Subgroups — #7010862

Order 512.

1487 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59382	C₂	1	1	yes	maximal, characteristic
2	#40101	C₂	1	1	yes	maximal, characteristic, complemented
3	#32264	C₂	1	1	yes	maximal, characteristic, complemented
4	#31690	C₂	1	1	yes	maximal, characteristic, complemented
5	#31610	C₂	1	1	yes	maximal, characteristic, complemented
6	#31608	C₂	1	1	yes	maximal, characteristic, complemented
7	#31559	C₂	1	1	yes	maximal, characteristic, complemented
8	#31466	C₂	1	1	yes	maximal, characteristic, complemented
9	#31235	C₂	1	1	yes	maximal, characteristic, complemented
10	#30408	C₂	1	1	yes	maximal, characteristic
11	#29156	C₂	1	1	yes	maximal, characteristic, complemented
12	#28944	C₂	1	1	yes	maximal, characteristic, complemented
13	#28841	C₂	1	1	yes	maximal, characteristic, complemented
14	#28094	C₂	1	1	yes	maximal, characteristic
15	#27838	C₂	1	1	yes	maximal, characteristic, complemented
16	#27523	C₂	1	1	yes	maximal, characteristic, complemented
17	#27433	C₂	1	1	yes	maximal, characteristic, complemented
18	#27363	C₂	1	1	yes	maximal, characteristic, complemented
19	#27035	C₂	1	1	yes	maximal, characteristic, complemented
20	#26379	C₂	1	1	yes	maximal, characteristic, complemented
21	#26096	C₂	1	1	yes	maximal, characteristic, complemented
22	#25950	C₂	1	1	yes	maximal, characteristic, complemented
23	#25343	C₂	1	1	yes	maximal, characteristic, complemented
24	#25031	C₂	1	1	yes	maximal, characteristic, complemented
25	#24901	C₂	1	1	yes	maximal, characteristic, complemented
26	#24700	C₂	1	1	yes	maximal, characteristic, complemented
27	#23701	C₂	1	1	yes	maximal, characteristic, complemented
28	#22900	C₂	1	1	yes	maximal, characteristic, complemented
29	#22874	C₂	1	1	yes	maximal, characteristic, complemented
30	#22767	C₂	1	1	yes	maximal, characteristic, complemented
31	#22185	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#479	C₂²	1	1	yes	characteristic, complemented
33	C₂×#474	C₂²	1	1	yes	characteristic
34	C₂×#465	C₂²	1	1	yes	characteristic
35	C₂×#450	C₂²	1	1	yes	characteristic
36	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
39	C₂×#431	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#102	C₂²	1	1	yes	characteristic
41	#2857	C₂²	1	1	yes	characteristic, complemented
42	#2791	—	2	1	no	—
43	#2771	—	2	1	no	—
44	#2743	—	2	1	no	—
45	#2735	—	2	1	no	—
46	#2689	—	2	1	no	—
47	#2680	—	2	1	no	—
48	#2666	—	2	1	no	—
49	#2598	—	2	1	no	—
50	#2578	—	2	1	no	—
51	#2577	—	2	1	no	—
52	#2570	C₂²	1	1	yes	characteristic, complemented
53	#2562	C₂²	1	1	yes	characteristic
54	#2553	—	2	1	no	—
55	#2536	C₂²	1	1	yes	characteristic
56	#2534	—	2	1	no	—
57	#2508	C₂²	1	1	yes	characteristic, complemented
58	#2497	C₂²	1	1	yes	characteristic
59	#2496	C₂²	1	1	yes	characteristic, complemented
60	#2495	C₂²	1	1	yes	characteristic
61	#2495	C₂²	1	1	yes	characteristic
62	#2486	C₂²	1	1	yes	characteristic
63	#2457	—	2	1	no	—
64	#2454	C₂²	1	1	yes	characteristic
65	#2454	C₂²	1	1	yes	characteristic
66	#2451	C₂²	1	1	yes	characteristic, complemented
67	#2440	C₂²	1	1	yes	characteristic
68	#2423	C₂²	1	1	yes	characteristic
69	#2422	C₂²	1	1	yes	characteristic
70	#2421	C₂²	1	1	yes	characteristic, complemented
71	#2420	C₂²	1	1	yes	characteristic
72	#2418	—	2	1	no	—
73	#2408	C₂²	1	1	yes	characteristic
74	#2360	C₂²	1	1	yes	characteristic
75	#2357	C₂²	1	1	yes	characteristic
76	#2354	C₂²	1	1	yes	characteristic
77	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	#2342	—	2	1	no	—
79	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
80	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	#2332	—	2	1	no	—
82	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₄×#123	C₂²	1	1	yes	characteristic
84	C₄×#121	C₂²	1	1	yes	characteristic
85	C₄×#121	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	#2100	C₂²	1	1	yes	characteristic, complemented
90	#2094	C₂²	1	1	yes	characteristic
91	#2093	C₂²	1	1	yes	characteristic
92	#2092	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic, complemented
94	#2087	C₂²	1	1	yes	characteristic, complemented
95	#2084	C₂²	1	1	yes	characteristic, complemented
96	#2083	C₂²	1	1	yes	characteristic, complemented
97	#2077	C₂²	1	1	yes	characteristic
98	#2077	C₂²	1	1	yes	characteristic
99	#2077	C₂²	1	1	yes	characteristic
100	#2077	C₂²	1	1	yes	characteristic, complemented
101	#2076	C₂²	1	1	yes	characteristic
102	#2075	C₂²	1	1	yes	characteristic, complemented
103	#2075	C₂²	1	1	yes	characteristic, complemented
104	#2074	C₂²	1	1	yes	characteristic, complemented
105	#2073	C₂²	1	1	yes	characteristic
106	#2073	C₂²	1	1	yes	characteristic
107	#2068	C₂²	1	1	yes	characteristic, complemented
108	#2068	C₂²	1	1	yes	characteristic, complemented
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	#2065	C₂²	1	1	yes	characteristic
114	#2059	C₂²	1	1	yes	characteristic, complemented
115	#2059	C₂²	1	1	yes	characteristic, complemented
116	#2058	C₂²	1	1	yes	characteristic, complemented
117	#2055	C₂²	1	1	yes	characteristic
118	#2036	C₂²	1	1	yes	characteristic
119	#2036	C₂²	1	1	yes	characteristic, complemented
120	#2035	C₂²	1	1	yes	characteristic
121	#2033	C₂²	1	1	yes	characteristic
122	#2033	C₂²	1	1	yes	characteristic
123	#2033	C₂²	1	1	yes	characteristic
124	#2023	C₂²	1	1	yes	characteristic
125	#2000	C₂²	1	1	yes	characteristic
126	#1991	C₂²	1	1	yes	characteristic, complemented
127	#1988	C₂²	1	1	yes	characteristic, complemented
128	#1968	C₂²	1	1	yes	characteristic
129	#1949	C₂²	1	1	yes	characteristic, complemented
130	#1949	C₂²	1	1	yes	characteristic, complemented
131	#1947	C₂²	1	1	yes	characteristic, complemented
132	#1942	C₂²	1	1	yes	characteristic, complemented
133	#1942	C₂²	1	1	yes	characteristic, complemented
134	#1942	C₂²	1	1	yes	characteristic, complemented
135	#1941	C₂²	1	1	yes	characteristic, complemented
136	#1939	C₂²	1	1	yes	characteristic, complemented
137	#1934	C₂²	1	1	yes	characteristic
138	#1934	C₂²	1	1	yes	characteristic
139	#1934	C₂²	1	1	yes	characteristic
140	#1934	C₂²	1	1	yes	characteristic
141	#1934	C₂²	1	1	yes	characteristic
142	#1928	C₂²	1	1	yes	characteristic, complemented
143	#1926	C₂²	1	1	yes	characteristic
144	#1925	C₂²	1	1	yes	characteristic
145	#1923	C₂²	1	1	yes	characteristic
146	#1923	C₂²	1	1	yes	characteristic
147	#1921	C₂²	1	1	yes	characteristic, complemented
148	#1920	C₂²	1	1	yes	characteristic, complemented
149	#1920	C₂²	1	1	yes	characteristic, complemented
150	#1920	C₂²	1	1	yes	characteristic, complemented
151	#1920	C₂²	1	1	yes	characteristic, complemented
152	#1919	C₂²	1	1	yes	characteristic, complemented
153	#1918	C₂²	1	1	yes	characteristic, complemented
154	#1916	C₂²	1	1	yes	characteristic, complemented
155	#1916	C₂²	1	1	yes	characteristic, complemented
156	#1893	C₂²	1	1	yes	characteristic
157	#1893	C₂²	1	1	yes	characteristic
158	#1893	C₂²	1	1	yes	characteristic
159	#1892	C₂²	1	1	yes	characteristic
160	#1892	C₂²	1	1	yes	characteristic, complemented
161	#1880	C₂²	1	1	yes	characteristic
162	#1880	C₂²	1	1	yes	characteristic
163	#1880	C₂²	1	1	yes	characteristic
164	#1880	C₂²	1	1	yes	characteristic
165	#1877	C₂²	1	1	yes	characteristic
166	#1877	C₂²	1	1	yes	characteristic
167	#1869	C₂²	1	1	yes	characteristic
168	#1864	C₂²	1	1	yes	characteristic
169	#1864	C₂²	1	1	yes	characteristic
170	#1864	C₂²	1	1	yes	characteristic
171	#1863	C₂²	1	1	yes	characteristic, complemented
172	#1863	C₂²	1	1	yes	characteristic, complemented
173	#1862	C₂²	1	1	yes	characteristic
174	#1862	C₂²	1	1	yes	characteristic
175	#1862	C₂²	1	1	yes	characteristic
176	#1853	C₂²	1	1	yes	characteristic
177	#1852	C₂²	1	1	yes	characteristic
178	#1850	C₂²	1	1	yes	characteristic
179	#1850	C₂²	1	1	yes	characteristic, complemented
180	#1846	C₂²	1	1	yes	characteristic, complemented
181	#1834	C₂²	1	1	yes	characteristic, complemented
182	#1823	C₂²	1	1	yes	characteristic
183	#1808	C₂²	1	1	yes	characteristic
184	#1808	C₂²	1	1	yes	characteristic
185	#1808	C₂²	1	1	yes	characteristic, complemented
186	#1807	C₂²	1	1	yes	characteristic, complemented
187	#1807	C₂²	1	1	yes	characteristic, complemented
188	#1804	C₂²	1	1	yes	characteristic
189	#1803	C₂²	1	1	yes	characteristic, complemented
190	#1802	C₂²	1	1	yes	characteristic
191	#1802	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	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
196	C₄×#103	C₂²	1	1	yes	characteristic, complemented
197	C₄×#103	C₂²	1	1	yes	characteristic, complemented
198	C₄×#102	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
201	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
202	C₂×#336	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#126	—	2	1	no	—
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#123	—	2	1	no	—
213	C₂×#123	—	2	1	no	—
214	C₂×#123	D₄	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	—	2	1	no	—
216	C₂×C₂²⋊Q₈	—	2	1	no	—
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×#121	C₂³	1	1	yes	characteristic
220	C₂×#121	C₂³	1	1	yes	characteristic
221	C₂×#120	—	2	1	no	—
222	C₂×C₄×Q₈	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×D₄	—	2	1	no	—
226	C₂×C₄×D₄	—	2	1	no	—
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
232	C₂×#117	—	2	1	no	—
233	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	—	2	1	no	—
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₄²	C₂³	1	1	yes	characteristic
237	#479	—	4	2	no	—
238	#474	—	4	2	no	—
239	#465	—	2	4	no	—
240	#450	—	2	4	no	—
241	C₄×SD₁₆	—	2	4	no	—
242	C₄×SD₁₆	—	4	2	no	—
243	C₈×D₄	—	4	2	no	—
244	#431	—	4	2	no	—
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	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#102	—	4	2	no	—
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
291	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
295	#400	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#400	—	2	1	no	—
302	#400	—	2	1	no	—
303	#399	—	2	1	no	—
304	#399	—	2	1	no	—
305	#399	—	2	1	no	—
306	#398	—	2	1	no	—
307	#398	—	2	1	no	—
308	#398	—	2	1	no	—
309	#398	—	2	1	no	—
310	#398	—	2	1	no	—
311	#398	—	2	1	no	—
312	#398	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	2	1	no	—
317	#397	—	2	1	no	—
318	#397	—	2	1	no	—
319	#397	—	2	1	no	—
320	#396	—	2	1	no	—
321	#396	—	2	1	no	—
322	#396	—	2	1	no	—
323	#395	—	2	1	no	—
324	#395	—	2	1	no	—
325	#394	—	2	1	no	—
326	#394	—	2	1	no	—
327	#394	—	2	1	no	—
328	#394	—	2	1	no	—
329	#394	—	2	1	no	—
330	#392	—	2	1	no	—
331	#391	—	2	1	no	—
332	#391	—	2	1	no	—
333	#391	C₂³	1	1	yes	characteristic
334	#391	C₂³	1	1	yes	characteristic
335	#390	C₂³	1	1	yes	characteristic
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	#389	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	—	2	1	no	—
344	#389	—	2	1	no	—
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#389	C₂³	1	1	yes	characteristic
351	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
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	D₄	1	1	yes	characteristic
373	#388	D₄	1	1	yes	characteristic
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	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	D₄	1	1	yes	characteristic
385	#387	D₄	1	1	yes	characteristic
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#386	—	2	1	no	—
389	#386	—	2	1	no	—
390	#386	—	2	1	no	—
391	#386	—	2	1	no	—
392	#386	—	2	1	no	—
393	#386	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
401	#384	—	2	1	no	—
402	#384	C₂³	1	1	yes	characteristic
403	#384	C₂³	1	1	yes	characteristic
404	#384	C₂³	1	1	yes	characteristic
405	#383	—	2	1	no	—
406	#383	—	2	1	no	—
407	#382	—	2	1	no	—
408	#382	C₂³	1	1	yes	characteristic
409	#382	C₂³	1	1	yes	characteristic
410	#382	C₂³	1	1	yes	characteristic
411	#381	—	2	1	no	—
412	#381	—	2	1	no	—
413	#381	—	2	1	no	—
414	#381	D₄	1	1	yes	characteristic
415	#380	—	2	1	no	—
416	#380	—	2	1	no	—
417	#380	—	2	1	no	—
418	#380	—	2	1	no	—
419	#380	C₂³	1	1	yes	characteristic
420	#380	C₂³	1	1	yes	characteristic
421	#380	C₂³	1	1	yes	characteristic
422	#380	C₂³	1	1	yes	characteristic
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	#380	C₂³	1	1	yes	characteristic
427	#380	C₂³	1	1	yes	characteristic
428	#380	C₂³	1	1	yes	characteristic
429	#379	—	2	1	no	—
430	#379	—	2	1	no	—
431	#379	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	—	2	1	no	—
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
490	C₂²×D₄	—	2	2	no	—
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂⁴	1	1	yes	characteristic
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×SD₁₆	#41	1	4	yes	—
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	—	4	1	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	—	4	1	no	—
524	C₂²×C₈	—	4	1	no	—
525	C₂²×C₈	—	4	1	no	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₄⋊Q₈	—	4	1	no	—
535	C₄⋊Q₈	—	4	1	no	—
536	#126	—	8	2	no	—
537	#125	—	4	1	no	—
538	#125	—	4	1	no	—
539	#123	—	2	4	no	—
540	#123	—	8	2	no	—
541	#123	—	8	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	4	1	no	—
545	C₂²⋊Q₈	—	4	1	no	—
546	C₂²⋊Q₈	—	4	4	no	—
547	C₂²⋊Q₈	—	8	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	4	1	no	—
551	#121	—	4	1	no	—
552	#120	—	8	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	4	1	no	—
557	C₄×Q₈	—	4	1	no	—
558	C₄×Q₈	—	4	1	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	4	1	no	—
562	C₄×D₄	—	4	1	no	—
563	C₄×D₄	—	4	1	no	—
564	C₄×D₄	—	4	1	no	—
565	C₄×D₄	—	4	1	no	—
566	C₄×D₄	—	4	1	no	—
567	C₄×D₄	—	4	1	no	—
568	C₄×D₄	—	4	1	no	—
569	C₄×D₄	—	8	2	no	—
570	C₄×D₄	—	8	2	no	—
571	#117	—	8	2	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	—	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	—	4	1	no	—
600	C₂×C₄⋊C₄	—	4	1	no	—
601	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂×D₄	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×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×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	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	4	4	no	—
650	C₂×C₂²⋊C₄	—	8	2	no	—
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×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	4	1	no	—
668	C₂×C₄²	—	4	1	no	—
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₂×D₄	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	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	#107	—	2	2	no	—
677	#107	—	4	1	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	#106	—	2	2	no	—
685	#106	—	2	2	no	—
686	#106	—	4	1	no	—
687	#106	—	4	1	no	—
688	#106	—	4	1	no	—
689	#106	—	4	1	no	—
690	C₄⋊C₈	—	2	2	no	—
691	C₄⋊C₈	—	2	2	no	—
692	C₄⋊C₈	—	4	1	no	—
693	C₄⋊C₈	—	4	1	no	—
694	C₄⋊C₈	—	4	1	no	—
695	#103	—	2	2	no	—
696	#103	—	2	2	no	—
697	#103	—	2	2	no	—
698	#103	—	4	1	no	—
699	#103	—	4	1	no	—
700	#103	—	4	1	no	—
701	#102	—	2	2	no	—
702	#102	—	2	2	no	—
703	#102	—	2	2	no	—
704	#102	—	2	2	no	—
705	#102	—	2	2	no	—
706	#102	—	2	2	no	—
707	#102	—	2	2	no	—
708	#102	—	4	1	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	C₂²⋊C₈	—	2	2	no	—
716	C₂²⋊C₈	—	2	2	no	—
717	C₂²⋊C₈	—	4	1	no	—
718	C₂²⋊C₈	—	4	1	no	—
719	C₂²⋊C₈	—	4	1	no	—
720	C₄×C₈	—	2	2	no	—
721	C₄×C₈	—	2	2	no	—
722	C₄×C₈	—	4	1	no	—
723	C₄×C₈	—	4	1	no	—
724	C₄×C₈	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	#95	C₂×D₄	1	1	yes	characteristic
767	#95	C₂×D₄	1	1	yes	characteristic
768	#95	C₂×D₄	1	1	yes	characteristic
769	#95	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	C₂⁴	—	2	1	no	—
773	C₂⁴	—	2	1	no	—
774	C₂⁴	—	4	2	no	—
775	C₂⁴	—	4	2	no	—
776	C₂⁴	—	4	2	no	—
777	C₂⁴	—	8	1	no	—
778	C₂⁴	—	8	1	no	—
779	C₂⁴	—	8	1	no	—
780	C₂⁴	—	8	1	no	—
781	C₂⁴	C₂²×D₄	1	1	yes	characteristic
782	C₂⁴	C₂²×D₄	1	1	yes	characteristic
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	4	2	no	—
789	C₂×Q₈	—	8	1	no	—
790	C₂×Q₈	—	8	1	no	—
791	C₂×Q₈	C₂×#41	1	2	yes	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	1	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	—	4	1	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	4	4	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	—	4	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	8	1	no	—
813	C₂×D₄	—	8	2	no	—
814	C₂×D₄	—	8	2	no	—
815	C₂×D₄	—	8	2	no	—
816	C₂×D₄	—	8	1	no	—
817	C₂×D₄	—	8	1	no	—
818	C₂×D₄	C₂×#41	1	2	yes	—
819	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	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	—	2	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	8	1	no	—
859	C₂²×C₄	—	8	1	no	—
860	C₂²×C₄	—	8	1	no	—
861	C₂²×C₄	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
868	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
869	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
880	SD₁₆	—	4	4	no	—
881	SD₁₆	—	4	4	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	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	—	8	2	no	—
905	C₂×C₈	—	8	2	no	—
906	C₂×C₈	—	8	2	no	—
907	C₂×C₈	C₂×#41	1	2	yes	—
908	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	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	—	4	1	no	—
939	C₄⋊C₄	—	4	1	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	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	—	8	1	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	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	4	1	no	—
972	C₂²⋊C₄	—	4	1	no	—
973	C₂²⋊C₄	—	4	1	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	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	#135	1	4	yes	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	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	—	4	1	no	—
1016	C₄²	—	4	1	no	—
1017	C₄²	—	4	2	no	—
1018	C₄²	—	4	2	no	—
1019	C₄²	—	4	2	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	1	no	—
1024	C₄²	—	8	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	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	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	4	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	—	8	4	no	—
1052	C₂³	—	8	4	no	—
1053	C₂³	—	8	4	no	—
1054	C₂³	—	16	2	no	—
1055	C₂³	—	16	2	no	—
1056	C₂³	—	16	2	no	—
1057	C₂³	—	16	2	no	—
1058	C₂³	C₂×#135	1	2	yes	—
1059	C₂³	#576	1	2	yes	—
1060	C₂³	C₂³×D₄	1	1	yes	characteristic
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	4	1	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	16	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	8	4	no	—
1076	D₄	—	8	4	no	—
1077	D₄	—	8	4	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	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	—	4	4	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	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	—	8	2	no	—
1163	C₂×C₄	—	8	4	no	—
1164	C₂×C₄	—	16	2	no	—
1165	C₂×C₄	—	16	2	no	—
1166	C₂×C₄	—	16	2	no	—
1167	C₂×C₄	—	16	2	no	—
1168	C₂×C₄	C₂×#135	1	2	yes	—
1169	C₂×C₄	C₂×#135	1	2	yes	—
1170	C₂×C₄	#577	1	2	yes	—
1171	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1172	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1174	C₂×C₄	#585	1	1	yes	characteristic
1175	C₂×C₄	#585	1	1	yes	characteristic
1176	C₂×C₄	#585	1	1	yes	characteristic
1177	C₈	—	2	2	no	—
1178	C₈	—	2	2	no	—
1179	C₈	—	4	1	no	—
1180	C₈	—	4	1	no	—
1181	C₈	—	4	1	no	—
1182	C₈	—	4	1	no	—
1183	C₈	—	4	1	no	—
1184	C₈	—	4	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	2	no	—
1204	C₂²	—	4	2	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	—	16	8	no	—
1214	C₂²	D₄×#41	1	1	yes	characteristic
1215	C₂²	#3489	1	1	yes	characteristic
1216	C₂²	#3496	1	1	yes	characteristic
1217	C₂²	C₂²×#135	1	1	yes	characteristic
1218	C₂²	C₂×#576	1	1	yes	characteristic
1219	C₂²	C₂×#577	1	1	yes	characteristic
1220	C₂²	#3586	1	1	yes	characteristic
1221	C₄	—	2	2	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	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	—	8	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	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	#3491	1	1	yes	characteristic
1248	C₄	#3520	1	1	yes	characteristic
1249	C₄	#3560	1	1	yes	characteristic
1250	C₄	#3564	1	1	yes	characteristic
1251	C₂	—	4	2	no	—
1252	C₂	—	4	2	no	—
1253	C₂	—	8	2	no	—
1254	C₂	—	8	2	no	—
1255	C₂	#43031	1	1	yes	characteristic
1256	C₂	#61432	1	1	yes	characteristic
1257	C₂	#61523	1	1	yes	characteristic
1258	C₂	#62097	1	1	yes	characteristic
1259	C₂	#62200	1	1	yes	characteristic
1260	C₂	#62251	1	1	yes	characteristic
1261	C₂	#62307	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 ◁ C₄×#123 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #40101	C₂	semidirect
3. #32264	C₂	semidirect
4. #31690	C₂	semidirect
5. #31610	C₂	semidirect
6. #31608	C₂	semidirect
7. #31559	C₂	semidirect
8. #31466	C₂	semidirect
9. #31235	C₂	semidirect
11. #29156	C₂	semidirect
12. #28944	C₂	semidirect
13. #28841	C₂	semidirect
15. #27838	C₂	semidirect
16. #27523	C₂	semidirect
17. #27433	C₂	semidirect
18. #27363	C₂	semidirect
19. #27035	C₂	semidirect
20. #26379	C₂	semidirect
21. #26096	C₂	semidirect
22. #25950	C₂	semidirect
23. #25343	C₂	semidirect
24. #25031	C₂	semidirect
25. #24901	C₂	semidirect
26. #24700	C₂	semidirect
27. #23701	C₂	semidirect
28. #22900	C₂	semidirect
29. #22874	C₂	semidirect
30. #22767	C₂	semidirect
31. #22185	C₂	semidirect
32. C₂×#479	C₂²	semidirect
39. C₂×#431	C₂²	semidirect
41. #2857	C₂²	semidirect
52. #2570	C₂²	semidirect
57. #2508	C₂²	semidirect
59. #2496	C₂²	semidirect
66. #2451	C₂²	semidirect
70. #2421	C₂²	semidirect
77. Q₈×C₄⋊C₄	C₂²	semidirect
82. C₄×C₂²⋊Q₈	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
88. #2100	C₂²	semidirect
89. #2100	C₂²	semidirect
93. #2088	C₂²	semidirect
94. #2087	C₂²	semidirect
95. #2084	C₂²	semidirect
96. #2083	C₂²	semidirect
100. #2077	C₂²	semidirect
102. #2075	C₂²	semidirect
103. #2075	C₂²	semidirect
104. #2074	C₂²	semidirect
107. #2068	C₂²	semidirect
108. #2068	C₂²	semidirect
114. #2059	C₂²	semidirect
115. #2059	C₂²	semidirect
116. #2058	C₂²	semidirect
119. #2036	C₂²	semidirect
126. #1991	C₂²	semidirect
127. #1988	C₂²	semidirect
129. #1949	C₂²	semidirect
130. #1949	C₂²	semidirect
131. #1947	C₂²	semidirect
132. #1942	C₂²	semidirect
133. #1942	C₂²	semidirect
134. #1942	C₂²	semidirect
135. #1941	C₂²	semidirect
136. #1939	C₂²	semidirect
142. #1928	C₂²	semidirect
147. #1921	C₂²	semidirect
148. #1920	C₂²	semidirect
149. #1920	C₂²	semidirect
150. #1920	C₂²	semidirect
151. #1920	C₂²	semidirect
152. #1919	C₂²	semidirect
153. #1918	C₂²	semidirect
154. #1916	C₂²	semidirect
155. #1916	C₂²	semidirect
160. #1892	C₂²	semidirect
171. #1863	C₂²	semidirect
172. #1863	C₂²	semidirect
179. #1850	C₂²	semidirect
180. #1846	C₂²	semidirect
181. #1834	C₂²	semidirect
185. #1808	C₂²	semidirect
186. #1807	C₂²	semidirect
187. #1807	C₂²	semidirect
189. #1803	C₂²	semidirect
194. C₄×#107	C₂²	semidirect
195. C₈×C₄⋊C₄	C₂²	semidirect
196. C₄×#103	C₂²	semidirect
197. C₄×#103	C₂²	semidirect
201. C₈×C₂²⋊C₄	C₂²	semidirect
202. C₂×#336	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#59382	2
#40101	2
#32264	2
#31690	2
#31610	2
#31608	2
#31559	2
#31466	2
#31235	2
#30408	2
#29156	2
#28944	2
#28841	2
#28094	2
#27838	2
#27523	2
#27433	2
#27363	2
#27035	2
#26379	2
#26096	2
#25950	2
#25343	2
#25031	2
#24901	2
#24700	2
#23701	2
#22900	2
#22874	2
#22767	2
#22185	2