C₂³	1	1	yes	characteristic
431	#380	C₂³	1	1	yes	characteristic
432	#379	—	2	1	no	—
433	#379	—	2	1	no	—
434	#379	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
439	C₄×C₄⋊C₄	D₄	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×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	C₂×#95	—	2	1	no	—
452	C₂×#95	—	2	1	no	—
453	C₂×#95	—	2	1	no	—
454	C₂×#95	—	2	1	no	—
455	C₄³	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	#340	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	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂⁵	—	2	1	no	—
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
502	C₂²×D₄	C₂⁴	1	1	yes	characteristic
503	C₂²×D₄	C₂⁴	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
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	C₂³×C₄	C₂⁴	1	1	yes	characteristic
515	C₂²×C₈	—	2	2	no	—
516	C₂²×C₈	—	2	2	no	—
517	C₂²×C₈	—	2	2	no	—
518	C₂²×C₈	—	2	2	no	—
519	C₂²×C₈	—	4	1	no	—
520	C₂²×C₈	—	4	1	no	—
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	#126	—	8	2	no	—
530	#125	—	4	1	no	—
531	#125	—	4	1	no	—
532	#125	—	4	1	no	—
533	#125	—	4	1	no	—
534	#125	—	4	1	no	—
535	#125	—	4	1	no	—
536	#125	—	4	1	no	—
537	#125	—	4	1	no	—
538	#124	—	4	1	no	—
539	#124	—	4	1	no	—
540	#124	—	4	1	no	—
541	#124	—	4	1	no	—
542	#123	—	8	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	4	1	no	—
546	C₂²⋊Q₈	—	4	1	no	—
547	#121	—	4	1	no	—
548	#121	—	4	1	no	—
549	#121	—	4	1	no	—
550	#121	—	4	1	no	—
551	#120	—	4	4	no	—
552	C₄×Q₈	—	4	1	no	—
553	C₄×Q₈	—	4	1	no	—
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	4	2	no	—
558	C₄×D₄	—	4	4	no	—
559	C₄×D₄	—	4	4	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	1	no	—
569	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
593	C₂×C₄⋊C₄	—	4	1	no	—
594	C₂×C₄⋊C₄	—	4	1	no	—
595	C₂×C₄⋊C₄	—	4	1	no	—
596	C₂×C₄⋊C₄	—	4	1	no	—
597	C₂×C₄⋊C₄	—	4	1	no	—
598	C₂×C₄⋊C₄	—	4	1	no	—
599	C₂×C₄⋊C₄	—	4	1	no	—
600	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	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×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	—	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	—	4	4	no	—
647	C₂×C₂²⋊C₄	—	8	2	no	—
648	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
659	C₂×C₄²	—	4	1	no	—
660	C₂×C₄²	—	4	1	no	—
661	C₂×C₄²	—	4	1	no	—
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₂⁴	1	1	yes	characteristic
671	C₂×C₄²	C₂⁴	1	1	yes	characteristic
672	C₂×C₄²	C₂⁴	1	1	yes	characteristic
673	C₂×C₄²	C₂⁴	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	#107	—	2	2	no	—
676	#107	—	2	2	no	—
677	#107	—	2	2	no	—
678	#107	—	4	1	no	—
679	#107	—	4	1	no	—
680	#107	—	4	1	no	—
681	#107	—	4	1	no	—
682	#107	—	4	1	no	—
683	#107	—	4	1	no	—
684	#107	—	4	1	no	—
685	#106	—	2	2	no	—
686	#106	—	2	2	no	—
687	#106	—	2	2	no	—
688	#106	—	4	1	no	—
689	#106	—	4	1	no	—
690	#106	—	4	1	no	—
691	#106	—	4	1	no	—
692	#106	—	4	1	no	—
693	#106	—	4	1	no	—
694	#106	—	4	1	no	—
695	C₄⋊C₈	—	4	1	no	—
696	C₄⋊C₈	—	4	1	no	—
697	#103	—	2	2	no	—
698	#103	—	2	2	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	—	4	1	no	—
710	#102	—	4	1	no	—
711	#102	—	4	1	no	—
712	#102	—	4	1	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	C₂²⋊C₈	—	2	2	no	—
722	C₂²⋊C₈	—	2	2	no	—
723	C₂²⋊C₈	—	2	2	no	—
724	C₂²⋊C₈	—	2	2	no	—
725	C₂²⋊C₈	—	4	1	no	—
726	C₂²⋊C₈	—	4	1	no	—
727	C₄×C₈	—	2	2	no	—
728	C₄×C₈	—	2	2	no	—
729	C₄×C₈	—	4	1	no	—
730	C₄×C₈	—	4	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	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	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	C₂⁴	—	2	1	no	—
777	C₂⁴	—	2	1	no	—
778	C₂⁴	—	4	2	no	—
779	C₂⁴	—	4	2	no	—
780	C₂⁴	—	4	2	no	—
781	C₂⁴	—	8	1	no	—
782	C₂⁴	—	8	1	no	—
783	C₂⁴	—	8	1	no	—
784	C₂⁴	—	8	1	no	—
785	C₂⁴	C₂²×D₄	1	1	yes	characteristic
786	C₂⁴	C₂²×D₄	1	1	yes	characteristic
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	4	4	no	—
808	C₂×D₄	—	4	4	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	—	4	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	8	2	no	—
813	C₂×D₄	—	8	2	no	—
814	C₂×D₄	—	8	1	no	—
815	C₂×D₄	—	8	1	no	—
816	C₂×D₄	—	8	1	no	—
817	C₂×D₄	—	8	1	no	—
818	C₂×D₄	—	8	1	no	—
819	C₂×D₄	—	8	1	no	—
820	C₂×D₄	#135	1	4	yes	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	8	1	no	—
863	C₂²×C₄	—	8	1	no	—
864	C₂²×C₄	—	8	1	no	—
865	C₂²×C₄	—	8	1	no	—
866	C₂²×C₄	—	8	1	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	—	8	1	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
871	C₂²×C₄	—	8	1	no	—
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	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	2₋¹⁺⁴	1	2	yes	—
885	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
886	C₂²×C₄	C₂⁵	1	1	yes	characteristic
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	4	4	no	—
910	C₂×C₈	—	4	4	no	—
911	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
912	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	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	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	—	8	1	no	—
950	C₄⋊C₄	—	8	1	no	—
951	C₄⋊C₄	—	8	1	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	no	—
958	C₄⋊C₄	—	8	1	no	—
959	C₄⋊C₄	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₄⋊C₄	—	8	1	no	—
962	C₄⋊C₄	—	8	1	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	—	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	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	4	1	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	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	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	4	1	no	—
1020	C₄²	—	4	1	no	—
1021	C₄²	—	4	1	no	—
1022	C₄²	—	4	1	no	—
1023	C₄²	—	4	1	no	—
1024	C₄²	—	4	1	no	—
1025	C₄²	—	4	1	no	—
1026	C₄²	—	4	2	no	—
1027	C₄²	—	4	2	no	—
1028	C₄²	—	8	1	no	—
1029	C₄²	—	8	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	—	4	1	no	—
1045	C₂³	—	4	1	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	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	—	8	4	no	—
1055	C₂³	—	8	4	no	—
1056	C₂³	—	8	4	no	—
1057	C₂³	—	16	2	no	—
1058	C₂³	—	16	2	no	—
1059	C₂³	—	16	2	no	—
1060	C₂³	—	16	2	no	—
1061	C₂³	#536	1	2	yes	—
1062	C₂³	C₂×#135	1	2	yes	—
1063	C₂³	C₂×#135	1	2	yes	—
1064	C₂³	#575	1	2	yes	—
1065	C₂³	C₂³×D₄	1	1	yes	characteristic
1066	Q₈	—	4	1	no	—
1067	Q₈	—	4	1	no	—
1068	Q₈	—	4	1	no	—
1069	Q₈	—	4	1	no	—
1070	D₄	—	2	8	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	1	no	—
1078	D₄	—	4	1	no	—
1079	D₄	—	8	4	no	—
1080	D₄	—	16	2	no	—
1081	D₄	—	16	2	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	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	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	—	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	—	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	—	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	—	8	2	no	—
1167	C₂×C₄	—	8	2	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	—	16	2	no	—
1171	C₂×C₄	—	16	2	no	—
1172	C₂×C₄	—	16	2	no	—
1173	C₂×C₄	—	16	2	no	—
1174	C₂×C₄	—	16	2	no	—
1175	C₂×C₄	#536	1	2	yes	—
1176	C₂×C₄	C₂×#135	1	2	yes	—
1177	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1178	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1179	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1180	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1181	C₂×C₄	#585	1	1	yes	characteristic
1182	C₂×C₄	#585	1	1	yes	characteristic
1183	C₈	—	2	2	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	4	1	no	—
1186	C₈	—	4	1	no	—
1187	C₈	—	4	1	no	—
1188	C₈	—	4	1	no	—
1189	C₈	—	4	1	no	—
1190	C₈	—	4	1	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	—	8	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	8	1	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	—	16	8	no	—
1219	C₂²	#3232	1	4	yes	—
1220	C₂²	C₂×#536	1	1	yes	characteristic
1221	C₂²	#3485	1	1	yes	characteristic
1222	C₂²	#3498	1	1	yes	characteristic
1223	C₂²	C₂²×#135	1	1	yes	characteristic
1224	C₂²	C₂×#575	1	1	yes	characteristic
1225	C₂²	#3584	1	1	yes	characteristic
1226	C₂²	#3585	1	1	yes	characteristic
1227	C₄	—	2	2	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	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	#3535	1	1	yes	characteristic
1254	C₄	#3535	1	1	yes	characteristic
1255	C₄	#3541	1	1	yes	characteristic
1256	C₄	#3541	1	1	yes	characteristic
1257	C₂	—	2	4	no	—
1258	C₂	—	4	2	no	—
1259	C₂	—	16	1	no	—
1260	C₂	—	16	1	no	—
1261	C₂	#41370	1	1	yes	characteristic
1262	C₂	C₂×#3232	1	1	yes	characteristic
1263	C₂	#60890	1	1	yes	characteristic
1264	C₂	#61702	1	1	yes	characteristic
1265	C₂	#61732	1	1	yes	characteristic
1266	C₂	#62419	1	1	yes	characteristic
1267	C₂	#62449	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2408	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄²×D₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #36165	C₂	semidirect
3. #32836	C₂	semidirect
4. #32778	C₂	semidirect
5. #32389	C₂	semidirect
6. #32385	C₂	semidirect
7. #31583	C₂	semidirect
8. #31579	C₂	semidirect
9. #30783	C₂	semidirect
10. #30781	C₂	semidirect
11. #30643	C₂	semidirect
12. #30641	C₂	semidirect
13. #30360	C₂	semidirect
14. #30282	C₂	semidirect
15. #30065	C₂	semidirect
16. #29956	C₂	semidirect
17. #29912	C₂	semidirect
18. #29516	C₂	semidirect
19. #29158	C₂	semidirect
20. #27912	C₂	semidirect
21. #27686	C₂	semidirect
22. #27256	C₂	semidirect
23. #27256	C₂	semidirect
24. #26132	C₂	semidirect
25. #26128	C₂	semidirect
26. #26067	C₂	semidirect
27. #26062	C₂	semidirect
30. C₂×#2092	C₂	semidirect
31. #22785	C₂	semidirect
32. C₂×#499	C₂²	semidirect
33. C₂×#499	C₂²	semidirect
36. C₂×#484	C₂²	semidirect
38. C₂×#483	C₂²	semidirect
46. #2859	C₂²	semidirect
49. #2851	C₂²	semidirect
54. #2571	C₂²	semidirect
55. #2571	C₂²	semidirect
70. #2442	C₂²	semidirect
71. #2442	C₂²	semidirect
83. C₄×#125	C₂²	semidirect
87. C₂×#382	C₂²	semidirect
89. #2101	C₂²	semidirect
90. #2101	C₂²	semidirect
91. #2101	C₂²	semidirect
92. #2097	C₂²	semidirect
93. #2097	C₂²	semidirect
94. #2097	C₂²	semidirect
95. #2096	C₂²	semidirect
96. #2095	C₂²	semidirect
109. #2085	C₂²	semidirect
110. #2085	C₂²	semidirect
111. #2085	C₂²	semidirect
112. #2085	C₂²	semidirect
113. #2084	C₂²	semidirect
114. #2083	C₂²	semidirect
115. #2077	C₂²	semidirect
116. #2076	C₂²	semidirect
125. #2059	C₂²	semidirect
126. #2059	C₂²	semidirect
127. #2059	C₂²	semidirect
128. #2059	C₂²	semidirect
129. #2059	C₂²	semidirect
134. #2036	C₂²	semidirect
135. #2035	C₂²	semidirect
140. #2026	C₂²	semidirect
147. #1949	C₂²	semidirect
148. #1949	C₂²	semidirect
149. #1942	C₂²	semidirect
150. #1942	C₂²	semidirect
151. #1941	C₂²	semidirect
152. #1941	C₂²	semidirect
157. #1928	C₂²	semidirect
158. #1927	C₂²	semidirect
163. #1923	C₂²	semidirect
164. #1923	C₂²	semidirect
165. #1921	C₂²	semidirect
166. #1920	C₂²	semidirect
167. #1920	C₂²	semidirect
168. #1918	C₂²	semidirect
169. #1916	C₂²	semidirect
170. #1916	C₂²	semidirect
179. #1865	C₂²	semidirect
180. #1863	C₂²	semidirect
183. #1853	C₂²	semidirect
186. #1852	C₂²	semidirect
187. #1846	C₂²	semidirect
188. #1846	C₂²	semidirect
189. #1839	C₂²	semidirect
190. #1817	C₂²	semidirect
193. #1805	C₂²	semidirect
194. #1805	C₂²	semidirect
200. C₄×C₂²⋊C₈	C₂²	semidirect
201. #1744	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36165	2
#35025	2
#32836	2
#32778	2
#32389	2
#32385	2
#31583	2
#31579	2
#30783	2
#30781	2
#30643	2
#30641	2
#30360	2
#30282	2
#30065	2
#29956	2
#29912	2
#29516	2
#29158	2
#27912	2
#27686	2
#27256	2
#26132	2
#26128	2
#26067	2
#26062	2
#24865	2
#24861	2
C₂×#2092	2
#22785	2