Subgroups — #7065382

Order 512.

1350 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#45365	C₂	1	1	yes	maximal, characteristic
2	#42955	C₂	1	1	yes	maximal, characteristic, complemented
3	#32643	C₂	1	1	yes	maximal, characteristic, complemented
4	#32588	C₂	1	1	yes	maximal, characteristic, complemented
5	#32484	C₂	1	1	yes	maximal, characteristic, complemented
6	#32475	C₂	1	1	yes	maximal, characteristic, complemented
7	#32236	C₂	1	1	yes	maximal, characteristic, complemented
8	#31983	C₂	1	1	yes	maximal, characteristic, complemented
9	#31965	C₂	1	1	yes	maximal, characteristic, complemented
10	#30820	C₂	1	1	yes	maximal, characteristic, complemented
11	#29116	C₂	1	1	yes	maximal, characteristic
12	#29031	C₂	1	1	yes	maximal, characteristic, complemented
13	#28641	C₂	1	1	yes	maximal, characteristic, complemented
14	#28044	C₂	1	1	yes	maximal, characteristic, complemented
15	#27724	C₂	1	1	yes	maximal, characteristic, complemented
16	#27363	C₂	1	1	yes	maximal, characteristic, complemented
17	#27256	C₂	1	1	yes	maximal, characteristic
18	#26760	C₂	1	1	yes	maximal, characteristic, complemented
19	#26468	C₂	1	1	yes	maximal, characteristic, complemented
20	#26032	C₂	1	1	yes	maximal, characteristic, complemented
21	#26013	C₂	1	1	yes	maximal, characteristic, complemented
22	#25952	C₂	1	1	yes	maximal, characteristic
23	#25473	C₂	1	1	yes	maximal, characteristic, complemented
24	#24849	C₂	1	1	yes	maximal, characteristic, complemented
25	#24584	C₂	1	1	yes	maximal, characteristic, complemented
26	#24493	C₂	1	1	yes	maximal, characteristic
27	#23612	C₂	1	1	yes	maximal, characteristic
28	#22958	C₂	1	1	yes	maximal, characteristic, complemented
29	#22614	C₂	1	1	yes	maximal, characteristic, complemented
30	#22580	C₂	1	1	yes	maximal, characteristic
31	#22092	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#488	C₂²	1	1	yes	characteristic
33	C₂×#485	C₂²	1	1	yes	characteristic
34	C₂×#477	C₂²	1	1	yes	characteristic, complemented
35	C₂×#478	C₂²	1	1	yes	characteristic
36	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×#427	C₂²	1	1	yes	characteristic
38	C₂×#424	C₂²	1	1	yes	characteristic
39	C₂×#418	C₂²	1	1	yes	characteristic
40	C₂²×#102	C₂²	1	1	yes	characteristic
41	#2843	—	2	1	no	—
42	#2768	—	2	1	no	—
43	#2768	—	2	1	no	—
44	#2763	—	2	1	no	—
45	#2757	—	2	1	no	—
46	#2742	—	2	1	no	—
47	#2737	—	2	1	no	—
48	#2736	—	2	1	no	—
49	#2735	—	2	1	no	—
50	#2666	—	2	1	no	—
51	#2666	—	2	1	no	—
52	#2628	C₂²	1	1	yes	characteristic
53	#2597	—	2	1	no	—
54	#2592	C₂²	1	1	yes	characteristic
55	#2584	C₂²	1	1	yes	characteristic, complemented
56	#2584	C₂²	1	1	yes	characteristic, complemented
57	#2580	C₂²	1	1	yes	characteristic
58	#2571	—	2	1	no	—
59	#2550	C₂²	1	1	yes	characteristic, complemented
60	#2550	C₂²	1	1	yes	characteristic, complemented
61	#2513	C₂²	1	1	yes	characteristic
62	#2512	C₂²	1	1	yes	characteristic
63	#2508	C₂²	1	1	yes	characteristic, complemented
64	#2508	C₂²	1	1	yes	characteristic, complemented
65	#2508	C₂²	1	1	yes	characteristic, complemented
66	#2508	C₂²	1	1	yes	characteristic, complemented
67	#2499	C₂²	1	1	yes	characteristic
68	#2482	—	2	1	no	—
69	#2480	—	2	1	no	—
70	#2479	—	2	1	no	—
71	#2448	C₂²	1	1	yes	characteristic
72	#2447	C₂²	1	1	yes	characteristic
73	#2442	C₂²	1	1	yes	characteristic
74	#2442	C₂²	1	1	yes	characteristic
75	#2435	C₂²	1	1	yes	characteristic
76	#2396	C₂²	1	1	yes	characteristic
77	#2367	C₂²	1	1	yes	characteristic
78	#2354	C₂²	1	1	yes	characteristic
79	#2347	C₂²	1	1	yes	characteristic
80	#2347	C₂²	1	1	yes	characteristic
81	#2347	C₂²	1	1	yes	characteristic
82	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
83	#2323	C₂²	1	1	yes	characteristic
84	#2317	C₂²	1	1	yes	characteristic
85	#2309	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2101	C₂²	1	1	yes	characteristic, complemented
88	#2100	C₂²	1	1	yes	characteristic, complemented
89	#2092	C₂²	1	1	yes	characteristic
90	#2088	C₂²	1	1	yes	characteristic, complemented
91	#2088	C₂²	1	1	yes	characteristic, complemented
92	#2087	C₂²	1	1	yes	characteristic, complemented
93	#2086	C₂²	1	1	yes	characteristic, complemented
94	#2085	C₂²	1	1	yes	characteristic, complemented
95	#2083	C₂²	1	1	yes	characteristic, complemented
96	#2074	C₂²	1	1	yes	characteristic, complemented
97	#2073	C₂²	1	1	yes	characteristic
98	#2073	C₂²	1	1	yes	characteristic
99	#2073	C₂²	1	1	yes	characteristic
100	#2068	C₂²	1	1	yes	characteristic, complemented
101	#2068	C₂²	1	1	yes	characteristic, complemented
102	#2067	C₂²	1	1	yes	characteristic
103	#2067	C₂²	1	1	yes	characteristic
104	#2067	C₂²	1	1	yes	characteristic
105	#2067	C₂²	1	1	yes	characteristic
106	#2067	C₂²	1	1	yes	characteristic
107	#2066	C₂²	1	1	yes	characteristic, complemented
108	#2066	C₂²	1	1	yes	characteristic, complemented
109	#2065	C₂²	1	1	yes	characteristic
110	#2065	C₂²	1	1	yes	characteristic
111	#2065	C₂²	1	1	yes	characteristic
112	#2065	C₂²	1	1	yes	characteristic
113	#2065	C₂²	1	1	yes	characteristic
114	#2065	C₂²	1	1	yes	characteristic
115	#2065	C₂²	1	1	yes	characteristic
116	#2059	C₂²	1	1	yes	characteristic, complemented
117	#2042	C₂²	1	1	yes	characteristic
118	#2042	C₂²	1	1	yes	characteristic
119	#2042	C₂²	1	1	yes	characteristic
120	#2042	C₂²	1	1	yes	characteristic
121	#2026	C₂²	1	1	yes	characteristic, complemented
122	#2025	C₂²	1	1	yes	characteristic
123	#2025	C₂²	1	1	yes	characteristic
124	#2023	C₂²	1	1	yes	characteristic
125	#2023	C₂²	1	1	yes	characteristic
126	#1991	C₂²	1	1	yes	characteristic, complemented
127	#1989	C₂²	1	1	yes	characteristic, complemented
128	#1988	C₂²	1	1	yes	characteristic, complemented
129	#1985	C₂²	1	1	yes	characteristic, complemented
130	#1983	C₂²	1	1	yes	characteristic
131	#1983	C₂²	1	1	yes	characteristic
132	#1958	C₂²	1	1	yes	characteristic
133	#1949	C₂²	1	1	yes	characteristic, complemented
134	#1949	C₂²	1	1	yes	characteristic, complemented
135	#1949	C₂²	1	1	yes	characteristic, complemented
136	#1948	C₂²	1	1	yes	characteristic, complemented
137	#1943	C₂²	1	1	yes	characteristic, complemented
138	#1942	C₂²	1	1	yes	characteristic, complemented
139	#1942	C₂²	1	1	yes	characteristic, complemented
140	#1941	C₂²	1	1	yes	characteristic, complemented
141	#1940	C₂²	1	1	yes	characteristic, complemented
142	#1939	C₂²	1	1	yes	characteristic, complemented
143	#1939	C₂²	1	1	yes	characteristic, complemented
144	#1936	C₂²	1	1	yes	characteristic
145	#1936	C₂²	1	1	yes	characteristic
146	#1936	C₂²	1	1	yes	characteristic
147	#1935	C₂²	1	1	yes	characteristic, complemented
148	#1935	C₂²	1	1	yes	characteristic, complemented
149	#1934	C₂²	1	1	yes	characteristic
150	#1934	C₂²	1	1	yes	characteristic
151	#1934	C₂²	1	1	yes	characteristic
152	#1934	C₂²	1	1	yes	characteristic
153	#1934	C₂²	1	1	yes	characteristic
154	#1933	C₂²	1	1	yes	characteristic, complemented
155	#1933	C₂²	1	1	yes	characteristic, complemented
156	#1928	C₂²	1	1	yes	characteristic, complemented
157	#1927	C₂²	1	1	yes	characteristic, complemented
158	#1926	C₂²	1	1	yes	characteristic
159	#1925	C₂²	1	1	yes	characteristic
160	#1925	C₂²	1	1	yes	characteristic
161	#1925	C₂²	1	1	yes	characteristic
162	#1921	C₂²	1	1	yes	characteristic, complemented
163	#1920	C₂²	1	1	yes	characteristic, complemented
164	#1920	C₂²	1	1	yes	characteristic, complemented
165	#1920	C₂²	1	1	yes	characteristic, complemented
166	#1919	C₂²	1	1	yes	characteristic, complemented
167	#1919	C₂²	1	1	yes	characteristic, complemented
168	#1919	C₂²	1	1	yes	characteristic, complemented
169	#1919	C₂²	1	1	yes	characteristic, complemented
170	#1916	C₂²	1	1	yes	characteristic, complemented
171	#1916	C₂²	1	1	yes	characteristic, complemented
172	#1894	C₂²	1	1	yes	characteristic
173	#1892	C₂²	1	1	yes	characteristic
174	#1872	C₂²	1	1	yes	characteristic
175	#1865	C₂²	1	1	yes	characteristic, complemented
176	#1865	C₂²	1	1	yes	characteristic, complemented
177	#1864	C₂²	1	1	yes	characteristic
178	#1864	C₂²	1	1	yes	characteristic
179	#1862	C₂²	1	1	yes	characteristic
180	#1862	C₂²	1	1	yes	characteristic
181	#1853	C₂²	1	1	yes	characteristic
182	#1851	C₂²	1	1	yes	characteristic
183	#1850	C₂²	1	1	yes	characteristic
184	#1836	C₂²	1	1	yes	characteristic, complemented
185	#1825	C₂²	1	1	yes	characteristic
186	#1825	C₂²	1	1	yes	characteristic
187	#1825	C₂²	1	1	yes	characteristic
188	#1809	C₂²	1	1	yes	characteristic
189	#1808	C₂²	1	1	yes	characteristic
190	#1805	C₂²	1	1	yes	characteristic, complemented
191	#1804	C₂²	1	1	yes	characteristic
192	#1786	C₂²	1	1	yes	characteristic
193	#1786	C₂²	1	1	yes	characteristic
194	C₄×#107	C₂²	1	1	yes	characteristic, complemented
195	C₄×#107	C₂²	1	1	yes	characteristic, complemented
196	#1771	C₂²	1	1	yes	characteristic, complemented
197	#1762	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
201	#1750	C₂²	1	1	yes	characteristic
202	#1736	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂×#126	—	2	1	no	—
208	C₂×#125	C₂³	1	1	yes	characteristic
209	C₂×#125	C₂³	1	1	yes	characteristic
210	C₂×#124	C₂³	1	1	yes	characteristic
211	C₂×#124	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
217	C₂×#117	—	2	1	no	—
218	C₂×#117	C₂³	1	1	yes	characteristic
219	C₂×#117	C₂³	1	1	yes	characteristic
220	C₂×#117	C₂³	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂²×C₂²⋊C₄	—	2	1	no	—
223	#488	—	4	2	no	—
224	#485	—	2	4	no	—
225	#478	—	4	2	no	—
226	#477	—	4	2	no	—
227	C₈×Q₈	—	4	2	no	—
228	#427	—	2	4	no	—
229	C₂×#107	C₂³	1	1	yes	characteristic
230	C₂×#107	C₂³	1	1	yes	characteristic
231	C₂×#107	C₂³	1	1	yes	characteristic
232	C₂×#107	C₂³	1	1	yes	characteristic
233	C₂×#107	C₂³	1	1	yes	characteristic
234	C₂×#107	C₂³	1	1	yes	characteristic
235	C₂×#106	C₂³	1	1	yes	characteristic
236	C₂×#106	C₂³	1	1	yes	characteristic
237	C₂×#106	C₂³	1	1	yes	characteristic
238	C₂×#106	C₂³	1	1	yes	characteristic
239	C₂×#106	C₂³	1	1	yes	characteristic
240	C₂×#106	C₂³	1	1	yes	characteristic
241	#424	—	4	2	no	—
242	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	#418	—	2	4	no	—
251	C₂×#103	C₂³	1	1	yes	characteristic
252	C₂×#103	C₂³	1	1	yes	characteristic
253	C₂×#103	C₂³	1	1	yes	characteristic
254	C₂×#103	C₂³	1	1	yes	characteristic
255	C₂×#103	C₂³	1	1	yes	characteristic
256	C₂×#103	C₂³	1	1	yes	characteristic
257	C₂×#103	C₂³	1	1	yes	characteristic
258	C₂×#103	C₂³	1	1	yes	characteristic
259	C₂×#102	—	4	2	no	—
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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×#97	C₂³	1	1	yes	characteristic
279	C₂×#97	C₂³	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
284	#400	—	2	1	no	—
285	#400	—	2	1	no	—
286	#400	—	2	1	no	—
287	#400	—	2	1	no	—
288	#400	—	2	1	no	—
289	#400	—	2	1	no	—
290	#400	—	2	1	no	—
291	#400	D₄	1	1	yes	characteristic
292	#399	—	2	1	no	—
293	#399	—	2	1	no	—
294	#399	—	2	1	no	—
295	#399	D₄	1	1	yes	characteristic
296	#398	—	2	1	no	—
297	#398	—	2	1	no	—
298	#398	—	2	1	no	—
299	#398	—	2	1	no	—
300	#398	—	2	1	no	—
301	#398	—	2	1	no	—
302	#398	—	2	1	no	—
303	#398	—	2	1	no	—
304	#398	—	2	1	no	—
305	#398	—	2	1	no	—
306	#398	D₄	1	1	yes	characteristic
307	#398	D₄	1	1	yes	characteristic
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#397	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	2	1	no	—
317	#396	—	2	1	no	—
318	#396	D₄	1	1	yes	characteristic
319	#396	D₄	1	1	yes	characteristic
320	#395	—	2	1	no	—
321	#395	—	2	1	no	—
322	#395	—	2	1	no	—
323	#395	—	2	1	no	—
324	#395	—	2	1	no	—
325	#395	D₄	1	1	yes	characteristic
326	#394	—	2	1	no	—
327	#394	—	2	1	no	—
328	#393	—	2	1	no	—
329	#393	—	2	1	no	—
330	#393	—	2	1	no	—
331	#393	D₄	1	1	yes	characteristic
332	#391	—	2	1	no	—
333	#391	—	2	1	no	—
334	#391	C₂³	1	1	yes	characteristic
335	#391	C₂³	1	1	yes	characteristic
336	#391	C₂³	1	1	yes	characteristic
337	#390	—	2	1	no	—
338	#390	—	2	1	no	—
339	#390	C₂³	1	1	yes	characteristic
340	#390	C₂³	1	1	yes	characteristic
341	#390	C₂³	1	1	yes	characteristic
342	#390	C₂³	1	1	yes	characteristic
343	#390	C₂³	1	1	yes	characteristic
344	#390	C₂³	1	1	yes	characteristic
345	#390	C₂³	1	1	yes	characteristic
346	#390	C₂³	1	1	yes	characteristic
347	#389	—	2	1	no	—
348	#389	—	2	1	no	—
349	#389	—	2	1	no	—
350	#389	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	—	2	1	no	—
353	#389	—	2	1	no	—
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	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#389	C₂³	1	1	yes	characteristic
365	#389	C₂³	1	1	yes	characteristic
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#389	C₂³	1	1	yes	characteristic
369	#389	C₂³	1	1	yes	characteristic
370	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
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	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#386	—	2	1	no	—
398	#386	—	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	#385	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#384	—	2	1	no	—
408	#384	C₂³	1	1	yes	characteristic
409	#383	—	2	1	no	—
410	#383	—	2	1	no	—
411	#383	—	2	1	no	—
412	#382	—	2	1	no	—
413	#382	—	2	1	no	—
414	#382	—	2	1	no	—
415	#382	—	2	1	no	—
416	#382	—	2	1	no	—
417	#382	C₂³	1	1	yes	characteristic
418	#382	C₂³	1	1	yes	characteristic
419	#382	C₂³	1	1	yes	characteristic
420	#382	C₂³	1	1	yes	characteristic
421	#381	—	2	1	no	—
422	#380	—	2	1	no	—
423	#380	—	2	1	no	—
424	#380	—	2	1	no	—
425	#380	C₂³	1	1	yes	characteristic
426	#380	C₂³	1	1	yes	characteristic
427	#380	C₂³	1	1	yes	characteristic
428	#379	—	2	1	no	—
429	#379	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	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	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
490	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
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	C₂⁴	1	1	yes	characteristic
504	C₂×M₁₆	—	2	2	no	—
505	C₂×M₁₆	—	4	1	no	—
506	C₂×M₁₆	—	4	1	no	—
507	C₂²×C₈	—	2	2	no	—
508	C₂²×C₈	—	2	2	no	—
509	C₂²×C₈	—	4	1	no	—
510	C₂²×C₈	C₂⁴	1	1	yes	characteristic
511	C₂²×C₈	C₂⁴	1	1	yes	characteristic
512	C₂²×C₈	C₂⁴	1	1	yes	characteristic
513	C₂²×C₈	C₂⁴	1	1	yes	characteristic
514	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	4	1	no	—
519	C₄⋊Q₈	—	4	1	no	—
520	#126	—	8	2	no	—
521	#125	—	4	1	no	—
522	#125	—	4	1	no	—
523	#125	—	4	1	no	—
524	#125	—	4	1	no	—
525	#124	—	2	2	no	—
526	#124	—	4	1	no	—
527	#124	—	4	1	no	—
528	#124	—	4	1	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₄×Q₈	—	4	1	no	—
532	C₄×Q₈	—	4	1	no	—
533	C₄×Q₈	—	4	1	no	—
534	C₄×Q₈	—	4	1	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	4	1	no	—
537	C₄×D₄	—	4	1	no	—
538	C₄×D₄	—	4	1	no	—
539	#117	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	—	4	1	no	—
543	#117	—	4	1	no	—
544	#117	—	8	2	no	—
545	#117	#41	1	4	yes	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	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	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	—	4	1	no	—
574	C₂×C₄⋊C₄	—	4	1	no	—
575	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	8	2	no	—
628	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	1	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂⁴	1	1	yes	characteristic
645	C₂×C₄²	C₂⁴	1	1	yes	characteristic
646	C₂×C₄²	C₂⁴	1	1	yes	characteristic
647	C₂×C₄²	C₂⁴	1	1	yes	characteristic
648	C₂×C₄²	C₂⁴	1	1	yes	characteristic
649	C₂×C₄²	C₂⁴	1	1	yes	characteristic
650	#107	—	2	2	no	—
651	#107	—	2	2	no	—
652	#107	—	2	2	no	—
653	#107	—	2	2	no	—
654	#107	—	4	1	no	—
655	#107	—	4	1	no	—
656	#106	—	2	2	no	—
657	#106	—	2	2	no	—
658	#106	—	2	2	no	—
659	#106	—	4	1	no	—
660	#106	—	4	1	no	—
661	#106	—	4	1	no	—
662	C₄⋊C₈	—	2	2	no	—
663	C₄⋊C₈	—	2	2	no	—
664	C₄⋊C₈	—	2	2	no	—
665	C₄⋊C₈	—	4	1	no	—
666	C₄⋊C₈	—	4	1	no	—
667	C₄⋊C₈	—	4	1	no	—
668	C₄⋊C₈	—	4	1	no	—
669	C₄⋊C₈	—	4	1	no	—
670	#103	—	2	2	no	—
671	#103	—	2	2	no	—
672	#103	—	2	2	no	—
673	#103	—	4	1	no	—
674	#103	—	4	1	no	—
675	#103	—	4	1	no	—
676	#103	—	4	1	no	—
677	#103	—	4	1	no	—
678	#102	—	2	2	no	—
679	#102	—	2	2	no	—
680	#102	—	2	2	no	—
681	#102	—	2	2	no	—
682	#102	—	2	2	no	—
683	#102	—	2	2	no	—
684	#102	—	2	2	no	—
685	#102	—	2	2	no	—
686	#102	—	4	1	no	—
687	#102	—	4	1	no	—
688	#102	—	4	1	no	—
689	#102	—	4	1	no	—
690	#102	—	4	1	no	—
691	#102	—	4	1	no	—
692	#102	—	4	1	no	—
693	#102	—	4	1	no	—
694	C₂²⋊C₈	—	2	2	no	—
695	C₂²⋊C₈	—	2	2	no	—
696	#97	—	4	1	no	—
697	#97	—	4	1	no	—
698	C₄×C₈	—	2	2	no	—
699	C₄×C₈	—	4	1	no	—
700	C₄×C₈	—	4	1	no	—
701	C₄×C₈	—	4	1	no	—
702	#95	—	2	1	no	—
703	#95	—	2	1	no	—
704	#95	—	2	1	no	—
705	#95	—	2	1	no	—
706	#95	—	2	1	no	—
707	#95	—	2	1	no	—
708	#95	—	2	1	no	—
709	#95	—	2	1	no	—
710	#95	—	2	1	no	—
711	#95	—	2	1	no	—
712	#95	—	2	1	no	—
713	#95	—	2	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	C₂⁴	—	2	1	no	—
754	C₂⁴	—	2	1	no	—
755	C₂⁴	—	4	2	no	—
756	C₂⁴	—	4	2	no	—
757	C₂⁴	—	8	1	no	—
758	C₂⁴	—	8	1	no	—
759	C₂⁴	—	8	1	no	—
760	C₂⁴	—	8	1	no	—
761	C₂⁴	—	8	1	no	—
762	C₂⁴	C₂²×D₄	1	1	yes	characteristic
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	4	1	no	—
770	C₂×Q₈	—	4	1	no	—
771	C₂×Q₈	—	4	1	no	—
772	C₂×Q₈	—	8	1	no	—
773	C₂×Q₈	—	8	1	no	—
774	C₂×Q₈	—	8	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	—	4	4	no	—
787	C₂×D₄	—	4	4	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	8	2	no	—
791	C₂×D₄	—	8	2	no	—
792	C₂×D₄	—	8	1	no	—
793	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	8	1	no	—
815	C₂²×C₄	—	8	1	no	—
816	C₂²×C₄	—	8	1	no	—
817	C₂²×C₄	—	8	1	no	—
818	C₂²×C₄	—	8	1	no	—
819	C₂²×C₄	—	8	1	no	—
820	C₂²×C₄	—	8	1	no	—
821	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
822	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
823	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
824	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
825	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
826	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
827	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
828	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
829	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
830	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
831	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
832	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
833	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂²×C₄	C₂×#41	1	2	yes	—
835	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
836	C₂²×C₄	C₂⁵	1	1	yes	characteristic
837	M₁₆	—	8	2	no	—
838	C₂×C₈	—	2	1	no	—
839	C₂×C₈	—	2	1	no	—
840	C₂×C₈	—	2	1	no	—
841	C₂×C₈	—	2	1	no	—
842	C₂×C₈	—	2	1	no	—
843	C₂×C₈	—	2	1	no	—
844	C₂×C₈	—	2	1	no	—
845	C₂×C₈	—	2	1	no	—
846	C₂×C₈	—	2	1	no	—
847	C₂×C₈	—	2	1	no	—
848	C₂×C₈	—	2	1	no	—
849	C₂×C₈	—	2	1	no	—
850	C₂×C₈	—	2	1	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	2	1	no	—
855	C₂×C₈	—	2	1	no	—
856	C₂×C₈	—	2	1	no	—
857	C₂×C₈	—	2	1	no	—
858	C₂×C₈	—	2	1	no	—
859	C₂×C₈	—	2	1	no	—
860	C₂×C₈	—	2	1	no	—
861	C₂×C₈	—	4	4	no	—
862	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	4	1	no	—
888	C₄⋊C₄	—	4	1	no	—
889	C₄⋊C₄	—	4	1	no	—
890	C₄⋊C₄	—	4	1	no	—
891	C₄⋊C₄	—	4	1	no	—
892	C₄⋊C₄	—	4	1	no	—
893	C₄⋊C₄	—	4	1	no	—
894	C₄⋊C₄	—	4	1	no	—
895	C₄⋊C₄	—	4	1	no	—
896	C₄⋊C₄	—	4	1	no	—
897	C₄⋊C₄	—	4	1	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	8	1	no	—
901	C₄⋊C₄	—	8	1	no	—
902	C₄⋊C₄	—	8	1	no	—
903	C₄⋊C₄	—	8	1	no	—
904	C₄⋊C₄	—	8	1	no	—
905	C₄⋊C₄	—	8	1	no	—
906	C₄⋊C₄	—	8	1	no	—
907	C₄⋊C₄	—	8	1	no	—
908	C₄⋊C₄	—	8	1	no	—
909	C₄⋊C₄	—	8	1	no	—
910	C₄⋊C₄	—	8	1	no	—
911	C₄⋊C₄	—	8	1	no	—
912	C₄⋊C₄	—	8	1	no	—
913	C₄⋊C₄	—	8	1	no	—
914	C₄⋊C₄	—	8	1	no	—
915	C₄⋊C₄	—	8	1	no	—
916	C₄⋊C₄	—	8	1	no	—
917	C₄⋊C₄	—	8	1	no	—
918	C₄⋊C₄	—	8	1	no	—
919	C₄⋊C₄	—	8	1	no	—
920	C₄⋊C₄	—	8	1	no	—
921	C₄⋊C₄	—	8	1	no	—
922	C₄⋊C₄	—	8	1	no	—
923	C₄⋊C₄	—	8	1	no	—
924	C₄⋊C₄	—	8	1	no	—
925	C₄⋊C₄	C₂×#41	1	2	yes	—
926	C₄⋊C₄	C₂×#41	1	2	yes	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	4	1	no	—
929	C₂²⋊C₄	—	4	1	no	—
930	C₂²⋊C₄	—	4	1	no	—
931	C₂²⋊C₄	—	4	1	no	—
932	C₂²⋊C₄	—	4	1	no	—
933	C₂²⋊C₄	—	4	1	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	8	1	no	—
941	C₂²⋊C₄	—	8	1	no	—
942	C₂²⋊C₄	—	8	1	no	—
943	C₂²⋊C₄	—	8	1	no	—
944	C₂²⋊C₄	—	8	1	no	—
945	C₂²⋊C₄	—	8	1	no	—
946	C₂²⋊C₄	—	8	1	no	—
947	C₂²⋊C₄	—	8	1	no	—
948	C₂²⋊C₄	—	8	1	no	—
949	C₂²⋊C₄	—	8	1	no	—
950	C₂²⋊C₄	—	8	1	no	—
951	C₂²⋊C₄	—	8	1	no	—
952	C₂²⋊C₄	—	8	1	no	—
953	C₂²⋊C₄	—	8	1	no	—
954	C₂²⋊C₄	—	8	1	no	—
955	C₂²⋊C₄	—	8	1	no	—
956	C₂²⋊C₄	—	8	1	no	—
957	C₂²⋊C₄	—	8	1	no	—
958	C₂²⋊C₄	—	8	1	no	—
959	C₂²⋊C₄	—	8	1	no	—
960	C₂²⋊C₄	—	8	1	no	—
961	C₄²	—	2	4	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	4	2	no	—
975	C₄²	—	8	1	no	—
976	C₄²	—	8	1	no	—
977	C₄²	—	8	1	no	—
978	C₄²	—	8	1	no	—
979	C₄²	—	8	1	no	—
980	C₄²	—	8	1	no	—
981	C₄²	—	8	1	no	—
982	C₄²	—	8	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	4	1	no	—
991	C₂³	—	4	1	no	—
992	C₂³	—	4	1	no	—
993	C₂³	—	4	1	no	—
994	C₂³	—	4	1	no	—
995	C₂³	—	4	1	no	—
996	C₂³	—	4	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	4	1	no	—
999	C₂³	—	4	1	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	—	4	1	no	—
1003	C₂³	—	8	4	no	—
1004	C₂³	—	8	4	no	—
1005	C₂³	—	16	2	no	—
1006	C₂³	—	16	2	no	—
1007	C₂³	—	16	2	no	—
1008	C₂³	—	16	2	no	—
1009	C₂³	—	16	2	no	—
1010	C₂³	#548	1	2	yes	—
1011	C₂³	C₂³×D₄	1	1	yes	characteristic
1012	Q₈	—	4	4	no	—
1013	Q₈	—	4	1	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	4	1	no	—
1016	Q₈	—	4	1	no	—
1017	Q₈	—	16	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	1	no	—
1024	D₄	—	4	1	no	—
1025	D₄	—	4	1	no	—
1026	D₄	—	8	4	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	1	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	8	4	no	—
1112	C₂×C₄	—	16	2	no	—
1113	C₂×C₄	—	16	2	no	—
1114	C₂×C₄	#548	1	2	yes	—
1115	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1116	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1117	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1118	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1119	C₂×C₄	#585	1	1	yes	characteristic
1120	C₂×C₄	#585	1	1	yes	characteristic
1121	C₈	—	2	2	no	—
1122	C₈	—	4	1	no	—
1123	C₈	—	4	1	no	—
1124	C₈	—	4	1	no	—
1125	C₈	—	4	1	no	—
1126	C₈	—	4	1	no	—
1127	C₈	—	4	1	no	—
1128	C₈	—	4	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	8	1	no	—
1140	C₂²	—	8	1	no	—
1141	C₂²	—	8	1	no	—
1142	C₂²	—	8	1	no	—
1143	C₂²	—	8	1	no	—
1144	C₂²	—	8	1	no	—
1145	C₂²	—	8	1	no	—
1146	C₂²	—	8	1	no	—
1147	C₂²	—	8	1	no	—
1148	C₂²	—	8	1	no	—
1149	C₂²	—	8	1	no	—
1150	C₂²	—	16	8	no	—
1151	C₂²	C₂×#548	1	1	yes	characteristic
1152	C₂²	#3489	1	1	yes	characteristic
1153	C₂²	#3496	1	1	yes	characteristic
1154	C₂²	#3584	1	1	yes	characteristic
1155	C₂²	#3584	1	1	yes	characteristic
1156	C₂²	#3584	1	1	yes	characteristic
1157	C₂²	#3585	1	1	yes	characteristic
1158	C₄	—	2	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	8	1	no	—
1174	C₄	—	8	1	no	—
1175	C₄	—	8	1	no	—
1176	C₄	—	8	1	no	—
1177	C₄	—	8	1	no	—
1178	C₄	—	8	1	no	—
1179	C₄	—	8	1	no	—
1180	C₄	—	8	1	no	—
1181	C₄	—	8	1	no	—
1182	C₄	—	8	1	no	—
1183	C₄	—	8	1	no	—
1184	C₄	—	8	1	no	—
1185	C₄	#3494	1	1	yes	characteristic
1186	C₄	#3495	1	1	yes	characteristic
1187	C₄	#3538	1	1	yes	characteristic
1188	C₄	#3564	1	1	yes	characteristic
1189	C₂	—	4	2	no	—
1190	C₂	—	8	2	no	—
1191	C₂	—	16	1	no	—
1192	C₂	#43908	1	1	yes	characteristic
1193	C₂	#61331	1	1	yes	characteristic
1194	C₂	#61349	1	1	yes	characteristic
1195	C₂	#62175	1	1	yes	characteristic
1196	C₂	#62208	1	1	yes	characteristic
1197	C₂	#62275	1	1	yes	characteristic
1198	C₂	#62347	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2396 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #42955	C₂	semidirect
3. #32643	C₂	semidirect
4. #32588	C₂	semidirect
5. #32484	C₂	semidirect
6. #32475	C₂	semidirect
7. #32236	C₂	semidirect
8. #31983	C₂	semidirect
9. #31965	C₂	semidirect
10. #30820	C₂	semidirect
12. #29031	C₂	semidirect
13. #28641	C₂	semidirect
14. #28044	C₂	semidirect
15. #27724	C₂	semidirect
16. #27363	C₂	semidirect
18. #26760	C₂	semidirect
19. #26468	C₂	semidirect
20. #26032	C₂	semidirect
21. #26013	C₂	semidirect
23. #25473	C₂	semidirect
24. #24849	C₂	semidirect
25. #24584	C₂	semidirect
28. #22958	C₂	semidirect
29. #22614	C₂	semidirect
31. #22092	C₂	semidirect
34. C₂×#477	C₂²	semidirect
36. C₂×C₈×Q₈	C₂²	semidirect
55. #2584	C₂²	semidirect
56. #2584	C₂²	semidirect
59. #2550	C₂²	semidirect
60. #2550	C₂²	semidirect
63. #2508	C₂²	semidirect
64. #2508	C₂²	semidirect
65. #2508	C₂²	semidirect
66. #2508	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
88. #2100	C₂²	semidirect
90. #2088	C₂²	semidirect
91. #2088	C₂²	semidirect
92. #2087	C₂²	semidirect
93. #2086	C₂²	semidirect
94. #2085	C₂²	semidirect
95. #2083	C₂²	semidirect
96. #2074	C₂²	semidirect
100. #2068	C₂²	semidirect
101. #2068	C₂²	semidirect
107. #2066	C₂²	semidirect
108. #2066	C₂²	semidirect
116. #2059	C₂²	semidirect
121. #2026	C₂²	semidirect
126. #1991	C₂²	semidirect
127. #1989	C₂²	semidirect
128. #1988	C₂²	semidirect
129. #1985	C₂²	semidirect
133. #1949	C₂²	semidirect
134. #1949	C₂²	semidirect
135. #1949	C₂²	semidirect
136. #1948	C₂²	semidirect
137. #1943	C₂²	semidirect
138. #1942	C₂²	semidirect
139. #1942	C₂²	semidirect
140. #1941	C₂²	semidirect
141. #1940	C₂²	semidirect
142. #1939	C₂²	semidirect
143. #1939	C₂²	semidirect
147. #1935	C₂²	semidirect
148. #1935	C₂²	semidirect
154. #1933	C₂²	semidirect
155. #1933	C₂²	semidirect
156. #1928	C₂²	semidirect
157. #1927	C₂²	semidirect
162. #1921	C₂²	semidirect
163. #1920	C₂²	semidirect
164. #1920	C₂²	semidirect
165. #1920	C₂²	semidirect
166. #1919	C₂²	semidirect
167. #1919	C₂²	semidirect
168. #1919	C₂²	semidirect
169. #1919	C₂²	semidirect
170. #1916	C₂²	semidirect
171. #1916	C₂²	semidirect
175. #1865	C₂²	semidirect
176. #1865	C₂²	semidirect
184. #1836	C₂²	semidirect
190. #1805	C₂²	semidirect
194. C₄×#107	C₂²	semidirect
195. C₄×#107	C₂²	semidirect
196. #1771	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#45365	2
#42955	2
#32643	2
#32588	2
#32484	2
#32475	2
#32236	2
#31983	2
#31965	2
#30820	2
#29116	2
#29031	2
#28641	2
#28044	2
#27724	2
#27363	2
#27256	2
#26760	2
#26468	2
#26032	2
#26013	2
#25952	2
#25473	2
#24849	2
#24584	2
#24493	2
#23612	2
#22958	2
#22614	2
#22580	2
#22092	2