Subgroups — #6482448

Order 512.

1493 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#35107	C₂	1	1	yes	maximal, characteristic
2	C₄×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	#33151	C₂	1	1	yes	maximal, characteristic, complemented
4	#33149	C₂	1	1	yes	maximal, characteristic, complemented
5	#33096	C₂	1	1	yes	maximal, characteristic, complemented
6	#33095	C₂	1	1	yes	maximal, characteristic, complemented
7	#30170	C₂	1	1	yes	maximal, characteristic, complemented
8	#30169	C₂	1	1	yes	maximal, characteristic, complemented
9	#30011	C₂	1	1	yes	maximal, characteristic, complemented
10	#30010	C₂	1	1	yes	maximal, characteristic, complemented
11	#27474	C₂	1	1	yes	maximal, characteristic, complemented
12	#27473	C₂	1	1	yes	maximal, characteristic, complemented
13	#27348	C₂	1	1	yes	maximal, characteristic, complemented
14	#27343	C₂	1	1	yes	maximal, characteristic, complemented
15	#27053	C₂	1	1	yes	maximal, characteristic, complemented
16	#27050	C₂	1	1	yes	maximal, characteristic, complemented
17	#26742	C₂	1	1	yes	maximal, characteristic, complemented
18	#26741	C₂	1	1	yes	maximal, characteristic, complemented
19	#26453	C₂	1	1	yes	maximal, characteristic, complemented
20	#26310	C₂	1	1	yes	maximal, characteristic, complemented
21	#26035	C₂	1	1	yes	maximal, characteristic, complemented
22	#25712	C₂	1	1	yes	maximal, characteristic, complemented
23	#25462	C₂	1	1	yes	maximal, characteristic, complemented
24	#24977	C₂	1	1	yes	maximal, characteristic
25	#24689	C₂	1	1	yes	maximal, characteristic, complemented
26	#24130	C₂	1	1	yes	maximal, characteristic
27	#22250	C₂	1	1	yes	maximal, characteristic, complemented
28	#22116	C₂	1	1	yes	maximal, characteristic, complemented
29	#22014	C₂	1	1	yes	maximal, characteristic, complemented
30	#21618	C₂	1	1	yes	maximal, characteristic, complemented
31	#21124	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#554	C₂²	1	1	yes	characteristic
33	C₂×#501	C₂²	1	1	yes	characteristic
34	C₂×#479	C₂²	1	1	yes	characteristic
35	C₂×#474	C₂²	1	1	yes	characteristic
36	C₂×#440	C₂²	1	1	yes	characteristic
37	#2857	C₂²	1	1	yes	characteristic
38	#2854	C₂²	1	1	yes	characteristic
39	#2854	C₂²	1	1	yes	characteristic
40	#2851	C₂²	1	1	yes	characteristic
41	#2650	—	2	1	no	—
42	#2630	—	2	1	no	—
43	#2566	C₂²	1	1	yes	characteristic
44	#2562	C₂²	1	1	yes	characteristic
45	#2550	C₂²	1	1	yes	characteristic
46	#2535	C₂²	1	1	yes	characteristic
47	#2525	—	2	1	no	—
48	#2497	C₂²	1	1	yes	characteristic
49	#2495	C₂²	1	1	yes	characteristic
50	#2491	C₂²	1	1	yes	characteristic
51	#2490	C₂²	1	1	yes	characteristic
52	#2477	—	2	1	no	—
53	#2470	—	2	1	no	—
54	#2461	—	2	1	no	—
55	#2370	—	2	1	no	—
56	#2369	C₂²	1	1	yes	characteristic
57	#2368	—	2	1	no	—
58	#2368	—	2	1	no	—
59	#2360	C₂²	1	1	yes	characteristic
60	#2360	C₂²	1	1	yes	characteristic
61	#2355	C₂²	1	1	yes	characteristic
62	#2349	—	2	1	no	—
63	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	#2345	C₂²	1	1	yes	characteristic
65	#2345	C₂²	1	1	yes	characteristic
66	#2337	—	2	1	no	—
67	#2335	—	2	1	no	—
68	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
69	C₄×#125	—	2	1	no	—
70	C₄×#125	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊Q₈	—	2	1	no	—
72	C₄×C₂²⋊Q₈	—	2	1	no	—
73	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
75	#2293	C₂²	1	1	yes	characteristic
76	C₄²×Q₈	C₂²	1	1	yes	characteristic
77	C₄²×D₄	—	2	1	no	—
78	C₄²×D₄	C₂²	1	1	yes	characteristic
79	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#2088	C₂²	1	1	yes	characteristic
82	#2086	C₂²	1	1	yes	characteristic
83	#2085	C₂²	1	1	yes	characteristic
84	#2083	C₂²	1	1	yes	characteristic
85	#2077	C₂²	1	1	yes	characteristic
86	#2077	C₂²	1	1	yes	characteristic
87	#2077	C₂²	1	1	yes	characteristic
88	#2076	C₂²	1	1	yes	characteristic
89	#2076	C₂²	1	1	yes	characteristic
90	#2075	C₂²	1	1	yes	characteristic
91	#2074	C₂²	1	1	yes	characteristic
92	#2072	C₂²	1	1	yes	characteristic
93	#2067	C₂²	1	1	yes	characteristic
94	#2066	C₂²	1	1	yes	characteristic
95	#2066	C₂²	1	1	yes	characteristic
96	#2065	C₂²	1	1	yes	characteristic
97	#2059	C₂²	1	1	yes	characteristic
98	#2057	C₂²	1	1	yes	characteristic
99	#2055	C₂²	1	1	yes	characteristic
100	#2055	C₂²	1	1	yes	characteristic
101	#2036	C₂²	1	1	yes	characteristic
102	#2036	C₂²	1	1	yes	characteristic
103	#2036	C₂²	1	1	yes	characteristic
104	#2036	C₂²	1	1	yes	characteristic
105	#2035	C₂²	1	1	yes	characteristic
106	#2035	C₂²	1	1	yes	characteristic
107	#2034	C₂²	1	1	yes	characteristic
108	#2033	C₂²	1	1	yes	characteristic
109	#2026	C₂²	1	1	yes	characteristic
110	#2024	C₂²	1	1	yes	characteristic
111	#2000	C₂²	1	1	yes	characteristic
112	#2000	C₂²	1	1	yes	characteristic
113	#1993	C₂²	1	1	yes	characteristic
114	#1992	C₂²	1	1	yes	characteristic
115	#1989	C₂²	1	1	yes	characteristic
116	#1989	C₂²	1	1	yes	characteristic
117	#1989	C₂²	1	1	yes	characteristic
118	#1988	C₂²	1	1	yes	characteristic
119	#1987	C₂²	1	1	yes	characteristic
120	#1987	C₂²	1	1	yes	characteristic
121	#1955	C₂²	1	1	yes	characteristic
122	#1955	C₂²	1	1	yes	characteristic
123	#1949	C₂²	1	1	yes	characteristic
124	#1949	C₂²	1	1	yes	characteristic
125	#1949	C₂²	1	1	yes	characteristic
126	#1948	C₂²	1	1	yes	characteristic
127	#1947	C₂²	1	1	yes	characteristic
128	#1947	C₂²	1	1	yes	characteristic
129	#1943	C₂²	1	1	yes	characteristic
130	#1943	C₂²	1	1	yes	characteristic
131	#1940	C₂²	1	1	yes	characteristic
132	#1940	C₂²	1	1	yes	characteristic
133	#1936	C₂²	1	1	yes	characteristic
134	#1936	C₂²	1	1	yes	characteristic
135	#1926	C₂²	1	1	yes	characteristic
136	#1926	C₂²	1	1	yes	characteristic
137	#1926	C₂²	1	1	yes	characteristic
138	#1926	C₂²	1	1	yes	characteristic
139	#1926	C₂²	1	1	yes	characteristic
140	#1925	C₂²	1	1	yes	characteristic
141	#1925	C₂²	1	1	yes	characteristic
142	#1925	C₂²	1	1	yes	characteristic
143	#1924	C₂²	1	1	yes	characteristic
144	#1924	C₂²	1	1	yes	characteristic
145	#1924	C₂²	1	1	yes	characteristic
146	#1924	C₂²	1	1	yes	characteristic
147	#1921	C₂²	1	1	yes	characteristic
148	#1921	C₂²	1	1	yes	characteristic
149	#1921	C₂²	1	1	yes	characteristic
150	#1921	C₂²	1	1	yes	characteristic
151	#1921	C₂²	1	1	yes	characteristic
152	#1921	C₂²	1	1	yes	characteristic
153	#1920	C₂²	1	1	yes	characteristic
154	#1920	C₂²	1	1	yes	characteristic
155	#1919	C₂²	1	1	yes	characteristic
156	#1919	C₂²	1	1	yes	characteristic
157	#1919	C₂²	1	1	yes	characteristic
158	#1919	C₂²	1	1	yes	characteristic
159	#1919	C₂²	1	1	yes	characteristic
160	#1919	C₂²	1	1	yes	characteristic
161	#1919	C₂²	1	1	yes	characteristic
162	#1918	C₂²	1	1	yes	characteristic
163	#1918	C₂²	1	1	yes	characteristic
164	#1918	C₂²	1	1	yes	characteristic
165	#1880	C₂²	1	1	yes	characteristic
166	#1880	C₂²	1	1	yes	characteristic
167	#1874	C₂²	1	1	yes	characteristic
168	#1874	C₂²	1	1	yes	characteristic
169	#1874	C₂²	1	1	yes	characteristic
170	#1874	C₂²	1	1	yes	characteristic
171	#1865	C₂²	1	1	yes	characteristic
172	#1865	C₂²	1	1	yes	characteristic
173	#1863	C₂²	1	1	yes	characteristic
174	#1863	C₂²	1	1	yes	characteristic
175	#1853	C₂²	1	1	yes	characteristic
176	#1853	C₂²	1	1	yes	characteristic
177	#1853	C₂²	1	1	yes	characteristic
178	#1853	C₂²	1	1	yes	characteristic
179	#1852	C₂²	1	1	yes	characteristic
180	#1852	C₂²	1	1	yes	characteristic
181	#1852	C₂²	1	1	yes	characteristic
182	#1852	C₂²	1	1	yes	characteristic
183	#1836	C₂²	1	1	yes	characteristic
184	#1824	C₂²	1	1	yes	characteristic
185	#1824	C₂²	1	1	yes	characteristic
186	#1823	C₂²	1	1	yes	characteristic
187	#1823	C₂²	1	1	yes	characteristic
188	#1817	C₂²	1	1	yes	characteristic
189	#1817	C₂²	1	1	yes	characteristic
190	#1805	C₂²	1	1	yes	characteristic
191	#1802	C₂²	1	1	yes	characteristic
192	#1797	C₂²	1	1	yes	characteristic
193	#1797	C₂²	1	1	yes	characteristic
194	#1776	C₂²	1	1	yes	characteristic
195	#1776	C₂²	1	1	yes	characteristic
196	#1776	C₂²	1	1	yes	characteristic
197	#1767	C₂²	1	1	yes	characteristic
198	#1763	C₂²	1	1	yes	characteristic
199	#1763	C₂²	1	1	yes	characteristic
200	#1763	C₂²	1	1	yes	characteristic
201	#1762	C₂²	1	1	yes	characteristic
202	#1745	C₂²	1	1	yes	characteristic
203	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
204	#554	—	2	4	no	—
205	#554	—	2	4	no	—
206	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	C₂×#125	—	2	1	no	—
209	C₂×#125	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×#123	—	2	1	no	—
213	C₂×#123	—	2	1	no	—
214	C₂×C₂²⋊Q₈	—	2	1	no	—
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×C₄×Q₈	—	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	D₄	1	1	yes	characteristic
228	C₂×C₄×D₄	D₄	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
231	C₂×#117	—	2	1	no	—
232	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₄²	—	2	1	no	—
237	C₂²×C₄²	—	2	1	no	—
238	C₂²×C₄²	C₂³	1	1	yes	characteristic
239	C₂²×C₄²	C₂³	1	1	yes	characteristic
240	#501	—	2	4	no	—
241	#479	—	2	4	no	—
242	#474	—	2	4	no	—
243	#440	—	2	4	no	—
244	C₂×#107	C₂³	1	1	yes	characteristic
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#106	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×C₄⋊C₈	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×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	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×#97	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	#400	—	2	1	no	—
292	#400	—	2	1	no	—
293	#400	—	2	1	no	—
294	#398	—	2	1	no	—
295	#397	—	2	1	no	—
296	#397	—	2	1	no	—
297	#397	—	2	1	no	—
298	#396	—	2	1	no	—
299	#396	—	2	1	no	—
300	#396	—	2	1	no	—
301	#395	—	2	1	no	—
302	#394	—	2	1	no	—
303	#394	—	2	1	no	—
304	#394	—	2	1	no	—
305	#393	—	2	1	no	—
306	#392	—	2	1	no	—
307	#391	—	2	1	no	—
308	#391	—	2	1	no	—
309	#391	—	2	1	no	—
310	#391	—	2	1	no	—
311	#391	—	2	1	no	—
312	#391	C₂³	1	1	yes	characteristic
313	#391	C₂³	1	1	yes	characteristic
314	#390	—	2	1	no	—
315	#390	C₂³	1	1	yes	characteristic
316	#390	C₂³	1	1	yes	characteristic
317	#390	C₂³	1	1	yes	characteristic
318	#390	C₂³	1	1	yes	characteristic
319	#389	—	2	1	no	—
320	#389	—	2	1	no	—
321	#389	—	2	1	no	—
322	#389	—	2	1	no	—
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	C₂³	1	1	yes	characteristic
327	#389	C₂³	1	1	yes	characteristic
328	#389	C₂³	1	1	yes	characteristic
329	#389	C₂³	1	1	yes	characteristic
330	#389	C₂³	1	1	yes	characteristic
331	#389	C₂³	1	1	yes	characteristic
332	#389	C₂³	1	1	yes	characteristic
333	#389	C₂³	1	1	yes	characteristic
334	#389	C₂³	1	1	yes	characteristic
335	#389	C₂³	1	1	yes	characteristic
336	#388	—	2	1	no	—
337	#388	—	2	1	no	—
338	#388	—	2	1	no	—
339	#388	—	2	1	no	—
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#387	—	2	1	no	—
349	#387	—	2	1	no	—
350	#387	—	2	1	no	—
351	#387	—	2	1	no	—
352	#387	—	2	1	no	—
353	#387	—	2	1	no	—
354	#387	—	2	1	no	—
355	#387	—	2	1	no	—
356	#387	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
363	#386	—	2	1	no	—
364	#386	—	2	1	no	—
365	#386	—	2	1	no	—
366	#386	—	2	1	no	—
367	#385	—	2	1	no	—
368	#385	—	2	1	no	—
369	#385	—	2	1	no	—
370	#385	—	2	1	no	—
371	#385	—	2	1	no	—
372	#385	—	2	1	no	—
373	#385	—	2	1	no	—
374	#385	—	2	1	no	—
375	#385	—	2	1	no	—
376	#385	—	2	1	no	—
377	#384	C₂³	1	1	yes	characteristic
378	#384	C₂³	1	1	yes	characteristic
379	#383	—	2	1	no	—
380	#382	—	2	1	no	—
381	#382	C₂³	1	1	yes	characteristic
382	#382	C₂³	1	1	yes	characteristic
383	#380	—	2	1	no	—
384	#380	—	2	1	no	—
385	#380	—	2	1	no	—
386	#380	C₂³	1	1	yes	characteristic
387	#380	C₂³	1	1	yes	characteristic
388	#380	C₂³	1	1	yes	characteristic
389	#380	C₂³	1	1	yes	characteristic
390	#380	C₂³	1	1	yes	characteristic
391	#380	C₂³	1	1	yes	characteristic
392	#380	C₂³	1	1	yes	characteristic
393	#380	C₂³	1	1	yes	characteristic
394	C₄×C₄⋊C₄	—	2	1	no	—
395	C₄×C₄⋊C₄	—	2	1	no	—
396	C₄×C₄⋊C₄	—	2	1	no	—
397	C₄×C₄⋊C₄	—	2	1	no	—
398	C₄×C₄⋊C₄	—	2	1	no	—
399	C₄×C₄⋊C₄	—	2	1	no	—
400	C₄×C₄⋊C₄	—	2	1	no	—
401	C₄×C₄⋊C₄	—	2	1	no	—
402	C₄×C₄⋊C₄	—	2	1	no	—
403	C₄×C₄⋊C₄	—	2	1	no	—
404	C₄×C₄⋊C₄	—	2	1	no	—
405	C₄×C₄⋊C₄	—	2	1	no	—
406	C₄×C₄⋊C₄	—	2	1	no	—
407	C₄×C₄⋊C₄	—	2	1	no	—
408	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
409	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₂²⋊C₄	—	2	1	no	—
424	C₄×C₂²⋊C₄	—	2	1	no	—
425	C₄×C₂²⋊C₄	—	2	1	no	—
426	C₄×C₂²⋊C₄	—	2	1	no	—
427	C₄×C₂²⋊C₄	—	2	1	no	—
428	C₄×C₂²⋊C₄	—	2	1	no	—
429	C₄×C₂²⋊C₄	—	2	1	no	—
430	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
436	C₂×#95	—	2	1	no	—
437	C₂×#95	—	2	1	no	—
438	C₄³	—	2	1	no	—
439	C₄³	C₂³	1	1	yes	characteristic
440	#340	C₂³	1	1	yes	characteristic
441	#340	C₂³	1	1	yes	characteristic
442	#340	C₂³	1	1	yes	characteristic
443	#340	C₂³	1	1	yes	characteristic
444	#340	C₂³	1	1	yes	characteristic
445	#340	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	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	#336	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	C₂²×Q₈	—	2	1	no	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
490	C₂²×D₄	C₂⁴	1	1	yes	characteristic
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
497	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
498	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
500	C₂³×C₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×SD₁₆	—	2	2	no	—
503	C₂×SD₁₆	—	4	1	no	—
504	C₂×SD₁₆	—	4	1	no	—
505	C₂²×C₈	C₂⁴	1	1	yes	characteristic
506	C₂²×C₈	C₂⁴	1	1	yes	characteristic
507	C₂²×C₈	C₂⁴	1	1	yes	characteristic
508	C₂²×C₈	C₂⁴	1	1	yes	characteristic
509	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
514	C₄⋊Q₈	—	4	1	no	—
515	C₄⋊Q₈	—	4	1	no	—
516	C₄⋊Q₈	#41	1	4	yes	—
517	#125	—	2	8	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	4	1	no	—
521	#125	—	4	1	no	—
522	#124	—	4	4	no	—
523	#123	—	4	4	no	—
524	#123	—	8	2	no	—
525	C₂²⋊Q₈	—	2	8	no	—
526	C₂²⋊Q₈	—	2	8	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	8	2	no	—
532	#121	—	4	1	no	—
533	#121	—	4	1	no	—
534	#121	—	4	1	no	—
535	#121	—	4	1	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	4	1	no	—
539	C₄×Q₈	—	4	1	no	—
540	C₄×Q₈	—	4	1	no	—
541	C₄×Q₈	—	8	2	no	—
542	C₄×Q₈	#41	1	4	yes	—
543	C₄×D₄	—	2	8	no	—
544	C₄×D₄	—	2	4	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	4	2	no	—
550	C₄×D₄	—	4	4	no	—
551	#117	—	8	2	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	2	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	—	2	2	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	2	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	4	1	no	—
588	C₂×C₄⋊C₄	—	4	1	no	—
589	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×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	C₂×D₄	1	1	yes	characteristic
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×C₄²	—	2	1	no	—
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	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	4	1	no	—
649	C₂×C₄²	—	4	1	no	—
650	C₂×C₄²	—	4	1	no	—
651	C₂×C₄²	—	4	1	no	—
652	C₂×C₄²	—	8	2	no	—
653	C₂×C₄²	—	8	2	no	—
654	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	1	yes	characteristic
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	#107	—	2	2	no	—
668	#107	—	2	2	no	—
669	#107	—	2	2	no	—
670	#107	—	2	2	no	—
671	#107	—	2	2	no	—
672	#107	—	2	2	no	—
673	#107	—	4	1	no	—
674	#107	—	4	1	no	—
675	#106	—	2	2	no	—
676	#106	—	2	2	no	—
677	#106	—	2	2	no	—
678	#106	—	2	2	no	—
679	#106	—	4	1	no	—
680	#106	—	4	1	no	—
681	#106	—	4	1	no	—
682	C₄⋊C₈	—	2	2	no	—
683	C₄⋊C₈	—	2	2	no	—
684	C₄⋊C₈	—	4	1	no	—
685	C₄⋊C₈	—	4	1	no	—
686	C₄⋊C₈	—	4	1	no	—
687	C₄⋊C₈	—	4	1	no	—
688	#103	—	2	2	no	—
689	#103	—	2	2	no	—
690	#103	—	2	2	no	—
691	#103	—	4	1	no	—
692	#103	—	4	1	no	—
693	#103	—	4	1	no	—
694	#103	—	4	1	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	2	2	no	—
699	#102	—	4	1	no	—
700	#102	—	4	1	no	—
701	#102	—	4	1	no	—
702	C₂²⋊C₈	—	4	1	no	—
703	C₂²⋊C₈	—	4	1	no	—
704	C₂²⋊C₈	—	4	1	no	—
705	C₂²⋊C₈	—	4	1	no	—
706	C₂²⋊C₈	—	4	1	no	—
707	C₂²⋊C₈	—	4	1	no	—
708	C₂²⋊C₈	—	4	1	no	—
709	C₂²⋊C₈	—	4	1	no	—
710	#97	—	2	2	no	—
711	#97	—	2	2	no	—
712	#97	—	4	1	no	—
713	#97	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
753	#95	C₂×D₄	1	1	yes	characteristic
754	#95	C₂×D₄	1	1	yes	characteristic
755	#95	C₂×D₄	1	1	yes	characteristic
756	#95	C₂×D₄	1	1	yes	characteristic
757	#95	C₂×D₄	1	1	yes	characteristic
758	C₂⁴	—	2	1	no	—
759	C₂⁴	C₂²×D₄	1	1	yes	characteristic
760	C₂⁴	C₂²×D₄	1	1	yes	characteristic
761	C₂×Q₈	—	2	4	no	—
762	C₂×Q₈	—	2	1	no	—
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	—	4	2	no	—
768	C₂×Q₈	—	8	1	no	—
769	C₂×Q₈	—	8	1	no	—
770	C₂×Q₈	—	8	1	no	—
771	C₂×Q₈	—	8	1	no	—
772	C₂×Q₈	C₂×#41	1	2	yes	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	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	—	4	2	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	8	1	no	—
785	C₂×D₄	—	8	1	no	—
786	C₂×D₄	—	8	1	no	—
787	C₂×D₄	—	8	1	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	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	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	—	4	1	no	—
822	C₂²×C₄	—	4	1	no	—
823	C₂²×C₄	—	4	1	no	—
824	C₂²×C₄	—	4	1	no	—
825	C₂²×C₄	—	4	1	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	8	1	no	—
834	C₂²×C₄	—	8	1	no	—
835	C₂²×C₄	—	8	1	no	—
836	C₂²×C₄	—	8	1	no	—
837	C₂²×C₄	—	8	1	no	—
838	C₂²×C₄	—	8	1	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
841	C₂²×C₄	#137	1	4	yes	—
842	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
843	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
844	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
845	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
846	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
847	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂⁵	1	1	yes	characteristic
855	SD₁₆	—	4	4	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	—	2	1	no	—
862	C₂×C₈	—	2	1	no	—
863	C₂×C₈	—	2	1	no	—
864	C₂×C₈	—	2	1	no	—
865	C₂×C₈	—	2	1	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₄⋊C₄	—	2	4	no	—
881	C₄⋊C₄	—	2	4	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	4	1	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	8	1	no	—
925	C₄⋊C₄	—	8	1	no	—
926	C₄⋊C₄	—	8	1	no	—
927	C₄⋊C₄	—	8	1	no	—
928	C₄⋊C₄	—	8	1	no	—
929	C₄⋊C₄	—	8	1	no	—
930	C₄⋊C₄	—	8	1	no	—
931	C₄⋊C₄	—	8	1	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	C₂×#41	1	2	yes	—
937	C₄⋊C₄	C₂×#41	1	2	yes	—
938	C₄⋊C₄	C₂×#41	1	2	yes	—
939	C₄⋊C₄	2₋¹⁺⁴	1	2	yes	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	2	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	8	1	no	—
959	C₂²⋊C₄	—	8	1	no	—
960	C₂²⋊C₄	—	8	1	no	—
961	C₂²⋊C₄	—	8	1	no	—
962	C₂²⋊C₄	—	8	1	no	—
963	C₂²⋊C₄	—	8	1	no	—
964	C₂²⋊C₄	—	8	1	no	—
965	C₂²⋊C₄	—	8	1	no	—
966	C₂²⋊C₄	—	8	1	no	—
967	C₄²	—	2	4	no	—
968	C₄²	—	2	2	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	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	4	1	no	—
978	C₄²	—	4	1	no	—
979	C₄²	—	4	1	no	—
980	C₄²	—	4	1	no	—
981	C₄²	—	4	1	no	—
982	C₄²	—	4	1	no	—
983	C₄²	—	4	1	no	—
984	C₄²	—	4	2	no	—
985	C₄²	—	4	2	no	—
986	C₄²	—	4	2	no	—
987	C₄²	—	4	2	no	—
988	C₄²	—	4	2	no	—
989	C₄²	—	4	2	no	—
990	C₄²	—	4	2	no	—
991	C₄²	—	8	1	no	—
992	C₄²	—	8	1	no	—
993	C₄²	—	8	1	no	—
994	C₄²	—	8	1	no	—
995	C₄²	—	8	1	no	—
996	C₄²	—	8	1	no	—
997	C₄²	—	8	1	no	—
998	C₄²	C₂×#41	1	2	yes	—
999	C₄²	C₂×#41	1	2	yes	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	4	1	no	—
1013	C₂³	—	4	1	no	—
1014	C₂³	—	4	1	no	—
1015	C₂³	—	4	1	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	C₂×#137	1	2	yes	—
1020	C₂³	#575	1	2	yes	—
1021	C₂³	C₂³×D₄	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	4	1	no	—
1025	Q₈	—	4	1	no	—
1026	Q₈	—	8	4	no	—
1027	Q₈	—	16	2	no	—
1028	D₄	—	2	8	no	—
1029	D₄	—	4	1	no	—
1030	D₄	—	4	1	no	—
1031	D₄	—	4	1	no	—
1032	D₄	—	4	1	no	—
1033	D₄	—	16	2	no	—
1034	D₄	—	16	2	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	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	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	2	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	—	2	1	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	4	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	—	4	1	no	—
1112	C₂×C₄	—	4	1	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	—	8	4	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	—	8	4	no	—
1125	C₂×C₄	—	8	4	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	4	no	—
1128	C₂×C₄	—	8	4	no	—
1129	C₂×C₄	#525	1	2	yes	—
1130	C₂×C₄	#525	1	2	yes	—
1131	C₂×C₄	C₂×#137	1	2	yes	—
1132	C₂×C₄	C₂×#137	1	2	yes	—
1133	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1134	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1135	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1136	C₂×C₄	#585	1	1	yes	characteristic
1137	C₂×C₄	#585	1	1	yes	characteristic
1138	C₂×C₄	#585	1	1	yes	characteristic
1139	C₈	—	4	1	no	—
1140	C₈	—	4	1	no	—
1141	C₈	—	4	1	no	—
1142	C₈	—	4	1	no	—
1143	C₈	—	4	1	no	—
1144	C₈	—	4	1	no	—
1145	C₈	—	4	1	no	—
1146	C₈	—	4	1	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	8	1	no	—
1162	C₂²	—	8	1	no	—
1163	C₂²	—	8	1	no	—
1164	C₂²	—	8	1	no	—
1165	C₂²	—	8	1	no	—
1166	C₂²	—	8	1	no	—
1167	C₂²	—	8	1	no	—
1168	C₂²	C₂×#525	1	1	yes	characteristic
1169	C₂²	#3485	1	1	yes	characteristic
1170	C₂²	#3489	1	1	yes	characteristic
1171	C₂²	C₂²×#137	1	1	yes	characteristic
1172	C₂²	C₂×#575	1	1	yes	characteristic
1173	C₂²	#3585	1	1	yes	characteristic
1174	C₂²	#3585	1	1	yes	characteristic
1175	C₄	—	2	2	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	2	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	2	no	—
1192	C₄	—	8	1	no	—
1193	C₄	—	8	1	no	—
1194	C₄	—	8	1	no	—
1195	C₄	—	8	1	no	—
1196	C₄	—	8	1	no	—
1197	C₄	—	8	1	no	—
1198	C₄	—	8	1	no	—
1199	C₄	—	8	1	no	—
1200	C₄	—	8	1	no	—
1201	C₄	—	8	1	no	—
1202	C₄	#3455	1	1	yes	characteristic
1203	C₄	#3461	1	1	yes	characteristic
1204	C₄	#3518	1	1	yes	characteristic
1205	C₄	#3524	1	1	yes	characteristic
1206	C₂	—	4	2	no	—
1207	C₂	—	4	2	no	—
1208	C₂	—	16	1	no	—
1209	C₂	#35155	1	1	yes	characteristic
1210	C₂	#60560	1	1	yes	characteristic
1211	C₂	#60574	1	1	yes	characteristic
1212	C₂	#61709	1	1	yes	characteristic
1213	C₂	#61714	1	1	yes	characteristic
1214	C₂	#62114	1	1	yes	characteristic
1215	C₂	#62119	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2535	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄²×D₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₄×#554	C₂	semidirect
3. #33151	C₂	semidirect
4. #33149	C₂	semidirect
5. #33096	C₂	semidirect
6. #33095	C₂	semidirect
7. #30170	C₂	semidirect
8. #30169	C₂	semidirect
9. #30011	C₂	semidirect
10. #30010	C₂	semidirect
11. #27474	C₂	semidirect
12. #27473	C₂	semidirect
13. #27348	C₂	semidirect
14. #27343	C₂	semidirect
15. #27053	C₂	semidirect
16. #27050	C₂	semidirect
17. #26742	C₂	semidirect
18. #26741	C₂	semidirect
19. #26453	C₂	semidirect
20. #26310	C₂	semidirect
21. #26035	C₂	semidirect
22. #25712	C₂	semidirect
23. #25462	C₂	semidirect
25. #24689	C₂	semidirect
27. #22250	C₂	semidirect
28. #22116	C₂	semidirect
29. #22014	C₂	semidirect
30. #21618	C₂	semidirect
31. #21124	C₂	semidirect

Maximal subgroups

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

subgroup	index
#35107	2
C₄×#554	2
#33151	2
#33149	2
#33096	2
#33095	2
#30170	2
#30169	2
#30011	2
#30010	2
#27474	2
#27473	2
#27348	2
#27343	2
#27053	2
#27050	2
#26742	2
#26741	2
#26453	2
#26310	2
#26035	2
#25712	2
#25462	2
#24977	2
#24689	2
#24130	2
#22250	2
#22116	2
#22014	2
#21618	2
#21124	2