Subgroups — #7512732

Order 512.

1641 conjugacy classes of subgroups.

The subgroup lattice has 1233 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34938	C₂	1	1	yes	maximal, characteristic, complemented
2	#34914	C₂	1	1	yes	maximal, characteristic
3	#32378	C₂	1	1	yes	maximal, characteristic, complemented
4	#32314	C₂	1	1	yes	maximal, characteristic, complemented
5	#32230	C₂	1	1	yes	maximal, characteristic, complemented
6	#32134	C₂	1	1	yes	maximal, characteristic, complemented
7	#31740	C₂	1	1	yes	maximal, characteristic, complemented
8	#31688	C₂	1	1	yes	maximal, characteristic, complemented
9	#31574	C₂	1	1	yes	maximal, characteristic, complemented
10	#31458	C₂	1	1	yes	maximal, characteristic, complemented
11	#31424	C₂	1	1	yes	maximal, characteristic, complemented
12	#31352	C₂	1	1	yes	maximal, characteristic, complemented
13	#31118	C₂	1	1	yes	maximal, characteristic
14	#31086	C₂	1	1	yes	maximal, characteristic, complemented
15	#30954	C₂	1	1	yes	maximal, characteristic, complemented
16	#30813	C₂	1	1	yes	maximal, characteristic, complemented
17	#30775	C₂	1	1	yes	maximal, characteristic, complemented
18	#30631	C₂	1	1	yes	maximal, characteristic
19	#23837	C₂	1	1	yes	maximal, characteristic, complemented
20	#23815	C₂	1	1	yes	maximal, characteristic, complemented
21	#23775	C₂	1	1	yes	maximal, characteristic, complemented
22	#23775	C₂	1	1	yes	maximal, characteristic, complemented
23	#23755	C₂	1	1	yes	maximal, characteristic, complemented
24	#23755	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#498	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#486	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#476	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#476	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#481	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#481	C₂	1	1	yes	maximal, characteristic, complemented
31	#21430	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#533	—	2	1	no	—
33	C₂×#529	—	2	1	no	—
34	C₂×#498	C₂²	1	1	yes	characteristic
35	C₂×#486	C₂²	1	1	yes	characteristic
36	C₂×#481	C₂²	1	1	yes	characteristic
37	C₂×#481	C₂²	1	1	yes	characteristic
38	C₂×#476	C₂²	1	1	yes	characteristic
39	C₂×#476	C₂²	1	1	yes	characteristic
40	#2560	—	2	1	no	—
41	#2559	—	2	1	no	—
42	#2558	—	2	1	no	—
43	#2557	—	2	1	no	—
44	#2552	C₂²	1	1	yes	characteristic
45	#2552	C₂²	1	1	yes	characteristic
46	#2551	C₂²	1	1	yes	characteristic
47	#2551	C₂²	1	1	yes	characteristic
48	#2550	—	2	1	no	—
49	#2550	—	2	1	no	—
50	#2549	—	2	1	no	—
51	#2549	—	2	1	no	—
52	#2512	C₂²	1	1	yes	characteristic
53	#2506	C₂²	1	1	yes	characteristic
54	#2496	C₂²	1	1	yes	characteristic
55	#2491	C₂²	1	1	yes	characteristic
56	#2452	C₂²	1	1	yes	characteristic
57	#2445	C₂²	1	1	yes	characteristic
58	#2440	C₂²	1	1	yes	characteristic
59	#2440	C₂²	1	1	yes	characteristic
60	#2440	C₂²	1	1	yes	characteristic
61	#2440	C₂²	1	1	yes	characteristic
62	#2428	C₂²	1	1	yes	characteristic
63	#2422	C₂²	1	1	yes	characteristic
64	#2399	—	2	1	no	—
65	#2399	—	2	1	no	—
66	#2398	—	2	1	no	—
67	#2392	—	2	1	no	—
68	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
73	C₄×#127	C₂²	1	1	yes	characteristic
74	C₄×#121	C₂²	1	1	yes	characteristic
75	C₄×#121	C₂²	1	1	yes	characteristic
76	#2296	—	2	1	no	—
77	#2293	C₂²	1	1	yes	characteristic
78	#2290	—	2	1	no	—
79	#2285	C₂²	1	1	yes	characteristic
80	C₄²×D₄	C₂²	1	1	yes	characteristic
81	C₄×#117	C₂²	1	1	yes	characteristic
82	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	#2100	C₂²	1	1	yes	characteristic
84	#2100	C₂²	1	1	yes	characteristic
85	#2100	C₂²	1	1	yes	characteristic
86	#2100	C₂²	1	1	yes	characteristic
87	#2099	C₂²	1	1	yes	characteristic
88	#2099	C₂²	1	1	yes	characteristic
89	#2094	C₂²	1	1	yes	characteristic
90	#2094	C₂²	1	1	yes	characteristic
91	#2094	C₂²	1	1	yes	characteristic
92	#2094	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic
94	#2088	C₂²	1	1	yes	characteristic
95	#2088	C₂²	1	1	yes	characteristic
96	#2088	C₂²	1	1	yes	characteristic
97	#2084	C₂²	1	1	yes	characteristic
98	#2084	C₂²	1	1	yes	characteristic
99	#2084	C₂²	1	1	yes	characteristic
100	#2084	C₂²	1	1	yes	characteristic
101	#2084	C₂²	1	1	yes	characteristic
102	#2084	C₂²	1	1	yes	characteristic
103	#2077	C₂²	1	1	yes	characteristic
104	#2077	C₂²	1	1	yes	characteristic
105	#2077	C₂²	1	1	yes	characteristic
106	#2077	C₂²	1	1	yes	characteristic
107	#2071	C₂²	1	1	yes	characteristic
108	#2071	C₂²	1	1	yes	characteristic
109	#2071	C₂²	1	1	yes	characteristic
110	#2071	C₂²	1	1	yes	characteristic
111	#2065	C₂²	1	1	yes	characteristic
112	#2065	C₂²	1	1	yes	characteristic
113	#2065	C₂²	1	1	yes	characteristic
114	#2065	C₂²	1	1	yes	characteristic
115	#2058	C₂²	1	1	yes	characteristic
116	#2058	C₂²	1	1	yes	characteristic
117	#2058	C₂²	1	1	yes	characteristic
118	#2058	C₂²	1	1	yes	characteristic
119	#2058	C₂²	1	1	yes	characteristic
120	#2058	C₂²	1	1	yes	characteristic
121	#2041	C₂²	1	1	yes	characteristic
122	#2041	C₂²	1	1	yes	characteristic
123	#2034	C₂²	1	1	yes	characteristic
124	#2034	C₂²	1	1	yes	characteristic
125	#2034	C₂²	1	1	yes	characteristic
126	#2034	C₂²	1	1	yes	characteristic
127	#2023	C₂²	1	1	yes	characteristic
128	#2023	C₂²	1	1	yes	characteristic
129	#2023	C₂²	1	1	yes	characteristic
130	#2023	C₂²	1	1	yes	characteristic
131	#1990	C₂²	1	1	yes	characteristic
132	#1990	C₂²	1	1	yes	characteristic
133	#1990	C₂²	1	1	yes	characteristic
134	#1987	C₂²	1	1	yes	characteristic
135	#1987	C₂²	1	1	yes	characteristic
136	#1957	C₂²	1	1	yes	characteristic
137	#1948	C₂²	1	1	yes	characteristic
138	#1948	C₂²	1	1	yes	characteristic
139	#1941	C₂²	1	1	yes	characteristic
140	#1941	C₂²	1	1	yes	characteristic
141	#1941	C₂²	1	1	yes	characteristic
142	#1941	C₂²	1	1	yes	characteristic
143	#1934	C₂²	1	1	yes	characteristic
144	#1934	C₂²	1	1	yes	characteristic
145	#1934	C₂²	1	1	yes	characteristic
146	#1934	C₂²	1	1	yes	characteristic
147	#1926	C₂²	1	1	yes	characteristic
148	#1926	C₂²	1	1	yes	characteristic
149	#1926	C₂²	1	1	yes	characteristic
150	#1926	C₂²	1	1	yes	characteristic
151	#1923	C₂²	1	1	yes	characteristic
152	#1923	C₂²	1	1	yes	characteristic
153	#1923	C₂²	1	1	yes	characteristic
154	#1923	C₂²	1	1	yes	characteristic
155	#1920	C₂²	1	1	yes	characteristic
156	#1920	C₂²	1	1	yes	characteristic
157	#1920	C₂²	1	1	yes	characteristic
158	#1920	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	#1919	C₂²	1	1	yes	characteristic
163	#1916	C₂²	1	1	yes	characteristic
164	#1916	C₂²	1	1	yes	characteristic
165	#1916	C₂²	1	1	yes	characteristic
166	#1916	C₂²	1	1	yes	characteristic
167	#1874	C₂²	1	1	yes	characteristic
168	#1874	C₂²	1	1	yes	characteristic
169	#1864	C₂²	1	1	yes	characteristic
170	#1864	C₂²	1	1	yes	characteristic
171	#1864	C₂²	1	1	yes	characteristic
172	#1864	C₂²	1	1	yes	characteristic
173	#1853	C₂²	1	1	yes	characteristic
174	#1853	C₂²	1	1	yes	characteristic
175	#1844	C₂²	1	1	yes	characteristic
176	#1834	C₂²	1	1	yes	characteristic
177	#1824	C₂²	1	1	yes	characteristic
178	#1824	C₂²	1	1	yes	characteristic
179	#1802	C₂²	1	1	yes	characteristic
180	#1802	C₂²	1	1	yes	characteristic
181	C₄×#106	C₂²	1	1	yes	characteristic
182	C₄×#106	C₂²	1	1	yes	characteristic
183	C₄×#106	C₂²	1	1	yes	characteristic
184	C₄×#106	C₂²	1	1	yes	characteristic
185	C₄×#106	C₂²	1	1	yes	characteristic
186	C₄×#106	C₂²	1	1	yes	characteristic
187	C₄×#106	C₂²	1	1	yes	characteristic
188	C₄×#106	C₂²	1	1	yes	characteristic
189	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
190	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
191	C₄×#102	C₂²	1	1	yes	characteristic
192	C₄×#102	C₂²	1	1	yes	characteristic
193	C₄×#102	C₂²	1	1	yes	characteristic
194	C₄×#102	C₂²	1	1	yes	characteristic
195	C₄×#102	C₂²	1	1	yes	characteristic
196	C₄×#102	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
200	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
201	#1744	C₂²	1	1	yes	characteristic
202	C₄²×C₈	C₂²	1	1	yes	characteristic
203	#533	—	4	8	no	—
204	C₂×C₄⋊Q₈	—	2	1	no	—
205	C₂×C₄⋊Q₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂×#127	C₂³	1	1	yes	characteristic
212	#529	—	4	8	no	—
213	C₂×#126	—	2	1	no	—
214	C₂×#126	—	2	1	no	—
215	C₂×#125	—	2	1	no	—
216	C₂×#125	—	2	1	no	—
217	C₂×#125	—	2	1	no	—
218	C₂×#124	—	2	1	no	—
219	C₂×#123	—	2	1	no	—
220	C₂×#123	—	2	1	no	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	—	2	1	no	—
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×C₂²⋊Q₈	—	2	1	no	—
226	C₂×#121	—	2	1	no	—
227	C₂×#121	C₂³	1	1	yes	characteristic
228	C₂×#121	C₂³	1	1	yes	characteristic
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	—	2	1	no	—
231	C₂×C₄×Q₈	—	2	1	no	—
232	C₂×C₄×Q₈	—	2	1	no	—
233	C₂×C₄×Q₈	—	2	1	no	—
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	—	2	1	no	—
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
242	C₂×#117	—	2	1	no	—
243	C₂×#117	—	2	1	no	—
244	C₂×#117	D₄	1	1	yes	characteristic
245	C₂×#117	D₄	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂²×C₄²	—	2	1	no	—
249	C₂²×C₄²	—	2	1	no	—
250	C₂²×C₄²	C₂³	1	1	yes	characteristic
251	#498	—	2	4	no	—
252	#486	—	2	4	no	—
253	#481	—	2	4	no	—
254	#481	—	2	4	no	—
255	#476	—	2	4	no	—
256	#476	—	2	4	no	—
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×#106	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	C₂×#106	C₂³	1	1	yes	characteristic
262	C₂×#106	C₂³	1	1	yes	characteristic
263	C₂×#106	C₂³	1	1	yes	characteristic
264	C₂×#106	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
304	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
305	#400	—	2	1	no	—
306	#400	—	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	#398	—	2	1	no	—
314	#398	—	2	1	no	—
315	#398	—	2	1	no	—
316	#397	—	2	1	no	—
317	#397	—	2	1	no	—
318	#397	—	2	1	no	—
319	#396	—	2	1	no	—
320	#396	—	2	1	no	—
321	#395	—	2	1	no	—
322	#395	—	2	1	no	—
323	#395	—	2	1	no	—
324	#395	—	2	1	no	—
325	#395	—	2	1	no	—
326	#395	—	2	1	no	—
327	#395	—	2	1	no	—
328	#395	—	2	1	no	—
329	#394	—	2	1	no	—
330	#394	—	2	1	no	—
331	#394	—	2	1	no	—
332	#394	—	2	1	no	—
333	#394	—	2	1	no	—
334	#393	—	2	1	no	—
335	#393	—	2	1	no	—
336	#392	—	2	1	no	—
337	#391	—	2	1	no	—
338	#391	—	2	1	no	—
339	#391	—	2	1	no	—
340	#391	—	2	1	no	—
341	#391	—	2	1	no	—
342	#390	—	2	1	no	—
343	#390	—	2	1	no	—
344	#390	C₂³	1	1	yes	characteristic
345	#390	C₂³	1	1	yes	characteristic
346	#390	C₂³	1	1	yes	characteristic
347	#390	C₂³	1	1	yes	characteristic
348	#390	C₂³	1	1	yes	characteristic
349	#390	C₂³	1	1	yes	characteristic
350	#389	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	—	2	1	no	—
353	#389	—	2	1	no	—
354	#389	—	2	1	no	—
355	#389	—	2	1	no	—
356	#389	—	2	1	no	—
357	#389	—	2	1	no	—
358	#389	—	2	1	no	—
359	#389	C₂³	1	1	yes	characteristic
360	#389	C₂³	1	1	yes	characteristic
361	#389	C₂³	1	1	yes	characteristic
362	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#389	C₂³	1	1	yes	characteristic
365	#389	C₂³	1	1	yes	characteristic
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#389	C₂³	1	1	yes	characteristic
369	#389	C₂³	1	1	yes	characteristic
370	#389	C₂³	1	1	yes	characteristic
371	#389	C₂³	1	1	yes	characteristic
372	#389	C₂³	1	1	yes	characteristic
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#388	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#386	—	2	1	no	—
382	#386	—	2	1	no	—
383	#386	—	2	1	no	—
384	#386	—	2	1	no	—
385	#385	—	2	1	no	—
386	#385	—	2	1	no	—
387	#385	—	2	1	no	—
388	#385	—	2	1	no	—
389	#385	—	2	1	no	—
390	#385	—	2	1	no	—
391	#384	C₂³	1	1	yes	characteristic
392	#384	C₂³	1	1	yes	characteristic
393	#384	C₂³	1	1	yes	characteristic
394	#384	C₂³	1	1	yes	characteristic
395	#384	C₂³	1	1	yes	characteristic
396	#384	C₂³	1	1	yes	characteristic
397	#384	C₂³	1	1	yes	characteristic
398	#384	C₂³	1	1	yes	characteristic
399	#382	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	C₂³	1	1	yes	characteristic
402	#380	C₂³	1	1	yes	characteristic
403	#380	C₂³	1	1	yes	characteristic
404	#380	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
409	C₄×C₄⋊C₄	—	2	1	no	—
410	C₄×C₄⋊C₄	—	2	1	no	—
411	C₄×C₄⋊C₄	—	2	1	no	—
412	C₄×C₄⋊C₄	—	2	1	no	—
413	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
414	C₄×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
431	C₄×C₂²⋊C₄	—	2	1	no	—
432	C₄×C₂²⋊C₄	—	2	1	no	—
433	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
437	#376	D₄	1	1	yes	characteristic
438	#376	D₄	1	1	yes	characteristic
439	C₂×#95	—	2	1	no	—
440	C₄³	C₂³	1	1	yes	characteristic
441	C₄³	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	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	C₂²×Q₈	—	2	1	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	C₂⁴	1	1	yes	characteristic
496	C₂²×D₄	C₂⁴	1	1	yes	characteristic
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
505	C₂³×C₄	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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
514	C₄⋊Q₈	—	2	2	no	—
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	—	4	1	no	—
520	C₄⋊Q₈	—	4	1	no	—
521	C₄⋊Q₈	—	4	1	no	—
522	C₄⋊Q₈	—	4	1	no	—
523	C₄⋊Q₈	—	4	1	no	—
524	C₄⋊Q₈	—	4	4	no	—
525	C₄⋊Q₈	—	4	4	no	—
526	#127	—	2	2	no	—
527	#127	—	4	1	no	—
528	#126	—	4	4	no	—
529	#126	—	4	4	no	—
530	#125	—	4	4	no	—
531	#125	—	4	4	no	—
532	#125	—	4	4	no	—
533	#124	—	4	4	no	—
534	#123	—	4	4	no	—
535	#123	—	4	4	no	—
536	C₂²⋊Q₈	—	4	4	no	—
537	C₂²⋊Q₈	—	4	4	no	—
538	C₂²⋊Q₈	—	4	4	no	—
539	C₂²⋊Q₈	—	4	4	no	—
540	C₂²⋊Q₈	—	4	4	no	—
541	#121	—	2	2	no	—
542	#121	—	2	2	no	—
543	#121	—	4	1	no	—
544	#121	—	4	1	no	—
545	#121	—	4	4	no	—
546	C₄×Q₈	—	4	4	no	—
547	C₄×Q₈	—	4	4	no	—
548	C₄×Q₈	—	4	4	no	—
549	C₄×Q₈	—	4	4	no	—
550	C₄×Q₈	—	4	4	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	4	1	no	—
558	C₄×D₄	—	4	1	no	—
559	C₄×D₄	—	4	4	no	—
560	C₄×D₄	—	4	4	no	—
561	C₄×D₄	—	4	4	no	—
562	C₄×D₄	—	4	4	no	—
563	#117	—	2	4	no	—
564	#117	—	4	4	no	—
565	#117	—	4	4	no	—
566	#117	SD₁₆	1	8	yes	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	—	2	2	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	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	—	2	1	no	—
606	C₂×C₄⋊C₄	—	4	1	no	—
607	C₂×C₄⋊C₄	—	4	1	no	—
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	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×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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₄²	—	2	2	no	—
653	C₂×C₄²	—	2	2	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
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	—	4	4	no	—
665	C₂×C₄²	—	4	4	no	—
666	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	C₂×C₄²	C₂⁴	1	1	yes	characteristic
678	C₂×C₄²	C₂⁴	1	1	yes	characteristic
679	C₂×C₄²	C₂⁴	1	1	yes	characteristic
680	C₂×C₄²	C₂⁴	1	1	yes	characteristic
681	C₂×C₄²	C₂⁴	1	1	yes	characteristic
682	#106	—	2	2	no	—
683	#106	—	2	2	no	—
684	#106	—	2	2	no	—
685	#106	—	2	2	no	—
686	#106	—	2	2	no	—
687	#106	—	2	2	no	—
688	#106	—	2	2	no	—
689	#106	—	2	2	no	—
690	#106	—	2	2	no	—
691	#106	—	4	1	no	—
692	#106	—	4	1	no	—
693	#106	—	4	1	no	—
694	#106	—	4	1	no	—
695	#106	—	4	1	no	—
696	#106	—	4	1	no	—
697	#106	#41	1	4	yes	—
698	C₄⋊C₈	—	2	2	no	—
699	C₄⋊C₈	—	2	2	no	—
700	C₄⋊C₈	—	4	1	no	—
701	C₄⋊C₈	—	4	1	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	—	2	2	no	—
709	#102	—	2	2	no	—
710	#102	—	2	2	no	—
711	#102	—	4	1	no	—
712	#102	—	4	1	no	—
713	#102	—	4	1	no	—
714	#102	—	4	1	no	—
715	#102	—	4	1	no	—
716	#102	—	4	1	no	—
717	#102	#41	1	4	yes	—
718	C₂²⋊C₈	—	2	2	no	—
719	C₂²⋊C₈	—	2	2	no	—
720	C₂²⋊C₈	—	4	1	no	—
721	C₂²⋊C₈	—	4	1	no	—
722	C₄×C₈	—	2	2	no	—
723	C₄×C₈	—	2	2	no	—
724	C₄×C₈	—	2	2	no	—
725	C₄×C₈	—	2	2	no	—
726	C₄×C₈	—	2	2	no	—
727	C₄×C₈	—	2	2	no	—
728	C₄×C₈	—	4	1	no	—
729	C₄×C₈	—	4	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	C₂×D₄	1	1	yes	characteristic
759	#95	C₂×D₄	1	1	yes	characteristic
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	—	2	1	no	—
767	C₂⁴	—	2	1	no	—
768	C₂⁴	C₂²×D₄	1	1	yes	characteristic
769	C₂×Q₈	—	4	2	no	—
770	C₂×Q₈	—	4	2	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	—	4	2	no	—
773	C₂×Q₈	—	4	2	no	—
774	C₂×Q₈	—	4	2	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	—	4	2	no	—
779	C₂×Q₈	—	8	1	no	—
780	C₂×Q₈	—	8	1	no	—
781	C₂×Q₈	—	8	1	no	—
782	C₂×Q₈	—	8	1	no	—
783	C₂×Q₈	—	8	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	2	no	—
803	C₂×D₄	—	8	1	no	—
804	C₂×D₄	—	8	1	no	—
805	C₂×D₄	—	8	1	no	—
806	C₂×D₄	—	8	1	no	—
807	C₂×D₄	C₂×#41	1	2	yes	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	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	—	2	2	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	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	—	4	1	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	8	1	no	—
848	C₂²×C₄	—	8	1	no	—
849	C₂²×C₄	—	8	1	no	—
850	C₂²×C₄	—	8	1	no	—
851	C₂²×C₄	C₂×SD₁₆	1	4	yes	—
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
865	C₂²×C₄	C₂⁵	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	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	C₂×#41	1	2	yes	—
889	C₂×C₈	C₂×#41	1	2	yes	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	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	—	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	—	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	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	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	C₂×SD₁₆	1	4	yes	—
955	C₄⋊C₄	C₂×SD₁₆	1	4	yes	—
956	C₄⋊C₄	C₂×#41	1	2	yes	—
957	C₄⋊C₄	C₂×#41	1	2	yes	—
958	C₄⋊C₄	C₂×#41	1	2	yes	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
980	C₂²⋊C₄	—	8	1	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	C₂×SD₁₆	1	4	yes	—
984	C₂²⋊C₄	C₂×SD₁₆	1	4	yes	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	4	1	no	—
999	C₄²	—	4	1	no	—
1000	C₄²	—	4	1	no	—
1001	C₄²	—	4	1	no	—
1002	C₄²	—	4	2	no	—
1003	C₄²	—	4	2	no	—
1004	C₄²	—	4	2	no	—
1005	C₄²	—	4	2	no	—
1006	C₄²	—	4	2	no	—
1007	C₄²	—	4	2	no	—
1008	C₄²	—	4	2	no	—
1009	C₄²	—	4	2	no	—
1010	C₄²	—	4	2	no	—
1011	C₄²	—	4	2	no	—
1012	C₄²	C₂×SD₁₆	1	4	yes	—
1013	C₄²	C₂×SD₁₆	1	4	yes	—
1014	C₄²	AGL(1,ℤ/8)	1	4	yes	—
1015	C₄²	2₋¹⁺⁴	1	2	yes	—
1016	C₄²	2₋¹⁺⁴	1	2	yes	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	1	no	—
1030	C₂³	—	4	1	no	—
1031	C₂³	—	4	1	no	—
1032	C₂³	—	4	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	C₂²×SD₁₆	1	2	yes	—
1038	C₂³	C₂³×D₄	1	1	yes	characteristic
1039	Q₈	—	8	4	no	—
1040	Q₈	—	8	4	no	—
1041	Q₈	—	8	4	no	—
1042	Q₈	—	8	4	no	—
1043	Q₈	—	8	4	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	4	1	no	—
1047	D₄	—	4	1	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	4	1	no	—
1050	D₄	—	4	1	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	8	4	no	—
1053	D₄	—	8	4	no	—
1054	D₄	—	8	4	no	—
1055	D₄	—	8	4	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	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	8	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	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	—	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	—	8	2	no	—
1132	C₂×C₄	—	8	4	no	—
1133	C₂×C₄	—	8	4	no	—
1134	C₂×C₄	—	8	4	no	—
1135	C₂×C₄	—	8	4	no	—
1136	C₂×C₄	—	8	4	no	—
1137	C₂×C₄	—	8	4	no	—
1138	C₂×C₄	#536	1	2	yes	—
1139	C₂×C₄	#536	1	2	yes	—
1140	C₂×C₄	C₂²×SD₁₆	1	2	yes	—
1141	C₂×C₄	C₂²×SD₁₆	1	2	yes	—
1142	C₂×C₄	C₂²×SD₁₆	1	2	yes	—
1143	C₂×C₄	C₂²×SD₁₆	1	2	yes	—
1144	C₂×C₄	C₂²×SD₁₆	1	2	yes	—
1145	C₂×C₄	C₂²×SD₁₆	1	2	yes	—
1146	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
1147	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
1148	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
1149	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1150	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1151	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1152	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1153	C₂×C₄	#585	1	1	yes	characteristic
1154	C₂×C₄	#585	1	1	yes	characteristic
1155	C₈	—	2	2	no	—
1156	C₈	—	2	2	no	—
1157	C₈	—	4	1	no	—
1158	C₈	—	4	1	no	—
1159	C₈	—	4	1	no	—
1160	C₈	—	4	1	no	—
1161	C₈	—	4	1	no	—
1162	C₈	—	4	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	8	1	no	—
1174	C₂²	—	8	1	no	—
1175	C₂²	—	8	1	no	—
1176	C₂²	—	8	1	no	—
1177	C₂²	—	8	1	no	—
1178	C₂²	—	8	1	no	—
1179	C₂²	—	8	1	no	—
1180	C₂²	—	8	1	no	—
1181	C₂²	—	8	1	no	—
1182	C₂²	—	8	1	no	—
1183	C₂²	—	8	1	no	—
1184	C₂²	C₂×#536	1	1	yes	characteristic
1185	C₂²	D₄×#41	1	1	yes	characteristic
1186	C₂²	D₄×#41	1	1	yes	characteristic
1187	C₂²	C₂³×SD₁₆	1	1	yes	characteristic
1188	C₂²	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
1189	C₂²	#3584	1	1	yes	characteristic
1190	C₂²	#3584	1	1	yes	characteristic
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	8	1	no	—
1207	C₄	—	8	1	no	—
1208	C₄	—	8	1	no	—
1209	C₄	—	8	1	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	—	8	1	no	—
1213	C₄	—	8	1	no	—
1214	C₄	—	8	1	no	—
1215	C₄	—	8	1	no	—
1216	C₄	—	8	1	no	—
1217	C₄	#3227	1	4	yes	—
1218	C₄	#3461	1	1	yes	characteristic
1219	C₄	#3461	1	1	yes	characteristic
1220	C₄	#3482	1	1	yes	characteristic
1221	C₄	#3531	1	1	yes	characteristic
1222	C₂	—	4	2	no	—
1223	C₂	—	8	2	no	—
1224	C₂	—	16	1	no	—
1225	C₂	#52166	1	1	yes	characteristic
1226	C₂	C₂×#3227	1	1	yes	characteristic
1227	C₂	#60859	1	1	yes	characteristic
1228	C₂	SD₁₆×#41	1	1	yes	characteristic
1229	C₂	SD₁₆×#41	1	1	yes	characteristic
1230	C₂	#61437	1	1	yes	characteristic
1231	C₂	#61439	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
socle	C₂³	C₂³×D₄
prime radical	#2428	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #34938	C₂	semidirect
3. #32378	C₂	semidirect
4. #32314	C₂	semidirect
5. #32230	C₂	semidirect
6. #32134	C₂	semidirect
7. #31740	C₂	semidirect
8. #31688	C₂	semidirect
9. #31574	C₂	semidirect
10. #31458	C₂	semidirect
11. #31424	C₂	semidirect
12. #31352	C₂	semidirect
14. #31086	C₂	semidirect
15. #30954	C₂	semidirect
16. #30813	C₂	semidirect
17. #30775	C₂	semidirect
19. #23837	C₂	semidirect
20. #23815	C₂	semidirect
21. #23775	C₂	semidirect
22. #23775	C₂	semidirect
23. #23755	C₂	semidirect
24. #23755	C₂	semidirect
25. C₄×#498	C₂	semidirect
26. C₄×#486	C₂	semidirect
27. C₄×#476	C₂	semidirect
28. C₄×#476	C₂	semidirect
29. C₄×#481	C₂	semidirect
30. C₄×#481	C₂	semidirect
31. #21430	C₂	semidirect

Maximal subgroups

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

subgroup	index
#34938	2
#34914	2
#32378	2
#32314	2
#32230	2
#32134	2
#31740	2
#31688	2
#31574	2
#31458	2
#31424	2
#31352	2
#31118	2
#31086	2
#30954	2
#30813	2
#30775	2
#30631	2
#23837	2
#23815	2
#23775	2
#23755	2
C₄×#498	2
C₄×#486	2
C₄×#476	2
C₄×#481	2
#21430	2