Subgroups — #7010288

Order 512.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59424	C₂	1	1	yes	maximal, characteristic, complemented
2	#40034	C₂	1	1	yes	maximal, characteristic, complemented
3	#32659	C₂	1	1	yes	maximal, characteristic, complemented
4	#32624	C₂	1	1	yes	maximal, characteristic, complemented
5	#32536	C₂	1	1	yes	maximal, characteristic, complemented
6	#32401	C₂	1	1	yes	maximal, characteristic, complemented
7	#31928	C₂	1	1	yes	maximal, characteristic, complemented
8	#31922	C₂	1	1	yes	maximal, characteristic, complemented
9	#31579	C₂	1	1	yes	maximal, characteristic, complemented
10	#31217	C₂	1	1	yes	maximal, characteristic, complemented
11	#28893	C₂	1	1	yes	maximal, characteristic, complemented
12	#28361	C₂	1	1	yes	maximal, characteristic, complemented
13	#28312	C₂	1	1	yes	maximal, characteristic
14	#28275	C₂	1	1	yes	maximal, characteristic, complemented
15	#28025	C₂	1	1	yes	maximal, characteristic, complemented
16	#27945	C₂	1	1	yes	maximal, characteristic, complemented
17	#27195	C₂	1	1	yes	maximal, characteristic, complemented
18	#26611	C₂	1	1	yes	maximal, characteristic, complemented
19	#26543	C₂	1	1	yes	maximal, characteristic, complemented
20	#26087	C₂	1	1	yes	maximal, characteristic, complemented
21	#25298	C₂	1	1	yes	maximal, characteristic, complemented
22	#25219	C₂	1	1	yes	maximal, characteristic, complemented
23	#25101	C₂	1	1	yes	maximal, characteristic
24	#24757	C₂	1	1	yes	maximal, characteristic, complemented
25	#24590	C₂	1	1	yes	maximal, characteristic, complemented
26	#24539	C₂	1	1	yes	maximal, characteristic
27	#23618	C₂	1	1	yes	maximal, characteristic, complemented
28	#22955	C₂	1	1	yes	maximal, characteristic, complemented
29	#22931	C₂	1	1	yes	maximal, characteristic, complemented
30	#22864	C₂	1	1	yes	maximal, characteristic, complemented
31	#22083	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#485	C₂²	1	1	yes	characteristic
33	C₂×#483	C₂²	1	1	yes	characteristic
34	C₂×#480	C₂²	1	1	yes	characteristic
35	C₂×#470	C₂²	1	1	yes	characteristic
36	C₂×#468	C₂²	1	1	yes	characteristic
37	C₂×#464	C₂²	1	1	yes	characteristic, complemented
38	C₂×#463	C₂²	1	1	yes	characteristic
39	C₂×#450	C₂²	1	1	yes	characteristic
40	C₂×#447	C₂²	1	1	yes	characteristic
41	C₂×#446	C₂²	1	1	yes	characteristic, complemented
42	C₂×#440	C₂²	1	1	yes	characteristic
43	C₂×#428	C₂²	1	1	yes	characteristic
44	C₂×#423	C₂²	1	1	yes	characteristic
45	C₂×#418	C₂²	1	1	yes	characteristic
46	C₂×#418	C₂²	1	1	yes	characteristic
47	#2850	C₂²	1	1	yes	characteristic
48	#2796	—	2	1	no	—
49	#2786	—	2	1	no	—
50	#2782	—	2	1	no	—
51	#2750	—	2	1	no	—
52	#2740	—	2	1	no	—
53	#2723	—	2	1	no	—
54	#2650	—	2	1	no	—
55	#2601	—	2	1	no	—
56	#2596	—	2	1	no	—
57	#2592	C₂²	1	1	yes	characteristic
58	#2581	C₂²	1	1	yes	characteristic, complemented
59	#2580	C₂²	1	1	yes	characteristic, complemented
60	#2575	—	2	1	no	—
61	#2571	C₂²	1	1	yes	characteristic, complemented
62	#2571	C₂²	1	1	yes	characteristic, complemented
63	#2560	—	2	1	no	—
64	#2538	C₂²	1	1	yes	characteristic
65	#2512	C₂²	1	1	yes	characteristic
66	#2512	C₂²	1	1	yes	characteristic
67	#2512	C₂²	1	1	yes	characteristic, complemented
68	#2511	C₂²	1	1	yes	characteristic, complemented
69	#2502	C₂²	1	1	yes	characteristic
70	#2500	C₂²	1	1	yes	characteristic
71	#2499	C₂²	1	1	yes	characteristic
72	#2480	—	2	1	no	—
73	#2480	—	2	1	no	—
74	#2448	C₂²	1	1	yes	characteristic
75	#2448	C₂²	1	1	yes	characteristic, complemented
76	#2447	C₂²	1	1	yes	characteristic
77	#2447	C₂²	1	1	yes	characteristic, complemented
78	#2437	—	2	1	no	—
79	#2435	C₂²	1	1	yes	characteristic
80	#2367	C₂²	1	1	yes	characteristic
81	#2363	C₂²	1	1	yes	characteristic
82	#2362	C₂²	1	1	yes	characteristic
83	#2354	C₂²	1	1	yes	characteristic
84	#2345	C₂²	1	1	yes	characteristic
85	#2342	—	2	1	no	—
86	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	#2334	—	2	1	no	—
88	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
90	#2296	C₂²	1	1	yes	characteristic
91	C₂×#390	C₂²	1	1	yes	characteristic
92	#2097	C₂²	1	1	yes	characteristic, complemented
93	#2095	C₂²	1	1	yes	characteristic, complemented
94	#2094	C₂²	1	1	yes	characteristic
95	#2094	C₂²	1	1	yes	characteristic, complemented
96	#2093	C₂²	1	1	yes	characteristic, complemented
97	#2092	C₂²	1	1	yes	characteristic
98	#2092	C₂²	1	1	yes	characteristic
99	#2092	C₂²	1	1	yes	characteristic
100	#2085	C₂²	1	1	yes	characteristic, complemented
101	#2084	C₂²	1	1	yes	characteristic, complemented
102	#2084	C₂²	1	1	yes	characteristic, complemented
103	#2073	C₂²	1	1	yes	characteristic
104	#2072	C₂²	1	1	yes	characteristic, complemented
105	#2071	C₂²	1	1	yes	characteristic
106	#2068	C₂²	1	1	yes	characteristic, complemented
107	#2068	C₂²	1	1	yes	characteristic, complemented
108	#2067	C₂²	1	1	yes	characteristic
109	#2067	C₂²	1	1	yes	characteristic
110	#2067	C₂²	1	1	yes	characteristic
111	#2067	C₂²	1	1	yes	characteristic
112	#2067	C₂²	1	1	yes	characteristic
113	#2066	C₂²	1	1	yes	characteristic, complemented
114	#2066	C₂²	1	1	yes	characteristic, complemented
115	#2065	C₂²	1	1	yes	characteristic
116	#2065	C₂²	1	1	yes	characteristic
117	#2065	C₂²	1	1	yes	characteristic
118	#2065	C₂²	1	1	yes	characteristic
119	#2065	C₂²	1	1	yes	characteristic, complemented
120	#2056	C₂²	1	1	yes	characteristic, complemented
121	#2056	C₂²	1	1	yes	characteristic, complemented
122	#2055	C₂²	1	1	yes	characteristic, complemented
123	#2054	C₂²	1	1	yes	characteristic
124	#2054	C₂²	1	1	yes	characteristic
125	#2054	C₂²	1	1	yes	characteristic
126	#2042	C₂²	1	1	yes	characteristic
127	#2015	C₂²	1	1	yes	characteristic
128	#2015	C₂²	1	1	yes	characteristic
129	#2012	C₂²	1	1	yes	characteristic
130	#2012	C₂²	1	1	yes	characteristic
131	#2012	C₂²	1	1	yes	characteristic
132	#1985	C₂²	1	1	yes	characteristic, complemented
133	#1983	C₂²	1	1	yes	characteristic
134	#1983	C₂²	1	1	yes	characteristic, complemented
135	#1973	C₂²	1	1	yes	characteristic
136	#1973	C₂²	1	1	yes	characteristic
137	#1973	C₂²	1	1	yes	characteristic
138	#1973	C₂²	1	1	yes	characteristic, complemented
139	#1972	C₂²	1	1	yes	characteristic
140	#1972	C₂²	1	1	yes	characteristic
141	#1968	C₂²	1	1	yes	characteristic
142	#1968	C₂²	1	1	yes	characteristic
143	#1968	C₂²	1	1	yes	characteristic, complemented
144	#1959	C₂²	1	1	yes	characteristic
145	#1958	C₂²	1	1	yes	characteristic
146	#1949	C₂²	1	1	yes	characteristic, complemented
147	#1949	C₂²	1	1	yes	characteristic, complemented
148	#1948	C₂²	1	1	yes	characteristic, complemented
149	#1948	C₂²	1	1	yes	characteristic, complemented
150	#1944	C₂²	1	1	yes	characteristic, complemented
151	#1943	C₂²	1	1	yes	characteristic, complemented
152	#1942	C₂²	1	1	yes	characteristic, complemented
153	#1940	C₂²	1	1	yes	characteristic, complemented
154	#1940	C₂²	1	1	yes	characteristic, complemented
155	#1939	C₂²	1	1	yes	characteristic, complemented
156	#1936	C₂²	1	1	yes	characteristic
157	#1936	C₂²	1	1	yes	characteristic, complemented
158	#1935	C₂²	1	1	yes	characteristic, complemented
159	#1935	C₂²	1	1	yes	characteristic, complemented
160	#1928	C₂²	1	1	yes	characteristic, complemented
161	#1927	C₂²	1	1	yes	characteristic, complemented
162	#1927	C₂²	1	1	yes	characteristic, complemented
163	#1925	C₂²	1	1	yes	characteristic
164	#1925	C₂²	1	1	yes	characteristic
165	#1925	C₂²	1	1	yes	characteristic, complemented
166	#1921	C₂²	1	1	yes	characteristic, complemented
167	#1921	C₂²	1	1	yes	characteristic, complemented
168	#1919	C₂²	1	1	yes	characteristic, complemented
169	#1918	C₂²	1	1	yes	characteristic, complemented
170	#1917	C₂²	1	1	yes	characteristic, complemented
171	#1916	C₂²	1	1	yes	characteristic, complemented
172	#1895	C₂²	1	1	yes	characteristic
173	#1894	C₂²	1	1	yes	characteristic
174	#1880	C₂²	1	1	yes	characteristic
175	#1879	C₂²	1	1	yes	characteristic
176	#1879	C₂²	1	1	yes	characteristic
177	#1879	C₂²	1	1	yes	characteristic
178	#1878	C₂²	1	1	yes	characteristic, complemented
179	#1877	C₂²	1	1	yes	characteristic
180	#1873	C₂²	1	1	yes	characteristic
181	#1865	C₂²	1	1	yes	characteristic, complemented
182	#1864	C₂²	1	1	yes	characteristic
183	#1864	C₂²	1	1	yes	characteristic, complemented
184	#1863	C₂²	1	1	yes	characteristic, complemented
185	#1854	C₂²	1	1	yes	characteristic
186	#1851	C₂²	1	1	yes	characteristic
187	#1851	C₂²	1	1	yes	characteristic
188	#1847	C₂²	1	1	yes	characteristic, complemented
189	#1845	C₂²	1	1	yes	characteristic, complemented
190	#1825	C₂²	1	1	yes	characteristic
191	#1805	C₂²	1	1	yes	characteristic, complemented
192	#1804	C₂²	1	1	yes	characteristic
193	#1803	C₂²	1	1	yes	characteristic, complemented
194	#1802	C₂²	1	1	yes	characteristic
195	#1776	C₂²	1	1	yes	characteristic, complemented
196	#1771	C₂²	1	1	yes	characteristic, complemented
197	C₄×#102	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic, complemented
199	#1753	C₂²	1	1	yes	characteristic
200	#1753	C₂²	1	1	yes	characteristic
201	#1749	C₂²	1	1	yes	characteristic
202	#1736	C₂²	1	1	yes	characteristic
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	C₂²×D₈	C₂³	1	1	yes	characteristic
209	C₂²×D₈	C₂³	1	1	yes	characteristic
210	C₂²×M₁₆	C₂³	1	1	yes	characteristic
211	C₂²×M₁₆	C₂³	1	1	yes	characteristic
212	C₂×#126	—	2	1	no	—
213	C₂×#126	—	2	1	no	—
214	C₂×#126	—	2	1	no	—
215	C₂×#124	C₂³	1	1	yes	characteristic
216	C₂×#124	C₂³	1	1	yes	characteristic
217	C₂×#124	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×#121	C₂³	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂×#117	—	2	1	no	—
230	C₂×#117	C₂³	1	1	yes	characteristic
231	C₂×#117	C₂³	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	C₂²×C₂²⋊C₄	—	2	1	no	—
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₄²	C₂³	1	1	yes	characteristic
237	#485	—	2	4	no	—
238	#483	—	4	2	no	—
239	#480	—	2	4	no	—
240	#470	—	4	2	no	—
241	#468	—	4	2	no	—
242	#464	—	4	2	no	—
243	#463	—	4	2	no	—
244	#450	—	2	4	no	—
245	#447	—	4	2	no	—
246	#446	—	4	2	no	—
247	#440	—	4	2	no	—
248	#428	—	4	2	no	—
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×#107	C₂³	1	1	yes	characteristic
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#107	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	#423	—	4	2	no	—
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	#418	—	4	2	no	—
273	#418	—	4	2	no	—
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#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×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂×#97	C₂³	1	1	yes	characteristic
305	C₂×#97	C₂³	1	1	yes	characteristic
306	C₂×#97	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
310	#400	—	2	1	no	—
311	#400	—	2	1	no	—
312	#400	—	2	1	no	—
313	#400	—	2	1	no	—
314	#400	—	2	1	no	—
315	#400	—	2	1	no	—
316	#400	—	2	1	no	—
317	#399	—	2	1	no	—
318	#399	—	2	1	no	—
319	#399	—	2	1	no	—
320	#398	—	2	1	no	—
321	#398	—	2	1	no	—
322	#397	—	2	1	no	—
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#397	—	2	1	no	—
326	#397	—	2	1	no	—
327	#397	—	2	1	no	—
328	#397	—	2	1	no	—
329	#397	—	2	1	no	—
330	#397	—	2	1	no	—
331	#397	—	2	1	no	—
332	#397	—	2	1	no	—
333	#397	—	2	1	no	—
334	#396	—	2	1	no	—
335	#396	—	2	1	no	—
336	#396	—	2	1	no	—
337	#396	—	2	1	no	—
338	#396	—	2	1	no	—
339	#395	—	2	1	no	—
340	#394	—	2	1	no	—
341	#394	—	2	1	no	—
342	#394	—	2	1	no	—
343	#394	—	2	1	no	—
344	#393	—	2	1	no	—
345	#393	—	2	1	no	—
346	#391	D₄	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	#391	C₂³	1	1	yes	characteristic
354	#390	—	2	1	no	—
355	#390	—	2	1	no	—
356	#390	—	2	1	no	—
357	#390	C₂³	1	1	yes	characteristic
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	#390	C₂³	1	1	yes	characteristic
367	#390	C₂³	1	1	yes	characteristic
368	#390	C₂³	1	1	yes	characteristic
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	D₄	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	#389	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#388	—	2	1	no	—
398	#388	—	2	1	no	—
399	#388	—	2	1	no	—
400	#388	—	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	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	D₄	1	1	yes	characteristic
412	#387	D₄	1	1	yes	characteristic
413	#386	—	2	1	no	—
414	#386	—	2	1	no	—
415	#386	—	2	1	no	—
416	#386	—	2	1	no	—
417	#386	—	2	1	no	—
418	#385	—	2	1	no	—
419	#385	—	2	1	no	—
420	#385	—	2	1	no	—
421	#385	—	2	1	no	—
422	#385	—	2	1	no	—
423	#385	—	2	1	no	—
424	#385	—	2	1	no	—
425	#385	—	2	1	no	—
426	#385	—	2	1	no	—
427	#385	—	2	1	no	—
428	#385	D₄	1	1	yes	characteristic
429	#385	D₄	1	1	yes	characteristic
430	#384	C₂³	1	1	yes	characteristic
431	#384	C₂³	1	1	yes	characteristic
432	#384	C₂³	1	1	yes	characteristic
433	#384	C₂³	1	1	yes	characteristic
434	#382	—	2	1	no	—
435	#382	—	2	1	no	—
436	#382	C₂³	1	1	yes	characteristic
437	#382	C₂³	1	1	yes	characteristic
438	#382	C₂³	1	1	yes	characteristic
439	#381	—	2	1	no	—
440	#381	—	2	1	no	—
441	#380	—	2	1	no	—
442	#380	—	2	1	no	—
443	#380	—	2	1	no	—
444	#380	D₄	1	1	yes	characteristic
445	#380	C₂³	1	1	yes	characteristic
446	#379	—	2	1	no	—
447	#379	—	2	1	no	—
448	#379	—	2	1	no	—
449	C₄×C₄⋊C₄	—	2	1	no	—
450	C₄×C₄⋊C₄	—	2	1	no	—
451	C₄×C₄⋊C₄	—	2	1	no	—
452	C₄×C₄⋊C₄	—	2	1	no	—
453	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
461	C₄×C₂²⋊C₄	—	2	1	no	—
462	C₄×C₂²⋊C₄	—	2	1	no	—
463	C₄×C₂²⋊C₄	—	2	1	no	—
464	C₄×C₂²⋊C₄	—	2	1	no	—
465	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
466	C₄×C₂²⋊C₄	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	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	C₂⁵	—	2	1	no	—
494	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
495	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂⁴	1	1	yes	characteristic
515	C₂×Q₁₆	—	4	1	no	—
516	C₂×Q₁₆	—	4	1	no	—
517	C₂×Q₁₆	—	4	1	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×D₈	—	2	2	no	—
528	C₂×D₈	—	4	1	no	—
529	C₂×D₈	—	4	1	no	—
530	C₂×D₈	—	4	1	no	—
531	C₂×D₈	—	4	1	no	—
532	C₂×D₈	—	4	1	no	—
533	C₂×M₁₆	—	2	2	no	—
534	C₂×M₁₆	—	2	2	no	—
535	C₂×M₁₆	—	2	2	no	—
536	C₂×M₁₆	—	4	1	no	—
537	C₂×M₁₆	—	4	1	no	—
538	C₂×M₁₆	—	4	1	no	—
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	#126	—	4	4	no	—
548	#126	—	8	2	no	—
549	#126	—	8	2	no	—
550	#124	—	2	2	no	—
551	#124	—	4	1	no	—
552	#124	—	4	1	no	—
553	#124	—	4	1	no	—
554	#124	—	4	1	no	—
555	#124	—	4	1	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	4	2	no	—
561	C₂²⋊Q₈	—	8	2	no	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	C₄×Q₈	—	4	1	no	—
565	C₄×Q₈	—	4	1	no	—
566	C₄×Q₈	—	4	1	no	—
567	C₄×Q₈	—	4	1	no	—
568	C₄×Q₈	—	4	1	no	—
569	C₄×Q₈	—	4	1	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	4	1	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	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	—	4	1	no	—
579	#117	—	4	1	no	—
580	#117	—	8	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	4	4	no	—
665	C₂×C₂²⋊C₄	—	8	2	no	—
666	C₂×C₂²⋊C₄	—	8	2	no	—
667	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	—	2	1	no	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	4	1	no	—
681	C₂×C₄²	—	4	1	no	—
682	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
683	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
684	C₂×C₄²	C₂⁴	1	1	yes	characteristic
685	C₂×C₄²	C₂⁴	1	1	yes	characteristic
686	C₂×C₄²	C₂⁴	1	1	yes	characteristic
687	C₂×C₄²	C₂⁴	1	1	yes	characteristic
688	C₂×C₄²	C₂⁴	1	1	yes	characteristic
689	C₂×C₄²	C₂⁴	1	1	yes	characteristic
690	#107	—	2	2	no	—
691	#107	—	2	2	no	—
692	#107	—	2	2	no	—
693	#107	—	4	1	no	—
694	#107	—	4	1	no	—
695	#107	—	4	1	no	—
696	#107	—	4	1	no	—
697	#106	—	2	2	no	—
698	#106	—	4	1	no	—
699	#106	—	4	1	no	—
700	#106	—	4	1	no	—
701	#106	—	4	1	no	—
702	#106	—	4	1	no	—
703	#106	—	4	1	no	—
704	C₄⋊C₈	—	2	2	no	—
705	C₄⋊C₈	—	2	2	no	—
706	C₄⋊C₈	—	2	2	no	—
707	C₄⋊C₈	—	4	1	no	—
708	C₄⋊C₈	—	4	1	no	—
709	C₄⋊C₈	—	4	1	no	—
710	C₄⋊C₈	—	4	1	no	—
711	C₄⋊C₈	—	4	1	no	—
712	#103	—	2	2	no	—
713	#103	—	2	2	no	—
714	#103	—	2	2	no	—
715	#103	—	4	1	no	—
716	#103	—	4	1	no	—
717	#103	—	4	1	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#102	—	2	2	no	—
724	#102	—	2	2	no	—
725	#102	—	2	2	no	—
726	#102	—	2	2	no	—
727	#102	—	2	2	no	—
728	#102	—	2	2	no	—
729	#102	—	4	1	no	—
730	#102	—	4	1	no	—
731	#102	—	4	1	no	—
732	#102	—	4	1	no	—
733	#102	—	4	1	no	—
734	#102	—	4	1	no	—
735	#102	—	4	1	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	—	4	1	no	—
739	#102	—	4	1	no	—
740	C₂²⋊C₈	—	2	2	no	—
741	C₂²⋊C₈	#41	1	4	yes	—
742	#97	—	2	2	no	—
743	#97	—	4	1	no	—
744	#97	—	4	1	no	—
745	#97	—	4	1	no	—
746	C₄×C₈	—	4	1	no	—
747	C₄×C₈	—	4	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	#95	C₂×D₄	1	1	yes	characteristic
792	#95	C₂×D₄	1	1	yes	characteristic
793	C₂⁴	—	2	1	no	—
794	C₂⁴	—	2	1	no	—
795	C₂⁴	—	2	1	no	—
796	C₂⁴	—	4	2	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	—	4	2	no	—
800	C₂⁴	—	8	1	no	—
801	C₂⁴	—	8	1	no	—
802	C₂⁴	—	8	1	no	—
803	C₂⁴	C₂²×D₄	1	1	yes	characteristic
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	4	1	no	—
817	C₂×Q₈	—	4	1	no	—
818	C₂×Q₈	—	4	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	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	4	4	no	—
837	C₂×D₄	—	4	4	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	8	2	no	—
842	C₂×D₄	—	8	2	no	—
843	C₂×D₄	—	8	1	no	—
844	C₂×D₄	—	8	1	no	—
845	C₂×D₄	—	8	1	no	—
846	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	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	—	4	1	no	—
865	C₂²×C₄	—	4	1	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	8	1	no	—
875	C₂²×C₄	—	8	1	no	—
876	C₂²×C₄	—	8	1	no	—
877	C₂²×C₄	—	8	1	no	—
878	C₂²×C₄	—	8	1	no	—
879	C₂²×C₄	—	8	1	no	—
880	C₂²×C₄	—	8	1	no	—
881	C₂²×C₄	—	8	1	no	—
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂×#41	1	2	yes	—
896	C₂²×C₄	H(5,𝔽₂)	1	2	yes	—
897	C₂²×C₄	C₂⁵	1	1	yes	characteristic
898	Q₁₆	—	8	2	no	—
899	SD₁₆	—	4	4	no	—
900	SD₁₆	—	8	2	no	—
901	SD₁₆	—	8	2	no	—
902	D₈	—	8	2	no	—
903	D₈	—	8	2	no	—
904	M₁₆	—	4	4	no	—
905	M₁₆	—	8	2	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	C₂×#41	1	2	yes	—
928	C₂×C₈	C₂×#41	1	2	yes	—
929	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	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	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	4	1	no	—
955	C₄⋊C₄	—	4	1	no	—
956	C₄⋊C₄	—	4	1	no	—
957	C₄⋊C₄	—	4	1	no	—
958	C₄⋊C₄	—	4	1	no	—
959	C₄⋊C₄	—	4	1	no	—
960	C₄⋊C₄	—	4	1	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	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	—	8	1	no	—
979	C₄⋊C₄	—	8	1	no	—
980	C₄⋊C₄	—	8	1	no	—
981	C₄⋊C₄	—	8	1	no	—
982	C₄⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	4	1	no	—
985	C₂²⋊C₄	—	4	1	no	—
986	C₂²⋊C₄	—	4	1	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	2	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
1017	C₂²⋊C₄	—	8	1	no	—
1018	C₂²⋊C₄	—	8	1	no	—
1019	C₂²⋊C₄	—	8	1	no	—
1020	C₂²⋊C₄	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	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	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	4	1	no	—
1039	C₄²	—	4	1	no	—
1040	C₄²	—	4	2	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	—	8	1	no	—
1044	C₄²	—	8	1	no	—
1045	C₄²	—	8	1	no	—
1046	C₄²	—	8	1	no	—
1047	C₄²	—	8	1	no	—
1048	C₄²	—	8	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	2	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	—	4	1	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	8	4	no	—
1077	C₂³	—	8	4	no	—
1078	C₂³	—	8	4	no	—
1079	C₂³	—	8	4	no	—
1080	C₂³	—	16	2	no	—
1081	C₂³	—	16	2	no	—
1082	C₂³	—	16	2	no	—
1083	C₂³	#550	1	2	yes	—
1084	C₂³	C₂³×D₄	1	1	yes	characteristic
1085	Q₈	—	4	1	no	—
1086	Q₈	—	4	1	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	8	2	no	—
1094	D₄	—	2	2	no	—
1095	D₄	—	2	2	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	—	4	1	no	—
1102	D₄	—	4	1	no	—
1103	D₄	—	4	1	no	—
1104	D₄	—	4	1	no	—
1105	D₄	—	4	1	no	—
1106	D₄	—	8	4	no	—
1107	D₄	—	16	2	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	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	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	1	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	1	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	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	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	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	8	4	no	—
1189	C₂×C₄	—	8	2	no	—
1190	C₂×C₄	—	8	2	no	—
1191	C₂×C₄	—	16	2	no	—
1192	C₂×C₄	—	16	2	no	—
1193	C₂×C₄	—	16	2	no	—
1194	C₂×C₄	#550	1	2	yes	—
1195	C₂×C₄	#575	1	2	yes	—
1196	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1197	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1198	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1199	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1200	C₂×C₄	#585	1	1	yes	characteristic
1201	C₂×C₄	#585	1	1	yes	characteristic
1202	C₈	—	2	2	no	—
1203	C₈	—	2	2	no	—
1204	C₈	—	2	2	no	—
1205	C₈	—	4	1	no	—
1206	C₈	—	4	1	no	—
1207	C₈	—	4	1	no	—
1208	C₈	—	4	1	no	—
1209	C₈	—	4	1	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	2	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	—	8	1	no	—
1236	C₂²	—	8	1	no	—
1237	C₂²	—	8	1	no	—
1238	C₂²	—	16	8	no	—
1239	C₂²	C₂×#550	1	1	yes	characteristic
1240	C₂²	#3489	1	1	yes	characteristic
1241	C₂²	#3496	1	1	yes	characteristic
1242	C₂²	C₂×#575	1	1	yes	characteristic
1243	C₂²	#3585	1	1	yes	characteristic
1244	C₂²	#3585	1	1	yes	characteristic
1245	C₂²	#3586	1	1	yes	characteristic
1246	C₄	—	2	2	no	—
1247	C₄	—	2	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	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	—	8	1	no	—
1270	C₄	—	8	1	no	—
1271	C₄	—	8	1	no	—
1272	C₄	#3520	1	1	yes	characteristic
1273	C₄	#3521	1	1	yes	characteristic
1274	C₄	#3534	1	1	yes	characteristic
1275	C₄	#3535	1	1	yes	characteristic
1276	C₂	—	4	2	no	—
1277	C₂	—	8	2	no	—
1278	C₂	—	16	1	no	—
1279	C₂	—	16	1	no	—
1280	C₂	#43029	1	1	yes	characteristic
1281	C₂	#61403	1	1	yes	characteristic
1282	C₂	#61417	1	1	yes	characteristic
1283	C₂	#62119	1	1	yes	characteristic
1284	C₂	#62224	1	1	yes	characteristic
1285	C₂	#62294	1	1	yes	characteristic
1286	C₂	#62304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#447	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊Q₈ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #59424	C₂	semidirect
2. #40034	C₂	semidirect
3. #32659	C₂	semidirect
4. #32624	C₂	semidirect
5. #32536	C₂	semidirect
6. #32401	C₂	semidirect
7. #31928	C₂	semidirect
8. #31922	C₂	semidirect
9. #31579	C₂	semidirect
10. #31217	C₂	semidirect
11. #28893	C₂	semidirect
12. #28361	C₂	semidirect
14. #28275	C₂	semidirect
15. #28025	C₂	semidirect
16. #27945	C₂	semidirect
17. #27195	C₂	semidirect
18. #26611	C₂	semidirect
19. #26543	C₂	semidirect
20. #26087	C₂	semidirect
21. #25298	C₂	semidirect
22. #25219	C₂	semidirect
24. #24757	C₂	semidirect
25. #24590	C₂	semidirect
27. #23618	C₂	semidirect
28. #22955	C₂	semidirect
29. #22931	C₂	semidirect
30. #22864	C₂	semidirect
31. #22083	C₂	semidirect
37. C₂×#464	C₂²	semidirect
41. C₂×#446	C₂²	semidirect
58. #2581	C₂²	semidirect
59. #2580	C₂²	semidirect
61. #2571	C₂²	semidirect
62. #2571	C₂²	semidirect
67. #2512	C₂²	semidirect
68. #2511	C₂²	semidirect
75. #2448	C₂²	semidirect
77. #2447	C₂²	semidirect
92. #2097	C₂²	semidirect
93. #2095	C₂²	semidirect
95. #2094	C₂²	semidirect
96. #2093	C₂²	semidirect
100. #2085	C₂²	semidirect
101. #2084	C₂²	semidirect
102. #2084	C₂²	semidirect
104. #2072	C₂²	semidirect
106. #2068	C₂²	semidirect
107. #2068	C₂²	semidirect
113. #2066	C₂²	semidirect
114. #2066	C₂²	semidirect
119. #2065	C₂²	semidirect
120. #2056	C₂²	semidirect
121. #2056	C₂²	semidirect
122. #2055	C₂²	semidirect
132. #1985	C₂²	semidirect
134. #1983	C₂²	semidirect
138. #1973	C₂²	semidirect
143. #1968	C₂²	semidirect
146. #1949	C₂²	semidirect
147. #1949	C₂²	semidirect
148. #1948	C₂²	semidirect
149. #1948	C₂²	semidirect
150. #1944	C₂²	semidirect
151. #1943	C₂²	semidirect
152. #1942	C₂²	semidirect
153. #1940	C₂²	semidirect
154. #1940	C₂²	semidirect
155. #1939	C₂²	semidirect
157. #1936	C₂²	semidirect
158. #1935	C₂²	semidirect
159. #1935	C₂²	semidirect
160. #1928	C₂²	semidirect
161. #1927	C₂²	semidirect
162. #1927	C₂²	semidirect
165. #1925	C₂²	semidirect
166. #1921	C₂²	semidirect
167. #1921	C₂²	semidirect
168. #1919	C₂²	semidirect
169. #1918	C₂²	semidirect
170. #1917	C₂²	semidirect
171. #1916	C₂²	semidirect
178. #1878	C₂²	semidirect
181. #1865	C₂²	semidirect
183. #1864	C₂²	semidirect
184. #1863	C₂²	semidirect
188. #1847	C₂²	semidirect
189. #1845	C₂²	semidirect
191. #1805	C₂²	semidirect
193. #1803	C₂²	semidirect
195. #1776	C₂²	semidirect
196. #1771	C₂²	semidirect
198. C₄×#102	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#59424	2
#40034	2
#32659	2
#32624	2
#32536	2
#32401	2
#31928	2
#31922	2
#31579	2
#31217	2
#28893	2
#28361	2
#28312	2
#28275	2
#28025	2
#27945	2
#27195	2
#26611	2
#26543	2
#26087	2
#25298	2
#25219	2
#25101	2
#24757	2
#24590	2
#24539	2
#23618	2
#22955	2
#22931	2
#22864	2
#22083	2